diff --git "a/TAL-SCQ5K-EN/train.jsonl" "b/TAL-SCQ5K-EN/train.jsonl" new file mode 100644--- /dev/null +++ "b/TAL-SCQ5K-EN/train.jsonl" @@ -0,0 +1,3000 @@ +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1", "queId": "04a1962c6a554ccebe43f32e28d9cf5a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If a four-digit number $$5A2A$$ can be divisible by $20$, the digit that $$A$$ represents is . ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["We consider the last two-digit to see if a number is divisible by $4$. We consider the last one digit to see if a number is divisible by $5$. If $$\\overline{\\textasciitilde5A2A\\textasciitilde}$$ is divisible by $5$, the ones digit can only be $5$ or $0$. When the ones digit is $0$, the number that is formed by the last two digits, $20$, is divisible by $4$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2", "queId": "0045127337c842e1ac61fd2f853bf96d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$1994$$ is added to any odd number, the sum will always be． ", "answer_option_list": [[{"aoVal": "A", "content": "odd　 "}], [{"aoVal": "B", "content": "even　 "}], [{"aoVal": "C", "content": "$$1995$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers"], "answer_analysis": ["even number $$+$$ odd number $$=$$ odd number. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4", "queId": "0de9acf2eb584f4293873e9d82c87725", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many whole numbers are greater than $$9$$ and less than $$60$$?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$49$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$51$$ "}], [{"aoVal": "D", "content": "$$59$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["There are $$60$$ whole numbers from $$0$$ to $$59$$. That\\textquotesingle s $$50$$ without $$0$$ to $$9$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5", "queId": "04c4375ff4ce4868a284efaaefe1abbd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$a$$, $$b$$ are prime numbers, and $$3a+7b=41$$, then $$a+b=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Applying Special Prime Numbers"], "answer_analysis": ["Based on the laws relating to the parity in addition and multiplication, either $$a$$ or $$b$$ must be $$2$$. If $$a = 2$$, then $$b = 5$$, and $$a + b = 7$$; if $$b = 2$$, then $$a = 9$$; $$9$$ is not a prime number, which doesn\\textquotesingle t match the conditions in the question. Therefore, we choose B. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6", "queId": "0dedf1dbe7d94392a4960c76886ff3e3", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The hundreds digit of a three-digit number is $$2$$ more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["$$\\rm Method$$ $$1$$: Let the hundreds, tens, and units digits of the original three-digit number be $$a$$, $$b$$, and $$c$$, respectively. We are given that $$a=c+2$$. The original three-digit number is equal to $$100a+10b+c=100(c+2)+10b+c=101c+10b+200$$. The hundreds, tens, and units digits of the reversed three-digit number are $$c$$, $$b$$, and $$a$$, respectively. This number is equal to $$100c+10b+a=100c+10b+(c+2)=101c+10b+2$$. Subtracting this expression from the expression for the original number, we get $$(101c+10b+200)-(101c+10b+2)=198$$ . Thus, the units digit in the final result is $$8$$. $$\\rm Method$$ $$2$$: The result must hold for any three-digit number with its hundreds digit being $$2$$ more than the units digit. $$301$$ is such a number. Evaluating, we get $$301-103=198$$. Thus, the units digit in the final result is $$8$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11", "queId": "01265cb97ac64dd19c314c19b1322752", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Cindy prepares burgers with two slices of beef each. A box of beef has $20$ slices. How many burgers can she prepare with all the three and a half box of beef? (Adapted from 2013 Math Kangaroo Problem, Level 3-4, Question \\#7) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$25$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders"], "answer_analysis": ["There are $3\\times20+20\\div2=70$ slices of beef. $70\\div2=35$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "13", "queId": "1bf262c37cc54a2b8702ead261a2da56", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "$$\\overline{**45}$$, $$\\overline{19*8}$$, $$\\overline{23*1}$$, and $$\\overline{3*49}$$ are four $4-$digit numbers with some unknown digits. Which number is possible to be a perfect square? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\overline{**45}$$ "}], [{"aoVal": "B", "content": "$$\\overline{19*8}$$ "}], [{"aoVal": "C", "content": "$$\\overline{23*1}$$ "}], [{"aoVal": "D", "content": "$$\\overline{3*49}$$ "}], [{"aoVal": "E", "content": "None "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers"], "answer_analysis": ["According to the ones digit of perfect squares, we can eliminate choice $B$. A perfect square ending with $5$ must be a multiple of $25$, so we can eliminate choice $A$. $${{48}^{2}}=2304$$ and $${{49}^{2}}=2401$$ so we can eliminate choice $C$. ${57}^{2}=3249$. We choose option $D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "15", "queId": "253da63353f842cd9b5d8f3390e37d84", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Today is $$1^{st}$$ January $$2023$$, which is a Sunday. Teacher Angel has $$5$$ candies in her bag. Every time she completed her Tuesday and Thursday class, she will award herself with $$2$$ candies. On which date would she have $$15$$ candies in her bag? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15^{th}$$ January $$2023$$ "}], [{"aoVal": "B", "content": "$$16^{th}$$ January $$2023$$ "}], [{"aoVal": "C", "content": "$$17^{th}$$ January $$2023$$ "}], [{"aoVal": "D", "content": "$$18^{th}$$ January $$2023$$ "}], [{"aoVal": "E", "content": "$$19^{th}$$ January $$2023$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["$$16$$ days later. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "16", "queId": "054aa055e43247c1a2ffbcdab7af7a9b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$5$$, the remainder is $$1$$. When $$N$$ is divided by $$11$$, the remainder is $$1$$. The smallest possible value of $N$ is~\\uline{~~~~~~~~~~}~.(Adapted from $$2016$$ AMC $$8$$ Problem, Question \\#$$5$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$51$$ "}], [{"aoVal": "B", "content": "$$54$$ "}], [{"aoVal": "C", "content": "$$56$$ "}], [{"aoVal": "D", "content": "$$61$$ "}], [{"aoVal": "E", "content": "$$67$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["Among $1, 56, 111$, \\ldots~the smallest possible $$N$$ that satisfies the two conditions is $$56$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "17", "queId": "09a0a0796fe14457bacd973acc1b0bf7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Let $$N$$ be the greatest five$$-$$digit number whose digits have a product of $$120$$. What is the sum of the digits of $$N$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"], "answer_analysis": ["To make the largest possible five$$-$$digit $$N$$, you should make the number in the biggest digit as large as possible. $$120=8\\times5\\times3\\times1\\times1$$. So, the sum of digits is $$8+5+3+1+1=18$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "19", "queId": "0193777141ad4161ac1c7dcba19522ba", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The first $2018$ integers ($1$, $2$, $3$, $\\cdots$, $2017$, $2018$) are written on the blackboard. What is the minimum number of integers that should be erased from the blackboard, so that the last digit of the product of the remaining integers is $2$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$402$$ "}], [{"aoVal": "B", "content": "$$403$$ "}], [{"aoVal": "C", "content": "$$404$$ "}], [{"aoVal": "D", "content": "$$410$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders "], "answer_analysis": ["First, we need to remove all the integers which are multiples of $5$, otherwise the last digit of the products is $0$ or $5$. Hence, $403$ integers need to be removed. Next, note that the last digit of each of the products below is $6$. $1\\times2\\times3\\times4\\times6\\times7\\times8\\times9$, $11\\times12\\times13\\times14\\times16\\times17\\times18\\times19$, $\\cdots\\cdots$ $2001\\times2002\\times2003\\times2004\\times2006\\times2007\\times2008\\times2009$, and the last digit of the product $2011\\times2012\\times2013\\times2014\\times2016\\times2017\\times2018$ is $4$. Hence, we need to remove one more \"$2$\"and the last digit of the product will be $2$. So the answer is $404$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "20", "queId": "019a554ba9fe406293cd56509cbb7314", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Summer has some nuts and wants to divide them equally to $5$ kids. Everyone can get $7$ nuts at most. How many nuts does Summer have at most? ", "answer_option_list": [[{"aoVal": "A", "content": "$$34$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$39$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["There are $5-1=4$ nuts left after dividing at most. Thus, Summer has $5\\times7+4=39$ nuts at most. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "21", "queId": "056027dc7b2449daa05c4f0c33fe196b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The ones digit of $$9\\times 8\\times 7\\times 6\\times 5\\times 4\\times 3\\times 3\\times 4\\times 5\\times 6\\times 7\\times 8\\times 9$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["Since $$5\\times 4 = 20$$, the ones digit of the given product must be $$0$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "22", "queId": "01c24bdb9ec74dcdaca0376d99e5aa0f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Eleven members of the Middle School Math Club each paid the same integer amount for a guest speaker to talk about problem solving at their math club meeting. In all, they paid their guest speaker $$\\overline{1A2}$$. What is the missing digit $A$ of this $3$-digit number? (2014 AMC 8 Problem, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["$1+2-A=0$, $A=3$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "26", "queId": "021e67b73f4d456f845dd93532bbd70c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many 0s are there at the end of the product $$2\\times3\\times5\\times7\\times8\\times12\\times25$$. ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["3 set of 2$\\times$5. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "32", "queId": "027ffca1c108473597da507f092f7153", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of the ten-thousands\\textquotesingle{} digit and the millions\\textquotesingle{} digit of $$1234567890$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["The ten-thousands\\textquotesingle digit plus the millions\\textquotesingle~digit of $$1234567890$$ is $$6 + 4 = 10$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "34", "queId": "02c2ec7e62d54b1b8f30d30b3235dbc7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following numbers is the odd one out? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1138$$ "}], [{"aoVal": "B", "content": "$$1226$$ "}], [{"aoVal": "C", "content": "$$1324$$ "}], [{"aoVal": "D", "content": "$$1416$$ "}], [{"aoVal": "E", "content": "$$1854$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers"], "answer_analysis": ["$$1138 →1\\times1\\times3\\times8=24$$ $$1226 →1\\times2\\times2\\times6=24$$ $$1324 →1\\times3\\times2\\times4=24$$ $$1416~→1\\times4\\times1\\times6=24$$ $$1854 →1\\times8\\times5\\times4=160$$ $$1854$$ is the odd one out as the product of its digits is not $$24$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "35", "queId": "05ebb63ac0e249d19550df1d39a728dd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The greatest odd factor of the product $$1\\times 2\\times 3\\times 4\\times 5\\times 6$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$75$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$1\\times 2\\times 3\\times 4\\times 5\\times (2\\times 3)=2\\times 4\\times 2\\times (1\\times 3\\times 5\\times 3)=16\\times 45$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "41", "queId": "0308e2f8eadf487f8c2ee2f2ce93432e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of any two multiples of $$3$$ must be a multiple of． ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["Since $$3\\times3 =9$$, the product of two multiples of 3 is divisible by $$9$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "43", "queId": "a68956ecb7014b82a0bd9d6237b07573", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole numbers $A$, $B$ and $C$. $A\\times B=35$, $B\\times C=84$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$23$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$35=5\\times 7$ $84=2\\times 2\\times 3\\times 7$ Because $B$ is the factor both number contains, $B=7$ Thus, $A=5$, $C=12$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "45", "queId": "0a123c9b35cc40739eb08b8f2afbf1a3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Determine whether the following calculations give odd or even numbers. (a) $$14327+21462-3583$$ (b) $$9377\\times1525$$ ", "answer_option_list": [[{"aoVal": "A", "content": "Both Odd "}], [{"aoVal": "B", "content": "Both Even "}], [{"aoVal": "C", "content": "Odd, Even "}], [{"aoVal": "D", "content": "Even, Odd "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["Nil "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "46", "queId": "0e691b5588d84ed8a47685be173e7fe9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When $$106$$ is divided by $$3$$, the remainder is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders"], "answer_analysis": ["$$ 3\\times35 = 105$$; so $$106 \\div 3 =35$$ with remainder $$106-105=1$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "47", "queId": "06485722cb9946688b794c4b4f786f5f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the value for lcm $$\\left[ 4,6,8\\right]$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["List the prime factorization for $$4$$, $$6$$ and $$8$$ first. $$4=2^{2}$$, $$6=2\\times3$$, $$8=2^{3}$$. The largest exponent for $$2$$ is $$3$$,~~and the largest exponent for $$3$$ is $$1$$, thus the least common multiple for $$4$$, $$6$$, and $$8$$ is $$2^{3}\\times3=24$$. We choose $$\\rm C$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "48", "queId": "064c1eac3ed94925aeefd9463cbd3066", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "John, Mike, Emily and Nick want to buy some apples from Walmart where the apples are sold in pack of six. How many packs should they buy to get the same amount of apples for each one of them? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["For each one of them to get the same amount of apples, the total amount should be a multiple of $4$, because there are $4$ of them. The apples are sold in pack of six. $3$ packs contain $18$ apples; $5$ packs contain $30$; $6$ packs contain $36$; $7$ packs contain $42$. Among the number of $18, 30, 36, 42$, only $36$ can be divided by $4$. $36$ is a multiple of $4$. Therefore, they should buy $6$ packs. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "55", "queId": "04296e43b5e840838bcdc834c8067395", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "There is a book with 650 pages. Henry tears 31 paper from the book, each paper contains two pages. Is it possible that the sum of their page number equals to 2000? ", "answer_option_list": [[{"aoVal": "A", "content": "$$Yes.$$ "}], [{"aoVal": "B", "content": "$$No.$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["If there are odd number of odd page number, the sum of page numbers is odd. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "57", "queId": "2a06479fe20c4ec5a31ed7eff311324e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$1$$ thousand $$+9$$ hundreds $$+ 8$$ tens $$+ 18$$ ones $$=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1918$$ "}], [{"aoVal": "B", "content": "$$1988$$ "}], [{"aoVal": "C", "content": "$$1998$$ "}], [{"aoVal": "D", "content": "$$19818$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["$$1000+900+80+18=1980+18=1998$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "59", "queId": "bdc7996644914cc68a2007e9d478b32c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of all $$4$$ sides of a square is $$1296$$. The sum of all $$4$$ sides of the square is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$72$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["Let $x$ represent the length of each side of the square, then: $x^{4} = 1296 \\implies x^{2} = \\sqrt{1296} = 36$. Hence $x = \\sqrt{36} = 6$ and $4x = 4\\times 6 = 24$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "63", "queId": "0ea14919f55645f4ae31985ff1ce9152", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Change a digit of the number $45879$ to make the new five-digit number be divisible by $125$. What is the new five-digit number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$45870$$ "}], [{"aoVal": "B", "content": "$$45875$$ "}], [{"aoVal": "C", "content": "$$45579$$ "}], [{"aoVal": "D", "content": "$45875$ and $45870$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["The last three digits must be divisible by $125$, so it can only be $875$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "64", "queId": "a68d5611d46b4bf2b2b773399b7b9b6d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In this fictional \"Old Island\", all the numbers contain only odd digits. The order of the counting numbers is as follows: 1, 3, 5, 7, $\\cdots $ , 19, 31, 33, $\\cdots $ What is the 31st counting number in the island? ", "answer_option_list": [[{"aoVal": "A", "content": "$$101$$ "}], [{"aoVal": "B", "content": "$$111$$ "}], [{"aoVal": "C", "content": "$$99$$ "}], [{"aoVal": "D", "content": "$$113$$ "}], [{"aoVal": "E", "content": "None of the above. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["1,3,5,7,9 -\\/-\\/-\\/-\\/-\\/-\\/-\\/-\\/-\\/-⑤ 11,13,15,17,19-\\/-\\/-\\/-\\/-\\/-\\/-⑤ 31,33,35,37,39-\\/-\\/-\\/-\\/-⑤ 51,53,55,57,59-\\/-\\/-\\/-\\/-⑤ 71,73,75,77,79-\\/-\\/-\\/-\\/-⑤ 91,93,95,97,99-\\/-\\/-\\/-⑤ $$111$$ the 31st number is 111. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "65", "queId": "2a0f125d659e457f9321d33a493ca3ee", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Divide 5 numbers $$2$$、$$3$$、$$12$$、$$15$$ and $$30$$ into two groups to make the product of numbers in each group the same, so the two groups are ． ", "answer_option_list": [[{"aoVal": "A", "content": "（$$2$$, $$3$$, $$15$$），（$$12$$, $$30$$） "}], [{"aoVal": "B", "content": "（$$2$$, $$12$$, $$15$$），（$$3$$, $$30$$） "}], [{"aoVal": "C", "content": "（$$2$$, $$3$$, $$30$$），（$$12$$, $$15$$） "}], [{"aoVal": "D", "content": "（$$12$$, $$3$$, $$15$$），（$$2$$, $$30$$） "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->Finding Factors Given the Product"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "70", "queId": "de43b71338d54cb684cccb4dd906e7c4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many prime numbers are there between $120$ and $140$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["$127$, $131$, $137$, $139$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "74", "queId": "17b04685165d4e34b981c26ceb43e524", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is not a prime number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$41$$ "}], [{"aoVal": "B", "content": "$$51$$ "}], [{"aoVal": "C", "content": "$$61$$ "}], [{"aoVal": "D", "content": "$$71$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["Since $$51=3\\times17$$, $$51$$ is not a prime number. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "75", "queId": "586d6459b8004261a4757e69984ba6ce", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Mom was cooking at home with the lights on when suddenly the power went out. Dad came home and pressed the switch four times, and then Mason came home and pressed the switch three times. When the power came back on, were the lights off or on? ", "answer_option_list": [[{"aoVal": "A", "content": "On "}], [{"aoVal": "B", "content": "Off "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "77", "queId": "2ebccd26c02d457faf28406b3fbe1d77", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mike has $$17$$ apples and $$19$$ pears. He puts every $5$ fruits in each box. At least how many more fruits does he need to get $8$ boxes of fruits? (Adapted from 2001 Math Kangaroo Problem, Level 3-4, Question \\#7) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$(17+19)\\div5=7R1$ $5-1=4$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "78", "queId": "0ec6ba1606fe4b7d954b6b86d03331a8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A square has an area of $144\\text{cm}^{2}$, what is the length of each side of the square? ", "answer_option_list": [[{"aoVal": "A", "content": "$10\\text{cm}$ "}], [{"aoVal": "B", "content": "$11\\text{cm}$ "}], [{"aoVal": "C", "content": "$12\\text{cm}$ "}], [{"aoVal": "D", "content": "$13\\text{cm}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["The length of each side of the square is $\\sqrt{144} = 12\\text{cm}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "79", "queId": "0aaf151854bf47dd87dfa3a539e6041e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Vicky bought $26$ apples to divide to her $5$ cousins. If Vicky wants to give them all of the apples and also wants to make every cousin gets the same amount, at least how many more apples should Vicky buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["$6\\times5-26=4$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "80", "queId": "5d12e090ee00486a97d0ddc2e26c9e96", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$1\\times2\\times3\\times4\\times5\\times6\\times7\\times8\\times$$$$9\\times10\\times11\\times12\\times13\\times$$$$14\\times15 = 1307 674 368000$$, how many times does the digit \"$$0$$\" appear in the product $$10\\times20\\times30\\times40\\times50\\times60\\times$$$$70\\times80\\times90\\times100\\times110\\times120\\times130\\times140\\times150$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"], "answer_analysis": ["If $$1\\times2\\times3\\times4\\times5\\times6\\times7\\times$$$$8\\times9\\times10\\times11\\times12\\times13\\times14\\times15 = $$$$1307 674 368000$$, and we multiply each of these $$15$$ numbers by $$10$$, the new product will have an additional $$15$$ zeroes, and $$15+4=19$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "87", "queId": "07852ad0a5dd49099d246ecf18cc6b26", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If a natural number can be written as the sum of both two and three consecutive natural numbers, then we can call it a Think Number. What is the largest Think Number no larger than $5789$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5786$$ "}], [{"aoVal": "B", "content": "$$5787$$ "}], [{"aoVal": "C", "content": "$$5788$$ "}], [{"aoVal": "D", "content": "$$5789$$ "}], [{"aoVal": "E", "content": "$$5784$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["The number can be written as $$n+(n+1)=2n+1(n\\geqslant 1)$$ and $$x+(x+1)+(x+2)=3x+3$$. It must be a multiple of $3$ but leaves a remainder of $1$ when divided by $2$ but leaves a remainder of $1$. $5790$ can be divisible by both $2$ and $3$, so it is $5790-3=5787$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "90", "queId": "17c0e9afb1244d28bf3f1ed85a5b0c45", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of three $2-$digit consecutive numbers is the maximum 2-digit number. What is their product? ", "answer_option_list": [[{"aoVal": "A", "content": "$$99$$ "}], [{"aoVal": "B", "content": "$$25900$$ "}], [{"aoVal": "C", "content": "$$35904$$ "}], [{"aoVal": "D", "content": "$$34589$$ "}], [{"aoVal": "E", "content": "$$39804$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["$99\\div3=33$ $32+33+34=99$ $32\\times33\\times34=35904$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "92", "queId": "0ee4855c935442f1aea60daa349335e0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A student thinks of a natural number. She divides the number by $$9$$ and the remainder is $$7$$. What is the remainder when double that number is divided by $$9$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["The remainder of $$A$$ $$\\div9$$ is $$7$$, and $$2A=A+A$$. Therefore the remainder of $$2A\\div9$$ is $$7+7=14$$. $$14= 9+5$$, therefore the remainder is $$5$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "93", "queId": "d05b525d24e941939a340f9e31890c38", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Salah has collected more than $$20$$ football cards. When he puts his cards in piles of four, he has three cards left over. When he puts the cards in piles of five, he has four cards left over. Which of the following could be the number of cards he has in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$27$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$35$$ "}], [{"aoVal": "D", "content": "$$39$$ "}], [{"aoVal": "E", "content": "$$43$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["The number of Salah\\textquotesingle s cards is $$3$$ more than a multiple of $$4$$, and $$4$$ more than a multiple of $$5$$. Of the two-digit options given, the only one that satisfies both criteria is $$39(=9\\times4+3 =7\\times5+4)$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "94", "queId": "3ca92f90d377400880b73a0eecf799a2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Timothy writes down the number 24. He reverses the digits to make the number 42. He then works out that 42 is 18 more than his starting number, 24. Nicole writes down a whole number between 10 and 99. She also reverses the digits of her number. She finds that this makes a number that is 72 more than her starting number. What was the last digit of Nicole's starting number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["Let the original number be ab, and reverse it to be ba, calculated by the place value principle, ba-ab=72 10 + a - b (10) a + b = a = 9 b - 9, 72-8 a = b, b = 9, a = 1, the original number is 19, last digit is 9. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "98", "queId": "5d18daebf05f4e23afa130a4a322ba48", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many whole numbers greater than $$0$$ whose square is equal to its square root? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["The only positive whole number whose square is equal to its square root is $$1$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "101", "queId": "0b14c43cadd644cb841fb5c1f23e9393", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many numbers of the following are divisible by $3$? $$\\textasciitilde$$ $314\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} 528\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~899\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~1024\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~1356\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~3336$ $\\textasciitilde$ $\\textasciitilde$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["The sums of the digits of $528$, $1356$, and $3336$ are multiples of $3$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "104", "queId": "337959cea9bd45108e317f92daedc0a2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Of the following, which has the largest odd factor? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["Keep dividing each by $$2$$ until you get an odd number. $$\\text{A}$$.$$2\\times15$$. $$\\text{B}$$.$$2\\times2\\times 2 \\times 2\\times2\\times1$$. $$\\text{C}$$.$$2\\times2\\times9$$. $$\\text{D}$$.$$2\\times2 \\times 2\\times5$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "108", "queId": "7459d240ed5c454ba0033702e69b1703", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Is it possible to find two numbers such that if you add up the sum and the difference of these two numbers, you get $$999$$? If yes, please write it out. If not, please give your reason. ", "answer_option_list": [[{"aoVal": "A", "content": "Possible "}], [{"aoVal": "B", "content": "Not possible "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["For example you have number A and B. A+B = C A-B = D (A+B)+(A-B)=2A Thus, C+D must always be even number. Cannot be odd number. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "110", "queId": "138a883444a54268ba9e51acff7046d9", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Weili wanted to pack $60$ apples and $75$ pears into as many bags as possible, with no remainder. She packed the same number of fruit in each bag. The number of apples in each bag was the same. How many apples were there in each bag? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["Factors of $60$: $1$, $2$, $3$, $4$, $5$, $6$, $10$, $12$, $15$, $20$, $30$ and $60$, Factors of $75$: $1$, $3$, $5$, $15$, $25$ and $75$, Since Weili wanted to pack the apples and pears into as many bags as possible, we need to choose the largest common factor of both $60$ and $75$. Largest common factor $\\rightarrow 15$, Hence, Weili should use $15$ bags. Number of apples in each bag$\\rightarrow60\\div15$ $=4$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "113", "queId": "087ffa4c581a41dfafb354280510df95", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following integers is not a multiple of $$45$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$765$$ "}], [{"aoVal": "B", "content": "$$675$$ "}], [{"aoVal": "C", "content": "$$585$$ "}], [{"aoVal": "D", "content": "$$495$$ "}], [{"aoVal": "E", "content": "$$305$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["Note that $$45=5\\times 9$$. As $$5$$ and $$9$$ are coprime, a positive integer is a multiple of $$45$$ if and only if it is a multiple of both $$5$$ and $$9$$. The units digit of all five options is $$5$$, so they are all multiples of $$5$$. An integer is a multiple of $$9$$ if and only if the sum of its digits is also a multiple of $$9$$. The sums of the digits of the five options is $$18$$, $$18$$, $$18$$, $$18$$ and $$8$$. So $$305$$ is the only one of the options which is not a multiple of $$9$$ and hence is not a multiple of $$45$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "119", "queId": "25b69ee34dc04a4e8b32b76b80e172d9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A whole number is a perfect square if it can be expressed as the product of two equal whole numbers. What is the sum of the first $10$ perfect squares? ", "answer_option_list": [[{"aoVal": "A", "content": "$$384$$ "}], [{"aoVal": "B", "content": "$$385$$ "}], [{"aoVal": "C", "content": "$$386$$ "}], [{"aoVal": "D", "content": "$$387$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["We can list out the perfect squares: $1\\times 1 = 1$ $2\\times 2 = 4$ $3\\times 3 = 9$ $4\\times 4 = 16$ $5\\times 5 = 25$ $6\\times 6 = 36$ $7\\times 7 = 49$ $8\\times 8 = 64$ $9\\times 9 = 81$ $10\\times 10 = 100$ Hence the sum of the first $10$ perfect squares is $385$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "121", "queId": "3cc548da950c43e985868b667d5c2443", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many zeros does the number $$12^{2}\\times15^{3}$$ end with? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->The Number of Zeros at the end of a Product"], "answer_analysis": ["omitted "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "124", "queId": "1ca46b2d33e44987ab375415ac314f91", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Arthur writes down three two-digit integers. One is square, one is prime and one is triangular. She uses the digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ and $$6$$ exactly once each. Which largest prime does he write? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$13 $$ "}], [{"aoVal": "B", "content": "$$23 $$ "}], [{"aoVal": "C", "content": "$$31 $$ "}], [{"aoVal": "D", "content": "$$41 $$ "}], [{"aoVal": "E", "content": "$$43$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Applying Special Prime Numbers"], "answer_analysis": ["First note that Arthur can write down three squares, namely $$16$$, $$25$$ and $$36$$. Also, he can write down four triangular numbers, namely $$15$$, $$21$$, $$36$$ and $$45$$. If he chooses $$16$$ and $$45$$ for the square and triangular number respectively, then the remaining digits are $$2$$ and $$3$$, the prime is $$23$$. If he chooses $$25$$ and $$36$$ then the remaining digits are $$1$$ and $$4$$, the prime is $$41$$. If he chooses $$36$$ for the square number, the remaining difits can be a prime. So the largest prime he write is $$41$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "126", "queId": "090610b0093b4db287ce21c92fde9cc8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many three-digit positive integers have an odd number of even digits? ", "answer_option_list": [[{"aoVal": "A", "content": "$$150$$ "}], [{"aoVal": "B", "content": "$$250$$ "}], [{"aoVal": "C", "content": "$$350$$ "}], [{"aoVal": "D", "content": "$$450$$ "}], [{"aoVal": "E", "content": "$$550$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["There are only 2 ways for an odd number of even digits: 1 even digit or all even digits. Case 1: 1 even digit There are $5 \\cdot 5=25$ ways to choose the odd digits, 5 ways for the even digit, and 3 ways to order the even digit. So, $25 \\cdot 5 \\cdot 3=375$. However, there are $5 \\cdot 5=25$ ways that the hundred\\textquotesingle s digit is 0 and we must subtract this from 375 , leaving us with 350 ways. Case 2: all even digits There are $5 \\cdot 5 \\cdot 5=125$ ways to choose the even digits, and $5 \\cdot 5=25$ ways where the hundred\\textquotesingle s digit is 0 . So, $125-25=100$. Adding up the cases, the answer is $100+350=$ (D) 450 . "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "129", "queId": "667aa1112c2047eabd57b6781fb4daac", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many different primes are in the prime factorization of $$2016$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Prime Factorization (Equations)"], "answer_analysis": ["$$2016=2\\times2\\times2\\times2\\times2\\times3\\times3\\times7$$; there are $$3$$ different primes. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "131", "queId": "b92bf610c3a549dc90ab250dd473afc7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A whole number is a perfect square if it can be expressed as the product of two equal whole numbers. For example, $$9$$ is a perfect square since $$9= 3\\times 3$$. How many perfect squares are greater than $$0$$ and less than $$1000$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$33$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["A whole number is a perfect square if it is the product of two equal whole numbers. Thus, $$1\\times1$$ and $$2\\times 2$$ and $$3\\times 3$$ and $$4\\times 4$$ are perfect squares. Continue until the product is bigger than $$1000: 30\\times 30 = 900$$; $$31\\times 31 = 961$$; $$32\\times 32 = 1024$$ (too big). "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "135", "queId": "0f9e6ad41b1840a59c8ca6c7df0e0c73", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole numbers $A$, $B$ and $C$. $A\\times B=45$, $B\\times C=50$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$23$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$45=3\\times 3\\times 5$ $50=2\\times 5\\times 5$ Because $B$ is the factor both number contains, $B=5$ Thus, $A=9$, $C=10$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "136", "queId": "13d63cd420984e0ea737a8722ca5ce26", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eddie has some baseball cards from the $$1920$$s. If he divides the number of cards he has by $$4$$, then he will have $$3$$ remaining cards; if he divides the number of cards he has by $$5$$, he will have $$4$$ remaining cards; if he divides the number of cards he has by $$7$$, he will have $$6$$ remaining cards. How many cards does Eddie have at least? ", "answer_option_list": [[{"aoVal": "A", "content": "$$139$$ "}], [{"aoVal": "B", "content": "$$140$$ "}], [{"aoVal": "C", "content": "$$141$$ "}], [{"aoVal": "D", "content": "$$142$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["The number of cards after adding $$1$$ is divisible by $$4$$, $$5$$, and $$7$$. Since the least common multiple of $$4$$, $$5$$, and $$7$$ is $$4\\times5\\times7=140$$, Eddie has $$140-1=139$$ cards at least. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "138", "queId": "0bf3ece2c2544d78b8a4e6a1ffe926d6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of three $2-$digit consecutive even numbers is $$\\overline{\\textbackslash\\#\\textbackslash\\#\\textbackslash\\#2}$$. What is their sum? ", "answer_option_list": [[{"aoVal": "A", "content": "$$42$$ "}], [{"aoVal": "B", "content": "$$64$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$48$$ "}], [{"aoVal": "E", "content": "$$52$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["Considering the ones digit and the value of the product, which is less than $10000$, only $14, 16,$ and $18$ match the condition. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "139", "queId": "4ab20c5c7b66449fbf43b3e4a534f3f3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The square root of $$16$$ is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$64$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["The square root of $$16$$ is $$4$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "140", "queId": "183ebdb3da5842518bcd4158a1db450b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the smallest prime number that is greater than $$90$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$91$$ "}], [{"aoVal": "B", "content": "$$96$$ "}], [{"aoVal": "C", "content": "$$97$$ "}], [{"aoVal": "D", "content": "$$99$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["We only have one prime number between $$90$$ and $$100$$, which is $$97$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "142", "queId": "667e06a7e6d846bfb88f90807a8b2943", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Find the smallest whole number between $$14$$ and $$40$$ that is divisible by $$3$$ and by $$4$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["Multiple of $$3$$ and $$4$$ also a multiple of $$12$$. $$12, 24, 36, 48, \\cdots $$ Smallest multiple between $$14$$ and $$40$$ is $$24$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "143", "queId": "0fc733896f0941399ebe2fa12a71c962", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the prime factors of $$231$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$152$$ "}], [{"aoVal": "D", "content": "$$383$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Prime Factorization (Equations)"], "answer_analysis": ["Since $$231=3\\times7\\times11$$, the sum of its prime factors is $$3 +7+11=21$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "148", "queId": "21517993e5724e75ba514ce4dcc7de76", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I add up all even numbers between $$1$$ and $$101$$. Then from my total I subtract all odd numbers between $$0$$ and $$100$$. What is the result? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$255$$ "}], [{"aoVal": "E", "content": "$$2525$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers"], "answer_analysis": ["Let the required result be $$S$$. Then $$S= \\left( {2+4+6+\\cdots +100} \\right)- \\left( {1+3+5+\\cdots +99} \\right)~ $$ $$\\textasciitilde\\textasciitilde= \\left( {2-1} \\right) + \\left( {4-3} \\right) + \\left( {6-5} \\right) +\\cdots +\\left( {100-99} \\right) $$ $$\\textasciitilde\\textasciitilde=50\\times 1=50$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "158", "queId": "3857c604b5604d849b6e93d1c6c5435c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of two whole numbers is $$42$$. Their sum \\emph{cannot} be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$43$$ "}], [{"aoVal": "B", "content": "$$33$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["All but $$33$$ can be represented as required, as shown below. A. $$43=1+42$$ B. $$33$$ C. $$23=2+21$$ D. $$13=6+7$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "160", "queId": "0c9e113654bd4737bd294dd0622a3153", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of two prime numbers is $$99$$. What is the difference between the two prime numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$89$$ "}], [{"aoVal": "B", "content": "$$92$$ "}], [{"aoVal": "C", "content": "$$95$$ "}], [{"aoVal": "D", "content": "$$97$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Applying Special Prime Numbers"], "answer_analysis": ["Because $$99$$ is an odd number, one of these two prime numbers must be an even prime number. The only choice is $$2$$. So the other is $$99-2 = 97$$. So, the difference between the two numbers is $$95$$. Therefore, we choose $$\\rm C$$ . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "163", "queId": "144c1f84e77140e2865ea66f640ac983", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Andy writes down the largest two-digit prime such that each of its digits is prime. Baker writes down the smallest three-digit prime such that each of its digits is prime. Carl adds Andy\\textquotesingle s number and Baker\\textquotesingle s number. What answer does Carl obtain? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$174 $$ "}], [{"aoVal": "B", "content": "$$185 $$ "}], [{"aoVal": "C", "content": "$$198 $$ "}], [{"aoVal": "D", "content": "$$209 $$ "}], [{"aoVal": "E", "content": "$$296$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Applying Special Prime Numbers"], "answer_analysis": ["The prime digits are $$2$$, $$3$$, $$5$$ and $$7$$. So the largest two-digit integer whose digits are both prime is $$77$$. However, $$77$$ is not prime, nor is $$75$$, but $$73$$ is prime. So Andy writes down $$73$$. The smallest three-digit integer whose digits are both prime is $$222$$. However, $$222$$ is not prime, but $$223$$ is prime. So Baker writes down $$223$$. Therefore the answer which Carl obtains is $$73 +223 = 296$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "167", "queId": "5d4d5d4c6c2149488a788ddca4e97898", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Which of the following numbers cannot be written as the sum of $$4$$ consecutive whole numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1994$$ "}], [{"aoVal": "B", "content": "$$2042$$ "}], [{"aoVal": "C", "content": "$$2050$$ "}], [{"aoVal": "D", "content": "$$2060$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["$$497+498+499+500 =1994$$; $$509+510+511+512 = 2042$$; $$511+512+513+514=2050$$. (Divide by $$4$$, and \"start\"~near the quotient.) "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "168", "queId": "2620325e3a3a4ebaabd12ebd40934a7d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A multi-digit number$$\\underbrace{20092009\\cdot \\cdot \\cdot 2009}\\_{n 2009s}736$$, can be divisible by ~$$11$$ . The smallest value of $$n$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["$$3$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "170", "queId": "33d5ead5902b4215a92cf5234639525e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are some flowers along the corridor arranged in the following order: $5$ purple, $3$ red, $2$ yellow, $2$ pink, $3$ red, $2$ yellow, $2$ pink $\\cdots$ If there are $100$ flowers altogether, how many red flowers are there altogether? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$39$$ "}], [{"aoVal": "D", "content": "$$42$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["$$3+2+2=7$$; $100-5=95$ $95\\div7=13R4$; $$13$$$\\times$$$3$$+$$3$$=$$42$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "171", "queId": "3d05fd44b1194a60a6e2671fdeb773a9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the $${{9}^{\\text{th}}}$$ Century BC, an Indian mathematician named Al Khwarizmi wrote a book about math calculations. Since his calculations were always written on a clay tablet, he was afraid the calculation process might be lost. So, he created a system to determine whether his calculations were correct. Example: $$1234+18983+18922=39039$$, $$1234$$ divided by $$9$$ yields a remainder of $$1$$, $$18983$$ divided by $$9$$ yields a remainder of $$2$$, $$18922$$ divided by $$9$$ yields a remainder of $$4$$, When the remainders are added up and divided by $$9$$, the remainder is $$7$$. Dividing the number on the right-hand side of the equals sign by $$9$$ yields a remainder of $$6$$. Therefore, $$7$$ does not equal $$6$$, making the above equation incorrect. Use the method above to determine whether the following equations are correct or not:． ①$$2638457+3521983+6745785=12907225$$, ②$$7832145-2167953=5664192$$. ", "answer_option_list": [[{"aoVal": "A", "content": "√√ "}], [{"aoVal": "B", "content": "√$$\\times $$ "}], [{"aoVal": "C", "content": "$$\\times $$√ "}], [{"aoVal": "D", "content": "$$\\times $$$$\\times $$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Casting Out Nines"], "answer_analysis": ["$$(1)$$ Dividing the numbers on the left-hand side of the equals sign by $$9$$ yields remainders of $$8$$, $$4$$, and $$6$$. The sum of the remainders divided by $$9$$ is $$0$$. Dividing the right-hand side of the equals sign by $$9$$ yields a remainder of $$1$$. Therefore, $$0$$ does not equal $$1$$, making the equation incorrect. $$(2) $$The remainders on both sides of the equation are $$6$$. We can check by performing the calculation normally. It is correct. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "178", "queId": "10a3bd5a9e7e4c8aaab439a559fab821", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If a four-digit number $$5A2A$$ can be divisible by both $$4 $$ and $$5$$, the digit that $$A$$ represents is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["We consider the last two-digit to see if a number is divisible by $4$. We consider the last one digit to see if a number is divisible by $5$. If $$\\overline{\\textasciitilde5A2A\\textasciitilde}$$ is divisible by $5$, the ones digit can only be $5$ or $0$. When the ones digit is $0$, the number that is formed by the last two digits, $20$, is divisible by $4$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "181", "queId": "387e7b6d73084f81949cc6655cc1ee3f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If my school has four times as many girls as boys, then the number of girls minus the number of boys \\emph{could} be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2013$$ "}], [{"aoVal": "B", "content": "$$2011$$ "}], [{"aoVal": "C", "content": "$$2009$$ "}], [{"aoVal": "D", "content": "$$2008$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders"], "answer_analysis": ["For every $$4$$ girls and $$1$$ boy, the difference is $$3$$. The difference is always divisible by $$3$$. Of the choices, only $$2013$$ is divisible by $$3$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "184", "queId": "0d671eddbe1b4961bdcf1b01bff92fc7", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "The values of length and width of a rectangle are both prime numbers. If the area of that rectangle is $10$, what is its perimeter? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["$10=2\\times 5$, the length is $5$ and the width is $2$. $(2+5)\\times 2=14$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "190", "queId": "21c7d15fe7e34284babaaeef8b3929d7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is divisible by all of the integers from $$1$$ to $$10$$ inclusive? ", "answer_option_list": [[{"aoVal": "A", "content": "$$23\\times34$$ "}], [{"aoVal": "B", "content": "$$34\\times45$$ "}], [{"aoVal": "C", "content": "$$45\\times56$$ "}], [{"aoVal": "D", "content": "$$56\\times67$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"], "answer_analysis": ["Of the options given, $$23\\times 34$$, $$56\\times 67$$ and $$67\\times 78$$ are all not divisible by $$5$$, so may be discounted. Also $$34$$ is not divisible by $$4$$ and $$45$$ is odd, so $$34\\times 45$$ may also be discounted as it is not divisible by $$4$$. The only other option is $$45\\times 56$$. As a product of prime factors, $$45\\times 56=2^{3}\\times3^{2}\\times5\\times7$$, so it is clear that it is divisible by all of the integers from $$1$$ to $$10$$ inclusive. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "192", "queId": "10f119e529184ad9a006b6911dff2f40", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "John's age is a multiple of $$7$$ this year. His age next year will be a multiple of $$6$$. What is John's age this year? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$28$$ "}], [{"aoVal": "C", "content": "$$35$$ "}], [{"aoVal": "D", "content": "$$42$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "193", "queId": "21d3fdfdb74c4154bced08d42a146944", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the least possible remainder when an even number is divided by $$7$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders"], "answer_analysis": ["When $$14$$ (or any other even multiple of $$7$$) is divided by $$7$$, the remainder is $$0$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "195", "queId": "8add4bcaf8434eef8f27b437bfbb419b", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following is a multiple of $8$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$28$$ "}], [{"aoVal": "D", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["$3\\times 8=24$, so $24$ is a multiple of $8$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "199", "queId": "58cc498322ab4f44bd828644082cdd32", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole number $A$, $B$, $C$. $A\\times B=35$, $B\\times C=84$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$23$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$35=5\\times 7$ $84=2\\times 2\\times 3\\times 7$ Because $B$ is the factor both number contains, $B=7$ Thus, $A=5$, $C=12$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "205", "queId": "21f6d64af90745d5b924f25e5f2b2323", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If a whole number is divisible by $$111$$, then it must be divisible by ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$37$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["Of the following choices, only $$37$$ is a factor of $$111$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "209", "queId": "267e5f616b95459fb521f47f4b9b7441", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following is an odd number？ ", "answer_option_list": [[{"aoVal": "A", "content": "$$490$$ "}], [{"aoVal": "B", "content": "$$558$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$627$$ "}], [{"aoVal": "E", "content": "$$452$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["Odd numbers end with 1, 3, 5, 7, 9 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "210", "queId": "194addcb44c741538f37be4c5790c5ae", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the biggest prime number that is smaller than $$50$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$43$$ "}], [{"aoVal": "B", "content": "$$45$$ "}], [{"aoVal": "C", "content": "$$47$$ "}], [{"aoVal": "D", "content": "$$49$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["We have $$3$$ prime numbers between $$40$$ and $$50$$: $$41$$, $$43$$, $$47$$, so we choose $$\\text{C}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "212", "queId": "4fa106796f3a4082bf6f6c88051c845a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Divide an odd number by $$4$$. The remainder is always． ", "answer_option_list": [[{"aoVal": "A", "content": "odd　 "}], [{"aoVal": "B", "content": "even　 "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "prime　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers"], "answer_analysis": ["Eliminate choices. Try several examples. A good example is $$7\\div4$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "213", "queId": "220b0cbde5e148179aaa68928887f5db", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\left(\\sqrt{64}+\\sqrt{64}\\right)^{2}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$64$$ "}], [{"aoVal": "C", "content": "$$128$$ "}], [{"aoVal": "D", "content": "$$256$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["$$\\left(\\sqrt{64}+\\sqrt{64}\\right)^{2}=\\left(8+8\\right)^{2}=\\left(16\\right)^{2}=256$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "218", "queId": "6b618b1c1aaa4a3084ab66b4afd5636e", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "The product of two whole numbers is $$5$$. What is the sum of these two numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["If the product of two whole numbers is $$5$$, then one of the numbers is $$5$$ and the other is $$1$$. Their sum is $$6$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "223", "queId": "fa496985a7524ce996e4046f4afc2a43", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The thousands digit of the sum of 5+55+555+5555+55555 is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases"], "answer_analysis": ["$$61725$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "227", "queId": "58e74ab28cc94d75a8f7852e8b04e547", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of an odd number and an even number is always． ", "answer_option_list": [[{"aoVal": "A", "content": "an odd number "}], [{"aoVal": "B", "content": "an even number "}], [{"aoVal": "C", "content": "a prime number "}], [{"aoVal": "D", "content": "a multiple of $3$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers"], "answer_analysis": ["The sum is always odd. For example, $15 + 10 = 25$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "228", "queId": "8f95d36253214a9b8f2169bcdce07332", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is correct? $72=2^{x}\\times3^{y}$ $539=z^{2}\\times11$ ", "answer_option_list": [[{"aoVal": "A", "content": "$x\\textgreater y\\textgreater z$ "}], [{"aoVal": "B", "content": "$y\\textgreater z\\textgreater x$ "}], [{"aoVal": "C", "content": "$x\\textgreater y=z$ "}], [{"aoVal": "D", "content": "$z\\textgreater y\\textgreater x$ "}], [{"aoVal": "E", "content": "$z\\textgreater x\\textgreater y$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$x=3$, $y=2$, $z=7.$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "231", "queId": "795276ddcc114c868bc42ff31f54ed82", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The multiplication $$abc\\times de=7632$$ uses each of the digits $$1$$ to $$9$$ exactly once. What is the value of $$b$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"], "answer_analysis": ["Note first that $$7632 =2\\times2\\times2\\times2\\times3\\times3\\times53$$. Therefore either the two-digit number $$de = 53$$ or the three-digit number $$abc$$ is a multiple of $$53$$. Since the multiplication uses each of the digits $$1$$ to $$9$$ once and $$7632$$ contains a $$3$$, the option $$de= 53$$ is not allowable. Hence we need to find a three-digit multiple of $$53$$ that does not share any digits with $$7632$$ and divides into $$7632$$ leaving an answer that also does not share any digits with $$7632$$. We can reject $$2 \\times 53 = 106$$ since it contains a $$6$$ but $$3 \\times 53 = 159$$ is a possibility. The value of $$7632\\div159$$ is $$2\\times2\\times2\\times2\\times3 = 48$$ which does not have any digits in common with $$7632$$ nor with $$159$$. We can also check that no other multiple of $$53$$ will work. Therefore the required multiplication is $$159 \\times 48 = 7632$$ and hence the value of $$b$$ is $$5$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "235", "queId": "11ed2fcc137541a988097e78d4d2683c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If a natural number can be written as the sum of both two and three consecutive natural numbers, then we can call it a Think Number. What is the largest Think Number no larger than $2022$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2007$$ "}], [{"aoVal": "B", "content": "$$2009$$ "}], [{"aoVal": "C", "content": "$$2012$$ "}], [{"aoVal": "D", "content": "$$2015$$ "}], [{"aoVal": "E", "content": "$$2019$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["The number can be written as $$n+(n+1)=2n+1(n\\geqslant 1)$$ and $$x+(x+1)+(x+2)=3x+3$$. It must be a multiple of $3$ but leaves a remainder of $1$ when divided by $2$. $2022$ can be divisible by both $2$ and $3$, so it is $2022-3=2019$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "236", "queId": "38d6124f1426473ea2707454e46a10f8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "($$1999$$ Math League, Grade $$5$$, Question \\#$$16$$) The average of two odd numbers is always ． ", "answer_option_list": [[{"aoVal": "A", "content": "odd$$ $$ "}], [{"aoVal": "B", "content": "even$$ $$ "}], [{"aoVal": "C", "content": "prime$$ $$ "}], [{"aoVal": "D", "content": "whole$$ $$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Odd and Even Applications"], "answer_analysis": ["Avg of $$1$$ \\& $$5$$ is $$3$$. Avg of $$1$$ and $$7$$ is $$4$$. Both are whole numbers. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "238", "queId": "19baf57d2fba4f7f9f756ada2f1ff893", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the missing number in the box?~\\uline{~~~~~~~~~~}~ $$\\square \\div7=83 \\rm R 4$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$332$$ "}], [{"aoVal": "B", "content": "$$339$$ "}], [{"aoVal": "C", "content": "$$581$$ "}], [{"aoVal": "D", "content": "$$585$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders->Relationship between Dividend, Divisor, Quotient and Remainder in Division"], "answer_analysis": ["$$83\\times7=581$$ $$581+4=585$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "239", "queId": "623529589bc7469cbad311a6f05602a2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If the last $$2$$ digits of an integer are $$84$$, the integer must be divisible by． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders"], "answer_analysis": ["The sum of any multiple of $$100$$ and $$84$$ is divisible by $$4$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "244", "queId": "8afc802a8c304199b1040f11ffa2e92a", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A $14$-digit. number $666666 XY 444444$ is a multiple of $26$. If $X$ and $Y$ are both positive, what is the smallest vaue of $X+ Y$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["Since $1001$ is a multiple of $13$, $111111 = 111 \\times 1001$ is also a multiple of $13$. It follows that both $666666$ and $444444$ are both multiples of $26$. $666666XY 444444 = 66666600000000 + XY 000000 + 444444$ $\\Rightarrow XY$ must be divisible by $13$. Smallest $X+Y=1+3=4$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "246", "queId": "15daeda4d7d8493a86ce791dfd0e0c44", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following numbers are prime numbers? $$\\textasciitilde$$ $103$~ ~ ~ ~ ~ ~ ~ ~ ~$115$~ ~ ~ ~ ~ ~ ~ ~ ~$127$~ ~ ~ ~ ~ ~ ~ ~ ~$139$ $$\\textasciitilde$$ ", "answer_option_list": [[{"aoVal": "A", "content": "Only $103$ "}], [{"aoVal": "B", "content": "$103$ and $$127$$ "}], [{"aoVal": "C", "content": "$103$ and $139$ "}], [{"aoVal": "D", "content": "$103$, $127$, and $139$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["$115=5\\times23$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "247", "queId": "15e37bdbe0a54ceab08892246501262b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is a prime number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$39$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$79$$ "}], [{"aoVal": "D", "content": "$$87$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["We note that the other options are not prime numbers because: $39 = 3 \\times 13$ $50 = 5 \\times 10$ $87 = 3 \\times 29$ Hence by the process of elimination, $79$ is a prime number. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "249", "queId": "38efb4a2a3124347b63231d17ce29f19", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "It is known that the positive whole number $$n$$ is divisible by $$21$$ and by $$9$$. Which of the answers below can be the number of divisors of the number $$n$$? ($$2002$$ Math kangaroo Problems, Level $$7-8$$, Question \\#$$21$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Theorem of the Number of Factors of a Number->Applying Theorem of the Number of Factors of a Number Directly->The Total Number of Factors"], "answer_analysis": ["$n$ is divisible by $63$. $63=3^{2}\\times7$. $63$ has $(2+1)\\times(1+1)=6$ divisors. Thus, $n$ has at least $6$ divisors, and $n$ can\\textquotesingle t have an odd number of divisors. Option $D$ is the only possible answer. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "250", "queId": "26e86ced57414fa49c00adba305c3144", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A prime number is a number greater than $$1$$ whose only whole number factors are itself and $$1$$. What is the smallest prime number greater than $$50$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$51$$ "}], [{"aoVal": "B", "content": "$$52$$ "}], [{"aoVal": "C", "content": "$$53$$ "}], [{"aoVal": "D", "content": "$$59$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["A prime number is a number greater than $$1$$ whose only whole number factors are itself and $$1$$. Of the numbers greater than $$50$$, $$51 = 3\\times17$$ and $$52 = 2\\times26$$. The first prime is $$53$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "253", "queId": "79611e40be044d19a46f7909ef3fbd11", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The $7$-digit numbers $\\underline{74 A 52 B 1}$ and $\\underline{326 A B 4 C}$ are each multiples of $3$ . Which of the following could be the value of $C$ ? (2014 amc 8 Problem, Question \\#21) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["Since both numbers are divisible by $3$ , the sum of their digits has to be divisible by three. $7+4+5+2+1=19$. To be a multiple of $3$ , $A+B$ has to be either $2$ or $5$ or $8 \\ldots$ and so on. We add up the numerical digits in the second number; $3+2+6+4=15$. We then add two of the selected values, $5$ to $15$ , to get $20$ . We then see that $C=1,4$ or $7,10 \\ldots$ and so on, otherwise the number will not be divisible by three. We then add 8 to 15 , to get 23 , which shows us that $C=1$ or $4$ or $7 \\cdots$ and so on. To be a multiple of three, we select a few of the common numbers we got from both these equations, which could be $1,4$, and $7$ . However, in the answer choices, there is no $7$ or $4$ or anything greater than $7$ , but there is a $1$ , so $(\\mathbf{A}) 1$ is our answer. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "254", "queId": "12578a83726446f9a1cfa9ba08da18d8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the greatest prime number that is smaller than $$50$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$43$$ "}], [{"aoVal": "B", "content": "$$45$$ "}], [{"aoVal": "C", "content": "$$47$$ "}], [{"aoVal": "D", "content": "$$49$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["We have $$3$$ prime numbers between $$40$$ and $$50$$: $$41$$, $$43$$, $$47$$, so we choose $$\\text{C}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "255", "queId": "22802dfbd38446859fc56e4357436d8e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is the correct expression of quinary (base $5$ numeral system)? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\left (8231\\right )\\_5$ "}], [{"aoVal": "B", "content": "$\\left (2001\\right )\\_5$ "}], [{"aoVal": "C", "content": "$\\left (4341\\right )\\_7$ "}], [{"aoVal": "D", "content": "$\\left (2345\\right )\\_5$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Properties and Applications of Number Bases"], "answer_analysis": ["In quinary, the base number must be $5$, and all the digits in the brackets must be less than $5$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "256", "queId": "5da2e8c215384261b1d6df4e4cd99b4d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many zeros does the number $$14^{3}\\times15^{4}$$ end with? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->The Number of Zeros at the end of a Product"], "answer_analysis": ["omitted "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "259", "queId": "8fa98ae319f943ed9597748132d90a30", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many prime numbers are there between $90$ and $110$? $$\\textasciitilde$$ $$\\textasciitilde$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$3$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["$97$, $101$, $103$, $107$, $109$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "260", "queId": "1286dff0dd9143cbbc081271c29fb303", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many positive factors of $$36$$ are also multiples of $$4$$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$36={{2}^{2}}\\times {{3}^{2}}$$, so the number of its factors would be $$\\left( 2+1 \\right)\\times \\left( 2+1 \\right)=9$$, Among them, there are $$\\left( 2+1 \\right)\\times 1=3$$ factors which has $${{2}^{2}}$$ as its factors. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "263", "queId": "e7bd6a72b3b1488d87040777f149a7bd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of two different primes hasdivisors. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["For any $$2$$ such primes, the factors are $$1$$, the primes, and their product. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "268", "queId": "34857bf2e8604df5ae07ea01ecdf6e2b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$9$$, the remainder is $$1$$. When $$N$$ is divided by $$10$$, the remainder is $$3$$. What is the remainder when $$N$$ is divided by $$11$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["The smallest possible $$N$$ is $$73$$, and $$73 \\div 11\\rm R7$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "270", "queId": "1e5a5e4a0742456697b644b8e75922e5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What are the last $2$ digits on the right in the expansion of the expression $2^{2018201}- 8$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$44$$ "}], [{"aoVal": "D", "content": "$$88$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders "], "answer_analysis": ["$2^{10}=1024\\equiv24($mod$100)$ $\\left (2^{10}\\right )^{2}=1024^{2}\\equiv76($mod$100)$ $\\left (2^{10}\\right )^{3}\\equiv 76\\times24\\equiv24($mod$100)$ $\\left (2^{10}\\right )^{4}\\equiv76($mod$100)$ $\\cdots\\cdots$ $$2^{2018201}-8=2\\left (2^{2018200}\\right )-8 \\equiv 2\\left (76\\right )-8 \\equiv 44($$mod$$100)$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "271", "queId": "547d49015b884269b0abae24ad709cad", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A student thinks of a natural number. She divides the number by $$9$$ and the remainder is $$7$$. What is the remainder when double that number is divided by $$9$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["The remainder of $$A$$ $$\\div9$$ is $$7$$, and $$2A=A+A$$. Therefore the remainder of $$2A\\div9$$ is $$7+7=14$$. $$14= 9+5$$, therefore the remainder is $$5$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "274", "queId": "1e6d19bc761b4a43a6af8b99eec19c74", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many factors of $$36$$ are also multiples of $$4$$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$36={{2}^{2}}\\times {{3}^{2}}$$, so the number of its factors would be $$\\left( 2+1 \\right)\\times \\left( 2+1 \\right)=9$$, Among them, there are $$\\left( 2+1 \\right)\\times 1=3$$ factors which has $${{2}^{2}}$$ as its factors. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "276", "queId": "6b8f91228086409285112641c263825d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "♥ $$\\times$$ ☺ $$=$$ ♦ ☺ is an even number. which of the following gives an odd answer? ", "answer_option_list": [[{"aoVal": "A", "content": "♦ $$-\\textasciitilde3$$ "}], [{"aoVal": "B", "content": "☺ $$+$$ ♦ "}], [{"aoVal": "C", "content": "☺ $$\\times$$ ☺ "}], [{"aoVal": "D", "content": "♦ $$\\times$$~♦ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers"], "answer_analysis": ["♥ $$\\times$$ ☺ $$=$$ ♦ Since ☺ is an even number,~♦ must also be an even number. ♦ $$-\\textasciitilde3$$ is the only option to given an odd answer because even $$-$$ odd $$=$$ odd. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "277", "queId": "165c845bd9614b68809f686fdf67cae0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the remainder when we divide $19^{2021}$ by $4$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Congruence"], "answer_analysis": ["We note that $19^{2} \\equiv 1$ $( \\text{mod} \\textbackslash; 4)$ and hence: $19^{2021} \\equiv 1^{1010} \\times 3 \\equiv 3$ $( \\text{mod} \\textbackslash; 3)$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "279", "queId": "349794849e1c462dbac1ad35e306dd51", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Two whole numbers differ by $$1$$. If one number has $$3$$ digits and the other has $$4$$ digits, what is their sum? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1001$$ "}], [{"aoVal": "B", "content": "$$1100$$ "}], [{"aoVal": "C", "content": "$$1999$$ "}], [{"aoVal": "D", "content": "$$2001$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["If $$1$$ more than a $$3$$-digit number is a $$4$$-digit number, then the numbers are $$999$$ and $$1000$$ and their sum is $$1999$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "280", "queId": "3da95d6ffeb54b13852c46d737f81de7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the last digit of the smallest positive integer whose digits add to $$2022$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5 $$ "}], [{"aoVal": "B", "content": "$$6 $$ "}], [{"aoVal": "C", "content": "$$ 7 $$ "}], [{"aoVal": "D", "content": "$$8 $$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders"], "answer_analysis": ["For the number to be as small as possible, we need the number of digits to be as small as possible. For instance, $$111\\cdots 1 (2022\\textasciitilde1\\text{s})$$ has a digit sum of $$2022$$, but it is a much larger number than $$333\\cdots 3 (674\\textasciitilde3\\text{s})$$, which also has a digit sum of $$2022$$. Clearly, to reduce the number of digits in the number, we need to make as many as possible of the digits in the number equal to $$9$$. Now $$2022 \\div9 = 224$$ remainder $$6$$, so the smallest positive integer with digit sum of $$2022$$ is $$699\\cdots 9 (224\\textasciitilde9\\text{s})$$. Its last digit is $$9$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "284", "queId": "4ff67857ceae427a914f8bc7e82fcfc8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The greatest odd factor of $$30$$ is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["The factors of $$30$$ are $$1$$, $$30$$, $$2$$, $$15$$, $$3$$, $$10$$, $$5$$, $$6$$, so the greatest odd factor of $$30$$ is $$15$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "288", "queId": "424e71f4cb1742578a96c5a3d302217b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The greatest prime number that is a divisor of 16,384 is 2 because $16,384=2^{14}$. What is the sum of the digits of the greatest prime number that is a divisor of 16,383 ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$16$$ "}], [{"aoVal": "E", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["We have $$ \\begin{aligned} 16383 \\& =2^{14}-1 \\textbackslash\\textbackslash{} \\& =\\left(2^{7}+1\\right)\\left(2^{7}-1\\right) \\textbackslash\\textbackslash{} \\& =129 \\cdot 127 \\end{aligned} $$ Since 129 is composite, 127 is the largest prime divisible by 16383 . The sum of 127 \\textquotesingle s digits is $$ 1+2+7=\\text { (C) } 10 $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "292", "queId": "626b1bd276e8449c8e07afde26d60acb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Let $N$ be the greatest five-digit number whose digits have a product of $120$ . What is the sum of the digits of $N$ ? (2018 AMC 8 Problem, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["If we start off with the first digit, we know that it can\\textquotesingle t be $9$ since $9$ is not a factor of $120$ . We go down to the digit $8$ , which does work since it is a factor of $120$ . Now, we have to know what digits will take up the remaining four spots. To find this result, just divide $\\frac{120}{8}=15$. The next place can be $5$ , as it is the largest factor, aside from $15$ . Consequently, our next three values will be $3,1$ and $1$ if we use the same logic. Therefore, our five-digit number is $85311$ , so the sum is $8+5+3+1+1=18 \\Longrightarrow($ D) 18 . "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "297", "queId": "16cdb451cc3744ae8bde6471c70e056b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Dividing a certain number by $$13$$ leaves a quotient of $$8$$ with a remainder of $$7$$. Find this number. ", "answer_option_list": [[{"aoVal": "A", "content": "$$111$$ "}], [{"aoVal": "B", "content": "$$121$$ "}], [{"aoVal": "C", "content": "$$132$$ "}], [{"aoVal": "D", "content": "$$115$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders"], "answer_analysis": ["$$8\\times 13+7=111$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "298", "queId": "4b78b6a2b26c469db0b1e4afd9c988d2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A number can be xxxx and it will have a remainder of $2$ when divided by $4$. What is the maximum value of the number no larger than $2300$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2288$$ "}], [{"aoVal": "B", "content": "$$2290$$ "}], [{"aoVal": "C", "content": "$$2294$$ "}], [{"aoVal": "D", "content": "$$2098$$ "}], [{"aoVal": "E", "content": "$$2300$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["The number can be written as $$4n+2$$ and $$3x$$. It must be a multiple of $3$ but leaves a remainder of $2$ when divided by $4$. $2300$ can be divisible by both $2$ and $3$, so it is $2098$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "300", "queId": "231246fd9e8449368fe0639cd2fa341a", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A $6$-digit number starting with $18$, $18ABCD$, is a multiple of $6$, $7$, $9$ and $10$. Find $\\left (A +B + C+ D\\right )$ for the smallest such number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["The LCM of $6$, $7$, $9$ and $10$ is $2 \\times 3^{2}\\times 5 \\times7= 630$. $180 000=285 \\times 630 + 450$, ∴$$$$the$$$$ smallest number is $286 \\times 630=180 180$, Sum of the last 4 digits, $A + B + C+ D=9$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "306", "queId": "46f01c4c638345c9ae61f2db202abc2c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the followings is not a multiple of $3$? ", "answer_option_list": [[{"aoVal": "A", "content": "$213$ "}], [{"aoVal": "B", "content": "$214$ "}], [{"aoVal": "C", "content": "$216$ "}], [{"aoVal": "D", "content": "$219$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$\\text{A}$$. $$2+1+3=6=2\\times3$$; $$\\text{B}$$. $$2+1+4=7$$, and $$7$$ is not a multiple of $$3$$; $$\\text{C}$$. $$2+1+6=9=3\\times3$$; $$\\text{D}$$. $$2+1+9=12=4\\times3$$. We choose $$\\text{B}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "307", "queId": "4b857cc08fad4b29b9da2b87bbb1b17f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following products is an odd number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$23\\times24$$ "}], [{"aoVal": "B", "content": "$$24\\times35$$ "}], [{"aoVal": "C", "content": "$$42\\times53$$ "}], [{"aoVal": "D", "content": "$$53\\times45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers"], "answer_analysis": ["The product is odd if and only if every factor is odd. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "312", "queId": "7e2b629665d24a66aa7153754a1f6c2d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many positive factors of $$36$$ are also multiples of $$4$$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$36={{2}^{2}}\\times {{3}^{2}}$$, so the number of its factors would be $$\\left( 2+1 \\right)\\times \\left( 2+1 \\right)=9$$, Among them, there are $$\\left( 2+1 \\right)\\times 1=3$$ factors which has $${{2}^{2}}$$ as its factors. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "318", "queId": "1af3fff8d6f84c37875b1906cbcbb360", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A box contains gold coins. If the coins are equally divided among six people, four coins are left over. If the coins are equally divided among five people, three coins are left over. If the box holds the smallest number of coins that meets these two conditions, how many coins are left when equally divided among seven people? (2006 AMC 8 Problem, Question \\#23) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["The counting numbers that leave a remainder of 4 when divided by 6 are $4,10,16,22,28,34, \\cdots$ The counting numbers that leave a remainder of 3 when divided by 5 are $3,8,13,18,23,28,33, \\cdots$ So 28 is the smallest possible number of coins that meets both conditions. Because $4 \\cdot 7=28$, there are (A) 0 coins left when they are divided among seven people. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "320", "queId": "23451207e5254aa3a6086253d0f3a376", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Among numbers like $5$, $55$, $555$, $5555$, $$\\cdots$$, how many of them are perfect squares? ", "answer_option_list": [[{"aoVal": "A", "content": "$0$ "}], [{"aoVal": "B", "content": "$1$ "}], [{"aoVal": "C", "content": "$2$ "}], [{"aoVal": "D", "content": "Countless "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers"], "answer_analysis": ["Only $5$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "323", "queId": "1b0507be35e740e083516940c9edfe55", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Dividing a certain two$$-$$digit number by $$7$$ leaves a remainder of $$5$$; dividing it by $$11$$ leaves a remainder of $$9$$. What is the smallest possible value of this number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$54$$ "}], [{"aoVal": "C", "content": "$$75$$ "}], [{"aoVal": "D", "content": "$$152$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders"], "answer_analysis": ["The number when added by $$2$$ is divisible by $$7$$ and by $$11$$. Hence, the smallest value is $$7\\times 11-2=75$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "324", "queId": "b4d8fc095d4d4aa9a126f71222fa0a32", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If a four-digit number $$\\overline{5ab4}$$ is a perfect square number, then $$a+b=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers"], "answer_analysis": ["First of all $${{70}^{2}}=4900$$, So the number is between $$70$$ and $$80$$. According to the last digit, the number should be $$72 $$ or $$78 $$. $$\\because {{72}^{2}}=5184$$，$${{78}^{2}}=6084$$． $$\\therefore a+b=1+8=9$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "326", "queId": "8fd0b460aff741b7a66625604e9748b3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The natural numbers from $$1$$ to $$99$$ inclusive are divided into n groups such that the following conditions hold: Each number belongs to exactly one group. Each group contains at least two numbers. If two numbers belong to the same group, then their sum is not divisible by $$3$$. What is the smallest number $$n$$ which satisfies the above conditions? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$33$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$66$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["We can divide the $$99$$ numbers into $$3$$ groups according to their remainder when divided by $$3$$. $$1$$, $$4$$, $$7\\_\\cdots$$ they belong to the group $$A$$, since they leave a remainder of $$1$$ when divided by $$3$$. $$2$$, $$5$$, $$8\\_\\cdots$$ they belong to the group $$B$$, since they leave a remainder of $$2$$ when divided by $$3$$. $$3$$, $$6$$, $$9\\_\\cdots$$ they belong to the group $$C$$, since they leave a remainder of $$0$$ when divided by $$3$$. As we know, the members in group $$C$$ cannot get together. Also, when the member of group $$A$$ and the member of group $$B$$ get together, they will create the sum which is a multiple of $$3$$. So the $$33$$ members of group $$C$$ will be in $$33$$ groups. Group $$A$$ and group $$B$$ can join in the $$33$$ groups however they want. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "327", "queId": "1b1e909aabd44df5b1705c94e2d96dfc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If the four-digit number $$28X8$$ is divisible by $$3$$, how many possible values are there for $$X$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["$$2+8+8=18$$, $$18$$ is multiple of $$3$$ Thus, $$X$$ itself must be a multiple of $$3$$, or $$0$$. We have $$3, 6, 9$$ and $$0$$. Four possible value. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "340", "queId": "947e6c7b9b014008b2505f5982f0820b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many three-digit numbers have an odd number of factors? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["It can be shown that a positive integer has an odd number of factors if and only if it is square. ~The smallest three-digit square number is $${{10}^{2}}=100$$ and the largest is $${{31}^{2}}=961$$. Hence there are $$31-9=22$$ three-digit numbers which have an odd number of factors. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "341", "queId": "62961b5468034ea3bc961c6658efb18a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "♥ $$\\times$$ ☺ $$=$$ ♦ ☺ is an even number. Which of the following gives an odd answer? ", "answer_option_list": [[{"aoVal": "A", "content": "♦ $$-\\textasciitilde7$$ "}], [{"aoVal": "B", "content": "☺ $$+$$ ♦ "}], [{"aoVal": "C", "content": "☺ $$\\times$$ ☺ "}], [{"aoVal": "D", "content": "♦ $$\\times$$~♦ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers"], "answer_analysis": ["♥ $$\\times$$ ☺ $$=$$ ♦ Since ☺ is an even number,~♦ must also be an even number. ♦ $$-\\textasciitilde7$$ is the only option to given an odd answer because even $$-$$ odd $$=$$ odd. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "342", "queId": "54cd88f8af9547b49a7bc8a92f4337f0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Eleven members of the Middle School Math Club each paid the same amount for a guest speaker to talk about problem solving at their math club meeting. They paid their guest speaker $\\textbackslash$ 1 A 2$. What is the missing digit $A$ of this $3$ -digit number? (2014 AMC 8 Problem, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["We know that a number is divisible by $11$ if the odd numbers added together minus the even numbers added together(or vice versa) is a multiple of $11$ . So, we have $1+2-A=$ a multiple of $11$ . The only multiple that works here is $0$ , as $11 \\cdot 0=0$. Thus, $A=(D)$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "349", "queId": "b980de5db10a453989ff6f69895348e5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is not a factor of $$2016$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Prime Factorization (Equations)"], "answer_analysis": ["$$2016=7\\times288=8 \\times252=9\\times224$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "350", "queId": "629bacd9c7b7473f91c00e5e37ed2765", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Jam has some pieces of candy. He wants to share with some kids. If he shares the candy among $8$ kids on average, there will be $2$ pieces left. If he shares the candy among $9$ kids on average, there will be $3$ pieces left. If he shares the candy among $10$ kids on average, there will be $4$ pieces left. How many pieces of candy are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$321$ "}], [{"aoVal": "B", "content": "$354$ "}], [{"aoVal": "C", "content": "$720$ "}], [{"aoVal": "D", "content": "$360$ "}], [{"aoVal": "E", "content": "$240$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["$8\\times9\\times10\\div2=360$ $360-6=354$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "351", "queId": "ec7af5fd49f749f2aed2ebb53ffb2b80", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Chloe is working on this equation: $$475+17\\times 58+990-19\\times 32+33\\times 111$$. Her answer is $$5681$$. Without calculating, do you think Chloe\\textquotesingle s answer is correct or wrong? Explain why. ", "answer_option_list": [[{"aoVal": "A", "content": "Correct "}], [{"aoVal": "B", "content": "Wrong "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["Her calculation was wrong. The answer is supposed to be an even number. $$117\\times32$$，$$19\\times12$$ are even numbers and $$133\\times11$$ is an odd number. So in that case, we can think of the equation as: odd + even + even - even + odd = even Hence, the answer should be an even number! However, Chloe\\textquotesingle s answer is an odd number. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "355", "queId": "aba89df5372b490cbbdd252c3a4413d3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If the four-digit number $3P78$ is divisible by $3$, how many possible values are there for $P$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["use divisibility rule. 3+ 7+8+R = divisible by 3. 18 + R = divisible by 3. smallest possible number for R is 0, max possible amount for R is 9 3x6=18 - 18 =0 (can be divisible by 3) 3x7=21 -18 = 3 3x 8= 24 -18 =6 3x 9= 27 - 18 = 9 Total = 4 ways. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "363", "queId": "2c4a0091d2d242f086be8b8c29a044e2", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "John loves collecting stamps! If he divides the number of stamps he has by $$32$$, then he will have $$30$$ remaining stamps; if he divides the number of stamps he has by $$9$$, he will have $$7$$ remaining stamps; if he divides the number of stamps he has by $$7$$, he will have $$5$$ remaining stamps. How many stamps, at least, does John have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2014$$ "}], [{"aoVal": "B", "content": "$$2015$$ "}], [{"aoVal": "C", "content": "$$2016$$ "}], [{"aoVal": "D", "content": "$$2017$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["The total number of stamps when divided by $$32$$, $$9$$, and $$7$$ leaves remainders of $$30$$, $$7$$, and $$5$$, respectively. In other words, the number when added by $$2$$ is divisible by $$32$$, $$9$$, and $$7$$. Hence, the smallest such number is $$32\\times9\\times7-2=2014$$. The answer is $$\\rm A$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "366", "queId": "b046c96bebb94ec08273ce98347bf50e", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Prime factorise $$24\\times 105$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$${{2}^{3}}\\times {{3}^{2}}\\times 5\\times 7$$ "}], [{"aoVal": "B", "content": "$${{2}^{4}}\\times {{3}^{2}}\\times 5$$ "}], [{"aoVal": "C", "content": "$${{2}^{4}}\\times {{3}^{2}}\\times 5\\times 7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["$$24\\times 105={{2}^{3}}\\times {{3}^{2}}\\times 5\\times 7$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "369", "queId": "23b33f2ec1ca4817a5dedc24c6a96d60", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is the correct expression of quinary (base-$5$ numeral system)? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\left (8231\\right )\\_5$ "}], [{"aoVal": "B", "content": "$\\left (2001\\right )\\_5$ "}], [{"aoVal": "C", "content": "$\\left (4341\\right )\\_7$ "}], [{"aoVal": "D", "content": "$\\left (2345\\right )\\_5$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Properties and Applications of Number Bases"], "answer_analysis": ["In quinary, the base number must be $5$, and all the digits in the parentheses must be less than $5$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "371", "queId": "2c52074323c44ec28440bca4cef1ca3a", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "$$2010$$ is divided by $$N$$ and gets a remainder of $$15$$. There are~\\uline{~~~~~~~~~~}~possible values of $$N$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Theorem of the Number of Factors of a Number"], "answer_analysis": ["$$2010-15=1995=3\\times 5\\times 7\\times 19$$ $$\\left( 1+1 \\right)\\times \\left( 1+1 \\right)\\times \\left( 1+1 \\right)\\times \\left( 1+1 \\right)=16$$ factors. Remove $$1$$, $$3$$, $$5$$, $$7$$, and $$15$$ from them, we can get $$16-5=11$$ possible values. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "372", "queId": "62aa07be6a79498b92f9a5329af9f085", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Timothy writes down the number 24. He reverses the digits to make the number 42. He then works out that 42 is 18 more than his starting number, 24. Nicole writes down a whole number between 10 and 99. She also reverses the digits of her number. She finds that this makes a number that is 72 more than her starting number. What was the last digit of Nicole's starting number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["Let the original number be ab, and reverse it to be ba, calculated by the place value principle, ba-ab=72 10b+a-(10a+b)=72, 9b-9a=72, b-a=8, b=9 and a=1. So the original number is 19, last digit is 9. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "373", "queId": "1b9e4ee38e444d3ba604085a55af9026", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many three-digit numbers are divisible by $13$ ? (2004 AMC 8 Problem, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$67$$ "}], [{"aoVal": "C", "content": "$$69$$ "}], [{"aoVal": "D", "content": "$$76$$ "}], [{"aoVal": "E", "content": "$$77$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["Let $k$ be any positive integer so that $13 k$ is a multiple of 13 . For the smallest three-digit number, $13 k\\textgreater100$ and $k\\textgreater\\frac{100}{13} \\approx 7.7$. For the greatest three-digit number, $13 k\\textless999$ and $k\\textless\\frac{999}{13} \\approx 76.8$. The number $k$ can range from 8 to 76 so there are $(\\mathbf{C}) 69$ threedigit numbers. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "374", "queId": "6bdcc37396914afb94686c30ac999be3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following numbers are prime numbers? $$\\textasciitilde$$ $179$~ ~ ~ ~ ~ ~ ~ ~ ~$129$~ ~ ~ ~ ~ ~ ~ ~ ~$187$~ ~ ~ ~ ~ ~ ~ ~ ~$157$ $$\\textasciitilde$$ ", "answer_option_list": [[{"aoVal": "A", "content": "Only $179$ "}], [{"aoVal": "B", "content": "$179$ and $$187$$ "}], [{"aoVal": "C", "content": "$179$ and $157$ "}], [{"aoVal": "D", "content": "$179$, $157$, and $187$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["$129=3\\times43$. $187=11\\times17$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "376", "queId": "23c3e439e68f41a3a3111dd9f12b0d86", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The square root of the square root of $$16$$ is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$64$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["The square root of $$16$$ is $$4$$ and the square root of $$4$$ is $$2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "379", "queId": "1ba8fb6c2895403aaa3b8c4967b73d6c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Candy buys $$15$$ bottles of drinks, and they are placed in order on the counter in the following way: $$2$$ bottles of milk, a bottle of juice, a bottle of coke, $$2$$ bottles of milk, a bottle of juice, a bottle of coke$$\\ldots $$ According to the pattern, the $$15$$\\textsuperscript{th} bottle is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\text{milk}$$ "}], [{"aoVal": "B", "content": "$$\\text{juice}$$ "}], [{"aoVal": "C", "content": "$$\\text{coke}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["$$15\\div 4=3\\text{R}3$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "386", "queId": "79bef362d75645c69f53dbadbf00f263", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many factors $2000$ that have more than $2$ factors are there? (As an example, $12$ has $6$ factors, namely $1$, $2$, $3$, $4$, $6$ and $12$. But $2$ and $3$ only two factors.) ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$16$$ "}], [{"aoVal": "E", "content": "$$17$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$2000=2^{3}\\times5^{3}$, the number of its factors would be $(4+1)(3+1)=20$, but $1$, $2$, and $5$ do not meet the condition. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "388", "queId": "949570c9cb624a7dbba2f5c14a87e40a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following prime factorization is incorrect? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12=2\\times2\\times3$$ "}], [{"aoVal": "B", "content": "$$51=3\\times17$$ "}], [{"aoVal": "C", "content": "$$8=2\\times2\\times2$$ "}], [{"aoVal": "D", "content": "$$45=5\\times9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$$45=5\\times3\\times3$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "389", "queId": "5e2030e626f745468a91ab3f9adaf899", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "In Walmart, apples are sold in pack of eight. How many apples will you get, if you buy five packs? ", "answer_option_list": [[{"aoVal": "A", "content": "$$32$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$56$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["$5\\times 8=40$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "391", "queId": "e7e0dc6c42c14a5e8a69c650975774df", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the first four square numbers is $$30$$. What is the sum of the first five square numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$55$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$25$$ "}], [{"aoVal": "D", "content": "$$45$$ "}], [{"aoVal": "E", "content": "$$65$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["$30+25=55$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "396", "queId": "50740f8e5c704794a82424fcd10a684d", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "In the division expression $$28\\div$$~\\uline{~~~~~~~~~~}~$$=$$~\\uline{~~~~~~~~~~}~$$\\text{r}4$$, how many different pairs of number are there to fill the gaps? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["We can use the equation: divisor $$\\times$$ quotient $$=$$ dividend $$-$$ remainder, so here we can get divisor $$\\times$$ quotient $$=28-4=24$$. Therefore, the only possibilities are $$1$$ and $$24$$, $$2$$ and $$12$$, $$3$$ and $$8$$, and $$4$$ and $$6$$ for a total of four possible combinations. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "399", "queId": "2416eefdffb5435cb68e820fd16519d0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\sqrt{10^{2} - 6^{2}} + \\sqrt{3^{2} + 4^{2}}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["$$\\sqrt{10^{2} - 6^{2}} + \\sqrt{3^{2} + 4^{2}}=\\sqrt{64} + \\sqrt{25} = 8 + 5 = 13$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "401", "queId": "6bf6c8821a234e18b4a5e06096b4112e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole numbers $A$, $B$ and $C$ ($B\\neq 1$). $A\\times B=45$, $B\\times C=50$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$23$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$45=3\\times 3\\times 5$ $50=2\\times 5\\times 5$ Because $B$ is the factor both number contains, $B=5$ Thus, $A=9$, $C=10$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "402", "queId": "3e6065d727734f4988abb897421c3298", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$539-142$$ divided by $$4$$ has a remainder of~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["$$539\\div 4$$ R $$3$$；$$142\\div 4$$ R $$2$$；$$539-142$$ divided by $$4$$, the remainder is 3-2=1. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "408", "queId": "e346408b32dc4287998e046bcf3c4ff7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the followings is divisible by $$8$$ and $$7$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$56$$ "}], [{"aoVal": "B", "content": "$$49$$ "}], [{"aoVal": "C", "content": "$$42$$ "}], [{"aoVal": "D", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders"], "answer_analysis": ["$$56 = 8 \\times 7$$, $$56 = 7 \\times 8$$, so we choose $$\\rm A$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "417", "queId": "24420680ed84476f9d4856d77c14899d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Given $$a$$ is a factor of $37$, then ． ", "answer_option_list": [[{"aoVal": "A", "content": "$a$ can only be $1$ "}], [{"aoVal": "B", "content": "$a$ can only be $37$ "}], [{"aoVal": "C", "content": "$a$ can be 1 or $37$ "}], [{"aoVal": "D", "content": "$a$ can be any number "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["\"$$a$$ is a factor of $37$\" means $37$ is divisible by $a$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "423", "queId": "ec90ac45a801414a893640a524c1daa5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many $$2$$-digit whole numbers have no odd factor except $$1$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$49$$ "}], [{"aoVal": "B", "content": "$$45$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers"], "answer_analysis": ["The $$3$$ such whole numbers are $$16$$, $$32$$, and $$64$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "424", "queId": "dea568c51be24e08946353f48456eedf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Of the integers from $$1$$ to $$1000$$, how many are multiples of $$3$$, $$4$$, \\emph{and} $$5$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$17$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["A multiple of $$3$$, $$4$$, and $$5$$ is a multiple of $$60$$, and $$16\\times60\\textless{}1000 \\textless{}17\\times60$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "425", "queId": "245f2270e9d049b8938007042f915dc0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole numbers $A$, $B$ and $C$ $(B\\ne 1)$. $A\\times B=15$, $B\\times C=35$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$15=3\\times 5$ $35=5\\times 7$ Because $B$ is the factor both number contains, $B=5$ Thus, $A=3$, $C=7$, $A+B+C=15$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "426", "queId": "20588a8a922a4aa5866dbeb986961b3c", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "In the division expression $$28\\div$$~\\uline{~~~~~~~~~~}~$$=$$~\\uline{~~~~~~~~~~}~$$\\text{R}4$$, how many different combinations are there for the quotient and the divisor ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["We can use the equation: divisor $$\\times$$ quotient $$=$$ dividend $$-$$ remainder, so here we can get divisor $$\\times$$ quotient $$=28-4=24$$. Therefore, the only possibilities are $$1$$ and $$24$$, $$2$$ and $$12$$, $$3$$ and $$8$$, and $$4$$ and $$6$$ for a total of four possible combinations. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "427", "queId": "d566f074832149a5b6f7906833230b49", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of two prime numbers is $$99$$. What is the difference between the two numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$89$$ "}], [{"aoVal": "B", "content": "$$92$$ "}], [{"aoVal": "C", "content": "$$95$$ "}], [{"aoVal": "D", "content": "$$97$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Applying Special Prime Numbers"], "answer_analysis": ["Because $$99$$ is an odd number, one of these two prime numbers must be an even prime number. The only choice is $$2$$. So the other is $$99-2 = 97$$. So, the difference between the two numbers is $$95$$. Therefore, we choose $$\\rm C$$ . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "430", "queId": "cc2b46c66da64c66b91a9e328e0bba27", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The first $2018$ integers ($1$, $2$, $3$, $\\cdots$, $2017$, $2018$) are written on the blackboard. What is the minimum number of integers that should be erased from the blackboard, so that the last digit of the product of the remaining integers is $2$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$402$$ "}], [{"aoVal": "B", "content": "$$403$$ "}], [{"aoVal": "C", "content": "$$404$$ "}], [{"aoVal": "D", "content": "$$410$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders "], "answer_analysis": ["First, we need to remove all the integers which are multiples of $5$, otherwise the last digit of the products is $0$ or $5$. Hence, $403$ integers need to be removed. Next, note that the last digit of each of the products below is $6$. $1\\times2\\times3\\times4\\times6\\times7\\times8\\times9$, $11\\times12\\times13\\times14\\times16\\times17\\times18\\times19$, $\\cdots\\cdots$ $2001\\times2002\\times2003\\times2004\\times2006\\times2007\\times2008\\times2009$, and the last digit of the product $2011\\times2012\\times2013\\times2014\\times2016\\times2017\\times2018$ is $4$. Hence, we need to remove one more \"$2$\"and the last digit of the product will be $2$. So the answer is $404$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "433", "queId": "55394c85b3f14436b055693bfcdf6034", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The result of $$29+30+31+\\cdots\\cdots+87+88$$ is an~\\uline{~~~~~~~~~~}~number. ", "answer_option_list": [[{"aoVal": "A", "content": "odd "}], [{"aoVal": "B", "content": "even "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["$88-29+1=60$ $60\\div2=30$ Odd numbers all paired. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "435", "queId": "35be3c076e034ddc8ef203b1b16c5855", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A bag contains $$50$$ straws of two different colours. $$10$$ straws are yellow and the rest are red. What percentage of the straws are red? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$20\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$40\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$80\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Properties and Applications of Number Bases->Mixed Operations of Number Bases", "Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Word Problems Involving Fractions and Percentages->Finding the Percentage Given a Part and a Whole"], "answer_analysis": ["50-10=40；$$40\\div$$ 50=0.8；0.8=80\\% "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "438", "queId": "24994e3c05bb4739adb830e9f014e41a", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "How many solutions that can be expressed with positive integers does the equation below have? ($$1999$$ Math kangaroo Problems, Level $$7-8$$, Question \\#$$26$$) $$a^{2}b-1=1999$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->Finding Factors Given the Product"], "answer_analysis": ["$a^{2}b=2000=2^{4}\\times5^{3}$. Thus, the value of $a$ can be $1$, $2$, $4$, $5$, $10$, and $20$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "439", "queId": "87c40f9728dc42e68803fcc5bb5f2608", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the value for lcm $$[5,7,11]$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$385$$ "}], [{"aoVal": "B", "content": "$$1155$$ "}], [{"aoVal": "C", "content": "$$77$$ "}], [{"aoVal": "D", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["Since $$5=1\\times5$$, $$7=1\\times7$$, and $$11=1\\times11$$, we have one $$5$$, one $$7$$, and one $$11$$, thus the least common multiple for $$5$$, $$7$$, and $$11$$ is $$5\\times7\\times11=385$$. We choose $$\\rm A$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "442", "queId": "2d15d60fb7d247cc968d0f5d2238fc8c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A computer can do $$7\\times {{10}^{9}}$$ operations per second. Then, it can do~\\uline{~~~~~~~~~~}~operations in $$5\\times {{10}^{2}}$$ seconds. ", "answer_option_list": [[{"aoVal": "A", "content": "$$35\\times {{10}^{10}}$$ "}], [{"aoVal": "B", "content": "$$3.5\\times {{10}^{11}}$$ "}], [{"aoVal": "C", "content": "$$3.5\\times {{10}^{12}}$$ "}], [{"aoVal": "D", "content": "$$3.5\\times {{10}^{19}}$$ "}], [{"aoVal": "E", "content": "$$3.5\\times {{10}^{18}}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->The Relationship between Exponents and the Number of Factors"], "answer_analysis": ["$$7\\times {{10}^{9}}\\times 5\\times {{10}^{2}}=3.5\\times {{10}^{12}}$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "443", "queId": "f13c8e1991a84eb184a6518808e0299c", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "If you were to work out the answer to the sum $$2^{2016}+0^{2016}+1^{2016}+6^{2016}$$ you would get a number with $$1569$$ digits, starting with $$566$$ $$136$$ $$001$$ $$\\cdots$$ What is the last digit of this number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders "], "answer_analysis": ["We can find the last (units) digit by looking at the units digits of the four parts. We can quickly note that the units digits of $$0^{2016}$$ and $$1^{2016}$$ and $$6^{2016}$$are $$0$$, $$1$$ and$$6$$ respectively. Now then we have to look at powers of $$2:{{2}^{1}}=2$$, $${{2}^{2}}=4$$, $${{2}^{3}}=8$$, $${{2}^{4}}=16$$, and after this the units digits repeat ($${{2}^{5}}=3\\underline{2}$$, $${{2}^{6}}=6\\underline{4}$$, $${{2}^{7}}=12\\underline{8}$$, $${{2}^{8}}=25\\underline{6}$$, $$\\cdots $$). We notice that when the indices are multiples of 4 (eg. $${{2}^{4}}=16$$, $${{2}^{8}}=256$$, $$\\cdots $$) the units digit of the power of $$2$$ is $$6$$. Hence the units digit of $$2^{2016}+0^{2016}+1^{2016}+6^{2016}$$ is the same as the units digit of $$6 + 0 + 1 + 6$$, that is $$3$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "444", "queId": "9df81e661c30410293f9bce1ad7a48c2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $5$-digit number $\\overline{2018U}$ is divisible by $9$. What is the remainder when this number is divided by $8$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["We use the property that the digits of a number must sum to a multiple of $9$ if it is divisible by $9$. This means $2+0+1+8+U$ must be divisible by $9$. The only possible value for U then must be $7$. Since we are looking for the remainder when divided by $8$, we can ignore the thousands. The remainder when $187$ is divided by $8$ is $(\\rm B)$ $3$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "448", "queId": "9dfa17618bd54714bcb3a628c5b55c96", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the options below is equivalent to $${{({{2}^{2}}\\times {{3}^{3}}\\times {{5}^{5}})}^{4}}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$${{2}^{6}}\\times {{3}^{7}}\\times {{5}^{9}}$$ "}], [{"aoVal": "B", "content": "$${{2}^{2}}\\times {{3}^{3}}\\times {{5}^{20}}$$ "}], [{"aoVal": "C", "content": "$${{2}^{2}}\\times {{3}^{3}}\\times {{5}^{9}}$$ "}], [{"aoVal": "D", "content": "$${{2}^{8}}\\times {{3}^{12}}\\times {{5}^{20}}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->The Relationship between Exponents and the Number of Factors"], "answer_analysis": ["Answer $$={{2}^{2\\times 4}}\\times {{3}^{3\\times 4}}\\times {{5}^{5\\times 4}}={{2}^{8}}\\times {{3}^{12}}\\times {{5}^{20}}$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "449", "queId": "2d22ab8017c443918d3d1fb3d375d047", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of all factors of $$24$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$52$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$62$$ "}], [{"aoVal": "D", "content": "$$72$$ "}], [{"aoVal": "E", "content": "$$84$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Theorem of the Number of Factors of a Number"], "answer_analysis": ["The sum of the factors is $$(3^{0}+3^{1})$$$$\\times (2^{0}+2^{1}+2^{2}+2^{3})=60$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "453", "queId": "5e6c30bf347c4bee827e7e12a9a6933e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Add any two odd numbers. The ones\\textquotesingle{} digit of the sum is always． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2 $$ "}], [{"aoVal": "B", "content": "$$$$prime "}], [{"aoVal": "C", "content": "$$$$odd "}], [{"aoVal": "D", "content": "$$$$even "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers"], "answer_analysis": ["Add two numbers from: $$1$$, $$3$$, $$5$$, $$7$$, $$9$$. The result is always even. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "456", "queId": "5557975ee0824a2db7c5a3f47ab3d864", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "What is the smallest integer $$n$$ for which the number $$\\left(2^{2}-1\\right)\\cdot \\left(3^{2}-1\\right)\\cdot \\left(4^{2}-1\\right)\\cdots \\left(n^{2}-1\\right)$$ is the square of an integer? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "None of these. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Questions involving Square Numbers"], "answer_analysis": ["Using the difference of two squares, we can get: $$\\left(2^{2}-1\\right)\\cdot \\left(3^{2}-1\\right)\\cdot \\left(4^{2}-1\\right)\\cdots \\left(n^{2}-1\\right) = 1\\times 3\\times 2\\times 4\\times 3\\times 5\\times \\cdots \\times (n-1) \\times (n+1)$$ you will notice that this is equal to: $$1\\times 2\\times 3^{2} \\times 4^{2} \\times \\cdots \\times (n-1)^{2} \\times n \\times (n+1)$$ So this will only be a square if $2n(n+1)$ is a square, which happens when $n=8$ as $2n(n+1) = 144=12^{2}$. Answer: $B$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "461", "queId": "24d84f88a93a4e1480009fa37369f2dd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the greatest number of consecutive integers such that the sum of the digits of none of them is divisible by $$5$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["Five consecutive numbers can be: $$12$$, $$13$$, $$14$$, $$15$$, and $$16$$ (without carrying) or $$17$$, $$18$$, $$19$$, $$20$$, $$21$$ (with carrying in the tens place). Without carrying, among each of the $$5$$ consecutive integers, we can find one whose sum of digits is a multiple of $$5$$. So we need to carry. To make the number of integers the greatest, we can start from a number whose remainder is $$1$$ when divided by five. And the most important thing is, after we write the fourth number, the carry appears. For example: $$56$$, $$57$$, $$58$$, $$59$$, $$60$$, $$61$$, $$62$$, $$63$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "463", "queId": "2d4c0050cb854728b63114e473c1e44f", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The number $$95$$~\\uline{~~~~~~~~~~}~$$94775998$$ is divisible by $$198$$. What is the missing digit? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["Already divisible by $$2$$, so we must check it divides by $$9$$ by adding the digits together: $$9+5+x+9+4+7+7+5+9+9+8=54+x$$, this must be a multiple of $$9$$ so $$x$$ is $$0$$ or $$9$$. It should also be divisible by $$11$$, so the alternating sum of digits should too. $$9-5+x-9+4-7+7-5+9-9+8=2+x$$ is divisible by $$11$$. Hence $$x$$ is $$9$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "469", "queId": "4c587707443e4315b20740805dc3e0ef", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Lucas buys $24$ machines. But two of the digits of the total price on the invoice are not clear, which only show $\\overline{\\square 8\\square 2}$ dollars. The purchasing agent says the two unclear digits on the invoice are the same. Given that the unit price of this kind of machine is an integer, how much is it? ", "answer_option_list": [[{"aoVal": "A", "content": "$$76$$ "}], [{"aoVal": "B", "content": "$$160$$ "}], [{"aoVal": "C", "content": "$$202$$ "}], [{"aoVal": "D", "content": "$$328$$ "}], [{"aoVal": "E", "content": "$$412$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["The number of total price can be divided by $3$ and $8$. It can be divided by $8$ which means the tens digit must be $3$ or $7$. And when the tens digit is $7$, the number can be divided by $3$. Thus, the total price is $7872$ dollars, and each of the machine is $328$ dollars. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "471", "queId": "7a082c8d18f4425d966efa21d82c7ce8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many two-digit numbers can be divided by both 2 and 3 at the same time. ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$75$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["*and* = 2 x 3 = 6 Multiple of 6 with 2 digits = 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "477", "queId": "7a0cfb6a0e214e619912ea4804b38fb2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many of the whole numbers less than $$100$$ are $$10$$ greater than an odd whole number?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$46$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$91$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers"], "answer_analysis": ["Add $$10$$ to $$1$$, $$3$$, $$5$$, $$7$$, $$\\cdots $$, $$87$$, and $$89$$. None of these sums is more than $$99$$. There are $$45$$ such sums. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "486", "queId": "3629c97dbf63445ba101052cd2579033", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the remainder when $$\\frac{{{2}^{2019}}}{{{4}^{982}}-{{2}^{1963}}}$$ is divided by $$5$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->The Relationship between Exponents and the Number of Factors"], "answer_analysis": ["$$\\frac{{{2}^{2019}}}{{{2}^{1964}}-{{2}^{1963}}}$$ $$={{2}^{2019-1963}}$$ $$={{2}^{56}}$$， ∴$${{2}^{56}}:6$$， $$6\\div 5:1$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "489", "queId": "9e125e23b02549369e9ddc39214a30ae", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many of these four expressions are perfect squares? $$1^{3}+2^{3}$$~ ~ ~ ~ ~ ~$$1^{3}+2^{3}+3^{3}$$~ ~ ~ ~ ~$$1^{3}+2^{3}+3^{3}+4^{3}$$~ ~ ~ ~ ~$$1^{3}+2^{3}+3^{3}+4^{3}+5^{3}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["All four expressions are perfect squares: $$1^{3} + 2^{3} = 1 + 8 = 9 = 3^{2}$$; $$1^{3}+2^{3}+3^{3}=1+8+27=36=6^{2}$$; $$1^{3}+2^{3}+3^{3}+4^{3}=1+8+27+64=100=10^{2}$$; $$1^{3} + 2^{3} + 3^{3} + 4^{3} + 5^{3} = 1 + 8 + 27 + 64 + 125 = 225 = 15^{2}$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "490", "queId": "50fc5c9bedbc4e279e1929841cb95d8c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$135 798 642$$ is not divisible by~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["$$42$$ is not divisible by $$4$$, so neither is $$135 798 642$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "492", "queId": "7a1ca7756cf94fd2a744c85a86a3223c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$3^{2}+3^{2}+3^{2}+3^{2}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4^{2}$$ "}], [{"aoVal": "B", "content": "$$6^{2}$$ "}], [{"aoVal": "C", "content": "$$12^{2}$$ "}], [{"aoVal": "D", "content": "$$33^{2}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["$$3^{2}+3^{2}+3^{2}+3^{2}=9+9+9+9=36=6^{2}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "494", "queId": "e806a2a77d3b44299f7b224cd112ee4a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is \\emph{not} a factor of $$2016$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Prime Factorization (Equations)"], "answer_analysis": ["$$2016=7\\times288=8 \\times252=9\\times224$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "495", "queId": "4c7f65faa3c04ffda40fa416ad7c3f7b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the sum of the two smallest prime factors of $250$? (2007 AMC 8 Problems, Question \\#3) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["The smallest prime factors of $250$ are $2$ and $5$. Thus, the sum is $2 + 5 = 7$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "497", "queId": "67c4a869cb0345528d2675e45be4dd18", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the remainder when $$16+16+16+16$$ is divided by $$4$$ ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["Since $$16\\div 4$$ has a remainder of $$0$$, the remainder is $$0+0+0+0=0$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "501", "queId": "67c9a790cb18417892d62ccfc0967247", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $$2-$$digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the units digit of the number? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["We can think of the number as $$10a+b$$, where $$a$$ and $$b$$ are digits. Since the number is equal to the product of the digits $$(a\\cdot b)$$ plus the sum of the digits $$(a+b)$$, we can say that $$10a+b=a\\cdot b+a+b$$. We can simplify this to $$10a=a\\cdot b+a$$, and factor to $$(10)a=(b+1)a$$. Dividing by $$a$$, we have that $$b+1=10$$. Therefore, the units digit, $$b$$, is $$9$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "503", "queId": "9e1aa2a388134abdb1696a2bb22d9e87", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Lee counted by $$7$$\\textquotesingle s beginning with one of the whole numbers from $$1$$ through $$7$$, until Lee passed $$1000$$. If Lee counted three of the following numbers, which number did Lee not count? ", "answer_option_list": [[{"aoVal": "A", "content": "$$107$$ "}], [{"aoVal": "B", "content": "$$184$$ "}], [{"aoVal": "C", "content": "$$534$$ "}], [{"aoVal": "D", "content": "$$641$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders"], "answer_analysis": ["Each number on Lee\\textquotesingle s list must have the same remainder when divided by $$7$$. Divide each choice by $$7$$. The respective remainders are $$2$$, $$2$$, $$2$$, and $$4$$. Thus, $$107$$, $$184$$, and $$534$$ work. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "504", "queId": "31fa7ed485574b5b9d266bd98a8662ab", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A $14$-digit. number $666666 XY 444444$ is a multiple of $26$. If $X$ and $Y$ are both positive, what is the smallest vaue of $X+ Y$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["Since $1001$ is a multiple of $13$, $111111 = 111 \\times 1001$ is also a multiple of $13$. It follows that both $666666$ and $444444$ are both multiples of $26$. $666666XY 444444 = 66666600000000 + XY 000000 + 444444$ $\\Rightarrow XY$ must be divisible by $13$. Smallest $X+Y=1+3=4$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "506", "queId": "dec6dccdbe7c40a88fe0eec1fed0f88a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Leo prepares more than $400$ cupcakes for a party. Now he can divided all of them equally into $5$ piles. After his pet cat eats one of the cupcakes, he finds that now he can divide the remaining cupcakes equally into $6$ piles. Then, the naughty pet cat eat another one, and Leo divides the remaining cupcakes into $7$ piles. How many cupcakes did Leo prepare at least at the beginning? Find the sum of the three digits. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["The number is a multiple of $5$. When it is divided by $6$, it will have a remainder of $1$; when it is divided by $7$, it will have a remainder of $2$. Thus, if we add another $5$ to the number, it can be multiple of all the three numbers, which is $5\\times6\\times7=210$ at least. But the number is more than $400$, so we can get $210\\times2-5=415.$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "508", "queId": "559dde8bd71e4ad0b63c7b2e63b6569b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$1994$$ is added to any odd number, the sum will always be． ", "answer_option_list": [[{"aoVal": "A", "content": "odd　 "}], [{"aoVal": "B", "content": "even　 "}], [{"aoVal": "C", "content": "$$1995$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers"], "answer_analysis": ["even number $$+$$ odd number $$=$$ odd number. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "510", "queId": "2dc5182360394b649ee9157813653568", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ms Lee has many students. They can be split into $$5$$ groups, $$6$$ groups or $$9$$ groups equally. How many students might she possibly have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$120$$ "}], [{"aoVal": "B", "content": "$$150$$ "}], [{"aoVal": "C", "content": "$$180$$ "}], [{"aoVal": "D", "content": "$$240$$ "}], [{"aoVal": "E", "content": "$$300$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Word Problems Involving Factors and Multiples->Multiples Word Problems"], "answer_analysis": ["$6=2\\times3, 9=3\\times3, 2\\times3\\times3\\times5=90$. The number of students is a multiple of 90. $180\\div90=2$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "512", "queId": "7591fe5ccfb1426a985af90d4acaaa02", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A $6$-digit number starting with $18$, $18ABCD$, is a multiple of $6$, $7$, $9$ and $10$. Find $\\left (A +B + C+ D\\right )$ for the smallest such number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["The LCM of $6$, $7$, $9$ and $10$ is $2 \\times 3^{2}\\times 5 \\times7= 630$. $180 000=285 \\times 630 + 450$, ∴$$$$the$$$$ smallest number is $286 \\times 630=180 180$, Sum of the last 4 digits, $A + B + C+ D=9$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "514", "queId": "3666421ff7a4406db12951d92dd2e94d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "(US $$1998$$ Math kangaroo Problems, Level $$5-6$$, Question \\#$$15$$)When from any three-digit number we subtract that number written backwards, the difference will always be a number that is divisible by:． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Casting Out Nines"], "answer_analysis": ["No matter how we write the three-digit number, the sum of its three digits is always the same. Therefore, the remainders of the two numbers divided by $$9$$ are also the same. The difference will always be a number that is divisible by $$9$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "515", "queId": "3f30133a621c4a6083f19d9a332b5a04", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole number $A$, $B$, $C$. $A\\times B=45$, $B\\times C=50$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$23$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$45=3\\times 3\\times 5$ $50=2\\times 5\\times 5$ Because $B$ is the factor both number contains, $B=5$ Thus, $A=9$, $C=10$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "516", "queId": "367207bff5af417fb82e757ef26a2f93", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Miss Angel want to pack some candy for her students. She has a total of $$104$$ pieces of candy. Each of the goody bag will contain $$7$$ pieces of candy. In order to ensure all her students get a full bag of candy, how many more pieces of candy she needed? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders"], "answer_analysis": ["$$104\\div7=14R6$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "521", "queId": "4cada4ceecdb4a2ba4505800b4438fcb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If the sum of two whole numbers equals twice their difference, this sum cannot be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$222$$ "}], [{"aoVal": "B", "content": "$$444$$ "}], [{"aoVal": "C", "content": "$$888$$ "}], [{"aoVal": "D", "content": "$$1000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders"], "answer_analysis": ["If the sum is twice the difference, one \\# is triple the other. The sum is divisible by $$4$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "522", "queId": "998a4fae75c542c9a9a8cb3d2666a08c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The product of $$2860$$ and $$m$$ is a square number. Find the smallest possible value of $$m$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$65$$ "}], [{"aoVal": "B", "content": "$$572$$ "}], [{"aoVal": "C", "content": "$$715$$ "}], [{"aoVal": "D", "content": "$$2860$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "527", "queId": "2df524a8384149d285106c732a9e472d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Think Lab buys $24$ experimental apparatus. But two of the digits of the total price on the invoice are not clear, which only show $\\overline{\\square 8\\square 2}$ dollars. The purchasing agent says the two unclear digits on the invoice are the same. Given that the unit price of this kind of apparatus is an integer, how much is it? ", "answer_option_list": [[{"aoVal": "A", "content": "$$76$$ "}], [{"aoVal": "B", "content": "$$160$$ "}], [{"aoVal": "C", "content": "$$202$$ "}], [{"aoVal": "D", "content": "$$328$$ "}], [{"aoVal": "E", "content": "$$412$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["The number of total price can be divided by $3$ and $8$. It can be divided by $8$ which means the tens digit must be $3$ or $7$. And when the tens digit is $7$, the number can be divided by $3$. Thus, the total price is $7872$ dollars, and each of them is $328$ dollars. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "528", "queId": "5ec9e88f099c488aa525e5fed7257f73", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are over $$1000$$ students at my school. When~ the number of students is divided by $$10$$， the remainder is $$3$$． When~ the number is divided by $$13$$， the remainder is $$3$$. What is the remainder when the number is divided by $$130$$？ ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["When $$10$$ students or$$13$$ students are in a group, there are always $$3$$ students remained. It means that if we subtract $$3$$ from the total number, the result is a common multiple of $$10$$ and $$13$$. Therefore when there are $$130$$ in one group, there are still$$\\textasciitilde3$$ students remained. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "531", "queId": "51359b6d0ed242468fc3e0d70d53c764", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Olivia is thinking of a two-digit number. She says, \"If I divide the number by $$6$$, the remainder is $$3$$. If I divide the number by $$8$$, the remainder is also $$3$$.\" What is the smallest possible number that Olivia could be thinking of? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$27$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$51$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["The Lowest Common Multiple of $$6$$ and $$8$$ is $$24$$. $$24+3=27$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "538", "queId": "67f721dd3b3344589a364a78a48a18c2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Let $N=34 \\cdot 34 \\cdot 63 \\cdot 270$. What is the ratio of the sum of the odd divisors of $N$ to the sum of the even divisors of $N$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$1:16$ "}], [{"aoVal": "B", "content": "$1:15$ "}], [{"aoVal": "C", "content": "$1:14$ "}], [{"aoVal": "D", "content": "$1:8$ "}], [{"aoVal": "E", "content": "$1:3$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["Prime factorizing $N$, we see $N=2^{3} \\cdot 3^{5} \\cdot 5 \\cdot 7 \\cdot 17^{2}$. The sum of $N$ \\textquotesingle s odd divisors are the sum of the factors of $N$ without 2 , and the sum of the even divisors is the sum of the odds subtracted by the total sum of divisors. The sum of odd divisors is given by $$ a=\\left(1+3+3^{2}+3^{3}+3^{4}+3^{5}\\right)(1+5)(1+7)\\left(1+17+17^{2}\\right) $$ and the total sum of divisors is $$ (1+2+4+8)\\left(1+3+3^{2}+3^{3}+3^{4}+3^{5}\\right)(1+5)(1+7)\\left(1+17+17^{2}\\right)=15 a . $$ Thus, our ratio is $$ \\frac{a}{15 a-a}=\\frac{a}{14 a}=\\text { (C) } 1: 14 \\text {. } $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "539", "queId": "43defcaf2fe944db879e116ec21a5ad5", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A student wrote down a natural number. When she divided the number by $$9$$, the remainder was $$7$$. What is the~~remainder when twice that number is divided by $$9$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["The remainder of $$A$$ $$\\div9$$ is $$7$$, and $$2A=A+A$$. Therefore the remainder of $$2A\\div9$$ is $$7+7=14$$. $$14= 9+5$$, therefore the remainder is $$5$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "541", "queId": "3f6b40d1913440e58052b4051c95c5e9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following numbers has the smallest prime factor? (2003 AMC 8 Problem, Question \\#2) ", "answer_option_list": [[{"aoVal": "A", "content": "$$55$$ "}], [{"aoVal": "B", "content": "$$57$$ "}], [{"aoVal": "C", "content": "$$58$$ "}], [{"aoVal": "D", "content": "$$59$$ "}], [{"aoVal": "E", "content": "$$61$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["The smallest prime factor is $2$, and $58$ is the only multiple of $2$ among these five numbers. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "543", "queId": "325ca03c31a2445e87db19bc8209ccbc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that $$6$$ and $$9$$ are multiples of $$3$$, which of the followings might not be a multiple of $$3$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9 + 6$$ "}], [{"aoVal": "B", "content": "$$9 - 6$$ "}], [{"aoVal": "C", "content": "$$2 \\times 9$$ "}], [{"aoVal": "D", "content": "$$2 \\times 9 + 1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["$$\\text{A}$$: corresponding to $$\\text{a}+\\text{b}$$; $$\\text{B}$$: corresponding to $$\\text{a}-\\text{b}$$; $$\\text{C}$$: $$\\text{na}$$, where $$\\text{n}$$\\emph{\\emph{~}}is an integer. We choose $$\\text{D}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "545", "queId": "9067885c5242404cadc8267d40649401", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many square numbers and cube numbers are there in the list below? $18$, $27$, $64$, $72$, $81$, $162$, $196$, $324$, $343$, $496$, $529$, $675$, $729$, $784$, $841$, $951$, $1000$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers"], "answer_analysis": ["Square numbers: $64$, $81$, $196$, $324$, $529$, $729$, $784$, $841$ Cube numbers: $27$, $64$, $343$, $729$, $1000$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "546", "queId": "a2d57ba9e3294c80a3cdb257ef309c21", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The ones digit of $$9\\times 8\\times 7\\times 6\\times 5\\times 4\\times 3\\times 3\\times 4\\times 5\\times 6\\times 7\\times 8\\times 9$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["Since $$5\\times 4 = 20$$, the ones digit of the given product must be $$0$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "547", "queId": "43ec0f56dfdd4992bf3ab63daffb140f", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following is a composite number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$59$$ "}], [{"aoVal": "B", "content": "$$61$$ "}], [{"aoVal": "C", "content": "$$63$$ "}], [{"aoVal": "D", "content": "$$67$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["$63$ is a composite number. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "550", "queId": "be87698b58524a658ec8af43503295b4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many numbers of the following are divisible by $9$? $$\\textasciitilde$$ $452 \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} 387\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~1057\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~108\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~496\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~1233$ $\\textasciitilde$ $\\textasciitilde$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["$387, 108$, and $1233$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "552", "queId": "999fdde844e945fa82c3ef2a0e0ab0c7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the product of the least common multiple of $$6$$ and $$18$$ and the greatest common factor of $$6$$ and $$18$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$54$$ "}], [{"aoVal": "D", "content": "$$108$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["The least common multiple of $$6$$ and $$18$$ is $$18$$. The greatest common factor of $$6$$ and $$18$$ is $$6$$. Finally, $$6\\times18 = 108$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "553", "queId": "5eee697d3b0c4c718ab9ed27c3bcfb23", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following numbers are prime numbers? $137$~ ~ ~ ~ ~ ~ ~ ~ ~$151$~ ~ ~ ~ ~ ~ ~ ~ ~$237$~ ~ ~ ~ ~ ~ ~ ~ ~$301$ ", "answer_option_list": [[{"aoVal": "A", "content": "$137$ and $237$ "}], [{"aoVal": "B", "content": "$137$ and $301$ "}], [{"aoVal": "C", "content": "$237$ and $301$ "}], [{"aoVal": "D", "content": "$137$ and $151$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["$3$ is the factor of $237$ because $3 \\times79 = 237$; $7$ is the factor of $301$ because $7 \\times 43 = 301$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "554", "queId": "a77c39b3628648419e505eff88b4827a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The expression $$1\\times 2\\times 3\\times \\cdots \\times n$$ has exactly $$128$$ consecutive zeros at the end of its result, then the maximum value of $$n$$ is~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$405$$ "}], [{"aoVal": "B", "content": "$$109$$ "}], [{"aoVal": "C", "content": "$$500$$ "}], [{"aoVal": "D", "content": "$$524$$ "}], [{"aoVal": "E", "content": "$$539$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["There are $$128$$ zeros at the end of the result, and the estimated answer is close to $$500$$. $$\\left[ \\frac{500}{5} \\right]+\\left[ \\frac{500}{25} \\right]+\\left[ \\frac{500 }{125} \\right]=100+20+4=124$$, Just add $$4$$ numbers including $$5$$: $$505$$, $$510$$, $$515$$, $$520$$, so the maximum value of $$n$$ that satisfies the condition is $$524$$ . "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "561", "queId": "3b416a9d130d468694f9d9e7660ef8b4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Think Lab buys $24$ experimental apparatus. But two of the digits of the total price on the invoice are not clear, which only show $\\overline{\\square 8\\square 2}$ dollars. The purchasing agent says the two unclear numbers on the invoice are the same. Given that the single price of this kind of apparatus is an integer, how much is it? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$328$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["The number of total price can be divided by $3$ and $8$. It can be divided by $8$ which means the tens digit must be $3$ or $7$. And when the tens digit is $7$, the number can be divided by $3$. Thus, the total price is $7872$ dollars, and each of them is $328$ dollars. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "562", "queId": "36ef04f664b44136b8414c34bfdf3873", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The hundreds digit of a three-digit number is $$2$$ more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["$$\\rm Method$$ $$1$$: Let the hundreds, tens, and units digits of the original three-digit number be $$a$$, $$b$$, and $$c$$, respectively. We are given that $$a=c+2$$. The original three-digit number is equal to $$100a+10b+c=100(c+2)+10b+c=101c+10b+200$$. The hundreds, tens, and units digits of the reversed three-digit number are $$c$$, $$b$$, and $$a$$, respectively. This number is equal to $$100c+10b+a=100c+10b+(c+2)=101c+10b+2$$. Subtracting this expression from the expression for the original number, we get $$(101c+10b+200)-(101c+10b+2)=198$$ . Thus, the units digit in the final result is $$8$$. $$\\rm Method$$ $$2$$: The result must hold for any three-digit number with its hundreds digit being $$2$$ more than the units digit. $$301$$ is such a number. Evaluating, we get $$301-103=198$$. Thus, the units digit in the final result is $$8$$. ($$2010$$ AMC $$8$$ Problem, Question \\#$$22$$) "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "563", "queId": "71414ae032e14f0aa8b8eac76ea72baf", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "I think of a number. When I divide it by $$2$$, the remainder is $$1$$. When I divide it by $$3$$, the remainder is $$2$$. What is the smallest possible value of the number?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["$$2\\times3-1=5$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "564", "queId": "5f020e1a25cd41699b22a85414742035", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "375+753+537+357+573+735= ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$3330$$ "}], [{"aoVal": "B", "content": "$$1000$$ "}], [{"aoVal": "C", "content": "$$3333$$ "}], [{"aoVal": "D", "content": "$$1333$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["$$3+5+7=15$$， $$15+15=30$$， $$30+300+3000=3330$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "565", "queId": "99ae3ee138774a8dbe3b57d1e9eca4cd", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Jam has some pieces of candy. He wants to share with some kids. If he shares the candy among $8$ kids equally, there will be $2$ pieces left. If he shares the candy among $9$ kids equally, there will be $3$ pieces left. If he shares the candy among $10$ kids equally, there will be $4$ pieces left. How many pieces of candy are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$321$ "}], [{"aoVal": "B", "content": "$354$ "}], [{"aoVal": "C", "content": "$720$ "}], [{"aoVal": "D", "content": "$360$ "}], [{"aoVal": "E", "content": "$240$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["The LCF of $8, 9,$ and $10$ is $8\\times9\\times10\\div2=360$. $360-6=354$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "566", "queId": "714239a45f3a404b8bb225d29d7f9f88", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following number pairs do not contain any divisible relationship? ", "answer_option_list": [[{"aoVal": "A", "content": "$(12+78), 2$ "}], [{"aoVal": "B", "content": "$(39+61), 3$ "}], [{"aoVal": "C", "content": "$(44+82), 4$ "}], [{"aoVal": "D", "content": "$(25+5100), 5$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["If both numbers in the parentheses are multiple of the smaller number, the number in the parentheses should be divisible by the smaller number. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "568", "queId": "32abb43f945b441aaa75d264ffc39361", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Becky is separating 53 cherries into bag A, bag B and bag C. It is known that there are even number of cherries in both bag A and bag B. Could you tell whether the number of cherries in bag C is even or odd number? ", "answer_option_list": [[{"aoVal": "A", "content": "Odd "}], [{"aoVal": "B", "content": "Even "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["Number of cherries in bag C: 53 (odd number) - even - even Number of odd character = 1 Therefore, the number of cherries in bag C is odd. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "570", "queId": "8be0be7f789c43b997ea512be47e1a23", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Think Lab buys $24$ experimental apparatus. But two of the digits of the total price on the invoice are not clear, which only show $\\overline{\\square 8\\square 2}$ dollars. The purchasing agent says the two unclear digits on the invoice are the same. Given that the single price of this kind of apparatus is an integer, how much is it? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$328$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["The number of total price can be divided by $3$ and $8$. It can be divided by $8$ which means the tens digit must be $3$ or $7$. And when the tens digit is $7$, the number can be divided by $3$. Thus, the total price is $7872$ dollars, and each of them is $328$ dollars. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "571", "queId": "4d0261799f564fcb85df22aba9ab70fe", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of $$4$$ odd numbers is always． ", "answer_option_list": [[{"aoVal": "A", "content": "even "}], [{"aoVal": "B", "content": "odd "}], [{"aoVal": "C", "content": "less than $$20$$ "}], [{"aoVal": "D", "content": "greater than $$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers"], "answer_analysis": ["The product of odd numbers is always odd. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "572", "queId": "682225b6e5974776bb00ea32874ed249", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole numbers $A$, $B$ and $C$ ($B\\neq1$). $A\\times B=21$, $B\\times C=57$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$23$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$21=3\\times 7$ $57=3\\times 19$ Because $B$ is the factor both number contains, $B=3$ Thus, $A=7$, $C=19$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "573", "queId": "32b4f71f512c4cbbbe395e4fe37c16e4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Micky and Marcy want to make dumplings. They start with different speeds. There are two kinds of boxes. The smaller one of them could contain $9$ dumplings, and the bigger one could contain $17$ dumplings. Micky works with the smaller one, and Marcy works with the bigger one. What is the smallest number of dumplings that Micky needs to make until they start with a new box respectively at the same time? ", "answer_option_list": [[{"aoVal": "A", "content": "$$143$$ "}], [{"aoVal": "B", "content": "$$150$$ "}], [{"aoVal": "C", "content": "$$153$$ "}], [{"aoVal": "D", "content": "$$163$$ "}], [{"aoVal": "E", "content": "$$173$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Multiples and Least Common Multiples->Least Common Multiple of Two Numbers"], "answer_analysis": ["The least common multiple of $9$ and $17$: $9 \\times 17 = 153$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "574", "queId": "32b6afd8cb3c44be8c911a1c85bc3b72", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $5$-digit number $\\overline{2018U}$ is divisible by $9$. What is the remainder when this number is divided by $8$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["We use the property that the digits of a number must sum to a multiple of $9$ if it is divisible by $9$. This means $2+0+1+8+U$ must be divisible by $9$. The only possible value for U then must be $7$. Since we are looking for the remainder when divided by $8$, we can ignore the thousands. The remainder when $187$ is divided by $8$ is $(\\rm B)$ $3$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "575", "queId": "8be38644dee6484384b66b89cc18c0e1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\sqrt{41^{2} - 9^{2}} + \\sqrt{8^{2} + 15^{2}}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$56$$ "}], [{"aoVal": "B", "content": "$$57$$ "}], [{"aoVal": "C", "content": "$$58$$ "}], [{"aoVal": "D", "content": "$$58$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["$$\\sqrt{41^{2} - 9^{2}} + \\sqrt{8^{2} + 15^{2}}=\\sqrt{1600} + \\sqrt{289} = 40 + 17 = 57$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "576", "queId": "6cb7bae9da1349f6a6539d819d1de5dc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many prime numbers are less than $$10$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Prime Factorization (Equations)"], "answer_analysis": ["The prime numbers less than $$10$$ are $$2$$, $$3$$, $$5$$, and $$7$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "579", "queId": "839e166836fb4da990f3922e436d76e6", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "A two-digit prime number is still prime when the digits of its first and tenth digits are exchanged. There are such prime numbers. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["$$11$$，$$13$$，$$17$$，$$31$$，$$37$$，$$71$$，$$73$$，$$79$$，$$97$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "580", "queId": "32ccd280d6dc43be996836503fbf4a10", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "In a Fibonacci-like sequence $$1,3,4,7,11,18\\cdots $$(where each term is the sum of the two previous terms, starting from the third term), what is the remainder when the $$5555^{}\\text{th}$$ term is divided by $$5$$？ ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["Nil "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "582", "queId": "a78fcc518cdf4eac805a9742c75b76d5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $5$-digit number $\\overline{2018U}$ is divisible by $9$. What is the remainder when this number is divided by $8$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["We use the property that the digits of a number must sum to a multiple of $9$ if it is divisible by $9$. This means $2+0+1+8+U$ must be divisible by $9$. The only possible value for U then must be $7$. Since we are looking for the remainder when divided by $8$, we can ignore the thousands. The remainder when $187$ is divided by $8$ is $(\\rm B)$ $3$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "583", "queId": "75e17d65e3384337b4edaa6d90eef503", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "If the product of an even number and an odd number is $$840$$, what is the largest possible value of this odd number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$105$$ "}], [{"aoVal": "D", "content": "$$420$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers"], "answer_analysis": ["If the product of an even and an odd number is $$840={2^{3}}\\times105$$, then the largest possible value of the odd number is $$105$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "585", "queId": "cc743f7400f744b495eb41f6ec3050e1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Modify a digit in $$675479$$ so that this six-digit number is divisible by $$25$$. What is the modified six-digit number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$675480$$ "}], [{"aoVal": "B", "content": "$$675475$$ "}], [{"aoVal": "C", "content": "$$675470$$ "}], [{"aoVal": "D", "content": "$$625479$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders"], "answer_analysis": ["change the number on ones digit from $$9$$to$$5$$，$$675475$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "587", "queId": "b9fa511bbb8f4e688f429dd91a68c321", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is a factor of $$380$$?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["Since $$380 =10\\times38$$, $$10$$ is a factor of $$380$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "588", "queId": "51a035336cfa4cd89792b6eeb26402e7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$3^{2}+3^{2}+3^{2}+3^{2}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4^{2}$$ "}], [{"aoVal": "B", "content": "$$6^{2}$$ "}], [{"aoVal": "C", "content": "$$12^{2}$$ "}], [{"aoVal": "D", "content": "$$33^{2}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["$$3^{2}+3^{2}+3^{2}+3^{2}=9+9+9+9=36=6^{2}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "590", "queId": "908ffabc2d7e463388d04051126de9a0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$9$$, the remainder is $$1$$. When $$N$$ is divided by $$10$$, the remainder is $$3$$. What is the remainder when $$N$$ is divided by $$11$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["The smallest possible $$N$$ is $$73$$, and $$73 \\div 11\\rm R7$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "592", "queId": "ff591f93b84e4c278c48f857934bdf76", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the least possible remainder when an even number is divided by $$7$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders"], "answer_analysis": ["When $$14$$ (or any other even multiple of $$7$$) is divided by $$7$$, the remainder is $$0$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "594", "queId": "63b475d8986743d9a318d3e19919ac30", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$18$$ apples are equally given to $$9$$ kids. How many apples can every kid get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders"], "answer_analysis": ["$$18\\div9=2$$ $$18=2+2+2+2+2+2+2+2+2$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "596", "queId": "5a9f067862ad466b8516c36bce658b8b", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following numbers is not prime? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13 $$ "}], [{"aoVal": "B", "content": "$$19 $$ "}], [{"aoVal": "C", "content": "$$89$$ "}], [{"aoVal": "D", "content": "$$93$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["$$93=31\\times 3$$ , its factors are $1$，$31$，$3$，$93$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "599", "queId": "716675a0e9af4299962aefdaa69aa99d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $n$ and $m$ are integers and $n^{2}+m^{2}$ is even, which of the following is impossible? (2014 AMC 8 Problem, Question \\#13) ", "answer_option_list": [[{"aoVal": "A", "content": "$n$ and $m$ are even "}], [{"aoVal": "B", "content": "$n$ and $m$ are odd "}], [{"aoVal": "C", "content": "$n+m$ is even "}], [{"aoVal": "D", "content": "$n+m$ is odd "}], [{"aoVal": "E", "content": "none of these are impossible "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["The question asks which one is impossible, all we need to do is find one possible way that the others are possible. After trying, when $n$ and $m$ are both even or odd, the calculation works, so $D$ is not correct. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "604", "queId": "fabee4e3dd6240d3b1e6b55192cb4ae8", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following is not a factor of $48$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["$14$ can not divide $48$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "606", "queId": "5634385348724933ae49b4983a89c14a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the value for lcm $$\\left[ 12,18\\right]$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["List the prime factorization for $$12$$ and $$18$$ first. $$12=2^{2}\\times3$$ and $$18=3^{2}\\times2$$. The largest exponent for $$2$$ is $$2$$, and the larger exponent for $$3$$ is $$2$$, thus the least common multiple for $$12$$ and $$18$$ is $$2^{2}\\times3^{2}=36$$. We choose $$\\text{A}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "608", "queId": "684f922efc664011860b8f69d3faec5e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$a=1$$, $$b=2$$, and $$c=3$$, then $$\\overline{abc}=123$$. Find the value of $$m$$ according to this rule. $$\\overline{m21}=8\\times \\overline{m9}+3m$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["$$\\begin{eqnarray}\\overline{m21}\\&=\\&8\\times \\overline{m9}+3m\\textbackslash\\textbackslash{} 100m+21\\&=\\&80m+72+3m\\textbackslash\\textbackslash{} 17m\\&=\\&51\\textbackslash\\textbackslash{} m\\&=\\&3.\\end{eqnarray}$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "610", "queId": "375e4ea1c2c64564952bff0f8058c931", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Answer the question below: If $$a$$, $$b$$ are prime numbers, and $$3a+7b=41$$, then $$a+b=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Applying Special Prime Numbers"], "answer_analysis": ["Based on the laws relating to the parity in addition and multiplication, either $$a$$ or $$b$$ must be $$2$$. If $$a = 2$$, then $$b = 5$$, and $$a + b = 7$$; if $$b = 2$$, then $$a = 9$$; $$9$$ is not a prime number, which doesn\\textquotesingle t match the conditions in the question. Therefore, we choose B. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "611", "queId": "7a94aab4d24747c69907e93f9ab1c856", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A kind of water plant grows so fast that it doubles every day. If one plant is put into the pond on the first day, it will turn to two plants on the second day, and on the $26$\\textsuperscript{th} days, they can fill the pond. If $8$ water plants are put into the pond on the first day, how many days will it take to fill the pond? ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["It takes three days for one plant to turn to $8$ plants. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "614", "queId": "5ac2b47d84bb474ca9ea93b9dfdd71a7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A number has the same digit in its tens place and its hundredth place. How many times greater is the value of the digit in the tens place than the value of the digit in the hundredth place? ", "answer_option_list": [[{"aoVal": "A", "content": "$0.1$ "}], [{"aoVal": "B", "content": "$100$ "}], [{"aoVal": "C", "content": "$1000$ "}], [{"aoVal": "D", "content": "$10,000$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases"], "answer_analysis": ["Let the digit be $d$ $10d\\div 0.01d=1000$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "615", "queId": "ecdb187f8f5446a4b97760216e1c206e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If an equilateral triangle has in-teger sides, its perimeter \\emph{cannot} be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$915$$ "}], [{"aoVal": "B", "content": "$$615$$ "}], [{"aoVal": "C", "content": "$$315$$ "}], [{"aoVal": "D", "content": "$$115$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders"], "answer_analysis": ["The perimeter of an equilateral $$\\triangle $$ with integer sides is divisible by $$3$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "616", "queId": "b0dcbc585b31462aafe6c6d19e0604d7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many different primes are in the prime factorisation of $$2016$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Prime Factorization (Equations)"], "answer_analysis": ["$$2016=2\\times2\\times2\\times2\\times2\\times3\\times3\\times7$$; there are $$3$$ different primes. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "617", "queId": "51d7355e6f1b4cc8903463abcfdabdbf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$1\\times2\\times3\\times4\\times5\\times6\\times7\\times8\\times$$$$9\\times10\\times11\\times12\\times13\\times$$$$14\\times15 = 1307 674 368000$$, how many times does the digit \"$$0$$\" appear in the product $$10\\times20\\times30\\times40\\times50\\times60\\times$$$$70\\times80\\times90\\times100\\times110\\times120\\times130\\times140\\times150$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"], "answer_analysis": ["If $$1\\times2\\times3\\times4\\times5\\times6\\times7\\times$$$$8\\times9\\times10\\times11\\times12\\times13\\times14\\times15 = $$$$1307 674 368000$$, and we multiply each of these $$15$$ numbers by $$10$$, the new product will have an additional $$15$$ zeroes, and $$15+4=19$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "618", "queId": "760c60c12063487c846f1fadc8010ba0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $5$-digit number $\\overline{2018U}$ is divisible by $9$. What is the remainder when this number is divided by $8$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["We use the property that the digits of a number must sum to a multiple of $9$ if it is divisible by $9$. This means $2+0+1+8+U$ must be divisible by $9$. The only possible value for U then must be $7$. Since we are looking for the remainder when divided by $8$, we can ignore the thousands. The remainder when $187$ is divided by $8$ is $(\\rm B)$ $3$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "624", "queId": "4493dee2b75046bc9ce0378b59f92a2f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If add $$1994$$ to any odd number, the sum will always be． ", "answer_option_list": [[{"aoVal": "A", "content": "odd　 "}], [{"aoVal": "B", "content": "even　 "}], [{"aoVal": "C", "content": "$$1995$$ "}], [{"aoVal": "D", "content": "prime　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers"], "answer_analysis": ["even number $$+$$ odd number $$=$$ odd number. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "627", "queId": "5adba830ff3b46ec92b30e403d6aa2cc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Kate and Kerry are two dogs. Every $3$-hour, Kate goes to the dog park. Every $2$-hour, Kerry gos to the dog park. Today, Kate and Kerry first meet at $10:00\\text{am}$. When will they meet each other again? ", "answer_option_list": [[{"aoVal": "A", "content": "$12:00\\text{pm}$ "}], [{"aoVal": "B", "content": "$4:00\\text{pm}$ "}], [{"aoVal": "C", "content": "$6:00\\text{pm}$ "}], [{"aoVal": "D", "content": "$10:00\\text{pm}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Multiples and Least Common Multiples->Least Common Multiple of Two Numbers"], "answer_analysis": ["$LCM[2,3]=6$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "630", "queId": "a7b5f72c56164004b54c43e5b88481ea", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The characteristic of numbers that are divisible by $$4$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "Last digit is divisible by $$4$$. "}], [{"aoVal": "B", "content": "Last two digits are divisible by $$4$$. "}], [{"aoVal": "C", "content": "Last three digits are divisible by $$4$$. "}], [{"aoVal": "D", "content": "The sum of digits is divisible by $$4$$. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders"], "answer_analysis": ["$$1$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "631", "queId": "490d5358ce7046a4b9b81cb2fe5a90fa", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\sqrt {2\\times 4\\times 8}\\times \\sqrt {8\\times 8}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$64$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["$$\\sqrt {2\\times 4\\times 8}\\times \\sqrt {8\\times 8}=8\\times 8=64$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "634", "queId": "37b5bc085e0d460392df19ab9a41c416", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following numbers is not the square of a whole number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$144$$ "}], [{"aoVal": "C", "content": "$$196$$ "}], [{"aoVal": "D", "content": "$$200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["All choices except $$200$$ are perfect squares since: $$100=10^{2}$$ $$144=12^{2}$$ $$196=14^{2}$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "637", "queId": "6d0a18cdd59d4557a14f76ecd508eba5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many factors does $36$ have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["$1, 2, 3, 4, 6, 9, 12, 18, 36$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "639", "queId": "5f74f620bffe44f380949499e519b587", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When from any three-digit number we subtract that number written backwards, the difference will always be a number that is divisible by:． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Casting Out Nines"], "answer_analysis": ["No matter how we write the three-digit number, the sum of its three digits is always the same. Therefore, the remainders of the two numbers divided by $$9$$ are also the same. The difference will always be a number that is divisible by $$9$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "640", "queId": "7ac01a3bb1194ff7b78925d0d02f7485", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following has an odd number of whole-number factors? ", "answer_option_list": [[{"aoVal": "A", "content": "$$47$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$49$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers"], "answer_analysis": ["The whole-number factors of $$49$$ are $$1$$, $$7$$, and $$49$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "642", "queId": "5f8027a5003742e692777d0509b09153", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many positive integer factors of 2020 have more than 3 factors? (As an example, 12 has 6 factors, namely $1,2,3,4,6$, and 12 .) (2020 AMC 8 Problem, Question \\#17) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["Since $2020=2^{2} \\cdot 5 \\cdot 101$, we can simply list its factors: $$ 1,2,4,5,10,20,101,202,404,505,1010,2020 . $$ There are 12 of these; only $1,2,4,5,101$ (i.e. 5 of them) don\\textquotesingle t have over 3 factors, so the remaining $12-5=(\\text{B}) 7$ factors have more than 3 factors. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "643", "queId": "e3aaeda909b642009297690f00b114b3", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "From 202 to 2020 (including these two numbers), how many multiples of 9 are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$201$$ "}], [{"aoVal": "B", "content": "$$202$$ "}], [{"aoVal": "C", "content": "$$101$$ "}], [{"aoVal": "D", "content": "$$102$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["$[\\frac{2020}{9}]-[\\frac{201}{9}]=224-22=202$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "651", "queId": "d139cdcaffda4f6e921a448ed14b69ec", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Amy runs a lap around the track in $4$ minutes and Pawel in $5$ minutes. Amy and Pawel start to run around the track at the same time. After how many minutes will the boys meet at the starting point again? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "It depends on the distance around the track "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["The answer is the least common multiple of $4$ and $5$, which is $20$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "654", "queId": "df12c8ec69db488da6ffcaf5e0b9fa02", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many positive factors of $$144$$ are also multiples of $$4$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$144={{2}^{4}}\\times {{3}^{2}}=4\\times2^{2}\\times {{3}^{2}}$$. Among them, there are $$\\left( 2+1 \\right)\\times (2+1)=9$$ factors which has $$4$$ as its factor. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "655", "queId": "4953f555328044d6bf88c2402e0e952b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "John, Emily and Nick want to buy some apples from Walmart where the apples are sold in pack of four. If they buy six packs and share the apples evenly, how many apples will each one of them get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["$4\\times 6=24$; $24=3\\times 8$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "656", "queId": "56a8b35b148f432795b814652a9d54c0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Each of the following results in an even number except． ", "answer_option_list": [[{"aoVal": "A", "content": "$$952+136$$ "}], [{"aoVal": "B", "content": "$$952-136$$ "}], [{"aoVal": "C", "content": "$$952\\div 136$$ "}], [{"aoVal": "D", "content": "$$952\\times 136$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Odd and Even Applications"], "answer_analysis": ["The sum, difference, and product of even numbers are even, but $$952\\div 136=7$$ is odd. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "658", "queId": "ba36917be0014d168e2984e4500780b7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the smallest prime number greater than $$47$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$59$$ "}], [{"aoVal": "B", "content": "$$57$$ "}], [{"aoVal": "C", "content": "$$53$$ "}], [{"aoVal": "D", "content": "$$51$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["$$49 =7\\times7$$; $$51 = 3\\times17$$. The first prime is $$53$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "659", "queId": "88a00507342d47c1b0e19a72002f66af", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "For a positive integer $n$, the factorial notation $n!$ repressents the product of the integer from $n$ to $1$, (For example, $6!=6\\times5\\times4\\times3\\times2\\times1$.) What value of $N$ satisfies the following equation? $$6!\\times8!=8\\times N!$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["$6!=10\\times9\\times8$, $$6!\\times8!=8\\times 10!$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "663", "queId": "84092477536143fb9d381ed652715e82", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the smallest multiple of $$7$$ that is greater than or equal to $$20 $$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$22$$ "}], [{"aoVal": "D", "content": "$$28$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$2\\times7=14$$, $$3\\times7=21$$, since $$14$$ is smaller than $$20$$ and $$21$$ is the closest multiple of $$7$$ and greater than $$20$$, we choose $$\\text B$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "664", "queId": "765fa02e95c34931aefa0929857642ee", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole number $A$, $B$, $C$. $A\\times B=77$, $B\\times C=132$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$33$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$77=7\\times 11$ $132=2\\times 2\\times 3\\times 11$ Because $B$ is the factor both number contains, $B=11$ Thus, $A=7$, $C=12$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "670", "queId": "68d281debfa344ca90d42e8daaf20953", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following number is a multiple of $9$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$234$$ "}], [{"aoVal": "B", "content": "$$136$$ "}], [{"aoVal": "C", "content": "$256$ "}], [{"aoVal": "D", "content": "$$418$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders"], "answer_analysis": ["$2+3+4=9$, so $234$ is divisible by 9. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "673", "queId": "90f85ce1e78b4a008e9b93aea2c4b3d7", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The smallest number greater than $2$ that leaves a remainder of $2$ when divided by $3,4,5$, or $6$ lies between what numbers? (2012 AMC 8 Problem, Question \\# 15) ", "answer_option_list": [[{"aoVal": "A", "content": "$40$ and $50$ "}], [{"aoVal": "B", "content": "$51$ and $55$ "}], [{"aoVal": "C", "content": "$56$ and $60$ "}], [{"aoVal": "D", "content": "$61$ and $65$ "}], [{"aoVal": "E", "content": "$66$ and $99$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["First, list number that leaves a remainder of $2$ when divided by $6$: $8,14,20,26,32,38,44,50,56,62\\cdots $. Meanwhile, divide each number with $5$ to see it the number meets the condition. If the number divided by $5$ leaves a remainder of $2$, divide it by $4$ see if it still works. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "674", "queId": "d14f4b95c61d47f5a993a06a2c5c3422", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of $$2$$ odd numbers is always.　 ", "answer_option_list": [[{"aoVal": "A", "content": "divisible by $$3$$ "}], [{"aoVal": "B", "content": "odd　 "}], [{"aoVal": "C", "content": "prime　 "}], [{"aoVal": "D", "content": "even　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers"], "answer_analysis": ["The product of $$2$$ odd numbers, such as $$5\\times7=35$$, is always odd. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "675", "queId": "40ecd025d4234849a565eb6f20a21835", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What does the \"3\"~in 1234 mean? ", "answer_option_list": [[{"aoVal": "A", "content": "3 hundreds "}], [{"aoVal": "B", "content": "3 tens "}], [{"aoVal": "C", "content": "3 thousands "}], [{"aoVal": "D", "content": "3 ones "}], [{"aoVal": "E", "content": "3 millions "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits"], "answer_analysis": ["3 tens "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "677", "queId": "454bba4a33824efab618378ac8426ce0", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "A two-digit prime number is still prime when the digits of its first and tenth digits are exchanged. There are such prime numbers. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["$$11$$，$$13$$，$$17$$，$$31$$，$$37$$，$$71$$，$$73$$，$$79$$，$$97$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "681", "queId": "b5b5215a73eb4d8e93d34a0e05f7a435", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Fill in the blanks below with the largest possible numbers: ~\\uline{~~~~~~~~~~}~$$\\div16 = 5\\rm R$$~\\uline{~~~~~~~~~~}~. ~\\uline{~~~~~~~~~~}~$$\\div16 = 5\\rm$$ $\\cdots\\cdots$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "105, 15 "}], [{"aoVal": "B", "content": "95, 15 "}], [{"aoVal": "C", "content": "88, 13 "}], [{"aoVal": "D", "content": "64, 16 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders"], "answer_analysis": ["The largest possible remainder should be at least $$1$$ smaller than the divisor. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "684", "queId": "8c68c724c9934a358b17bc7a8403f6ea", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the missing number in the box? $$7063000 =7000000+\\boxed{?}+3000$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$600$$ ones "}], [{"aoVal": "B", "content": "$$600$$ tens "}], [{"aoVal": "C", "content": "$$600$$ hundreds "}], [{"aoVal": "D", "content": "$$600$$ thousands "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["$600$ hundreds has the same value as $600\\times100=60000$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "687", "queId": "9ec72666d4f5427bb1ae52f1facdc562", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following cases can\\textquotesingle t make an even number? ", "answer_option_list": [[{"aoVal": "A", "content": "An odd number$$+$$An even number "}], [{"aoVal": "B", "content": "An even number$$+$$An even number "}], [{"aoVal": "C", "content": "An odd number$$+$$An odd number "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers"], "answer_analysis": ["The sum of an odd number and an even number is always an odd~ number. The sum of two numbers which are both even or both odd is always an even number. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "688", "queId": "5b75f53e71c64811acdd402bbb5ac797", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Divide 8 numbers $$15$$、$$18$$、$$21$$、$$22$$、$$42$$、$$44$$、$$50$$ and $$60$$ into two groups with 4 numbers in each group to make the product of numbers in each group the same, so the two groups are ． ", "answer_option_list": [[{"aoVal": "A", "content": "（$$15$$, $$22$$, $$21$$, $$60$$），（$$18$$, $$44$$, $$42$$, $$50$$） "}], [{"aoVal": "B", "content": "（$$15$$, $$42$$, $$44$$, $$60$$），（$$18$$, $$22$$, $$21$$, $$50$$） "}], [{"aoVal": "C", "content": "（$$15$$, $$44$$, $$21$$, $$60$$），（$$18$$, $$22$$, $$42$$, $$50$$） "}], [{"aoVal": "D", "content": "（$$15$$, $$44$$, $$21$$, $$50$$），（$$18$$, $$22$$, $$42$$, $$60$$） "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->Finding Factors Given the Product"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "689", "queId": "456df3204842430d8a3e9cfae8938155", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A kind of water plant grows so fast that it doubles every day. If one plant is put into the pond on the first day, two plants will grow on the second day, and on the twenty-sixth days, they will just fill the pond. If eight water plants are put into the pond on the first day, how many days it will take to fill the pond? ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["It takes three days for one plant to develop to eight plants. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "691", "queId": "49c5137498984ceb90c520f6e5483bc7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the remainder when $$12+34+56+89+90$$ is divided by $$10$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders"], "answer_analysis": ["Add ones digits, then divide by $$10$$: $$2+4+6+9+0=21$$;~$$21\\div 10=2\\text{R}1$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "693", "queId": "570e665b4c784481b3bd0cc061cdd7d2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Only one of the following four numbers is a perfect square. Which one is it? ", "answer_option_list": [[{"aoVal": "A", "content": "$$76186$$ "}], [{"aoVal": "B", "content": "$$750235$$ "}], [{"aoVal": "C", "content": "$$921438$$ "}], [{"aoVal": "D", "content": "$$2660161$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["$$\\text{A}$$: $$76186\\div2=28093$$. But $$28093$$ is not divisible by $$2$$. So, $$76186$$ is divisible by $$2$$ but not $$4$$, $$76186$$ is not a perfect square. $$\\text{B}$$: $$750235\\div5=150047$$. But $$150047$$ is not divisible by $$5$$. So, $$750235$$ is divisible by $$5$$ but not $$25$$, $$750235$$ is not a perfect square. $$\\text{C}$$: $$921438\\div2=460719$$. But $$460719$$ is not divisible by $$2$$. So, $$921438$$ is divisible by $$2$$ but not $$4$$, $$921438$$ is not a perfect square. Thus, answer must be $$\\text{D}$$. In fact, $$2660161=7^{2}\\times233^{2}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "695", "queId": "ccc29422593e4417a518581693ae5b1c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of the prime factors of $2010$? (2010 AMC 8 Problems, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$67$$ "}], [{"aoVal": "B", "content": "$$75$$ "}], [{"aoVal": "C", "content": "$$77$$ "}], [{"aoVal": "D", "content": "$$201$$ "}], [{"aoVal": "E", "content": "$$210$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["First, we must find the prime factorization of $2010.2010=2 \\cdot 3 \\cdot 5 \\cdot 67$. We add the factors up to get $(\\mathbf{C}) 77$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "697", "queId": "7213f4b7283848b9a9aada3ddac57686", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The whole numbers from $$1$$ to $$2016$$ inclusive are written on a blackboard. Moritz underlines all the multiples of two in red, all the multiples of three in blue and all the multiples of four in green. How many numbers does Moritz underline exactly twice? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1008$$ "}], [{"aoVal": "B", "content": "$$1004$$ "}], [{"aoVal": "C", "content": "$$504$$ "}], [{"aoVal": "D", "content": "$$336$$ "}], [{"aoVal": "E", "content": "$$168$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["There is no number that is both a multiple of three and a multiple of four without also being a multiple of two. Hence, the numbers underlined exactly twice are those that are a multiple of two and of three but not of four and those that are a multiple of two and four but not of three. The first set of numbers consists of the set of odd multiples of six. Since $$2016 \\div 6 = 336$$, there are $$336$$ multiples of $$6$$ in the list of numbers and hence $$336 \\div 2 = 168$$ odd multiples of six that would be underlined in red and blue but not green. The second set of numbers consists of two out of every three multiples of four and, since $$2016 \\div 4 = 504$$, there are $$3\\times 504 = 336 $$ numbers that would be underlined in red and green but not blue. Hence there are $$168+ 336 = 504$$ numbers that Moritz would underline exactly twice. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "699", "queId": "571af844dc1c490eb785699428b35c6c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is a prime number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$38$$ "}], [{"aoVal": "B", "content": "$$45$$ "}], [{"aoVal": "C", "content": "$$53$$ "}], [{"aoVal": "D", "content": "$$57$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["We note that the other options are not prime numbers because: $38 = 2 \\times 19$ $45 = 4 \\times 9$ $57 = 3 \\times 19$ Hence by the process of elimination, $53$ is a prime number. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "700", "queId": "6d8d8cf0a281433dbf23cfc2674320f2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A student wrote down a natural number. When she divided the number by $$9$$, the remainder was $$7$$. What is the~~remainder when twice that number is divided by $$9$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["The remainder of $$A$$ $$\\div9$$ is $$7$$, and $$2A=A+A$$. Therefore the remainder of $$2A\\div9$$ is $$7+7=14$$. $$14= 9+5$$, therefore the remainder is $$5$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "701", "queId": "f1b28656354347dd871ba79d11525dd9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "is a factor of $$100110011001$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$100110011001$$ is divisible by $$3$$, since the sum of its digits is $6$ which is divisible by $3$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "702", "queId": "571eafff8fb2450087a8eef4928cd018", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of any $$3$$-digit whole number and any $$2$$-digit whole number can contain at most how many digits? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["The largest product of a $$3$$-digit number and a $$2$$-digit number is $$999\\times99 = 98901$$. That product has $$5$$ digits. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "704", "queId": "648b4f56ce59455198880d8914b485c0", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "What is the greatest natural number $$n$$ such that $$n+27$$ and $$n-62$$ are squares of natural number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$598$$ "}], [{"aoVal": "B", "content": "$$1598$$ "}], [{"aoVal": "C", "content": "$$3998$$ "}], [{"aoVal": "D", "content": "$$1998$$ "}], [{"aoVal": "E", "content": "Such a number does not exist "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Questions involving Square Numbers"], "answer_analysis": ["Let $a^{2} = n+27$ and $b^{2} = n-62$. Taking the difference: $a^{2}-b^{2} = (a+b)(a-b) = n+27-(n-62) = 89$ Since $89$ is prime, that means $a+b=89$ and $a-b=1$, which means $a=45$ and $b=44$. That means $n=a^{2}-27 = 45^{2}-27 = 2025-27=1998$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "706", "queId": "ba5f15593e6f4c7aa8ce42e1f7dfcd04", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If I write all the whole numbers from $$1$$ to $$100$$ in words, how many times will I write the letter V? ", "answer_option_list": [[{"aoVal": "A", "content": "$$19$$ "}], [{"aoVal": "B", "content": "$$29$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$31$$ "}], [{"aoVal": "E", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["There are $$10$$ sevens in the unit digit, $$10$$ seventys, $$9$$ fives in the units (as fifteen is not fiveteen) plus eleven and twelve. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "708", "queId": "9a4528f59c2643a3936b64f8f8823092", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many multiples of $5$ are there from $1$ to $50$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$5$, $10$, $15$, $20$, $25$, $30$, $35$, $40$, $45$, $50$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "715", "queId": "69259a06ea8b4ca0a5a83423ffef5774", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following prime factorizations below is correct? ", "answer_option_list": [[{"aoVal": "A", "content": "$$97=1\\times97$$ "}], [{"aoVal": "B", "content": "$$85=5\\times 17$$ "}], [{"aoVal": "C", "content": "$$64=8\\times 8$$ "}], [{"aoVal": "D", "content": "$$52=1\\times 2\\times 2\\times 13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["①A prime number is a natural number greater than $$1$$ that has no other factors than $$1$$ and itself. ②Decomposing a composite number into the product of several prime factors is called decomposing prime factors. ③$$1$$ is neither a prime number nor a composite number. So $$\\text{D}$$ is not correct. The $$\\text{A}$$ option is also incorrect. $$8$$ is not a prime number, so $$\\text{C}$$ is incorrect. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "716", "queId": "5bae882a875b414ba8614df071ff4265", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the followings is the least common multiple for $$25$$ and $$125$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$125$$ "}], [{"aoVal": "C", "content": "$$130$$ "}], [{"aoVal": "D", "content": "$$600$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["We do prime factorization for $$25$$ and $$125$$ first. $$25={{5}^{2}}$$ and $$125={{5}^{3}}$$. We have three $$5$$'s, thus the least common multiple for $$25$$ and $$125$$ is $$125$$. We choose $$\\text{B}$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "717", "queId": "7233ba7cbb984793931332c2552a76a2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Of the multiples of $$7$$ that exceed $$7$$, how many are factors of $$700$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$99$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Theorem of the Number of Factors of a Number"], "answer_analysis": ["Multiply $$7$$ by any of these: $$2$$, $$2^{2}$$, $$5$$, $$5^{2}$$, $$2\\times 5$$, $$2^{2}\\times 5$$, $$2\\times 5^{2}$$, or $$2^{2}\\times 5^{2}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "723", "queId": "9a54586b8cc94a149968bab4a6f05882", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following has an odd number of whole-number factors? ", "answer_option_list": [[{"aoVal": "A", "content": "$$47$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$49$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers"], "answer_analysis": ["The whole-number factors of $$49$$ are $$1$$, $$7$$, and $$49$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "724", "queId": "e3dd6c2c4dea425d9a49122060ae6763", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole numbers $A$, $B$ and $C$. $A\\times B=55$, $B\\times C=100$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$34$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$55=5\\times 11$ $100=2\\times 2\\times 5\\times 5$ Because $B$ is the factor both number contains, $B=5$ Thus, $A=11$, $C=20$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "730", "queId": "575386fd7f704fc48406725e383dbab6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the difference between the largest single-digit prime number and the smallest three-digit prime number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$94$$ "}], [{"aoVal": "B", "content": "$$95$$ "}], [{"aoVal": "C", "content": "$$96$$ "}], [{"aoVal": "D", "content": "$$97$$ "}], [{"aoVal": "E", "content": "$$98$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Prime Factorization (Equations)"], "answer_analysis": ["The largest single-digit prime number is $$7$$ and the smallest three-digit prime number is $$101$$; their difference is $$101 -7=94$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "731", "queId": "64b7fd55ae7b4d23bca28562e1c24a98", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of \\emph{all} the prime numbers less than $$10$$ is divisible by ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$70$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["The primes less than $$10$$ are $$2$$, $$3$$, $$5$$, and $$7$$. Their product is $$210$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "736", "queId": "9a5e994657ea49db8570629c4e7df31c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The square root of $$49$$ is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["The square root of $$49$$ is $$7$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "738", "queId": "a38e18aa86c9410da4b0f71cd07d74ab", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Danni wants to use the numbers $1$, $3$, $7$, and $9$ to make prime numbers less than $100$. How many different prime numbers can she make? (She can use the same number more than once.) $$\\textasciitilde$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["Using these $4$ numbers, we can make $20$ different numbers which are less than $100$. However, only these $12$ numbers are prime numbers. $3; 7; 11; 13; 17; 19; 31; 37; 71; 73; 79; 97$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "741", "queId": "72544468182740249441b487e08a1120", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The numberis divisible by $$3\\times3$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$663$$ "}], [{"aoVal": "B", "content": "$$603$$ "}], [{"aoVal": "C", "content": "$$336$$ "}], [{"aoVal": "D", "content": "$$303$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["Add the digits to test: for $$603$$, $$6+0+3 =9$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "746", "queId": "ccdf978bf5bd4b4abc75beb07644ef7e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Ivan is puting 13 cakes into box A, box B and box C. It is known that there are odd number of cakes in both box A and box B. Could you tell whether the number of cakes in box C is even or odd number? ", "answer_option_list": [[{"aoVal": "A", "content": "Odd "}], [{"aoVal": "B", "content": "Even "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["Number of cakes in box C: 13 (odd number) - odd - odd Number of odd character = 3 Therefore, the number of cakes in box C is odd. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "747", "queId": "dab0206dc920475bbed11b2c9c869187", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The ones digit of $$9\\times 8\\times 7\\times 6\\times 5\\times 4\\times 3\\times 3\\times 4\\times 5\\times 6\\times 7\\times 8\\times 9$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["Since $$5\\times 4 = 20$$, the ones digit of the given product must be $$0$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "748", "queId": "695405d5736e4f419e7a5b933f9ff96b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The largest whole-number multiple of $$7$$ less than $$200$$ is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$187$$ "}], [{"aoVal": "B", "content": "$$189$$ "}], [{"aoVal": "C", "content": "$$196$$ "}], [{"aoVal": "D", "content": "$$197$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$200\\div7\\textgreater28$$, so the largest such multiple is $$28\\times7 =196$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "749", "queId": "4a4eb9d18d2d43f38d028d5417f88304", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The smallest number greater than $2$ that leaves a remainder of $2$ when divided by $3,4,5$, or $6$ lies between what numbers? (2012 AMC 8 Problem, Question \\# 15) ", "answer_option_list": [[{"aoVal": "A", "content": "$40$ and $50$ "}], [{"aoVal": "B", "content": "$51$ and $55$ "}], [{"aoVal": "C", "content": "$56$ and $60$ "}], [{"aoVal": "D", "content": "$61$ and $65$ "}], [{"aoVal": "E", "content": "$66$ and $99$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["To find the answer to this problem, we need to find the least common multiple of $3,4,5,6$ and add $2$ to the result. The least common multiple of the four numbers is $60$ , and by adding $2$ , we find that that such number is $62$ . Now we need to find the only given range that contains $62$ . The only such range is answer (D), and so our final answer is $(\\text{D}) 61$ and $65$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "753", "queId": "76e2528658994742bf63f02fc66e6c96", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of all factors of $$24$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$52$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$84$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Theorem of the Number of Factors of a Number"], "answer_analysis": ["The sum of the factors is $$(3^{0}+3^{1})$$$$\\times (2^{0}+2^{1}+2^{2}+2^{3})=60$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "755", "queId": "60671c37eb4149de9d4690e0daf2a887", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the greatest number of consecutive integers such that the sum of the digits of none of them is divisible by $$5$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["Five consecutive numbers can be: $$12$$, $$13$$, $$14$$, $$15$$, and $$16$$ (without carrying) or $$17$$, $$18$$, $$19$$, $$20$$, $$21$$ (with carrying in the tens place). Without carrying, among each of the $$5$$ consecutive integers, we can find one whose sum of digits is a multiple of $$5$$. So we need to carry. To make the number of integers the greatest, we can start from a number whose remainder is $$1$$ when divided by five. And the most important thing is, after we write the fourth number, the carry appears. For example: $$56$$, $$57$$, $$58$$, $$59$$, $$60$$, $$61$$, $$62$$, $$63$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "758", "queId": "578c303085a945e29296c5c87d9ce108", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The number $$1$$ million is less than the number． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ thousand "}], [{"aoVal": "B", "content": "$$10$$ thousand "}], [{"aoVal": "C", "content": "$$100$$ thousand "}], [{"aoVal": "D", "content": "$$1$$ billion "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["The number $$1$$ billion is $$1$$ thousand times $$1$$ million. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "762", "queId": "d1846153d2f5412681d6acaa03506ea2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "$\\overline{392AB}$ is a multiple of $45$, and $\\overline{B34}$ is a three-digit even number. What is the sum of $A$ and $B$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$4$ or $13$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["$45=5\\times9$ $\\overline{392AB}$ should be ended with $0$ or $5.$ But $0$ cannot be the first digit. Thus, $B$ can only be $5$ and $A$ should be $8.$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "764", "queId": "579e41f44450470e8097b3ac0393be82", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole number $A$, $B$, $C$. $A\\times B=21$, $B\\times C=60$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$33$$ "}], [{"aoVal": "C", "content": "$$35$$ "}], [{"aoVal": "D", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$21=3\\times 7$ $60=2\\times 2\\times 3\\times 5$ Because $B$ is the factor both number contains, $B=3$ Thus, $A=7$, $C=20$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "767", "queId": "df58d69ab0c44a62a02667ad08fd6b28", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Two whole numbers have a least common multiple of $60$. -Each number is less than or equal to $12$. -The greatest common factor of the two number is $2$. What are the two numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$6$ and $10$ "}], [{"aoVal": "B", "content": "$5$ and $12$ "}], [{"aoVal": "C", "content": "$10$ and $12$ "}], [{"aoVal": "D", "content": "$12$ and $16$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["A: The least common multiple of $6$ and $10$ is $30$. B: Two numbers are relatively prime. C: The least common multiple is $60$, and the greatest common factor is $2$. D: The least common multiple is $48$, and the greatest common factor is $4$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "768", "queId": "7704a5540a5f46cfbf5c8cc053168414", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There are some books in the central library. If Adam divides the number of the books in the library by $32$, there will be $30$ books remained; if he divides the number of books in the library by $9$, there will be $7$ books remained; if he divides the number of books in the library by $7$, there will be $5$ books remained. How many books, at least, are there in the central library? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2014$$ "}], [{"aoVal": "B", "content": "$$2015$$ "}], [{"aoVal": "C", "content": "$$2016$$ "}], [{"aoVal": "D", "content": "$$2017$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["The total number of books when divided by $$32$$, $$9$$, and $$7$$ leaves remainders of $$30$$, $$7$$, and $$5$$, respectively. In other words, the number when added by $$2$$ is divisible by $$32$$, $$9$$, and $$7$$. Hence, the smallest such number is $$32\\times9\\times7-2=2014$$. The answer is $$\\rm A$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "769", "queId": "a847c9d85e8a4ea6a1ebc1f18ed91132", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Order all prime numbers from least to greatest. What is the sum of the next two prime numbers after $43$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$89$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$101$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["$47+53=100$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "774", "queId": "535de29b137046e9bc37f0b2839d2e92", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Pip swam $$3$$ back and forth in the lane for a total of $$156$$ meters, how long is the lane in this pool? ", "answer_option_list": [[{"aoVal": "A", "content": "$$52$$ "}], [{"aoVal": "B", "content": "$$104$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$234$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Short Division"], "answer_analysis": ["one back and forth $$156\\div3=52$$meters length of the lane$$52\\div2=26$$meters "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "778", "queId": "4f03ac1b7d1748ca8da7a5e554b41a0e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many positive factors of $$360$$ are also multiples of $$12$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$360={{2}^{3}}\\times {{3}^{2}}\\times5$$, so the number of its factors would be $$\\left( 3+1 \\right)\\times \\left( 2+1 \\right)\\times\\left( 1+1 \\right)=24$$. Among them, there are $$2\\times 2\\times(1+1)=8$$ factors which have $${{2}^{2}}\\times 3$$ as its factors. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "779", "queId": "9f2610eaa8724a11829aa42867ef16eb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the ones digit of the product $$80\\times 70\\times 60\\times 50\\times 40\\times 30\\times 20\\times 10\\times 5\\times 2$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders "], "answer_analysis": ["Since $$10$$ is a factor of this product, the ones digit is $$0$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "780", "queId": "9175f417f4224b92bb003378af2aaf00", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A recurring decimal can also be written by putting a bar over the digits that repeat. Thus, $$0.\\overline {123}$$ means $$0.123123\\cdots $$. The sum of $$0.\\overline {234}$$, $$0.\\overline {342}$$, and $$0.\\overline {432}$$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$1.01$$ "}], [{"aoVal": "C", "content": "$$1\\frac1{111}$$ "}], [{"aoVal": "D", "content": "$$1.009$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["$$0.\\overline{234} +0.\\overline{342} +0.\\overline{432} =1.\\overline{009} $$$$=1\\frac 1{111}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "781", "queId": "fb2116a38e1d43b4b0d4112385fbfc78", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Fill in the blank:~\\uline{~~~~~~~~~~}~is $$4$$ tens $$5$$ ones greater than $$2$$ tens $$7$$ ones. ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$28$$ "}], [{"aoVal": "C", "content": "$$62$$ "}], [{"aoVal": "D", "content": "$$72$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["$$4$$ tens $$5$$ ones: $$45$$ $$2$$ tens $$7$$ ones: $$27$$ Greater than: $$45 + 27 = 72$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "784", "queId": "77209fce5dac46e29d009df02b6ac8e0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the prime factors of $$231$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$152$$ "}], [{"aoVal": "D", "content": "$$383$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Prime Factorization (Equations)"], "answer_analysis": ["Since $$231=3\\times7\\times11$$, the sum of its prime factors is $$3 +7+11=21$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "786", "queId": "84b4fc8e42aa4cd490ec23815bd2d386", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If I multiply three different prime numbers, the product must have positive divisors. ", "answer_option_list": [[{"aoVal": "A", "content": "$$ 3 $$ "}], [{"aoVal": "B", "content": "$$5 $$ "}], [{"aoVal": "C", "content": "$$6 $$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["Multiply the three smallest primes: $$2\\times3 \\times5=30$$, whose $$8$$ divisors are $$1$$, $$2$$, $$3$$, $$5$$, $$6$$, $$10$$, $$15$$, and $$30$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "788", "queId": "917c6b7949e0422fbc698e835b14241f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Students\\textquotesingle~seat numbers are from $$1$$ to $$35$$. How many times does digit $$3$$ appear? (adapted from $$2002$$ Math Kangaroo Problem, Level $$3$$ - $4$, Question \\#$9$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$16$$ "}], [{"aoVal": "E", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Questions Involving Applying Place Value Principle"], "answer_analysis": ["The digit $3$ appears in the ones place: $3$, $13$, $23$, The digit $3$ appears in the tens place: $30, 31, 32, 33, 34, 35$ In total, $3 + 6 = 9$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "794", "queId": "df66dcdbd6844e80a21f4187f7967a1c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $$2-$$digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the units digit of the number? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["We can think of the number as $$10a+b$$, where $$a$$ and $$b$$ are digits. Since the number is equal to the product of the digits $$(a\\cdot b)$$ plus the sum of the digits $$(a+b)$$, we can say that $$10a+b=a\\cdot b+a+b$$. We can simplify this to $$10a=a\\cdot b+a$$, and factor to $$(10)a=(b+1)a$$. Dividing by $$a$$, we have that $$b+1=10$$. Therefore, the units digit, $$b$$, is $$9$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "798", "queId": "57ef80c87c11442c8e95d5e2e44b702b", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "An unknown number is an odd number greater than $$50$$ but less than $$100$$. The number is a multiple of $$3$$ and $$7$$. What is the value of the unknown number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$63$$ "}], [{"aoVal": "B", "content": "$$77$$ "}], [{"aoVal": "C", "content": "$$84$$ "}], [{"aoVal": "D", "content": "$$91$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["A multiple of $$3$$ and $$7$$ also a multiple of $$21$$ $$21\\times3=63$$ $$21\\times4=even$$ $$21\\times5=105$$, exceed Thus, only $$63$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "802", "queId": "804114fdb50e4afdbc7c04c2f6e29a5e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Among the numbers below, how many numbers can be divisible by $4$? $234$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $789$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $7756$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $8865$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $3728$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $8064$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["$7756, 3728,$ and $8064$ can be divisible by $4$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "804", "queId": "b619ada29a3b4021bb3adc39a940cdf9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Della has a box of ping-pong balls. No matter she counts the balls $8$ by $8$, $10$ by $10$, or $12$ by $12$, there are always $3$ balls left. How many ping-pong balls are there in the box at least? ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$120$$ "}], [{"aoVal": "C", "content": "$$123$$ "}], [{"aoVal": "D", "content": "$$240$$ "}], [{"aoVal": "E", "content": "$$243$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["If the ping pong balls in the box are reduced by $3$, then there will be no extra balls when you count them $8$ by $8$, $10$ by $10$, or $12$ by $12$. It means that the number of the ping pong balls is a common multiple of $8$, $10$, and $12$ after being reduced by $3$. If you want to know how many ping pong balls there are at least, you can first find the least common multiple of $8$, $10$ and $12$, and then add $3$ to get the answer. $$\\begin{array}{l} {2\\left\\textbar{} \\underline{\\textasciitilde8\\textasciitilde\\textasciitilde10\\textasciitilde\\textasciitilde12}\\right. }\\textbackslash\\textbackslash{\\textasciitilde2\\left\\textbar{} \\underline{4\\textasciitilde\\textasciitilde\\textasciitilde5\\textasciitilde\\textasciitilde\\textasciitilde6}\\right. }\\textbackslash\\textbackslash{\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde2\\textasciitilde\\textasciitilde\\textasciitilde5\\textasciitilde\\textasciitilde\\textasciitilde3} \\end{array}$$ $2\\times2\\times2\\times5\\times3=120$ $120+3=123$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "806", "queId": "60d6565b220247a49fa360fdf5a5658e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$1^{st}$$ November $$2016$$ is a Tuesday, what day will it be $$30^{th}$$ November of the same year? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Saturday "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["$$30-1+1=30$$ $$30\\div7=4R2$$ Tuesday -\\/-\\textgreater~Wednesday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "810", "queId": "60ea335438a3498eb8941b1fe4e698c1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "is a factor of $$123123123$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$123123123$$ is divisible by $$3$$, since the sum of its digits is $18$ which is divisible by $3$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "811", "queId": "7bd018e26ccf46588e6d5997034afe66", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many different prime numbers, when multiplied by $$11$$, have an even number as their product? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Applying Special Prime Numbers"], "answer_analysis": ["The product of two odd numbers is odd, so there is only one even product, $$2\\times 11$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "824", "queId": "611fb49ea51546a99aaf47663662c311", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following statement is correct? ", "answer_option_list": [[{"aoVal": "A", "content": "All prime numbers are odd numbers. "}], [{"aoVal": "B", "content": "In every $3$ consecutive numbers, there must be a composite number. "}], [{"aoVal": "C", "content": "All even numbers are composite numbers. "}], [{"aoVal": "D", "content": "The sum of two different odd number must be a composite number. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["A: Any non-$3$ multiple of 3 are composite B: $1$, $2$, $3$ does not have composite number C: $2$ is prime number D: $1+$any odd number is multiple of $2$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "826", "queId": "777a3955cafd485290ca26d96eabd615", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Let $a$ and $b$ be positive integers such that $a+a b=1443$ and $a b+b=1444$. Find $10 a+b$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$407$$ "}], [{"aoVal": "B", "content": "$$408$$ "}], [{"aoVal": "C", "content": "$$418$$ "}], [{"aoVal": "D", "content": "$$419$$ "}], [{"aoVal": "E", "content": "$$428$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["$$ \\left\\textbackslash{\\begin{array}{l} a(b+1)=1443=3 \\times 13 \\times 37=37 \\times 39 \\textbackslash\\textbackslash{} b(a+1)=1444=38^{2} \\end{array}\\right. $$ Compare and $a=37, b=38 .$ So $10 a+b=370+38=408$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "827", "queId": "c3fca1f8410e459480fe60103c2007ae", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "When Ringo places his marbles into bags with $6$ marbles per bag, he has $4$ marbles left over. When Paul does the same with his marbles, he has $3$ marbles left over. Ringo and Paul pool their marbles and place them into as many bags as possible, with $6$ marbles per bag. How many marbles will be leftover? (2012 AMC 10B Problems, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["In total, there were $3+4=7$ marbles left from both Ringo and Paul.We know that $7 \\equiv 1(\\bmod 6)$. This means that there would be $1$ marble leftover. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "829", "queId": "b643890b9fb24f7b999bc43ce215d9a4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is divisible by all of the integers from $$1$$ to $$10$$ inclusive? ", "answer_option_list": [[{"aoVal": "A", "content": "$$23\\times34$$ "}], [{"aoVal": "B", "content": "$$34\\times45$$ "}], [{"aoVal": "C", "content": "$$45\\times56$$ "}], [{"aoVal": "D", "content": "$$56\\times67$$ "}], [{"aoVal": "E", "content": "$$67\\times78$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"], "answer_analysis": ["Of the options given, $$23\\times 34$$, $$56\\times 67$$ and $$67\\times 78$$ are all not divisible by $$5$$, so may be discounted. Also $$34$$ is not divisible by $$4$$ and $$45$$ is odd, so $$34\\times 45$$ may also be discounted as it is not divisible by $$4$$. The only other option is $$45\\times 56$$. As a product of prime factors, $$45\\times 56=2^{3}\\times3^{2}\\times5\\times7$$, so it is clear that it is divisible by all of the integers from $$1$$ to $$10$$ inclusive. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "830", "queId": "8996e233fb5942d48706727c04ee40c1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When two numbers are divided and the quotient is $$11$$ and remainder is $$5$$, the smallest value of the dividend is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$55$$ "}], [{"aoVal": "B", "content": "$$71$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$66$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["$$6\\times 11+5=71$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "832", "queId": "f200cf48a6b5450ba3ca1d7d72dea22a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Leo prepares more than $400$ cupcakes for a party. Now he can divided all of them equally into $5$ piles. After his pet cat eats one of the cupcakes, he finds that now he can divide the remaining cupcakes equally into $6$ piles. Then, the naughty pet cat eat another one, and Leo divides the remaining cupcakes into $7$ piles. How many cupcakes did Leo make at least at the beginning? Find the sum of the three digits. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["The number is a multiple of $5$. When it is divided by $6$, it will have a remainder of $1$; when it is divided by $7$, it will have a remainder of $2$. Thus, if we add another $5$ to the number, it can be multiple of all the three numbers, which is $5\\times6\\times7=210$ at least. But the number is more than $400$, so we can get $210\\times2-5=415.$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "837", "queId": "809e1cc67bb64b639545f37231bad586", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are exactly $$3$$ prime numbers between． ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ and $$20 $$ "}], [{"aoVal": "B", "content": "$$20$$ and $$30$$ "}], [{"aoVal": "C", "content": "$$30$$ and $$40$$ "}], [{"aoVal": "D", "content": "$$40$$ and $$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["The $$3$$ prime numbers between $$40$$ and $$50$$ are $$41$$, $$43$$, and $$47$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "848", "queId": "6a43c7e6014342bf9d4a3aedb53c8a12", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The $4$-digit number $32B9$ is divisble by $3$. If $B$ is even, find the digit $B$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["$$3+2+B+9$$ = 14+B is divisble by 3. Max single digit possible is 9. Then 14+9 = 23. Range is between 15 to 23. Multiple of 3 - 3 x 7=21, 3 x 6 =18, 3 x 5 = 15. Since, it should be even number, 18-14=4. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "849", "queId": "65d6d5197cf94ad6b8a05f3f001ac799", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The hundreds digit of a three-digit number is $2$ more than the units digit. The digits of the three-digit number are reversed, and the result is subtracted from the original three-digit number. What is the units digit of the result? (2010 AMC 8 Problem, Question \\#22) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["The result must hold for any three-digit number with hundreds digit being 2 more than the units digit. $301$ is such a number. Evaluating, we get $301-103=198$. Thus, the units digit in the final result is $(\\mathbf{E}) 8$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "850", "queId": "65d98809332c4aec8056d40cdc5c7f30", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following is a factor of $30$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["$30=5 \\times 6$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "853", "queId": "89bae662b4cc4fbeb7ba33cfb2bf83fd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $$2-$$digit number is such that the product of the digits adding the sum of the digits is equal to the number itself. What is the ones digit of the number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["We can think of the number as $$10a+b$$, where $$a$$ and $$b$$ are digits. Since the number is equal to the product of the digits $$(a\\cdot b)$$ plus the sum of the digits $$(a+b)$$, we can say that $$10a+b=a\\cdot b+a+b$$. We can simplify this to $$10a=a\\cdot b+a$$, and factor to $$(10)a=(b+1)a$$. Dividing by $$a$$, we have that $$b+1=10$$. Therefore, the units digit, $$b$$, is $$9$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "855", "queId": "89c2c252365e488f80be9eda8bf0b9f2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Of the first $$100$$ whole numbers,~\\uline{~~~~~~~~~~}~use the digit $$2$$ at least once. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$19$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["$$2$$, $$12$$, $$20-29$$, $$32$$, $$42$$, $$52$$, $$62$$, $$72$$, $$82$$, and $$92$$ use a $$2$$; that\\textquotesingle s $$19$$ numbers. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "859", "queId": "df9ffd2021c3494dbc61b14e9c0e2520", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many positive factors of $$36$$ are also multiples of $$4$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$36={{2}^{2}}\\times {{3}^{2}}$$, so the number of its factors would be $$\\left( 2+1 \\right)\\times \\left( 2+1 \\right)=9$$. Among them, there are $$\\left( 2+1 \\right)\\times 1=3$$ factors which have $${{2}^{2}}$$ as its factors. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "862", "queId": "b1d7e3af7b37428d8308b91d86d0b4ff", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "What are the last three digits of the answer to the calculation below? $$123\\times 124\\times 125\\times 126\\times 127$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$000$$ "}], [{"aoVal": "B", "content": "$$222$$ "}], [{"aoVal": "C", "content": "$$444$$ "}], [{"aoVal": "D", "content": "$$666$$ "}], [{"aoVal": "E", "content": "$$888$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders "], "answer_analysis": ["The product $$123 \\times124\\times125\\times126 \\times127$$ is a multiple of $$125$$; moreover, it also has a factor of $$2$$ three times, from $$124\\left( 2\\times 2\\times 31 \\right)$$ and from $$126\\left( =2\\times 63 \\right)$$. Therefore it is a multiple of $$125 \\times2\\times2\\times2= 1000$$, and so it must end in $$000$$. Alternatively, working from the options, it is easily seen that the product is a certainly an even multiple of $$5$$-so its unit digit is $$0$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "867", "queId": "7362928c7e7a4d16af38b42359ceeed8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$1\\times2\\times3\\times4\\times5\\times6\\times7\\times8\\times$$$$9\\times10\\times11\\times12\\times13\\times$$$$14\\times15 = 1307 674 368000$$, how many times does the digit \"$$0$$\" appear in the product $$10\\times20\\times30\\times40\\times50\\times60\\times$$$$70\\times80\\times90\\times100\\times110\\times120\\times130\\times140\\times150$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"], "answer_analysis": ["If $$1\\times2\\times3\\times4\\times5\\times6\\times7\\times$$$$8\\times9\\times10\\times11\\times12\\times13\\times14\\times15 = $$$$1307 674 368000$$, and we multiply each of these $$15$$ numbers by $$10$$, the new product will have an additional $$15$$ zeroes, and $$15+4=19$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "871", "queId": "8d860c8460e6457aa6db190227299a66", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Malcolm wants to visit Isabella after school today and he knows the street where she lives but does not know her house number. She tells him,~\"My house number has two digits, and all of the following four statements about it are true.\" $(1)$ It is a prime number. $(2)$ It is less than $40$. $(3)$ One of its digits is $3$. $(4)$ Another digit is an even number. This information allows Malcolm to determine Isabella\\textquotesingle s house number. What is the house number? (adapted from 2017 AMC 8 problem, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$43$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$32$$ "}], [{"aoVal": "E", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["According to information $(3)$ and $(4)$, we know $3$ must be in the ones place and the digit in the tens place is an even number. Thus, it should be one of the numbers from $23$, $43$, $63$ and $83$. According to information $(1)$, it can be $23$, $43$, and $83$. According to information $(2)$, it can only be $23$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "876", "queId": "89ef2ef50f8845d6b936d533267da78b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Malcolm wants to visit Isabella after school today and he knows the street where she lives but doesn't know her house number. She tells him, ``My house number has two digits, and all of the following four statements about it are true.'' $(1)$ It is a prime number. $(2)$ It is less than $40$. $(3)$ One of its digits is $3$. $(4)$ Another digit is an even number. This information allows Malcolm to determine Isabella's house number. What is the house number? (adapted from 2017 AMC 8 problem, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$43$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$32$$ "}], [{"aoVal": "E", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["According to information $(3)$ and $(4)$, we know $3$ must be in the ones place and the digit on the tens place is an even number. Thus, it should be one of the numbers from $23$, $43$, $63$ and $83$. According to information $(1)$, it can be $23$, $43$, and $83$. According to information $(2)$, it can only be $23$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "877", "queId": "8d9117c72edd4a2fa3836f62da41132e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Without calculating, can you quickly choose the correct answer? $$1236 + 3217$$ = ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4451$$ "}], [{"aoVal": "B", "content": "$$4453$$ "}], [{"aoVal": "C", "content": "$$4450$$ "}], [{"aoVal": "D", "content": "$$4452$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["Odd + Even = Odd~~ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "878", "queId": "737ec7160efe4ce18bd971b192c11869", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "There is a book with 650 pages. Henry tears 31 paper from the book, each paper contains two pages. Is it possible that the sum of their page number equals to 953? ", "answer_option_list": [[{"aoVal": "A", "content": "$$Yes.$$ "}], [{"aoVal": "B", "content": "$$No.$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["If there are odd number of odd page number, the sum of page numbers is odd. Therefore, it could be 953. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "881", "queId": "921df28cfec946fa8cbeb34da2321f99", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many of the whole numbers less than $$100$$ are $$10$$ greater than an odd whole number?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$46$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$91$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers"], "answer_analysis": ["Add $$10$$ to $$1$$, $$3$$, $$5$$, $$7$$, $$\\cdots $$, $$87$$, and $$89$$. None of these sums is more than $$99$$. There are $$45$$ such sums. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "883", "queId": "80f9dd753d7846f9b5125b4e7300a315", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the smallest prime number greater than $$59$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$69$$ "}], [{"aoVal": "B", "content": "$$67$$ "}], [{"aoVal": "C", "content": "$$63$$ "}], [{"aoVal": "D", "content": "$$61$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["omitted "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "885", "queId": "6f172e9c552e4422989bea555ada33b1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the thousands\\textquotesingle{} digit and the tens\\textquotesingle{} digit of $$12345$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["The thousands\\textquotesingle{} digit is $$2$$ and the tens\\textquotesingle{} digit is $$4$$. The sum is $$6$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "889", "queId": "81055565a5a74834a45961f3d8674a6d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of the digits in the number one million? ", "answer_option_list": [[{"aoVal": "A", "content": "　one "}], [{"aoVal": "B", "content": "one hundred "}], [{"aoVal": "C", "content": "one thousand "}], [{"aoVal": "D", "content": "one million "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["One million $$= 1000000$$. Adding, $$1+0+0+0+0+0+0 = 1$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "894", "queId": "ed9074e33862488e959c979fb4c6b077", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Vivian bakes a cuboid cake with a dimension of $6\\times8\\times10$ and cuts it into many small cubical cakes with a dimension of $2\\times2\\times2$. She wants to equally divide the cake without remainder among $x$ people so that each person can get at least one small cake. How many possible values of $x$ are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$16$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["$6\\times8\\times10 \\div(2\\times2\\times2)=60.$ $60=2^{2}\\times3\\times5$, which means it has $3\\times2\\times2=12$ factors. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "898", "queId": "73a8c6679d4f4f98bcd827450fc24180", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Four numbers are chosen from the set $3$, $6$, $12$, $27$, $48$ so that the product is a perfect square. What is the number that was not chosen? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers"], "answer_analysis": ["Obsever that $3\\times27=9^{2}$ and $12\\times27=24^{2}$ are both squares. Hence, their product is also a perfect square and the fifth number must be $6$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "901", "queId": "6acabdbfd81a4029b170fab8b32e9495", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following statements in incorrect? ", "answer_option_list": [[{"aoVal": "A", "content": "$$108$$ is a multiple of $$3$$ and $$9$$ "}], [{"aoVal": "B", "content": "$$100$$ is a multiple of $$10$$, but it is not a multiple of $$5$$ "}], [{"aoVal": "C", "content": "$$164$$ is a multiple of $$4$$ "}], [{"aoVal": "D", "content": "$$132$$ is a multiple of $$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["$$\\rm A$$: $$1+0+8=9$$, it is a multiple of $$3$$ and $$9$$; $$\\rm B$$: $$100$$ ends with $$0$$, thus it is a multiple of $$10$$ and $$5$$; $$\\rm C$$: $$164$$ ends with $$64$$, and $$64$$ is a multiple of $$4$$, thus $$164$$ is also a multiple of $$4$$; $$\\rm D$$: $$132$$ is a multiple of $$2$$ and $$3$$, thus it is a multiple of $$6$$. So we choose $$\\rm B$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "904", "queId": "7ca0596ede77481e96f70b517b23b6f3", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The positive integers from $$1$$ to $$150$$ inclusive are placed in a $$10$$ by $$15$$ grid so that each cell contains exactly one integer. Then the multiples of $$3$$ are given a red mark, the multiples of $$5$$ are given a blue mark, and the multiples of $$7$$ are given a green mark. How many cells have more than $$1$$ mark? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$19$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["As $$3$$ and $$5$$ are coprime, the squares that have more than one mark are multiples of both $$3$$ and $$5$$, $$\\left( {} \\right.$$multiples of $$15$$$$\\left. {} \\right)$$; or multiples of both $$3$$ and $$7$$, $$\\left( {} \\right.$$multiples of $$21$$$$\\left. {} \\right)$$; or multiples of $$5$$ and $$7$$, $$\\left( {} \\right.$$multiples of $$35$$$$\\left. {} \\right)$$; or multiples of $$3$$, $$5$$ and $$7$$, $$\\left( {} \\right.$$multiples of $$105$$$$\\left. {} \\right)$$. However, the latter will be included in all of the first three categories. Between $$1$$ and $$150$$ inclusive, there are ten multiples of $$15$$, seven multiples of $$21$$ and four multiples of $$35$$, making a total of $$21$$ multiples. However, there is one multiple of $$3$$, $$5$$ and $$7$$ between $$1$$ and $$150$$, namely $$105$$. So $$105$$ has been counted three times in those $$21$$ multiples, but corresponds to exactly one marked square. Therefore the total number of marked squares is $$21−2=19$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "905", "queId": "fb75ab0629ba455997f75256a024eb5e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Is $$12722385$$ divisible by $$13$$? ", "answer_option_list": [[{"aoVal": "A", "content": "Yes "}], [{"aoVal": "B", "content": "No "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders"], "answer_analysis": ["$$722-12-385=325$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "906", "queId": "e463ed0c1bc14b49b57c70370df208ef", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$123+234+345$$ divided by $$4$$ has a remainder of~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["The sum of each numbers remainder can be divided by $$4$$ to get $$2$$: $$123\\div 4$$ R $$3$$；$$234\\div 4$$ R $$2$$；$$345\\div 4$$ R $$1$$; Therefore, $$\\left( 3+2+1 \\right)\\div 4$$ R $$2$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "908", "queId": "73c4f13be4bd49d6af57502c380237be", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When Clara totaled her scores, she inadvertently reversed the units digit and the tens digit of a two-digit score. By which of the following might her incorrect sum have differed from the correct one? ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$46$$ "}], [{"aoVal": "C", "content": "$$47$$ "}], [{"aoVal": "D", "content": "$$48$$ "}], [{"aoVal": "E", "content": "$$49$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["Let the two digits be $$a$$ and $$b$$. The correct score was $$10a+b$$. Clara misinterpreted it as $$10b+a$$. The difference between the two is $$\\left\\textbar{} 9a-9b\\right\\textbar$$ which factors into $$\\left\\textbar{} 9(a-b)\\right\\textbar$$. Therefore, since the difference is a multiple of $$9$$, the only answer choice that is a multiple of $$9$$ is $$45$$ . ( $$2013$$ AMC $$8$$ Problem, Question \\#$$13$$) "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "909", "queId": "c8ea9db5908541a993bc430ca8907de4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following prime factorization below is correct? ", "answer_option_list": [[{"aoVal": "A", "content": "$$97=1\\times97$$ "}], [{"aoVal": "B", "content": "$$85=5\\times 17$$ "}], [{"aoVal": "C", "content": "$$64=8\\times 8$$ "}], [{"aoVal": "D", "content": "$$52=1\\times 2\\times 2\\times 13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["①A prime number is a natural number greater than $$1$$ that has no other factors than $$1$$ and itself. ②Decomposing a composite number into the product of several prime factors is called decomposing prime factors. ③$$1$$ is neither a prime number nor a composite number. So $$\\text{D}$$ is not correct. The $$\\text{A}$$ option is also incorrect. $$8$$ is not a prime number, so $$\\text{C}$$ is incorrect. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "910", "queId": "fb7b150d058d43aa8442d7e56a679ac7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A whole number divisible by $$6$$ and by $$14$$ need \\emph{not} be divisible by． ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders"], "answer_analysis": ["As an example, $$42$$ is divisible by $$6$$ and by $$14$$ but not by $$12$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "911", "queId": "78423e8326dc418fb2ee109c167605a9", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Allen has some apples, and the number of apples is more than $2200$ but less than $2300$. If he distributes them among $12$ children evenly, there will be $11$ apples left. If he distributes them among $13$ children evenly, there will be $7$ apples left.~ If he distributes them among $14$ children evenly, there will be $3$ apples left. Which is the correct range of the number of pens? ", "answer_option_list": [[{"aoVal": "A", "content": "$2530\\sim2540$ "}], [{"aoVal": "B", "content": "$2540\\sim2550$ "}], [{"aoVal": "C", "content": "$2550\\sim2560$ "}], [{"aoVal": "D", "content": "$2570\\sim2590$ "}], [{"aoVal": "E", "content": "$2580\\sim2600$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["If he distributes them among $12$ children evenly, there will be $11+12\\times4=59$ apples left. If he distributes them among $13$ children evenly, there will be $7+13\\times4=59$ apples left.~ If he distributes them among $14$ children evenly, there will be $3+14\\times 4=59$ apples left. So at least he takes $59+12\\times 13\\times 14=2243$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "914", "queId": "9b61a139233e414eb13c9677fa16fb1a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Hasan writes down a two-digit number. He then writes the same two-digit number next to his original number to form a four-digit number. What is the ratio of his four-digit number to his two-digit number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2:1$$ "}], [{"aoVal": "B", "content": "$$100:1$$ "}], [{"aoVal": "C", "content": "$$101:1$$ "}], [{"aoVal": "D", "content": "$$1001:1$$ "}], [{"aoVal": "E", "content": "It depends on his number "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["Let Hasan\\textquotesingle s two-digit number be \\textquotesingle$$ab$$\\textquotesingle, which is equal to $$10 a + b$$. The four-digit number he forms is therefore \\textquotesingle$$abab$$\\textquotesingle, which is equal to $$1000 a + 100 b + 10 a + b$$ and hence to $$100 (10 a + b)+ 10 a + b = 101 \\times (10 a + b)$$. Therefore the ratio of his four-digit number to his two-digit number is $$101:1$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "917", "queId": "7863b88bae904d42a7191e8a71f604eb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$123+234+345$$ divided by $$4$$ has a remainder of~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["$$123\\div 4$$ R $$3$$；$$234\\div 4$$ R $$2$$；$$345\\div 4$$ R $$1$$; Therefore, $$\\left( 3+2+1 \\right)\\div 4$$ R $$2$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "918", "queId": "e475d2a31c6947d38b9e0f6e5c9de57f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following statement is correct? ", "answer_option_list": [[{"aoVal": "A", "content": "All prime numbers are odd numbers "}], [{"aoVal": "B", "content": "In every $3$ consecutive numbers, there must be a composite number "}], [{"aoVal": "C", "content": "All even numbers are composite numbers "}], [{"aoVal": "D", "content": "The sum of two different odd number must be a composite number "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["A: Any non-$3$ multiple of 3 are composite B: $1$, $2$, $3$ does not have composite number C: $2$ is prime number D: $1+$any odd number is multiple of $2$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "920", "queId": "c46b055ba6974e1ebac08690035cb9ef", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the square root of the number whose square is $$16$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$\\sqrt{{8}}$$ "}], [{"aoVal": "D", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["The number whose square is $$16$$ is $$4$$. The square root of $$4$$ is $$2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "921", "queId": "bb49ad86e1c44428b641f610731409ca", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Teacher divides $$365$$ coins among $$3$$ kids. One of them gets an odd number of coins, and another gets also an odd number of coins. Which of the following would be the possible number of coins that the last kid gets? ", "answer_option_list": [[{"aoVal": "A", "content": "$$232$$ "}], [{"aoVal": "B", "content": "$$168$$ "}], [{"aoVal": "C", "content": "$$247$$ "}], [{"aoVal": "D", "content": "$$94$$ "}], [{"aoVal": "E", "content": "$$132$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["Odd number $+$ Odd number $=$ Even number Odd number $-$ Even number $=$ Odd number "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "922", "queId": "a922fb6fa9f64a9a87041c55e09ce3a6", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "One day Randy was bored and he wrotre all the whole numbers from $49$ to $97$ on his paper. How many times did he write the digit \\textquotesingle\\textquotesingle$8$\\textquotesingle\\textquotesingle{} on his paper? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits"], "answer_analysis": ["$$14$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "923", "queId": "927ff442497c46e0b8da1ddf2979c684", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of two whole numbers is $$12$$, and the product is $$32$$. Find the difference between these numbers. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"], "answer_analysis": ["If the sum of $$2$$ whole numbers is $$12$$, and the product is $$32$$, then the numbers are $$8$$ and $$4$$; $$8-4 = 4$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "926", "queId": "9708fa35c7d243dda0a06919a1759e4e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If the sum of $$7$$ whole numbers is even, at mostof the numbers could be odd. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers"], "answer_analysis": ["If the sum of $$7$$ whole numbers is even, there must be an even number of odd numbers. The total number of odd numbers could be $$6$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "929", "queId": "8e128967d91547dcaa51bcce7fad99f4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If the four-digit number 3P78 is divisible by 3, how many possible values are there for P? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["use divisibility rule. 3+ 7+8+R = divisible by 3. 18 + R = divisible by 3. smallest possible number for R is 0, max possible amount for R is 9 3x6=18 - 18 =0 (can be divisible by 3) 3x7=21 -18 = 3 3x 8= 24 -18 =6 3x 9= 27 - 18 = 9 Total = 4 ways. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "930", "queId": "e921906621a94ac6843d701a277f8c47", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many prime numbers are there between $130$ and $150$? $$\\textasciitilde$$ $$\\textasciitilde$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$3$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["$131$, $137$, $139$, $149$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "933", "queId": "a4b22186ec924648b77e4713a96d8854", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the sum of the two smallest prime factors of $250$? (2007 AMC 8 Problems, Question \\#3) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["The two smallest prime factors of $250$ are $2$ and $5$. Thus, the sum is $2 + 5 = 7$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "934", "queId": "929ca18b8786491cb33d7612f8dc350c", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "When $$1001$$ is divided by a certain one-digit number, the remainder is $$5$$. What is the remainder when the same one-digit number divides $$2006$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->The additive property of the remainder"], "answer_analysis": ["$$1001\\div a=b~~\\text {R} 5$$, $a$ is a one-digit number bigger than $$5$$, so $a$ =6; $$1005\\div a=c~ \\text {R} 9$$; $$2006\\div a=d \\text {R} 14$$; $$14=2\\times6 + 2$$, so the remainder is $$2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "935", "queId": "85ff55a17f9749f3bb050959e3b97ec0", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "How many perfect cubes lie between $2^{8}+1$ and $2^{18}+1$, inclusive? (2018 AMC 8 Problem, Question \\#25) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$57$$ "}], [{"aoVal": "E", "content": "$$58$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["We compute $2^{8}+1=257$. We\\textquotesingle re all familiar with what $6^{3}$ is, namely, which is too small. The smallest cube greater than it is $7^{3}=343$. $2^{18}+1$ is too large to calculate, but we notice that $2^{18}=(2^{6})^{3}=64^{3}$, which therefore clearly will be the largest cube less than $2^{18}+1$. Therefore, the required number of cubes is $64-7+1=58$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "943", "queId": "81a4ed50adec4e06adcde28e46afb581", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When I rounded $$142.857$$ to the nearest hundred, ten, one, tenth and hundredth,was not one of my rounded numbers. ", "answer_option_list": [[{"aoVal": "A", "content": "$$140$$ "}], [{"aoVal": "B", "content": "$142.8$ "}], [{"aoVal": "C", "content": "$142.86$ "}], [{"aoVal": "D", "content": "$143$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["$$142.857$$ rounded to nearest: hundred($100$), ten($140$), one($143$), tenth($142.9$) and hundredth($142.86$). "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "949", "queId": "f2678528cfbd417698a5fef343f9ab60", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following is not a multiple of $12$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["$32$ can not be divided by $12$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "956", "queId": "bb807932a7a243c1957d8733a84f9010", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Let $N=34 \\cdot 34 \\cdot 63 \\cdot 270$. What is the ratio of the sum of the odd divisors of $N$ to the sum of the even divisors of $N$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "1:16 "}], [{"aoVal": "B", "content": "1:15 "}], [{"aoVal": "C", "content": "1:14 "}], [{"aoVal": "D", "content": "1:8 "}], [{"aoVal": "E", "content": "1:3 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["Prime factorizing $N$, we see $N=2^{3} \\cdot 3^{5} \\cdot 5 \\cdot 7 \\cdot 17^{2}$. The sum of $N$ \\textquotesingle s odd divisors are the sum of the factors of $N$ without 2 , and the sum of the even divisors is the sum of the odds subtracted by the total sum of divisors. The sum of odd divisors is given by $$ a=\\left(1+3+3^{2}+3^{3}+3^{4}+3^{5}\\right)(1+5)(1+7)\\left(1+17+17^{2}\\right) $$ and the total sum of divisors is $$ (1+2+4+8)\\left(1+3+3^{2}+3^{3}+3^{4}+3^{5}\\right)(1+5)(1+7)\\left(1+17+17^{2}\\right)=15 a . $$ Thus, our ratio is $$ \\frac{a}{15 a-a}=\\frac{a}{14 a}=\\text { (C) } 1: 14 \\text {. } $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "957", "queId": "a0589d50f66b47c292f8e83c1c55a012", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Suppose it is now the month of December. What month will it be $$100$$ calendar months from now? ", "answer_option_list": [[{"aoVal": "A", "content": "January "}], [{"aoVal": "B", "content": "February "}], [{"aoVal": "C", "content": "March "}], [{"aoVal": "D", "content": "April "}], [{"aoVal": "E", "content": "May "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["$$100\\div12=8R4$$ $$4$$ months after December will be April. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "960", "queId": "8644012c3cd645c182a3e7f59c24acd5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three ropes. One of them is $10$ inches long, the other two are $28$ and $30$ inches respectively. If we cut those ropes into small pieces with nothing left and each piece has the same length, how long is each piece at most? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Factors and the Greatest Common Factors->The Greatest Common Factor of Multiple Numbers"], "answer_analysis": ["The greatest common factor of $10$, $28$ and $30$ is $2$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "963", "queId": "864edf87d1684202af7aa45648d1b2aa", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A number divisible by both $$6$$ and $$20$$ must also be divisible by. ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["Divisibility by $$6$$ \\& $$20$$ does not promise divisibility by $$7$$, $$13$$, or $$8$$. $$\\rm A$$. $$12 = 4\\times3$$; $$\\rm B$$. $$14 = 2\\times7$$; $$\\rm C$$. $$26 = 2\\times13$$; $$\\rm D$$. $$120 = 8\\times15$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "964", "queId": "f715f78950f44821ae9b9177e4768fab", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "Every positive integer is congruent modulo $9$ to the sum of its decimal digits. Now, let $S(n)$ equal the sum of the digits of positive integer $n$. For example, $S(1507)=13$. For a particular positive integer $n, S(n)=691$. Which of the following could be the value of $S(n+2)$? (Adapted From 2017 AMC 12A Problems, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$17$$ "}], [{"aoVal": "C", "content": "$$143$$ "}], [{"aoVal": "D", "content": "$$116$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Congruence"], "answer_analysis": ["Note that $n \\equiv S(n) \\bmod 9$, so $S(n+2)-S(n) \\equiv n+2-n\\equiv2 \\bmod 9$. So, since $S(n)=691 \\equiv 7 \\bmod 9 $, we have that $S(n+2) \\equiv 9 \\equiv 0\\bmod 9$. Then, only one of the answer choices is congruent to $0 \\bmod 9$, which is $(A)=9$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "966", "queId": "cdcae6fd83f0446cbd240e1c8f4c344d", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "What is the number between $$37$$ and $$49$$ is exactly divisible by both $$3$$ and $$4$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$39$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$42$$ "}], [{"aoVal": "D", "content": "$$45$$ "}], [{"aoVal": "E", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["Common multiple of $$12$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "967", "queId": "7d7753b8fa5447199f01cfd137463175", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the length of the largest square that can be made from $$50$$ one-centimetre square tile? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5\\rm{cm}$$ "}], [{"aoVal": "B", "content": "$$6\\rm{cm}$$ "}], [{"aoVal": "C", "content": "$$7\\rm{cm}$$ "}], [{"aoVal": "D", "content": "$$8\\rm{cm}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers"], "answer_analysis": ["$$7\\times7=49\\rm{cm}^{2}$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "968", "queId": "a4f0327821974d5fb8da7244995fc434", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole numbers $A$, $B$ and $C$ ($B\\neq1$). $A\\times B=35$, $B\\times C=84$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$23$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$35=5\\times 7$ $84=2\\times 2\\times 3\\times 7$ Because $B$ is the factor both number contains, $B=7$ Thus, $A=5$, $C=12$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "970", "queId": "7d8510a648cd45c5bc2ae7a4670f1927", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Emily writes down the largest two-digit prime such that each of its digits is prime. Krish writes down the smallest two-digit prime such that each of its digits is prime. Kirsten subtracts Krish\\textquotesingle s number from Emily\\textquotesingle s number. What answer does Kirsten obtain? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$14 $$ "}], [{"aoVal": "B", "content": "$$20 $$ "}], [{"aoVal": "C", "content": "$$36 $$ "}], [{"aoVal": "D", "content": "$$45 $$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Applying Special Prime Numbers"], "answer_analysis": ["The prime digits are $$2$$, $$3$$, $$5$$ and $$7$$. So the largest two-digit integer whose digits are both prime is $$77$$. However, $$77$$ is not prime, nor is $$75$$, but $$73$$ is prime. So Emily writes down $$73$$. The smallest two-digit integer whose digits are both prime is $$22$$. However, $$22$$ is not prime, but $$23$$ is prime. So Krish writes down $$23$$. Therefore the answer which Kirsten obtains is $$73 - 23 = 50$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "974", "queId": "ae10a380bce949c583b2b39b650fdace", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $5$-digit number \"$2018U$\" is divisible by $9$, where $$U$$ is the ones digit. What is the remainder when this number is divided by $8$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["We use the property that the digits of a number must sum to a multiple of $9$ if it is divisible by $9$. This means $2+0+1+8+U$ must be divisible by $9$. The only possible value for U then must be $7$. Since we are looking for the remainder when divided by $8$, we can ignore the thousands. The remainder when $187$ is divided by $8$ is $(\\rm B)$ $3$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "975", "queId": "867668e256bf4aaa8670f4d69ec340dc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A kind of water plant grows so fast that it doubles every day. If one plant is put into the pond on the first day, it will turn to two plants on the second day, and on the $26$\\textsuperscript{th} days, they can fill the pond. If $8$ water plants are put into the pond on the first day, how many days it will take to fill the pond? ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["It takes three days for one plant to turn to $8$ plants. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "976", "queId": "e01cab5de3724f4c88c3c25501af312a", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "What is the total value of all the odd numbers between $$34$$ and $$42$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$35$$ "}], [{"aoVal": "B", "content": "$$72$$ "}], [{"aoVal": "C", "content": "$$111$$ "}], [{"aoVal": "D", "content": "$$152$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers"], "answer_analysis": ["$$35+37+39+41=152$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "977", "queId": "d27397311387456a816982282342cd6c", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "$$(2345678+3456782+4567823+5678234+6782345+7823456+8234567)\\div5$$=~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$5555555$$ "}], [{"aoVal": "B", "content": "$$6666666$$ "}], [{"aoVal": "C", "content": "$$7777777$$ "}], [{"aoVal": "D", "content": "$$8888888$$ "}], [{"aoVal": "E", "content": "$$9999999$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["$$(2+3+4+5+6+7+8)\\times1111111\\div5$$ $$=7777777 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "980", "queId": "978cd250a6e94bf689656c2005a6bdff", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many numbers can be divided by both $$3$$ and $$5$$ from $$50$$ to $$500$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$33$$ "}], [{"aoVal": "E", "content": "$$34$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["There are $$33$$ from $$1$$ to $$500$$. Remove number \"$$15$$\" and \"$$30$$\", thus $$33-2=31$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "981", "queId": "8e98b920df4443cfb51db69e849c5ce5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\sqrt {2\\times 4\\times 8}\\times \\sqrt {8\\times 8}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$64$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["$$\\sqrt {2\\times 4\\times 8}\\times \\sqrt {8\\times 8}=8\\times 8=64$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "989", "queId": "9c1bccb8611f41d6bcf5f90e76086e48", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A whole number is a perfect square if it can be expressed as the product of two equal whole numbers. How many perfect squares are greater than $$0$$ and less than $$1000$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$33$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["We note that $$31\\times 31 = 961$$ and $$32\\times 32 = 1024$$, hence there are $31$ perfect squares greater than $$0$$ and less than $$1000$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "997", "queId": "c971f82c38b947d081ac8e1066b43291", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many positive integer factors of $2020$ have more than $3$ factors? (2020 AMC 8 Problems, Question \\#17) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["Since $2020=2^{2} \\cdot 5 \\cdot 101$, we can simply list its factors: $$ 1,2,4,5,10,20,101,202,404,505,1010,2020 . $$ There are $12$ of these; only $1,2,4,5,101$ (i.e. $5$ of them) don\\textquotesingle t have over $3$ factors, so the remaining $12-5=(\\mathbf{B}) 7$ factors have more than $3$ factors. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "998", "queId": "bbcc6077c21245578e4d4730ca82f0f9", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "How many whole numbers between $$1$$ and $$100$$ are $$3$$ times a prime? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["The prime is $${}\\textless33$$, so it could be $$2$$, $$3$$, $$5$$, $$7$$, $$11$$, $$13$$, $$17$$, $$19$$, $$23$$, $$29$$, or $$31$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "999", "queId": "86c34b18a8bf422c9d4927db7d35d654", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "For how many positive integer values of $$N$$ is the expression $$\\frac{36}{N+2}$$ an integer? ($$1994$$ AHSME Problem, Question \\#$$10$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Theorem of the Number of Factors of a Number"], "answer_analysis": ["$$36={{2}^{2}}\\times {{3}^{2}}$$, so the number of its factors would be $$\\left( 2+1 \\right)\\times \\left( 2+1 \\right)=9$$. But $$\\textasciitilde N+2$$ cannot be $$1$$ or $$2$$, so the number of possible values of $$N$$ is$$\\textasciitilde9-2=7$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1005", "queId": "86ca0813853b478cbe73a09b30d658bf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $$5$$-digit number $$2018U$$ is divisible by $$9$$. What is the remainder when this number is divided by $$4$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["We use the property that the digits of a number must sum to a multiple of $9$ if it is divisible by $9$. This means $2+0+1+8+U$ must be divisible by $9$. The only possible value for U then must be $7$. Since we are looking for the remainder when divided by $4$, we can ignore the hundreds. The remainder when $87$ is divided by $4$ is $3$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1010", "queId": "e97988d21a564e999ed422afe2934f6a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The result of the calculation $$123456789\\times8$$ is almost the same as $$987654321$$ except that two of the digits are in a different order. What is the sum of these two digits? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders "], "answer_analysis": ["The units digit of $$123456789\\times8$$ is $$2$$, since $$9\\times 8=72$$ . So, if the statement in the question is correct then the two digits which are in a different order are $$1$$ and $$2$$, whose sum is $$3$$. As a check, $$123456789\\times8$$ is indeed $$987654312$$ . "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1012", "queId": "8eea627038474899bfc56247a715851c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the followings is a multiple of $$8$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["Since $$8=8\\times 1$$. We choose $$\\rm A$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1013", "queId": "c0738e7e3ded426dbd446a68fedec4f4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of $$1\\times 2\\times 3\\times 4\\times 5\\times 6\\times \\cdots \\times 25$$ ends withzeros． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->The Number of Zeros at the end of a Product"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1017", "queId": "b2e4b04bd7b348e98f6ab246054e3c7b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many numbers in the number set $16,17,18,19$ and $20$ have more than $3$ factors? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["$$16$$：$$1$$, $$2$$, $$4$$, $$8$$, $$16$$ $$17$$：$$1$$, $$17$$ $$18$$：$$1$$, $$2$$, $$3$$, $$6$$, $$9$$, $$18$$ $$19$$：$$1$$, $$19$$ $$20$$：$$1$$, $$2$$, $$4$$, $$5$$, $$10$$, $$20$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1020", "queId": "a9ea5abe1a514d70b49471fdd232f65f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$N$$ is a two$$-$$digit number. When $$N$$ is divided by $$9$$, the remainder is $$1$$. When $$N$$ is divided by $$10$$, the remainder is $$4$$. What is the remainder when $$N$$ is divided by $$11$$? (Adapted from $$2016$$ AMC $$8$$ Problem, Question \\#$$5$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["Among $64, 154$\\ldots~the smallest possible $$N$$ that satisfies the two conditions is $$64$$, and $$64 \\div 11\\rm R9$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1023", "queId": "ce1bcdd8c00c48f287024111015d0f24", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the digit in the ones place for $$2\\times2\\times5\\times5\\times5$$. ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["The product includes the factor $$5\\times2=10$$, so the digit in the ones place is $$0$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1025", "queId": "a0ef60a01a674f64be13bb0c74e7050f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I am thinking of a whole number greater than $$0$$ whose square equals its square root. How many such numbers are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["The only positive whole number whose square is equal to its square root is $$1$$, so the answer is $$\\text{B}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1029", "queId": "c50b07bd12044a6a902fc8458da5b2ff", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Some pirates found lots of gold coins. They divided all the coins equally into $5$ groups. Then, the leader of each group would divide the coins he got with his teammates. The $5$ groups had $4,$ $8,$ $9,$ $10,$ and $11$ pirates, respectively. In addition, all the leaders found that after they divided the coins evenly, there were always $2$ coins left. Which of the following could be the possible range where the number of coins of each group was in? ", "answer_option_list": [[{"aoVal": "A", "content": "$4150\\sim4160$ "}], [{"aoVal": "B", "content": "$3950\\sim3960$ "}], [{"aoVal": "C", "content": "$4500\\sim4600$ "}], [{"aoVal": "D", "content": "$7920\\sim7960$ "}], [{"aoVal": "E", "content": "$7970\\sim7980$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["$[4, 8, 9, 10, 11]=3960$, so the possible number of coins could be $3962$ or $7922$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1030", "queId": "d74008300fdd4692962b6279e5679fcb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "On one side of Long Street the houses are numbered with the consecutive odd numbers from $$1$$ to $$19$$. On the other side of that street, the houses are numbered with the consecutive even numbers from $$2$$ to $$14$$. How many houses are there on Long Street? (2006 Math Kangaroo Problem, Level 3-4, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$33$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["Odd numbers from $$1$$ to $$19$$: $$1, 3, 5, 7, 9, 11, 13, 15, 17, 19$$ Even numbers from $$2$$ to $$14$$: $$2, 4, 6, 8, 10, 12, 14$$ $$10+7=17$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1031", "queId": "ee1ef4999c274e0aafb12b560050fdb6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of three $2-$digit consecutive numbers is the largest $2-$digit number. What is their product? ", "answer_option_list": [[{"aoVal": "A", "content": "$$99$$ "}], [{"aoVal": "B", "content": "$$25900$$ "}], [{"aoVal": "C", "content": "$$35904$$ "}], [{"aoVal": "D", "content": "$$34589$$ "}], [{"aoVal": "E", "content": "$$39804$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["$99\\div3=33$ $32+33+34=99$ $32\\times33\\times34=35904$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1039", "queId": "d2c1beb35fc345b0a4c6246cb37b6155", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many $$0$$\\textquotesingle s does the product of $$1\\times 2\\times 3\\times 4\\times 5\\times 6\\times \\cdots \\times 25$$ end with? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["There are $$6$$ factors of $$5$$ when you prime factorise~ $$1\\times 2\\times 3\\times 4\\times 5\\times 6\\times \\cdots \\times 25$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1049", "queId": "ee3fd0f1940f4568b9c19cc353636346", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Among the eleven numbers from $$121$$ to $$131$$, how many prime numbers are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["Only two prime numbers: $$127$$, $$131$$. Therefore, we choose $$\\rm C$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1052", "queId": "b32ecd4c20bf4b4bb78444f1908f2c94", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Connie counts from $$1$$ to $$20$$. What is the sum of the prime numbers she counts? ", "answer_option_list": [[{"aoVal": "A", "content": "$$29$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$77$$ "}], [{"aoVal": "D", "content": "$$78$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers"], "answer_analysis": ["Connie counts from $$1$$ to $$20$$. The sum of the prime numbers she counts is $$2+3+5+7+11+13+17+19=77$$. (Note: $$1$$ is not prime.) "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1053", "queId": "a13a404d92af4ce7a628d871e11e53e9", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Divide $$4$$、$$9$$、$$10$$、$$14$$、$$15$$ and $$21$$ into 2 groups with 3 numbers in each group to make the product of numbers in each group the same. How can we divide the numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$(14,9,10), (21,15,4)$$ "}], [{"aoVal": "B", "content": "$$(14,21,10), (9,15,4)$$ "}], [{"aoVal": "C", "content": "$$(14,4,10), (21,15,9)$$ "}], [{"aoVal": "D", "content": "$$(14,15,9), (21,10,4)$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->The Number of Zeros at the end of a Product"], "answer_analysis": ["$$A$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1054", "queId": "93d81e3e84524ff1af2ce8e234f17431", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following numbers leaves a remainder of $$1$$ when divided by $$2$$ and $$3$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["When we divide by $$2$$, $$3$$, the remainder is $$1$$. Hence, if we first subtract $$1$$, the result will be divisible by $$2$$, $$3$$. $2\\times3+1=7$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1055", "queId": "fffebecff8fd417089d42143575f7c38", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Teacher Angel has $$87$$ apples. She want to pack the apples into container so she can keep them nicely in the fridge. Each fo the container can only hold $$8$$ apples. What is the least number of containers needed so that teacher Angel can pack all the apples in the fridge? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders"], "answer_analysis": ["$$87\\div 8=10$$ $\\text{R}$ $$7$$ $$10+1=11$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1056", "queId": "c0bfce7cd1374e1cb294a30da9511a24", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many 0s are there at the end of the product $$2\\times3\\times5\\times2\\times5\\times3\\times5\\times5$$. ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["2 set of 2$\\times$5. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1058", "queId": "aa396e97ea9c443d849f6b27f048c026", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A square of a positive number is $$500\\textbackslash\\%$$ greater than that number. What number is it? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["Let the number be $x$. Since $x^{2} = 6x$, therefore $x=6$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1060", "queId": "c0cb5bbb111d421d829d7015d48d51f5", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "What are the last three digits of the answer to the calculation below? $$123\\times 124\\times 125\\times 126\\times 127$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$000$$ "}], [{"aoVal": "B", "content": "$$222$$ "}], [{"aoVal": "C", "content": "$$444$$ "}], [{"aoVal": "D", "content": "$$666$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders "], "answer_analysis": ["The product $$123 \\times124\\times125\\times126 \\times127$$ is a multiple of $$125$$; moreover, it also has a factor of $$2$$ three times, from $$124\\left( 2\\times 2\\times 31 \\right)$$ and from $$126\\left( =2\\times 63 \\right)$$. Therefore it is a multiple of $$125 \\times2\\times2\\times2= 1000$$, and so it must end in $$000$$. Alternatively, working from the options, it is easily seen that the product is a certainly an even multiple of $$5$$-so its unit digit is $$0$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1065", "queId": "ee531a19fba94189a88ebf818a73e598", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "What are the last two digits of the result of $$1\\times 3\\times 5\\times 7\\times \\cdots \\times 101$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$05$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$55$$ "}], [{"aoVal": "E", "content": "$$75$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["The result must be a multiple of $25.$ $$a=0(\\text{mod}25)$$ According to the divisibility rule of $4$, the remainder of the result divided by $4$ is $$1\\times 3\\times 1\\times 3\\times \\cdots \\times 1\\times 3\\times 1={{3}^{25}}\\times 1=3(\\text{mod}4)$$. When the result is $$75(\\text{mod}100)$$, it can be divisible by $25$ and have a remainder of $3$ when divided by $4.$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1068", "queId": "98713f9b8edd461e9b31286e675bec43", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The multiplication $$abc\\times de=7632$$ uses each of the digits $$1$$ to $$9$$ exactly once. What is the value of $$b$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"], "answer_analysis": ["Note first that $$7632 =2\\times2\\times2\\times2\\times3\\times3\\times53$$. Therefore either the two-digit number $$de = 53$$ or the three-digit number $$abc$$ is a multiple of $$53$$. Since the multiplication uses each of the digits $$1$$ to $$9$$ once and $$7632$$ contains a $$3$$, the option $$de= 53$$ is not allowable. Hence we need to find a three-digit multiple of $$53$$ that does not share any digits with $$7632$$ and divides into $$7632$$ leaving an answer that also does not share any digits with $$7632$$. We can reject $$2 \\times 53 = 106$$ since it contains a $$6$$ but $$3 \\times 53 = 159$$ is a possibility. The value of $$7632\\div159$$ is $$2\\times2\\times2\\times2\\times3 = 48$$ which does not have any digits in common with $$7632$$ nor with $$159$$. We can also check that no other multiple of $$53$$ will work. Therefore the required multiplication is $$159 \\times 48 = 7632$$ and hence the value of $$b$$ is $$5$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1069", "queId": "bc528659dd6041b5a314e2a4022df617", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "The greatest common factor is smallest for which of the following pairs of numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ \\& $$18$$ "}], [{"aoVal": "B", "content": "$$5$$ \\&~$$25$$ "}], [{"aoVal": "C", "content": "$$6$$ \\&~$$33$$ "}], [{"aoVal": "D", "content": "$$8$$ \\&~$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["The greatest common factors of the $$4$$ pairs of numbers are $$2$$, $$5$$, $$3$$, and $$1$$, respectively. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1070", "queId": "d78376297ec64106a977cd47bcd0e372", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The students of a class can be divided into groups of $5$ or groups of $7$ when there is a groupwork to do. How many students at least are in that class? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$21$$ "}], [{"aoVal": "D", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Multiples and Least Common Multiples->Least Common Multiple of Two Numbers"], "answer_analysis": ["The least common multiple of $5$ and $7$ is $35$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1079", "queId": "e53cd823fbfe4c2983ee4844678ac72b", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "A two-digit prime number is still a prime number when its first and tenth digits are exchanged. There aresuch prime numbers. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["$$11$$，$$13$$，$$17$$，$$31$$，$$37$$，$$71$$，$$73$$，$$79$$，$$97$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1080", "queId": "c9f9169e4cca4b379e691b358f5d9cc4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Avril likes collecting baseball cards. The number of cards she has is divisible by $$2$$, $$3$$, and $$5$$. How many baseball cards does Avril have at least? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["The total number of baseball cards is the least common multiple of $$2$$, $$3$$, and $$5$$, i.e. $$\\left[ 2,3,5\\right]=2\\times3\\times5=30$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1083", "queId": "a5fc4b32817d4bca9a9b1de9dfc51a25", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\sqrt {3\\times 12}\\times \\sqrt {4\\times 9}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2\\times 18$$ "}], [{"aoVal": "B", "content": "$$18\\times 18$$ "}], [{"aoVal": "C", "content": "$$3\\times 2$$ "}], [{"aoVal": "D", "content": "$$36\\times 36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["$$\\sqrt {36}\\times \\sqrt {36}=6\\times 6=36 = 2\\times 18$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1084", "queId": "c0f5c577a4de4757857c8242df5a5b0a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Vivian has many barbie cards. If she puts $8$ cards in each group, there will be $5$ cards left. If she puts $9$ cards in each group, there will be $3$ cards left. If she puts $10$ cards in each group, there will be $1$ card left. How many cards at least should Vivian take away, so that the remaining number of cards can be divisible by $8,$ $9,$ and $10$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem"], "answer_analysis": ["$8+8+5=9+9+3=10+10+1=21$, so after we removing $21$ cards, the number of the remaining cards can be divisible by $8, 9,$ and $10.$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1087", "queId": "dc2b22c6189f40289782c088c3290090", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the first $$5$$ \\textbf{odd} positive numbers is $$25$$. What is the sum of the first $$5$$ \\textbf{even} positive numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$45$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers"], "answer_analysis": ["Each of five positive even numbers is $$1$$ larger than the corresponding odd number in $$1$$,$$3$$, $$5$$, $$7$$ and $$9$$, which we are told have a sum of $$25$$. So the sum of the first five positive even numbers is $$25 +5 =30$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1091", "queId": "f3050c52aa044a29b8fc6765468df30a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Cayden is drawing some words on a mural in his school. Everyday, he is only able to draw out one letter. He wants to draw: $$I$$ $$love$$ $$Mathematics$$ $$and$$ $$English$$ If he starts on a Tuesday, and during the weekend, he is not able to draw. When will he finish the drawing? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Wednesday "}], [{"aoVal": "D", "content": "Thursday "}], [{"aoVal": "E", "content": "Friday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["$$26\\div 5 = 5R1$$ Start from Tuesday, thus, it is Tuesday "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1092", "queId": "bc7c78cf88884e908013ee33a1712b93", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$123+234+345$$ divided by $$4$$ has a remainder of． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["The sum of each numbers remainder can be divided by $$4$$ to get $$2$$: $$123\\div 4$$ R $$3$$；$$234\\div 4$$ R $$2$$；$$345\\div 4$$ R $$1$$; Therefore, $$\\left( 3+2+1 \\right)\\div 4$$ R $$2$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1093", "queId": "ce8ecdfa3d6746399caccff488a35c94", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the squares of the first $$20$$ positive integers is $$2870$$. What is the sum of the squares of the first $$19$$ positive integers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2350$$ "}], [{"aoVal": "B", "content": "$$2361$$ "}], [{"aoVal": "C", "content": "$$2470$$ "}], [{"aoVal": "D", "content": "$$2850$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["The sum of the squares of the first $$20$$ positive integers is $$2870$$. The sum of the squares of the first $$19$$ is $$2870-20^{2}=2870-400=2470$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1094", "queId": "aa9237d4f2de432a9c2e30d29773e5ae", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the remainder of $$(223\\times311+198\\times273)\\div 5$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$1$ "}], [{"aoVal": "B", "content": "$2$ "}], [{"aoVal": "C", "content": "$3$ "}], [{"aoVal": "D", "content": "$4$ "}], [{"aoVal": "E", "content": "$5$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["According to the additive and multiplicative properties of remainders, the remainder of this expression equals the remainder of $$(3\\times1+3\\times3)\\div 5=12\\div5=2 \\text{R} 2$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1101", "queId": "d32cf2ba9cd44dfa9ade1eb2846b4f2a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many numbers of the following are divisible by $3$? $$\\textasciitilde$$ $213 \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} 422\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~741\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~971\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~1197\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash~ ~ ~2937$ $\\textasciitilde$ $\\textasciitilde$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["The sums of the digits of $422$ and $971$ are not multiple of $3$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1102", "queId": "a1aea2c3d18f44249407fbb9522c6061", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A positive number is called a perfect square whenever it is the square of a whole number. The first three perfect squares are $$1$$, $$4$$, and $$9$$. The $$100$$th perfect square is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$1000$$ "}], [{"aoVal": "C", "content": "$$10000$$ "}], [{"aoVal": "D", "content": "$$100000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["The first perfect square is $$1^{2}$$, the $$2$$nd is $$2^{2}$$, and the $$3$$rd is $$3^{2}$$. With this pattern, the $$100$$th perfect square is $$100^{2} = 100\\times100= 10000$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1104", "queId": "e55f5407b3ed4f198c7d5863e16539b3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole number $A$, $B$, $C$. $A\\times B=55$, $B\\times C=100$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$34$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$55=5\\times 11$ $100=2\\times 2\\times 5\\times 5$ Because $B$ is the factor both number contains, $B=5$ Thus, $A=11$, $C=20$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1111", "queId": "aab7556303ee4e57a321425b74c2fd8d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If I multiply four different prime numbers, the product must have positive divisors. ", "answer_option_list": [[{"aoVal": "A", "content": "$$ 8 $$ "}], [{"aoVal": "B", "content": "$$12 $$ "}], [{"aoVal": "C", "content": "$$16 $$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$10 $$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Theorem of the Number of Factors of a Number"], "answer_analysis": ["$$2\\times2 \\times2\\times2=16$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1112", "queId": "aab8547966164a369925c6732853e3d8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In this fictional \"Old Island\", all the numbers contain only odd digits. The order of the counting numbers is as follows: $1, 3, 5, 7, \\cdots , 19, 31, 33, \\cdots $ What is the 31st counting number in the island? ", "answer_option_list": [[{"aoVal": "A", "content": "$$101$$ "}], [{"aoVal": "B", "content": "$$111$$ "}], [{"aoVal": "C", "content": "$$99$$ "}], [{"aoVal": "D", "content": "$$113$$ "}], [{"aoVal": "E", "content": "None of the above. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["1,3,5,7,9 -\\/-\\/-\\/-\\/-\\/-\\/-\\/-\\/-\\/-⑤ 11,13,15,17,19-\\/-\\/-\\/-\\/-\\/-\\/-⑤ 31,33,35,37,39-\\/-\\/-\\/-\\/-⑤ 51,53,55,57,59-\\/-\\/-\\/-\\/-⑤ 71,73,75,77,79-\\/-\\/-\\/-\\/-⑤ 91,93,95,97,99-\\/-\\/-\\/-⑤ $$111$$ the 31st number is 111. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1113", "queId": "aab9f2ba1a28437fae361e32367c9b7d", "competition_source_list": ["其���"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the remainder of $$(223\\times311+198\\times273)\\div 5$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$1$ "}], [{"aoVal": "B", "content": "$2$ "}], [{"aoVal": "C", "content": "$3$ "}], [{"aoVal": "D", "content": "$4$ "}], [{"aoVal": "E", "content": "$5$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["According to the additive and multiplicative properties of remainders, the remainder of this expression equals the remainder of $$(3\\times1+3\\times3)\\div 5=12\\div5=2 \\text{R} 2$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1116", "queId": "c12f2b6893e84633b04b9f61010acc28", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Bill writes down all the numbers from $1$ to $60$ inclusive. How many times does he use the digit $5$? ", "answer_option_list": [[{"aoVal": "A", "content": "$16$ "}], [{"aoVal": "B", "content": "$$17$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$19$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["In tens place: there are ten $$5$$s: $$50\\sim59$$ In ones place: there are six $$5$$s: $$5, 15, 25, 35, 45, 55$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1120", "queId": "bcb21a79edd148f4a916ddd31a51191e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The greatest prime number that is a divisor of $16,384$ is $2$ because $16,384=2^{14}$. What is the sum of the digits of the greatest prime number that is a divisor of $16,383$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$16$$ "}], [{"aoVal": "E", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["We have $$16383=2^{14}-1=\\left(2^{7}+1\\right)\\left(2^{7}-1\\right) =129 \\cdot 127 $$. Since $129$ is composite, $127$ is the largest prime divisible by $16383$. The sum of $127$\\textquotesingle s digits is $$ 1+2+7=\\text { (C) } 10 $$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1121", "queId": "f32a2b315ef940f2bfb4bd623a989e8e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If a natural number can be written as the sum of both two and three consecutive natural numbers, then we can call it a Think Number. What is the largest Think Number no larger than $5789$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5786$$ "}], [{"aoVal": "B", "content": "$$5787$$ "}], [{"aoVal": "C", "content": "$$5788$$ "}], [{"aoVal": "D", "content": "$$5789$$ "}], [{"aoVal": "E", "content": "$$5784$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["The number can be written as $$n+(n+1)=2n+1(n\\geqslant 1)$$ and $$x+(x+1)+(x+2)=3x+3$$. It must be a multiple of $3$ . $5790$ can be divisible by both $2$ and $3$, so it is $5790-3=5787$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1127", "queId": "d35c6f70f9e04ecfa792878851013839", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Change a digit of the number $98760$ to make the new five-digit number be divisible by $250$. What is the new five-digit number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$98765$$ "}], [{"aoVal": "B", "content": "$$98750$$ "}], [{"aoVal": "C", "content": "$$98755$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["The last three digits must be divisible by $125$, and the ones place must be divisible by $2$, so it can only be $98750$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1128", "queId": "bcd7aa508da1440195f18aa2d46bb6e1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is divisible by all of the integers from $$1$$ to $$10$$ inclusive? ", "answer_option_list": [[{"aoVal": "A", "content": "$$23\\times34$$ "}], [{"aoVal": "B", "content": "$$34\\times45$$ "}], [{"aoVal": "C", "content": "$$45\\times56$$ "}], [{"aoVal": "D", "content": "$$56\\times67$$ "}], [{"aoVal": "E", "content": "$$67\\times78$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"], "answer_analysis": ["Of the options given, $$23\\times 34$$, $$56\\times 67$$ and $$67\\times 78$$ are all not divisible by $$5$$, so may be discounted. Also $$34$$ is not divisible by $$4$$ and $$45$$ is odd, so $$34\\times 45$$ may also be discounted as it is not divisible by $$4$$. The only other option is $$45\\times 56$$. As a product of prime factors, $$45\\times 56=2^{3}\\times3^{2}\\times5\\times7$$, so it is clear that it is divisible by all of the integers from $$1$$ to $$10$$ inclusive. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1130", "queId": "b8618a49831f460e87e61a2b17f33a5b", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "$$(14\\times 9\\times 8)\\div \\left( 9\\times 7\\times 8 \\right)=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$0$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders"], "answer_analysis": ["$$(14\\times 9\\times 8)\\div \\left( 9\\times 7\\times 8 \\right)=14\\times 9\\times 8\\div 9\\div 7\\div 8=14\\div 7\\times (9\\div 9)\\times (8\\div 8)=14\\div 7=2$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1132", "queId": "ca6fb22fb1a047548c81b0cb4148aa3b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A two-digit number can be divided by both $$1$$ and $$5$$. It is also an even number. How many such numbers are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$19$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["$$10, 20, 30, 40, 50, 60, 70, 80, 90$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1134", "queId": "d7ff0f4f299c4d6891cf6a5a09db9e10", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "♥ $$\\times$$ ☺ $$=$$ ♦ ☺ is an even number. which of the following gives an odd answer? ", "answer_option_list": [[{"aoVal": "A", "content": "♦ $$-\\textasciitilde3$$ "}], [{"aoVal": "B", "content": "☺ $$+$$ ♦ "}], [{"aoVal": "C", "content": "☺ $$\\times$$ ☺ "}], [{"aoVal": "D", "content": "♦ $$\\times$$~♦ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers"], "answer_analysis": ["♥ $$\\times$$ ☺ $$=$$ ♦ Since ☺ is an even number,~♦ must also be an even number. ♦ $$-\\textasciitilde3$$ is the only option to given an odd answer because even $$-$$ odd $$=$$ odd. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1138", "queId": "d380c5ac43bb4948a98a3127e5bb5868", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many $$0$$\\textquotesingle s does the product of $$1\\times 2\\times 3\\times 4\\times 5\\times 6\\times \\cdots \\times 25$$ end with? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["There are $$6$$ factors of $$5$$ when you prime factorise~ $$1\\times 2\\times 3\\times 4\\times 5\\times 6\\times \\cdots \\times 25$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1144", "queId": "f803121d36274ffd85f972871cbc8c37", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The largest possible sum of two different two$$-$$digit numbers is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$99$$ "}], [{"aoVal": "C", "content": "$$197$$ "}], [{"aoVal": "D", "content": "$$198$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["$$99 + 98 = 197$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1145", "queId": "bd00ecc4856140d7b3ae29bb8ca33415", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Julie shares a bag of 70 carrots among some rabbits. Each rabbit has exactly the same number of carrots. If Julie doesn\\textquotesingle t have any carrots left, how many rabbits might she have fed? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["Among $$3,4,5,6,8$$, only $$5$$ is a factor of $$70$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1148", "queId": "f80c8a00b34f46b6bb74a945fd6a015e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jason has some baseball cards from the $$1920$$s. If he divides the number of cards he has by $$3$$, then he will have $$1$$ remaining cards; if he divides the number of cards he has by $$5$$, he will have $$3$$ remaining cards; if he divides the number of cards he has by $$7$$, he will have $$5$$ remaining cards. How many cards does Jason have at least? ", "answer_option_list": [[{"aoVal": "A", "content": "$$101$$ "}], [{"aoVal": "B", "content": "$$102$$ "}], [{"aoVal": "C", "content": "$$103$$ "}], [{"aoVal": "D", "content": "$$104$$ "}], [{"aoVal": "E", "content": "$$105$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["The number of cards after adding $$2$$ is divisible by $$3$$, $$5$$, and $$7$$. Since the least common multiple of $$3$$, $$5$$, and $$7$$ is $$3\\times5\\times7=105$$, Jason has $$105-2=103$$ cards at least. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1151", "queId": "f36fb2a7c50449b9a733313d1bde50a9", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Two(different) numbers are selected from $$0$$，$$1$$，$$3$$，$$5$$，$$8$$ and $$9$$. How many two-digit even mumbers can be formed？ ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["$$10$$、$$30$$、$$50$$、$$80$$、$$90$$、$$18$$、$$38$$、$$58$$、$$98$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1153", "queId": "c60e798a831a473cbadf2e9052ca64ad", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many whole numbers are greater than $$9$$ and less than $$60$$?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$49$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$51$$ "}], [{"aoVal": "D", "content": "$$59$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["There are $$60$$ whole numbers from $$0$$ to $$59$$. That\\textquotesingle s $$50$$ without $$0$$ to $$9$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1154", "queId": "bd13628819064521bfdca3e99ba3166f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of $$2016$$ integers is even. At mostof them can be odd. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2016$$ "}], [{"aoVal": "B", "content": "$$2015$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers"], "answer_analysis": ["The sum of any even number of odd integers is always even. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1161", "queId": "dcbdd91f061745bebdfaacf9a0f387cb", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "The greatest common factor of $$23$$ and $$24$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["The only common factor of any two consecutive whole numbers is $$1$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1165", "queId": "b4366eac8e5840d49b3bdbcbc5f2071f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following statements is incorrect? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2350$$ is a multiple of $$2$$, $$5$$ and $$10$$ "}], [{"aoVal": "B", "content": "$$1284$$ is a multiple of $$4$$ "}], [{"aoVal": "C", "content": "$$9972$$ is not a multiple of $$9$$ "}], [{"aoVal": "D", "content": "$$5742$$ is a multiple of $$6$$ and $$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["A: $$2350$$ is even, thus it is a multiple of $$2. 2350$$ ends with $$0$$, thus it is a multiple of $$5$$ and $$10$$; B: $$1284$$ ends with $$84$$, and $$84$$ is a multiple of $$4$$, thus $$1284$$ is a multiple of $$4$$; C: $$9 + 9 + 7 + 2 = 27$$ is a multiple of $$9$$, thus $$9972$$ is a multiple of $$9$$; D: $$5 + 7 + 4 + 2 = 18$$, it is a multiple of $$9$$ and $$3$$; since it ends with $$2$$, it is also a multiple of $$2$$, and thus a multiple of $$6$$; Hence the incorrect statement is C. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1167", "queId": "eefe14336a5744a7a910404efdf4c2a3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole number $A$, $B$, $C$. $A\\times B=77$, $B\\times C=364$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$70$$ "}], [{"aoVal": "D", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$77=7\\times 11$ $364=2\\times 2\\times 7\\times 13$ Because $B$ is the factor both number contains, $B=7$ Thus, $A=11$, $C=52$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1172", "queId": "cac0fb1ece41488bb4f9e5557c69da08", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which number between $$60$$ and $$80$$ is both a multiple of $$3$$ and $$8$$?~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$63$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$96$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Multiples and Least Common Multiples->Least Common Multiple of Two Numbers"], "answer_analysis": ["$$72$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1173", "queId": "bd49c85bd92947dc80d359760285107c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Divide $$2000$$ by an odd number. The remainder must be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$even "}], [{"aoVal": "B", "content": "$$$$odd "}], [{"aoVal": "C", "content": "$$$$prime "}], [{"aoVal": "D", "content": "$$$$whole "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders"], "answer_analysis": ["$$2000\\div1001$$ and $$2000\\div999$$ leave whole \\# remainders $$999$$ and $$2$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1175", "queId": "cf5fdaec3e5a4d59a7130468cec31f67", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the remainder when 7,999,999,999 is divided by 8 ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["omitted PMC 2021 \\#7 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1177", "queId": "d3f281e751ce4341aa8964348025fada", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that $$M=\\overline{3abcd}$$, $$N=\\overline{abcd3}$$ , and $$M-N=3177$$, what is $$\\overline{abcd}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2940$$ "}], [{"aoVal": "B", "content": "$$2960$$ "}], [{"aoVal": "C", "content": "$$2980$$ "}], [{"aoVal": "D", "content": "$$3000$$ "}], [{"aoVal": "E", "content": "$$3020$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value"], "answer_analysis": ["$$M-N=3177$$ $$(30000+\\overline{abcd})-(10\\times \\overline{abcd}+3)=3177$$ $$30000-3177=9\\times \\overline{abcd}$$ $$\\overline{abcd}=2980$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1179", "queId": "e188e36e97ae4b44b5bcc482c392730e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I have equal numbers of quarters, dimes, and nickels. These coins could have a total value of any of the following $$EXCEPT$$． ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$2.40$$ "}], [{"aoVal": "B", "content": "＄$$3.80$$ "}], [{"aoVal": "C", "content": "＄$$4.40$$ "}], [{"aoVal": "D", "content": "＄$$5.20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders"], "answer_analysis": ["The value of $$1$$ quarter, $$1$$ dime, and $$1$$ nickel is $$40$$￠. My coins must have a total value divisible by $$40$$, but ＄$$3.80$$ is not divisible by $$40$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1182", "queId": "cf6ff40cf43447a4be0bfd1687c64e68", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The thousands digit of the sum of 5+55+555+5555 is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases"], "answer_analysis": ["$$6170$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1185", "queId": "fd1a84bf0a72424eaae1c532163c9260", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The thousands digit of the sum of 8+88+888+8888+88888 is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases"], "answer_analysis": ["$$8+88+888+8888+88888=98760$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1187", "queId": "cb0291b682974c899411cce6b762942a", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following is not a composite number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$47$$ "}], [{"aoVal": "C", "content": "$$49$$ "}], [{"aoVal": "D", "content": "$$51$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["$47$ is a prime number. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1191", "queId": "bd8c7a7b249c49c8ba208d10139f9c4b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Students guess that Norb's age is $28$, $30$, $34$, $36$, $38$, and $41$. Norb says, \"At least half of you guessed too low, two of your guesses are off by one, and my age is a prime number.\"~How old is Norb? (adapted from 2011 AMC 8 Problem, Question \\#21) ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$29$$ "}], [{"aoVal": "C", "content": "$$31$$ "}], [{"aoVal": "D", "content": "$$37$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"], "answer_analysis": ["If at least half the guesses are too low, the Norb\\textquotesingle s age must be greater than $34$. If two of the guesses are off by one, then his age is between two guesses whose difference is $2$. It could be $29$, $35$ or $37$, but because his age is greater than $34$, it can only be $35$ or $37$. Lastly, Norb\\textquotesingle s age is a prime number so the answer must be $37$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1192", "queId": "e1a799b1e47c404da82acf880fb10ccf", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Among numbers like $5$, $55$, $555$, $5555$, $$\\cdots$$, how many of them are perfect squares? ", "answer_option_list": [[{"aoVal": "A", "content": "$0$ "}], [{"aoVal": "B", "content": "$1$ "}], [{"aoVal": "C", "content": "$2$ "}], [{"aoVal": "D", "content": "Countless "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers"], "answer_analysis": ["None of them "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1193", "queId": "bd94a222966f468fb42b4f4ff304beb2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the remainder when $$222 222 222$$ is divided by $$4$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders"], "answer_analysis": ["In division by $$4$$, the last $$2$$ digits determine the remainder, use $$22\\div4$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1196", "queId": "e1be5ea872254e7c82e0110367e74558", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "If the sum of two prime numbers is $$39$$, the difference between these two prime numbers will be ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$29$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$35$$ "}], [{"aoVal": "E", "content": "$$37$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["Because $$39$$ is an odd number, one of the two numbers must be an even prime number $$2$$. The other number is $$39-2=37$$, and their difference is $$35$$. So the answer is $$\\text{B}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1199", "queId": "cb300feddb254727b91e83ff585f0218", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of the distinct prime integer divisors of $2016 ?$ (2016 AMC 8 Problem, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$49$$ "}], [{"aoVal": "E", "content": "$$63$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["The prime factorization is $2016=2^{5} \\times 3^{2} \\times 7$. Since the problem is only asking us for the distinct prime factors, we have $2,3,7$. Their desired sum is then (B) 12 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1201", "queId": "dd555005e7e647f382b5669b30486a82", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which pair of numbers has a common factor greater than $$1$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ and $$9$$ "}], [{"aoVal": "B", "content": "$$6$$ and $$27$$ "}], [{"aoVal": "C", "content": "$$27$$ and $$50$$ "}], [{"aoVal": "D", "content": "$$33$$ and $$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["The greatest common factors for the choices are $$1$$, $$3$$, $$1$$, $$1$$, respectively. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1202", "queId": "c6bbd5474e144e75840e6b5fbc067802", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Suppose it is now the month of February. What month will it be $$90$$ calendar months from now? ", "answer_option_list": [[{"aoVal": "A", "content": "April "}], [{"aoVal": "B", "content": "May "}], [{"aoVal": "C", "content": "June "}], [{"aoVal": "D", "content": "July "}], [{"aoVal": "E", "content": "August "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["$$90\\div12=7R6$$ $$6$$ months afterFebruary will be August "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1203", "queId": "f42a79433f954facbd768e84bb9639ae", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The greatest odd factor of $$30$$ is .　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["The smallest even factor is $$2$$; $$30\\div2= 15$$, the greatest odd factor. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1206", "queId": "d8e8972b627249b194dc63166de864cb", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There are two reading rooms at Think Town\\textquotesingle s Library: Tulip\\textquotesingle s and Lily\\textquotesingle s. There are two lamps on every table in Tulip\\textquotesingle s Reading Room. As for Lily\\textquotesingle s Reading Room, there are three lamps on every table. Nini knows that the total number of lamps in the two reading rooms is an odd number, and the total number of tables in the two reading rooms is also an odd number. Which reading room has an odd number of tables? ", "answer_option_list": [[{"aoVal": "A", "content": "Tulip\\textquotesingle s Reading Room "}], [{"aoVal": "B", "content": "Lily\\textquotesingle s Reading Room "}], [{"aoVal": "C", "content": "Both rooms "}], [{"aoVal": "D", "content": "None of the rooms "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Odd and Even Applications"], "answer_analysis": ["There are two lamps on every table in Tulip\\textquotesingle s Reading Room, so the number of lamps in it is an even number. The total number of lamps in the two rooms is odd, and thus the number of lamps in Lily\\textquotesingle s Reading Room is an odd number. Since there are three lamps on every table in Lily\\textquotesingle s Reading Room, the number of tables in it is also an odd number. However, the total number of tables in the two rooms is odd, so the number of tables in Tulip\\textquotesingle s is even. Therefore, the answer is $$\\text{B}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1208", "queId": "eb1e5575606749f2959e842379d9b8a1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Any number that is divisible by both $$12$$ and $$5$$ must also be divisible by． ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders"], "answer_analysis": ["A number divisible by $$12$$ \\& $$5$$ is divisible by a product of their factors, such as $$3\\times5$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1211", "queId": "cfe214dd15f84d8d84b170e4b93e8e86", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Linda wrote down a natural number. When she divided the number by $$7$$, the remainder was $$5$$. What is the remainder when twice that number is divided by $$7$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder "], "answer_analysis": ["The remainder of $$A$$ $$\\div7$$ is $$5$$, and $$2A=A+A$$. Therefore the remainder of $$2A\\div7$$ is $$5+5=10$$. $$10= 7+3$$, therefore the remainder is $$3$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1212", "queId": "e2011f278c5842e9b7699d859706cfe1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following cases can\\textquotesingle t make an even number? ", "answer_option_list": [[{"aoVal": "A", "content": "An odd number + An even number "}], [{"aoVal": "B", "content": "An even number + An even number "}], [{"aoVal": "C", "content": "An odd number + An odd number "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers"], "answer_analysis": ["The sum of an odd number and an even number is always an odd number. The sum of two numbers which are both even or both odd is always an even number. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1213", "queId": "c6e1baf21dbb470ebeb08c54b17fbbd0", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "How many numbers listed below are positive? $$23$$, $$32$$, $$-56$$, $$-98$$, $$7$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers"], "answer_analysis": ["$$23$$, $$32$$, and $$7$$ are positive; $$-56$$, $$-98$$ are negative. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1214", "queId": "fd847e36d38f427e8d2bba466e087f7d", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "In the division expression $$28\\div$$~\\uline{~~~~~~~~~~}~$$=$$~\\uline{~~~~~~~~~~}~$$\\text{R}4$$, how many different combinations are there for the quotient and the divisor? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["We can use the equation: divisor $$\\times$$ quotient $$=$$ dividend $$-$$ remainder, so here we can get divisor $$\\times$$ quotient $$=28-4=24$$. Therefore, the only possibilities are $$1$$ and $$24$$, $$2$$ and $$12$$, $$3$$ and $$8$$, and $$4$$ and $$6$$ for a total of four possible combinations. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1219", "queId": "eb47b49f5d2940de94cb697242c5c459", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Pip swam $$3$$ back and forth in the lane for a total of $$156$$ metres, how long is the lane in this pool? ", "answer_option_list": [[{"aoVal": "A", "content": "$$52$$ "}], [{"aoVal": "B", "content": "$$104$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$234$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Short Division"], "answer_analysis": ["one back and forth $$156\\div3=52$$metres length of the lane$$52\\div2=26$$metres "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1220", "queId": "d0079149418f49818f9002bbafe25deb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of three different positive even numbers could be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$19$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Addition and Subtraction Rules of Odd and Even Numbers"], "answer_analysis": ["The sum must be even, and it could be $$2+4+8=14$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1222", "queId": "fdb2555fb109470698636626803ab0d4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Della has a box of ping pong balls. Each time she counts the balls $8$ by $8$, $10$ by $10$, or $12$ by $12$, there are always $3$ balls left. How many ping pong balls are there in the box at least? ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$120$$ "}], [{"aoVal": "C", "content": "$$123$$ "}], [{"aoVal": "D", "content": "$$240$$ "}], [{"aoVal": "E", "content": "$$243$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples"], "answer_analysis": ["If the ping pong balls in the box are reduced by $3$, then there will be no extra balls when you count them $8$ by $8$, $10$ by $10$, or $12$ by $12$. It means that the number of the ping pong balls is a common multiple of $8$, $10$, and $12$ after being reduced by $3$. If you want to know how many ping pong balls there are at least, you can first find the least common multiple of $8$, $10$ and $12$, and then add $3$ to get the answer. $$\\begin{array}{l} {2\\left\\textbar{} \\underline{\\textasciitilde8\\textasciitilde\\textasciitilde10\\textasciitilde\\textasciitilde12}\\right. }\\textbackslash\\textbackslash{\\textasciitilde2\\left\\textbar{} \\underline{4\\textasciitilde\\textasciitilde\\textasciitilde5\\textasciitilde\\textasciitilde\\textasciitilde6}\\right. }\\textbackslash\\textbackslash{\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde2\\textasciitilde\\textasciitilde\\textasciitilde5\\textasciitilde\\textasciitilde\\textasciitilde3} \\end{array}$$ $2\\times2\\times2\\times5\\times3=120$ $120+3=123$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1223", "queId": "f922d32ce692422f89b2f4e4653c1c88", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many factors of $$36$$ are also multiples of $$4$$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"], "answer_analysis": ["$$36={{2}^{2}}\\times {{3}^{2}}$$, so the number of its factors would be $$\\left( 2+1 \\right)\\times \\left( 2+1 \\right)=9$$, Among them, there are $$\\left( 2+1 \\right)\\times 1=3$$ factors which has $${{2}^{2}}$$ as its factors. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1228", "queId": "eb7ab4a6fb3a4367b972ae999083e1b5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are some flowers along the corridor, arranged in the following order: $3$ red flowers, $2$ yellow flowers, $2$ pink flowers$\\cdots$ If there are $100$ flowers altogether, how many red flowers are there altogether? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$42$$ "}], [{"aoVal": "D", "content": "$$44$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"], "answer_analysis": ["$$3+2+2=7$$; $100\\div7=14R2$; $$14$$$\\times$$$3$$+$$2$$=$$44$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1231", "queId": "ddd6dae3f05744cfbcaabfef8ca06989", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three whole numbers $A$, $B$ and $C$ ($B\\neq1$). $A\\times B=55$, $B\\times C=100$. $A+B+C=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$34$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization"], "answer_analysis": ["$55=5\\times 11$ $100=2\\times 2\\times 5\\times 5$ Because $B$ is the factor both number contains, $B=5$ Thus, $A=11$, $C=20$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1234", "queId": "d962bfb1d185418291679a0df6aa8369", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In how many ways can we represent the number $$2003$$ as a sum of two prime numbers? ($$2003$$ Math Kangaroo Problems, Level $$7-8$$, Question \\#$$15$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "Such a representation is impossible. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers->Knowing Prime and Composite Numbers"], "answer_analysis": ["If so, $2$ must be one of the prime numbers, and the other must be $2003-2=2001$, which is not prime. Thus, such a representation is impossible. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1238", "queId": "d97f7924d96e4fa5a14fa572958cb541", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many of the numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, and $$9$$ can be written as a sum of exactly two of the other numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders"], "answer_analysis": ["I wrote $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, and $$9$$ on my page. Adding $$1$$ to $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, and $$8$$ results in $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, and $$9$$. We cannot get a sum of $$1$$ or $$2$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1242", "queId": "ebbf3dbaa1ce463aaed5fbbf6153ec30", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\sqrt {2\\times 4\\times 8}\\times \\sqrt {8\\times 8}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$64$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["$$\\sqrt {2\\times 4\\times 8}\\times \\sqrt {8\\times 8}=8\\times 8=64$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1243", "queId": "f04c4a3226374614ac0de3892acb8ee9", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following is an even number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$321$$ "}], [{"aoVal": "B", "content": "$$489$$ "}], [{"aoVal": "C", "content": "$$644$$ "}], [{"aoVal": "D", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers"], "answer_analysis": ["even numbers end with 0,2,4,6,8 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1246", "queId": "e2ae0df02be740c082fe6ef47bb72c8c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A three-digit number can be written as $\\overline{6\\square4}$~and this three-digit number is divisble by $4$. How many different digits can we fill in this square? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules"], "answer_analysis": ["$0, 2, 4, 6,$ and $8$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1247", "queId": "f05a81e6ae3844e99d911a1b30eaf3cc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jason has some baseball cards from the $$1920$$s. If he divides the number of cards he has by $$3$$, the remainder is $1$; if he divides the number of cards he has by $$5$$, the remainder is $3$; if he divides the number of cards he has by $$7$$, the remainder is $5$. Suppose Jason has at least $k$ cards, the sum of digits of $k$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples"], "answer_analysis": ["The number of cards after adding $$2$$ is divisible by $$3$$, $$5$$, and $$7$$. Since the least common multiple of $$3$$, $$5$$, and $$7$$ is $$3\\times5\\times7=105$$, Jason has $$105-2=103$$ cards at least. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1248", "queId": "e744c4f61a6a43049eba4ea02c64f693", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$1\\times2\\times3\\times4\\times5\\times6\\times7\\times8\\times$$$$9\\times10\\times11\\times12\\times13\\times$$$$14\\times15 = 1307 674 368000$$, how many times does the digit \"$$0$$\" appear in the product $$10\\times20\\times30\\times40\\times50\\times60\\times$$$$70\\times80\\times90\\times100\\times110\\times120\\times130\\times140\\times150$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"], "answer_analysis": ["If $$1\\times2\\times3\\times4\\times5\\times6\\times7\\times$$$$8\\times9\\times10\\times11\\times12\\times13\\times14\\times15 = $$$$1307 674 368000$$, and we multiply each of these $$15$$ numbers by $$10$$, the new product will have an additional $$15$$ zeroes, and $$15+4=19$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1250", "queId": "fe3dfc3dcc024e8fb4b995708209962b", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "Every positive integer is congruent modulo $9$ to the sum of its decimal digits. Now, let $S(n)$ equal the sum of the digits of positive integer $n$. For example, $S(1507)=13$. For a particular positive integer $n, S(n)=1274$. Which of the following could be the value of $S(n+1)$? (Adapted From 2017 AMC 12A Problems, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$1239$$ "}], [{"aoVal": "E", "content": "$$1265$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Congruence"], "answer_analysis": ["Note that $n \\equiv S(n) \\bmod 9$, so $S(n+1)-S(n) \\equiv n+1-n=1 \\bmod 9$. So, since $S(n)=1274 \\equiv 5 \\bmod 9 $, we have that $S(n+1) \\equiv 6 \\bmod 9$. Then, only one of the answer choices is congruent to $6 \\bmod 9$, which is $(D)=1239$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1253", "queId": "f52648adca084650b87310ea44861079", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many different ways are there to form a $3-$digit number without repeating digits, using $1, 2, 3, 4,$ and $0$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$125$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers"], "answer_analysis": ["$4\\times 4\\times3=48$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1255", "queId": "f52b288b0e794a4e976a98fe1aef0a9c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Arthur writes down three two-digit integers. One is square, one is prime and one is triangular. He uses the digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ and $$6$$ exactly once each. Which largest prime does he write? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$13 $$ "}], [{"aoVal": "B", "content": "$$23 $$ "}], [{"aoVal": "C", "content": "$$31 $$ "}], [{"aoVal": "D", "content": "$$41 $$ "}], [{"aoVal": "E", "content": "$$43$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Applying Special Prime Numbers"], "answer_analysis": ["First note that Arthur can write down three squares, namely $$16$$, $$25$$ and $$36$$. Also, he can write down four triangular numbers, namely $$15$$, $$21$$, $$36$$ and $$45$$. If he chooses $$16$$ and $$45$$ for the square and triangular number respectively, then the remaining digits are $$2$$ and $$3$$, the prime is $$23$$. If he chooses $$25$$ and $$36$$ then the remaining digits are $$1$$ and $$4$$, the prime is $$41$$. If he chooses $$36$$ for the square number, the remaining difits can be a prime. So the largest prime he write is $$41$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1261", "queId": "f9fc56acd87f4b108ea6959e360a450f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Each of the following products is an even number except． ", "answer_option_list": [[{"aoVal": "A", "content": "$$11\\times99$$ "}], [{"aoVal": "B", "content": "$$44\\times33$$ "}], [{"aoVal": "C", "content": "$$55\\times22$$ "}], [{"aoVal": "D", "content": "$$88\\times66$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers"], "answer_analysis": ["The product is even $$except$$ when both numbers you multiply are odd. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1263", "queId": "f0cf46c0828a4c04a06b1ca969fedc8a", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Of the following, which has an odd quotient when divided by $$2$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$456456456456456$$ "}], [{"aoVal": "B", "content": "$$678 678678678678$$ "}], [{"aoVal": "C", "content": "$$432432432432432$$ "}], [{"aoVal": "D", "content": "$$876876876 876876$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers"], "answer_analysis": ["To check for an odd quotient, divide only the last two digits by $$2$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1264", "queId": "fa18f89642e142258f81557a6e446c50", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Three different numbers are chosen from the numbers 3, 5, 6 and 8. They are then added together. Which of these statements is/are correct? \\textbf{1} The total cannot be a multiple of 8. \\textbf{2} The total can be a multiple of 3. \\textbf{3} The total is always odd. ", "answer_option_list": [[{"aoVal": "A", "content": "none of them "}], [{"aoVal": "B", "content": "statement 1 only "}], [{"aoVal": "C", "content": "statement 2 only "}], [{"aoVal": "D", "content": "statement 3 only "}], [{"aoVal": "E", "content": "statements 2 and 3 only "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules"], "answer_analysis": ["3+5+8=16，$$3+5+6=14$$，$$5+6+8=19$$，$$16$$ is a multiple of 8, (1) wrong; No multiples of 3, (2) wrong, 14,16 is even, 19 is odd. (3) Wrong "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1265", "queId": "04bd800e844c4eb98318cd63bccc406b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the angle between the hour hand and the minute hand at seven o\\textquotesingle clock? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$50^{}\\circ $ "}], [{"aoVal": "B", "content": "$120^{}\\circ $ "}], [{"aoVal": "C", "content": "$135^{}\\circ $ "}], [{"aoVal": "D", "content": "$150^{}\\circ $ "}], [{"aoVal": "E", "content": "$165^{}\\circ $ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Reading the Clock"], "answer_analysis": ["The smaller angle is $\\frac 5{12}$ of a full circle. A full circle has $360$ degrees, so the angle is $\\frac 5{12}\\times 360^{}\\circ =150^{}\\circ $. So, the answer is $\\rm D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1267", "queId": "0952e2f7c1e04e0a968c14d9ae2b5a1c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Five balls are arranged around a circle. Chris chooses two adjacent balls at random and interchanges them. Then Silva does the same, with her choice of adjacent balls to interchange being independent of Chris\\textquotesingle s. What is the expected number of balls that occupy their original positions after these two successive transpositions? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1.6$$ "}], [{"aoVal": "B", "content": "$$1.8$$ "}], [{"aoVal": "C", "content": "$$2.0$$ "}], [{"aoVal": "D", "content": "$$2.2$$ "}], [{"aoVal": "E", "content": "$$2.4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["After the first swap, we do casework on the next swap. Case 1: Silva swaps the two balls that were just swapped There is only one way for Silva to do this, and it leaves 5 balls occupying their original position. Case 2: Silva swaps one ball that has just been swapped with one that hasn\\textquotesingle t swapped There are two ways for Silva to do this, and it leaves 2 balls occupying their original positions. Case 3 : Silva swaps two balls that have not been swapped There are two ways for Silva to do this, and it leaves 1 ball occupying their original positions. Our answer is the average of all 5 possible swaps, so we get $$ \\frac{5+2 \\cdot 2+2 \\cdot 1}{5}=\\frac{11}{5}=(\\text { D) } 2.2 $$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1269", "queId": "095c9365a11842bd8ec02693f041234d", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "A robot is facing south-east. It makes 58 quarter-turns clockwise, then 93 quarter-turns anti-clockwise. In which direction is the robot now facing? ", "answer_option_list": [[{"aoVal": "A", "content": "north "}], [{"aoVal": "B", "content": "north-east "}], [{"aoVal": "C", "content": "north-west "}], [{"aoVal": "D", "content": "south-east "}], [{"aoVal": "E", "content": "south-west "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["58 quarter-turn clockwise, 93 quarter-turn anti-clockwise, is the same thing as 35 and 1/4 quarter-turn counterclockwise, 35*1/4=8 turns more than 3/4, so it is facing southwest. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1272", "queId": "00b5aa8c8c054d97ad710e37a22dda80", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "$$2006$$ students participated in a survey. The survey stated that $$1500$$ of them participated in the Math Kangaroo contest, and $$1200$$ of them participated in an English Language contest. Out of the students who participated in the survey, how many participated in both contests if it is known that $$6$$ people did not take part in either of the competitions? ($$2006$$ Math Kangaroo Problems, Level $$7-8$$, Question \\#$$5$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$300$$ "}], [{"aoVal": "B", "content": "$$500$$ "}], [{"aoVal": "C", "content": "$$600$$ "}], [{"aoVal": "D", "content": "$$700$$ "}], [{"aoVal": "E", "content": "$$1000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["$(1200+1500)-(2006-6)=700$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1276", "queId": "29dfb0c1af3749b8b0d252ca20fa93d4", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In how many ways can the letters in $BEEKBBPERPP$ be rearranged so that two or more $E$s do not appear together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$49200$$ "}], [{"aoVal": "B", "content": "$$94080$$ "}], [{"aoVal": "C", "content": "$$564480$$ "}], [{"aoVal": "D", "content": "$$1800$$ "}], [{"aoVal": "E", "content": "$$98400$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["There are $3$ $E$s in total now with other $8$ letters remaining. But pay attention to $B$ and $P$: there are $3$ $B$s and $3$ $P$ here. There are $\\_8P\\_5 \\div \\_3P\\_3$ ways for us to arrange the $8$ letters\\textquotesingle{} positions. Then, we can put the $3$ $E$s in the $9$ intervals. So the answer is $\\_8P\\_5 \\div \\_3P\\_3 \\times \\_9C\\_3=94080$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1277", "queId": "12ad6e19deca45a58a37ca39edfdd0a1", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "I have $$11$$ pieces of candy in each of three baskets. From each basket I take out one piece of candy in the following order: from the left, from the middle, from the right, from the middle, from the left, from the middle, from the right, and so on. What is the largest number of pieces of candy left in one of the baskets when the middle basket is empty? (2001 Math Kangaroo Problem, Level 3-4, Question \\#23) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"], "answer_analysis": ["Start from either the left or the right and follow the steps until the basket in the middle has $$0$$ candy. And you can see that one side has $$5$$ pieces and the other side has $$6$$ pieces. So the largest number of pieces of candy is $$6$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1278", "queId": "0154af661caf493489685fdeed9cefe8", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A positive integer divisor of $12 !$ is chosen at random. The probability that the divisor chosen is a perfect square can be expressed as $\\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. What is $m+n$?~ (2020 AMC 10A Problem, Question \\#15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The prime factorization of $12 !$ is $2^{10} \\cdot 3^{5} \\cdot 5^{2} \\cdot 7 \\cdot 11$. This yields a total of $11 \\cdot 6 \\cdot 3 \\cdot 2 \\cdot 2$ divisors of $12 !$. In order to produce a perfect square divisor, there must be an even exponent for each number in the prime factorization. Note that 7 and 11 can not be in the prime factorization of a perfect square because there is only one of each in $12 !$. Thus, there are $6 \\cdot 3 \\cdot 2$ perfect squares. (For $2$ , you can choose $0,2,4,6,8,$ or $10$, etc. The probability that the divisor chosen is a perfect square is $$ \\frac{6 \\cdot 3 \\cdot 2}{11 \\cdot 6 \\cdot 3 \\cdot 2 \\cdot 2}=\\frac{1}{22} \\Longrightarrow \\frac{m}{n}=\\frac{1}{22} \\Longrightarrow m+n=1+22=\\text { (E) } 23 $$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1279", "queId": "0157035f5a0e46019a3bb815da4c16e6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Abe has $1$ green and $1$ red jelly beans in his hand. Bob has $1$ green and $2$ yellow jelly beans in his hand. Each randomly picks a jelly bean to show to the other. What is the probability that the colours match? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "C", "content": "$\\dfrac{3}{4}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{6}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The probability that both show a green bean is $\\dfrac{1}{2}\\cdot \\dfrac{1}{3}=\\dfrac{1}{6}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1281", "queId": "053f30a1a70d45da9500bd7302b49148", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If the sum of $$9$$ consecutive odd integers is $$1935$$, what is the sum of the next $$9$$ consecutive odd integers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2015$$ "}], [{"aoVal": "B", "content": "$$2017$$ "}], [{"aoVal": "C", "content": "$$2097$$ "}], [{"aoVal": "D", "content": "$$2099$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Each number in the second sum is $$18$$ greater than the corresponding number in the first sum. Thus the second sum is $$1935 +18 \\times9 = 2097$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1288", "queId": "0205d979c62646c79a8cb2a67f24e728", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A box contains $11$ cards, numbered from $1$ to $11$. One card is selected randomly from the box. What is the probability that the number on the selected card is greater than $7$? (adapted from 2017 AMC 8 Problem, Question \\#10) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac1{11}$ "}], [{"aoVal": "B", "content": "$\\frac4{11}$ "}], [{"aoVal": "C", "content": "$\\frac7{11}$ "}], [{"aoVal": "D", "content": "$\\frac{10}{11}$ "}], [{"aoVal": "E", "content": "$\\frac2{11}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $4$ numbers greater than $7$. Thus, the probability is $\\frac4{11}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1291", "queId": "37e3034e8021449b9dd891930cc80424", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Three kids line up to play games. In how many different ways can they form the line? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$3\\times 2\\times 1=6$ There are six different ways for three kids to line up. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1292", "queId": "05d66c77d9d444ad8731ca971a2bac4d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A city has a bicycle hire scheme where it is possible to hire a bicycle for short journeys. Last year I hired a bicycle $$60$$ times and rode for $$13$$ hours altogether. For how long on average did I hire the bicycle on each ride? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ minutes "}], [{"aoVal": "B", "content": "$$23$$ minutes "}], [{"aoVal": "C", "content": "$$39$$ minutes "}], [{"aoVal": "D", "content": "$$47$$ minutes "}], [{"aoVal": "E", "content": "$$73$$ minutes "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Using Formulas"], "answer_analysis": ["The rider travels for $$13$$ hours over $$60$$ rides, which is anaverage time of $$\\frac{13}{60}$$ of an hour per ride, hence $$13$$ minutes. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1293", "queId": "05db83c4e29f42d18210eca4f2f014e3", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A $$3$$-digit integer is called a \\textquotesingle V-number\\textquotesingle{} if the digits go \\textquotesingle high-low-high\\textquotesingle{} $$-$$ that is, if the tens digit is smaller than both the hundreds digit and the units (or \\textquotesingle ones\\textquotesingle) digit. How many $$3$$-digit \\textquotesingle V-numbers\\textquotesingle{} are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$120$$ "}], [{"aoVal": "B", "content": "$$240$$ "}], [{"aoVal": "C", "content": "$$285$$ "}], [{"aoVal": "D", "content": "$$320$$ "}], [{"aoVal": "E", "content": "$$400$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers"], "answer_analysis": ["The smallest \\textquotesingle V-number\\textquotesingle{} is $$101$$ and the largest \\textquotesingle V-mumber\\textquotesingle{} is $$989$$. Consider the tens digits. The smallest tens digit is $$0$$ and the largest tens digit is $$8$$. If the tens digit is $$0$$, the hundreds digit can be $$1$$ to $$9$$, and the units digit can be $$1$$ to $$9$$, giving $$9 \\times 9$$ possible \\textquotesingle V-numbers\\textquotesingle. If the tens digit is $$1$$, then the hundreds digit can be $$2$$ to $$9$$ and the units digit can be $$2$$ to $$9$$, giving $$8 \\times 8$$ possible \\textquotesingle V-numbers\\textquotesingle. If the tens digit is $$d$$, where $$d$$ can be any digit from $$0$$ to $$8$$, the hundreds digit can be $$(d + 1)$$ to $$9$$ and the units digit can be $$(d + 1)$$ to $$9$$, giving $$(9-d)\\times (9-d)$$ possible \\textquotesingle V-numbers\\textquotesingle. The greatest value of $$d$$ is $$8$$. In this case, the hundreds digit can only be $$9$$ and the units digit can only be $$9$$, which gives just $$1 \\times 1$$ possibilities. This gives the total number of possible \\textquotesingle V-numbers\\textquotesingle{} to be $$9\\times9+8\\times8+\\cdots +1\\times1 = 285$$, which is the sum of the squares from $$1$$ to $$9$$ inclusive. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1310", "queId": "039ba083041b454d9daf238d303e28a4", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "On $2021$ December $31$\\textsuperscript{st}, Lucas, Jeremy, and Irene visited their grandpa together. Then Lucas visited him every $4$ days, Jeremy visited him every $5$ days, and Irene visited him every $6$ days. In the first three months of $2022$, how many days could the grandpa be visited by at least one person? ", "answer_option_list": [[{"aoVal": "A", "content": "$$42$$ "}], [{"aoVal": "B", "content": "$$52$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$46$$ "}], [{"aoVal": "E", "content": "$$56$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle"], "answer_analysis": ["In $31+28+31=90$ days, they could visit the grandpa in $[90\\div4]+[90\\div5]+[90\\div6]-[90\\div20]-[90\\div12]-[90\\div30]+[90\\div60]=42$ days. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1312", "queId": "067ae38142314765b853e2df8c4afe7f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Harriet tells Topaz that she is thinking of three positive integers, not necessarily all different. She tells her that the product of her three integers is $$36$$. She also tells her the sum of her three integers. However, Topaz still cannot work out what the three integers are. What is the sum of Harriet\\textquotesingle s three integers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["The possible groups of three integers with product $$36$$ are $$(1,1,36)$$, $$(1,2,18)$$, $$(1,3,12)$$, $$(1,4,9)$$, $$(1,6,6)$$, $$(2,2,9)$$, $$(2,3,6)$$ and $$(3,3,4)$$ with sums $$38$$, $$21$$, $$16$$, $$14$$, $$13$$, $$13$$, $$11$$ and $$10$$ respectively. The only value for the sum that occurs twice is $$13$$. Hence, since Topaz does not know what the three integers chosen are, the sum of Harriet\\textquotesingle s three integers is $$13$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1313", "queId": "03f24e2b684947ddad137237e64da9a0", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Find the number of positive integers from $100$ to $300$ which is divisible by $6$, $8$ and $10$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$55$$ "}], [{"aoVal": "C", "content": "$$65$$ "}], [{"aoVal": "D", "content": "$$75$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle"], "answer_analysis": ["E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1315", "queId": "0411edfcac194fb68a68370d5b91ecd8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jack, Sarah, and Jimmy participated in a maths competition. Jack says: \"I won the competition.\" Sarah says: \"I didn\\textquotesingle t win the competition.\" Jimmy says: \"Jack didn\\textquotesingle t win the competition.\" Only one of them told the truth. Who won the maths competition? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$Jack "}], [{"aoVal": "B", "content": "Sarah "}], [{"aoVal": "C", "content": "Jimmy "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis"], "answer_analysis": ["We can spot that Jack\\textquotesingle s statement and Jimmy\\textquotesingle s statement contradict each other, so one of them is telling the truth. Therefore, Sarah tells a lie. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1316", "queId": "5d090b8a9b264200a5f3a8b93136aa0b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Manjari\\textquotesingle s average score on six tests is $$82$$. Her average score on the $$7^{}\\text{th}$$ and $$8^{}\\text{th}$$ tests is $$98$$. What is her average score on all eight tests? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$86$$ "}], [{"aoVal": "B", "content": "$$88$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$94$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)"], "answer_analysis": ["Total score on the first six tests is $$6\\times82=492$$. Her total score on all eight tests is $$492+2\\times98=688$$, and her average score is $$688\\div8=86$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1317", "queId": "d99e227a9e304bad9d8c88910a642d1a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If three couples stand in a row for taking a photo, how many ways are there for only one couple to stand next to each other? ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$72$$ "}], [{"aoVal": "C", "content": "$$144$$ "}], [{"aoVal": "D", "content": "$$240$$ "}], [{"aoVal": "E", "content": "$$288$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$\\_{3}C\\_1\\times \\_{2}C\\_1\\times \\_{3}A\\_3\\times \\_{2}C\\_1=72$$, $$\\_{3}C\\_1\\times \\_{2}C\\_1\\times \\_{3}A\\_3\\times \\_{2}C\\_1\\times \\_{3}C\\_1=216$$, $$72+216=288$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1318", "queId": "06a4909db2714ddfbc124c1e99c4b849", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There is a ball in a box and three kids are guessing what colour it is. \\textbf{Val says: \"The ball is white.\"} \\textbf{John says: \"The ball is blue.\"} \\textbf{Elvis says: \"I agree with Val.\"} They open the box and find only one of them guessed right. What colour is the ball? ", "answer_option_list": [[{"aoVal": "A", "content": "white "}], [{"aoVal": "B", "content": "blue "}], [{"aoVal": "C", "content": "Uncertain "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["We can spot that Val\\textquotesingle s guess and Elvis\\textquotesingle{} guess are the same, so both of them must be wrong. Therefore, John guessed it right. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1320", "queId": "0465d313366248a38f32d92f67194828", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ming, Fanny and other $$6$$ classmates sit at a row. Ming and Fanny cannot sit at $$2$$ ends at the same time. How many sitting arrangements are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30000$$ "}], [{"aoVal": "B", "content": "$$32800$$ "}], [{"aoVal": "C", "content": "$$34800$$ "}], [{"aoVal": "D", "content": "$$38800$$ "}], [{"aoVal": "E", "content": "$$40000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"], "answer_analysis": ["$$(6\\times7+2\\times6)\\times6!=54\\times720=38800$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1321", "queId": "0472be3f385843e5a1e6469e31f9df53", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Professor Chang has ten different language books lined up on a bookshelf: three Arabic, three German, and four Spanish. How many ways are there to arrange the ten books on the shelf keeping the Arabic books together and keeping the Spanish books together? (Adapted from $2018$ AMC $8$ Problem, Question \\#$16$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1440$$ "}], [{"aoVal": "B", "content": "$$2880$$ "}], [{"aoVal": "C", "content": "$$5760$$ "}], [{"aoVal": "D", "content": "$$17280$$ "}], [{"aoVal": "E", "content": "$$34560$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["Since the three Arabic books and four Spanish books have to be kept together, respectively, we can treat them both as just one book. That means we\\textquotesingle re trying to find the number of ways you can arrange one Arabic book, one Spanish book, and three German books, which is just $\\_5P\\_5$. Now we multiply this product by $\\_3P\\_3\\times \\_4P\\_4$~because there are $\\_3P\\_3$~ways to arrange just three Arabic books, and $\\_4P\\_4$~ways to arrange just four Spanish books. Multiplying all these together, we have the answer $D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1325", "queId": "0a6eb427433742f19d55fc6459eee0c9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Marcie is $4$ years old, and Sara is $6$ years old this year. $8$ years later, what is the sum of their ages? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$26$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$4+6+8+8=26$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1330", "queId": "076002623700430abafa7409d9a67f3e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Annie has four cards of different colors. She writes letter $B$ on the red card and blue card, and writes letter $O$ on the yellow card and green card. Now Annie puts the four cards in a box. Bob is going to draw three of them from the box randomly. How many different possible results can Bob get? Among them, how many can Bob get his name? ", "answer_option_list": [[{"aoVal": "A", "content": "$6$; $3$ "}], [{"aoVal": "B", "content": "$4$; $3$ "}], [{"aoVal": "C", "content": "$6$; $2$ "}], [{"aoVal": "D", "content": "$4$; $2$ "}], [{"aoVal": "E", "content": "$6$; $1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["There are $4$ ways to choose three from four. Two $B$s with one $O$ can form Bob\\textquotesingle s name. Thus, $2$ of the $4$ ways can get Bob\\textquotesingle s name. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1331", "queId": "5d13a75eabb34e62859adb7dcb55ed31", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Among the natural numbers from $1$ to $600$, how many numbers are multiples of $3$ or $5$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$260$$ "}], [{"aoVal": "B", "content": "$$280$$ "}], [{"aoVal": "C", "content": "$$300$$ "}], [{"aoVal": "D", "content": "$$320$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["There are $200$ multiples of $3$ and there are $120$ multiples of of $5$. There are also $40$ multiples of $15$. By the Inclusion Exclusion Principle, there are $200+120-40=280$ numbers which are multiples of $3$ or $5$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1333", "queId": "133a08a2a41c43499e46350d764429d4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eddie is ordering lunch at a fast food restaurant that has sandwiches and burgers on the lunch menu, along with coffee, milk, and tea as drink options. If Eddie chooses one food item and one drink item from the lunch menu, he hasdifferent ways to order lunch. ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"], "answer_analysis": ["$$2\\times 3=6$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1336", "queId": "0ada806bb3314ed58c8a89affb1fa7c8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$17$$ balls in a bag. Each ball has a number from $$1$$ to $$17$$ on it. We randomly pick a ball from the bag. What is the smallest number of balls we have to pick in order to be sure that we have at least one pair of balls with a sum equal to $$18$$? ($$2005$$ Math Kangaroo Problem, Level $$9-10$$, Question $$ \\textbackslash\\# $$$$15$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$17$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems"], "answer_analysis": ["Among these numbers, there are $$8$$ pairs of numbers can get the sum of $$18$$($$1+17=2+16=3+15=4+14=5+13=6+12=7+11=$$$$8+10$$), and $$9$$ is useless. So in the worst case, after we choose $$9$$, we need $$8+1=9$$ more numbers to make sure a pair appears. Thus, the answer is $$1+8+1=10$$. Copyrighted material used with permission from Math Kangaroo in USA, NFP Inc. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1338", "queId": "134c9613b2024c40add3b52275740a03", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$14.81+19.28$$~\\uline{~~~~~~~~~~}~$$19.82+14.21$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\textgreater$$ "}], [{"aoVal": "B", "content": "$$\\textless$$ "}], [{"aoVal": "C", "content": "$$=$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["Isolate the decimals and whole number parts "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1340", "queId": "07b96502d055450da699b0bae764082b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A bus was supposed to arrive at Think Station at $$5:30$$ PM, but it arrived $45$ minutes earlier by changing another route because of a traffic accident. When did the bus reach Think Station? ", "answer_option_list": [[{"aoVal": "A", "content": "$5:00$ PM "}], [{"aoVal": "B", "content": "$4:30$ PM "}], [{"aoVal": "C", "content": "$4:00$ PM "}], [{"aoVal": "D", "content": "$5:30$ PM "}], [{"aoVal": "E", "content": "$4:45$ PM "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$5:30$-$45$ minutes=$4:45$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1345", "queId": "e2ee1102056d40d8b52e434231c70b40", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Miruna had to multiply two $$2$$-digit numbers together, but she accidentally reversed the digits of both of them before multiplying and reached the answer $$209$$. Which of the following answers should she have obtained? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1001$$ "}], [{"aoVal": "B", "content": "$$1003$$ "}], [{"aoVal": "C", "content": "$$1005$$ "}], [{"aoVal": "D", "content": "$$1007$$ "}], [{"aoVal": "E", "content": "$$1009$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The prime factors of $$209$$ are $$11$$ and $$19$$, so these must have been the reversed numbers that Miruna multiplied. The correct multiplication was $$11 \\times 91=1001$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1348", "queId": "f0ddab49e52748488874d3c8763f5ca1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My average score on $$8$$ math tests is $$90$$. If my average score on the first $$5$$ tests was $$87$$, what was my average score on the last $$3$$ tests? ", "answer_option_list": [[{"aoVal": "A", "content": "$$96$$ "}], [{"aoVal": "B", "content": "$$95$$ "}], [{"aoVal": "C", "content": "$$94$$ "}], [{"aoVal": "D", "content": "$$93$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["I scored a total of $$720$$ on all $$8$$ tests. The total of $$435$$ on the first $$5$$ tests leaves a total of $$285$$ for the last $$3$$ tests, so the average is $$285\\div3 = 95$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1351", "queId": "fed023e1716a41e8be1611f2ff9cf9b9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Tiffany wants to pack $$9$$ shirts into several bags. There are at least $$2$$ shirts in each bag, and the number of shirts in each bag should be different. There are~\\uline{~~~~~~~~~~}~ways to pack the shirts. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$$9=2+7=3+6=4+5$$ $$9=2+3+4$$ So there are $$3+1=4$$ ways "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1352", "queId": "c716db41d02147d6959cb8597c43b1d6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A fair $6$-sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number? (2011 AMC 8 Problems, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{6}$ "}], [{"aoVal": "B", "content": "$\\dfrac{5}{12}$ "}], [{"aoVal": "C", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "D", "content": "$\\dfrac{7}{12}$ "}], [{"aoVal": "E", "content": "$\\dfrac{5}{6}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["There are $6\\cdot 6=36$ ways to roll the two dice, and $6$ of them result in two of the same number. Out of the remaining $36-6=30$ ways, the number of rolls where the first dice is greater than the second should be the same as the number of rolls where the second dice is greater than the first. In other words, there are $\\dfrac{30}{2}=15$ ways the first roll can be greater than the second. The probability the first number is greater than or equal to the second number is $\\dfrac{15+6}{36}=\\dfrac{21}{36}=\\boxed {\\left (\\text{D}\\right )\\dfrac{7}{12}}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1354", "queId": "a6953722b07c4278bce74e9312d2334f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sophia's average score on six tests is $$82$$. Her average scores on the $$7^{}\\text{th}$$ and $$8^{}\\text{th}$$ tests is $$98$$. What is her average score on all eight tests? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$86$$ "}], [{"aoVal": "B", "content": "$$88$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$94$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Sophia\\textquotesingle s total score on the first six tests is $$6\\times82=492$$. Her total score on all eight tests is $$492+2\\times98=688$$, and her average score is $$688\\div8=86$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1355", "queId": "080c5a6a841d44479460c1fa9cf30af8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eddie finished reading a story book last week. He read an average of $19$ pages per day in the first six days of the week and $26$ pages in the last day. How many pages on average did Eddie read per day? ", "answer_option_list": [[{"aoVal": "A", "content": "$$26$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)"], "answer_analysis": ["$(19\\times6+26)\\div7=140\\div7=20$ pages. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1356", "queId": "a1f027b73aee480abb4342a10b3a9c6b", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Amy picks some number cards as shown below: $13, 20, 14, 15, 19, 20, 20, 19, 19, 15, 19, 19, 20, 13, 15$. What is the difference between their mode and median? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$19$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["She picks two $13$s, one $14$, three $15$s, five $19$s, and four $20$s. The mode is $19.$ The median is $19.$ Thus, their difference should be $0.$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1357", "queId": "0f20330907bf4b4590eb717ea38228da", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Maria arrived at the market at $$9:35$$. She spent $$1$$ hour $30$ minutes at the market, and it took her an hour to arrive home. When did she arrive home? ", "answer_option_list": [[{"aoVal": "A", "content": "$11:05$ "}], [{"aoVal": "B", "content": "$12:05$ "}], [{"aoVal": "C", "content": "$11:45$ "}], [{"aoVal": "D", "content": "$11:55$ "}], [{"aoVal": "E", "content": "$12:00$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$9:35+1:30+1=12:05$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1358", "queId": "4a9a7339031c41b5bbf6f4ac1f5986ff", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Granny has $$10$$ grandchildren. Alice is the oldest. One day, Granny notices that her grandchildren all have different ages. If the sum of her grandchildren\\textquotesingle s ages is $$180$$, what is the youngest Alice can be? (2014 Math Kangaroo Problem, Level 5-6, Question \\#30) ", "answer_option_list": [[{"aoVal": "A", "content": "$$19$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$21$$ "}], [{"aoVal": "D", "content": "$$22$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Try to consider the problem of the youngest Alice in such way: make each grandchild has a similar age as possible, and the age of each grandchild should be different, that is, $$1 + 2 + 3 +\\cdots 9 + 10 = 55$$; then $$180 - 55 = 125$$, $$125 \\div 10 = 12R5$$, and $$5$$ is left. If every child\\textquotesingle s age is added by $$12$$, then $$5$$ is left. Give the extra year to each of the $$5$$ oldest children. In doing so, the minimum age of Alice is $$10+12+1=23$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1359", "queId": "0844a58fdc814c21a814d4378ae6260b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$624\\times14 =$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$8866$$ "}], [{"aoVal": "B", "content": "$$8976$$ "}], [{"aoVal": "C", "content": "$$8736$$ "}], [{"aoVal": "D", "content": "$$8636$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["624x14=624x(10+4)=624x10+624x4=6240+2496=8736 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1375", "queId": "53e969db0c9a4d3987e65079c691e430", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Throw two dice of the same quality and size. The six sides of each die are marked with number of dots from $$1$$ to $$6$$, respectively. Among the following options,~\\uline{~~~~~~~~~~}~is an impossible event. ", "answer_option_list": [[{"aoVal": "A", "content": "The sum of dots is $$12$$. "}], [{"aoVal": "B", "content": "The sum of dots is smaller than $$3$$. "}], [{"aoVal": "C", "content": "The sum of dots is larger than $$4$$ but smaller than $$8$$. "}], [{"aoVal": "D", "content": "The sum of dots is $$13$$. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The maximum sum is $$6+6=12$$, so \"the sum of dots is $$13$$\" is an impossible event. So $$\\text{D}$$ is the answer. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1377", "queId": "b488570dfc4d42d2a506d203ff29544d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are different ways for a librarian, lending six different books to three students, given that each student gets only a book. ", "answer_option_list": [[{"aoVal": "A", "content": "$$120$$ "}], [{"aoVal": "B", "content": "$$100$$ "}], [{"aoVal": "C", "content": "$$96$$ "}], [{"aoVal": "D", "content": "$$72$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The first student has six choices of books; the second has five; and the third has four. By the Rule of product, there is a total of $$6\\times5\\times4=120$$ways. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1379", "queId": "4aa9a446b25649408e0cb10ff9f1a803", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the smallest possible sum of two positive integers whose product is $$240$$？ ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$34$$ "}], [{"aoVal": "E", "content": "$$38$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Since the product of the two positive integers is $$240$$, the possible pairs of integers are $$\\left( 1,240 \\right)$$, $$\\left( 2,120 \\right)$$, $$\\left( 3,80 \\right)$$, $$\\left( 4,60 \\right)$$, $$\\left( 5,48 \\right)$$, $$\\left( 6,40 \\right)$$, $$\\left( 8,30 \\right)$$, $$\\left( 10,24 \\right)$$, $$\\left( 12,20 \\right)$$ and $$\\left( 15,16 \\right)$$. The respective sums of these pairs are $$241$$, $$122$$, $$83$$, $$64$$, $$53$$, $$46$$, $$38$$, $$34$$, $$32$$ and $$31$$. Of these, the smallest value is $$31$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1381", "queId": "2ef69351da9f4553a18c681216ed7966", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A three-digit integer contains one of each of the digits $1,3$ , and $5$ . What is the probability that the integer is divisible by $5$ ? (2009 AMC 8 Problem, Question \\#13) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{6}$ "}], [{"aoVal": "B", "content": "$\\frac{1}{3}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{2}$ "}], [{"aoVal": "D", "content": "$\\frac{2}{3}$ "}], [{"aoVal": "E", "content": "$\\frac{5}{6}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["The three digit numbers are $135,153,351,315,513,531$. The numbers that end in 5 are divisible are 5 , and the probability of choosing those numbers is (B) $\\frac{1}{3}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1385", "queId": "0f8e863ac92a4e6fad641e6b7d9c36e8", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Timi has $8$ paintings: $3$ of them are drawing landscape, and $5$ of them are drawing figure. Among the $5$ figure paintings, there are $3$ drawing the whole family of Timi, and the other $2$ are drawing himself. Now, Timi wants to put those painting in a line. The $3$ landscape paintings cannot be adjacent. How many ways can he do this? ", "answer_option_list": [[{"aoVal": "A", "content": "$$288$$ "}], [{"aoVal": "B", "content": "$$72$$ "}], [{"aoVal": "C", "content": "$$144$$ "}], [{"aoVal": "D", "content": "$$96$$ "}], [{"aoVal": "E", "content": "$$252$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["$\\_2P\\_2\\times \\_3P\\_3 \\times \\_2P\\_2 \\times \\_3P\\_3=144$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1387", "queId": "c2774811e7cf4492bab7358efec8328a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Pip and Bud are playing a game. Each time Pip has to flip a £$$1$$ coin. If Pip gets a head, Bud will pay him £$$1$$. If Pip gets a tail, Bud will take one of her coins. After they played $$50$$ rounds, how much would you expect Pip to gain or lose? ", "answer_option_list": [[{"aoVal": "A", "content": "Gaining £$$50$$ "}], [{"aoVal": "B", "content": "Losing £$$50$$ "}], [{"aoVal": "C", "content": "Gaining £$$25$$ "}], [{"aoVal": "D", "content": "Losing £$$25$$ "}], [{"aoVal": "E", "content": "Break Even "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Nil "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1390", "queId": "339c701ce4814241aa89d67da2cf9135", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$624\\times14 =$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$8866$$ "}], [{"aoVal": "B", "content": "$$8976$$ "}], [{"aoVal": "C", "content": "$$8736$$ "}], [{"aoVal": "D", "content": "$$8636$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["624x14=624x(10+4)=624x10+624x4=6240+2496=8736 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1391", "queId": "940eb710bf0e4c969f0a6d80683aa747", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A cup costs ￡$$8$$. Which of the following payment is not correct?． ", "answer_option_list": [[{"aoVal": "A", "content": "One £5 note and three~£1 coins "}], [{"aoVal": "B", "content": "Eight £1 coins "}], [{"aoVal": "C", "content": "One £5 note and four 50p coins "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1393", "queId": "0bf9046f754a4471b80f959fc1deab1c", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Molly, Dolly, Sally, Elly and Kelly are sitting on a park bench. Molly is not sitting on the far right and Dolly is not sitting on the far left. Sally is not sitting at either end. Kelly is not sitting next to Sally and Sally is not sitting next to Dolly. Elly is sitting to the right of Dolly but not necessarily next to her. Who is sitting at the far right end? ", "answer_option_list": [[{"aoVal": "A", "content": "Molly　 "}], [{"aoVal": "B", "content": "Dolly　 "}], [{"aoVal": "C", "content": "Sally　 "}], [{"aoVal": "D", "content": "Kelly　 "}], [{"aoVal": "E", "content": "Elly　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions"], "answer_analysis": ["The question tells us that Sally is not sitting at either end. This leaves three possible positions for Sally, which we will call positions $$2$$, $$3$$ and $$4$$ from the left-hand end. Were Sally to sit in place $$2$$, neither Dolly nor Kelly could sit in places $$1$$ or $$3$$ as they cannot sit next to Sally and, since Elly must sit to the right of Dolly, there would be three people to fit into places $$4$$ and $$5$$ which is impossible. Similarly, were Sally to sit in place $$3$$, Dolly could not sit in place $$2$$ or $$4$$ and the question also tells us she cannot sit in place $$1$$ so Dolly would have to sit in place $$5$$ making it impossible for Elly to sit to the right of Dolly. However, were Sally to sit in place $$4$$, Dolly could sit in place $$2$$, Kelly in place $$1$$, Molly (who cannot sit in place $$5$$) in place $$3$$ leaving Elly to sit in place $$5$$ at the right-hand end. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1395", "queId": "25d9b777edbb40bb9133312c7fddfc9a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Only $$1$$ of the $$3$$ boys Abel, Ben and Cain can swim. Abel says, \"I can swim.\" Ben says, \"I cannot swim.\" Cain says, \"Abel cannot swim.\" Only $$1$$ boy is telling the truth. Who can swim? ． ", "answer_option_list": [[{"aoVal": "A", "content": "Abel "}], [{"aoVal": "B", "content": "Ben "}], [{"aoVal": "C", "content": "Cain "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Only $$1$$ of the $$3$$ boys can swim. Only $$1$$ of the $$3$$ boys is telling the truth! Since Abel and Cain contradict each other, there must be one who is telling the truth! If Abel is true, Ben is lying and Ben can swim. Then we have $$2$$ boys (Abel and Ben) who can swim. Contradiction. Hence, Cain is true. Abel is lying and so is Ben. Then, Ben can swim. Abel cannot swim and we are not sure if Cain can swim. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1396", "queId": "98ae7d893726419e851d82d9bd8e579e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many $3$-digit positive integers have digits whose product equals $24$ ? (2009 AMC 8 Problem, Question \\#16) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["With the digits listed from least to greatest, the $3$-digit integers are $138,146,226,234.$ $226$ can be arranged in $3$ ways, and the other three can be arranged in $6$ ways. There are $3+6(3)=(\\mathbf{D}) 21$ 3-digit positive integers. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1399", "queId": "4ab85b5025484c4e81f46e97f2783e3e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Summer has $100$ number cards each with a different number from $0$ to $99$. What is the probability that when she chooses two cards randomly, the sum of those two is an even number? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac12$ "}], [{"aoVal": "B", "content": "$\\frac13$ "}], [{"aoVal": "C", "content": "$\\frac14$ "}], [{"aoVal": "D", "content": "$\\frac16$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $50$ even number cards and $50$ odd number cards here. If she chooses odd+odd or even+even, she will get an even sum. But if she chooses odd+even or even+odd, she will get an odd sum. So each of the two probabilities is equal. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1401", "queId": "2a723ca496a240faa05641c47b6958be", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Karl, Lim, Mary and Navin are each competing in a different sporting event at the Olympic Games - basketball, swimming, taekwondo and women\\textquotesingle s rhythmic gymnastics. Karl and Navin do not know how to swim. Mary is the only female. Karl\\textquotesingle s event does not require a ball. Which event is Navin competing in? ", "answer_option_list": [[{"aoVal": "A", "content": "Basketball　 "}], [{"aoVal": "B", "content": "Swimming　 "}], [{"aoVal": "C", "content": "Taekwondo　 "}], [{"aoVal": "D", "content": "Rhythmic gymnastics　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Since \\textbf{Mary} is the only female, she must have participated in the women\\textquotesingle s\\textbf{~Rhythmic gymnastics} as the rest are males. Since Karl and Navin do not know how to swim, \\textbf{Lim} is the only male left and thus he participated in the S\\textbf{wimming} event. And since \\textbf{Karl}\\textquotesingle s event does not require a ball, he must have participated in \\textbf{Taekwondo}. We can thus conclude that \\textbf{Navin}~participated in \\textbf{Basketball}. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1402", "queId": "8f67db24827346908154ae22744a6c0e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The average of the first ten odd whole numbers is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Using Formulas"], "answer_analysis": ["We have $$\\left( 1+3+5+7+9+11+13+15+17+19 \\right)\\div 10 = 10$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1404", "queId": "6fcfbf28ebfa46e8af8e8ba5c7e9748a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Una rolls $6$ standard $6$-sided dice simultaneously and calculates the product of the $6$ numbers obtained. What is the probability that the product is divisible by $4$? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{3}{4}$ "}], [{"aoVal": "B", "content": "$\\frac{57}{64}$ "}], [{"aoVal": "C", "content": "$\\frac{59}{64}$ "}], [{"aoVal": "D", "content": "$\\frac{187}{192}$ "}], [{"aoVal": "E", "content": "$\\frac{63}{64}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["We will use complementary counting to find the probability that the product is not divisible by $4$ . Then, we can find the probability that we want by subtracting this from $1$. We split this into two cases. Case 1: The product is not divisible by $2$. We need every number to be odd, and since the chance we roll an odd number is $\\frac{1}{2}$, our probability is $\\left(\\frac{1}{2}\\right)^{6}=\\frac{1}{64}$. Case 2: The product is divisible by $2$, but not by $4$. We need 5 numbers to be odd, and one to be divisible by $2$, but not by $4$. There is a $\\frac{1}{2}$ chance that an odd number is rolled, a $\\frac{1}{3}$ chance that we roll a number satisfying the second condition (only $2$ and $6$ work), and $6$ ways to choose the order in which the even number appears. Our probability is $\\left(\\frac{1}{2}\\right)^{5}\\left(\\frac{1}{3}\\right) \\cdot 6=\\frac{1}{16}$. Therefore, the probability the product is not divisible by 4 is $\\frac{1}{64}+\\frac{1}{16}=\\frac{5}{64}$. Our answer is $1-\\frac{5}{64}=$ (C) $\\frac{59}{64}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1405", "queId": "33b032116d9c47f9a365d20e27119367", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eight students from Think Academy School take a Mathematics test. Unfortunately, none of the students wrote his/her name on the test paper. As a result, the tests are handed back to the students at random. In how many ways can exactly $5$ of the $8$ students get the correct test back? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$56$$ "}], [{"aoVal": "D", "content": "$$112$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["If exactly $5$ pupils get the correct test, then exactly $3$ pupils must get the wrong test. No. of ways to choose $5$ pupils to get the correct test is $$\\frac{8 \\times 7 \\times 6 \\times 5 \\times 4}{5 \\times 4 \\times 3 \\times 2 \\times 1}-56.$$ To make sure that the other $3$ pupils get the wrong tests, the correct number is $2$. Hence, the total no, of ways $=56 \\times2=112$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1412", "queId": "54050ebe2d11415886e5dfd23e832f54", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In how many ways can the letters in $BEEKEEPER$ be rearranged so that two or more $E$s do not appear together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["There are $5$ $E$s in total, which have $4$ intervals leaving for the other $4$ letters. Thus, the answer is $\\_4P\\_4=24$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1413", "queId": "61ecf80436b841f99f5b7ea0944d7dc6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two tiles numbered $5$ and $6$ are turned face down, respectively. One tile is turned up at random, and throw a die to get a number from $1$ to $6$. What is the probability that the product of the numbers on the tile and the die is smaller than $6$? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac {1}{2}$ "}], [{"aoVal": "B", "content": "$\\frac {1}{3}$ "}], [{"aoVal": "C", "content": "$\\frac {1}{4}$ "}], [{"aoVal": "D", "content": "$\\frac {1}{6}$ "}], [{"aoVal": "E", "content": "$\\frac {1}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $2\\times6=12$ different combinations. The product of two numbers is smaller than $6$ will be $5\\times1$. Thus, the probability is $\\frac 1{12}$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1415", "queId": "2178f62e4d294aaba57277c3e74c4223", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The mean, median, and unique mode of the positive integers $3,4,5,6,6,7$, and $x$ are all equal. What is the value of $x$ ? (2012 AMC8, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Basic Concepts of Statistics"], "answer_analysis": ["unique mode: $6$ median: $6$ $(3+4+5+6+6+7+x)\\div7=6$ $x=11$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1416", "queId": "0ca313e40ee74f7ebabdddb18382676c", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Frieda the frog begins a sequence of hops on a $3 \\times 3$ grid of squares, moving one square on each hop and choosing at random the direction of each hop-up, down, left, or right. She does not hop diagonally. When the direction of a hop would take Frieda off the grid, she \"wraps around\" and jumps to the opposite edge. For example if Frieda begins in the center square and makes two hops \"up\", the first hop would place her in the top row middle square, and the second hop would cause Frieda to jump to the opposite edge, landing in the bottom row middle square. Suppose Frieda starts from the center square, makes at most four hops at random, and stops hopping if she lands on a corner square. What is the probability that she reaches a corner square on one of the four hops? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{9}{16}$ "}], [{"aoVal": "B", "content": "$\\frac{5}{8}$ "}], [{"aoVal": "C", "content": "$\\frac{3}{4}$ "}], [{"aoVal": "D", "content": "$\\frac{25}{32}$ "}], [{"aoVal": "E", "content": "$\\frac{13}{16}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["We will use complementary counting. First, the frog can go left with probability $\\frac{1}{4}$. We observe symmetry, so our final answer will be multiplied by $4$ for the $4$ directions, and since $4 \\cdot \\frac{1}{4}=1$, we will ignore the leading probability. From the left, she either goes left to another edge $\\left(\\frac{1}{4}\\right)$ or back to the center $\\left(\\frac{1}{4}\\right)$. Time for some casework. Case 1: She goes back to the center. Now, she can go in any $4$ directions, and then has $2$ options from that edge. This gives $\\frac{1}{2}$. Case 2: She goes to another edge (rightmost). Subcase 1: She goes back to the left edge. She now has $2$ places to go, giving $\\frac{1}{2}$ Subcase 2: She goes to the center. Now any move works. $\\frac{1}{4} \\cdot \\frac{1}{2}+\\frac{1}{4} \\cdot 1=\\frac{1}{8}+\\frac{1}{4}=\\frac{3}{8}$ for this case. She goes back to the center in Case 1 with probability $\\frac{1}{4}$, and to the right edge with probability $\\frac{1}{4}$ So, our answer is $\\frac{1}{4} \\cdot \\frac{1}{2}+\\frac{1}{4} \\cdot \\frac{3}{8}=\\frac{1}{4}\\left(\\frac{1}{2}+\\frac{3}{8}\\right)=\\frac{1}{4} \\cdot \\frac{7}{8}=\\frac{7}{32}$ But, don\\textquotesingle t forget complementary counting. So, we get $1-\\frac{7}{32}=\\frac{25}{32} \\Longrightarrow D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1417", "queId": "1d05c438ac4040049c28585c96adf293", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Calculate the value of 7 + 16 + 34 + 45 + 50 - 6 - 15 - 4 - 7 ", "answer_option_list": [[{"aoVal": "A", "content": "$$70$$ "}], [{"aoVal": "B", "content": "$$120$$ "}], [{"aoVal": "C", "content": "$$127$$ "}], [{"aoVal": "D", "content": "$$124$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["7-7 + 16-6 + 34-4 + 45-15 +50 = 0+10+30+30+50 = 120 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1419", "queId": "0cc06257931d4867ab5f77b1de728476", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many whole numbers between $$1$$ and $$500$$ are divisible by $$6$$ but are not divisible by $$8$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$83$$ "}], [{"aoVal": "B", "content": "$$73$$ "}], [{"aoVal": "C", "content": "$$63$$ "}], [{"aoVal": "D", "content": "$$53$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["Every $$6$$th number $$\\left( 83 \\right.$$ of them$$\\left. {} \\right)$$ is divisible by $$6$$. Every $$24$$th number $$\\left( 20 \\right.$$ of them$$\\left. {} \\right)$$ is divisible by $$6$$ and $$8$$, and $$83-20 = 63$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1420", "queId": "189b9fa5deb741989842abeb38253e7d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There is a ball in a box and three kids are guessing what colour it is. Val says: \"The ball is white.\" John says: \"The ball is blue.\" Elvis says: \"I agree with Val.\" They open the box and find only one of them guessed right. What colour is the ball? ", "answer_option_list": [[{"aoVal": "A", "content": "white "}], [{"aoVal": "B", "content": "blue "}], [{"aoVal": "C", "content": "Uncertain "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing"], "answer_analysis": ["We can spot that Val\\textquotesingle s guess and Elvis\\textquotesingle{} guess are the same, so both of them must be wrong. Therefore, John is right. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1421", "queId": "26155f57df1044fe8b65d80d157e3d1e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A train was supposed to arrive at a $$MRT$$ station at $$5:30 \\rm pm.$$ But the train arrived half an hour early because of a traffic accident and changed another line. What time did the train reach the $$MRT$$ station? (adapted from 2008 Math kangaroo Problems, Level 3-4 , Question \\#6） ", "answer_option_list": [[{"aoVal": "A", "content": "$5:00$ pm "}], [{"aoVal": "B", "content": "$4:30$ pm "}], [{"aoVal": "C", "content": "$4:00$ pm "}], [{"aoVal": "D", "content": "$5:30$ pm "}], [{"aoVal": "E", "content": "$4:40$ pm "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$5:30$-$30$ minutes=$5:00$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1422", "queId": "2f34ef57dbb54978beb23915e44429c6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many multiples of $6$ are there between $14$ and $100$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1424", "queId": "4635e0ffe64b4ad1b58eea820cec11d1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Rose is $$150\\rm cm$$ tall. Rose\\textquotesingle s older brother Quentin is $$10 \\rm cm$$ taller than Rose is. Rose\\textquotesingle s younger brother Sam is $$4 \\rm cm$$ shorter than Rose is. What is the average of the heights of Rose, Sam, and Quentin? ", "answer_option_list": [[{"aoVal": "A", "content": "$$148\\rm cm$$ "}], [{"aoVal": "B", "content": "$$150\\rm cm$$ "}], [{"aoVal": "C", "content": "$$152\\rm cm$$ "}], [{"aoVal": "D", "content": "$$154\\rm cm$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Rose is $$150\\rm cm$$ tall. Quentin is $$10 \\rm cm$$ taller than Rose, so Quentin is $$160 \\rm cm$$ tall. Sam is $$4 \\rm cm$$ shorter than Rose, so Sam is $$146 \\rm cm$$ tall. Their average height is $$ (150+160+146)\\div3 =152 \\rm cm$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1426", "queId": "cbcf0fe7e4064cefb4735aacb69d8337", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$24$$ four-digit numbers which use each of the digits $$3$$, $$5$$, $$6$$ and $$9$$ once only. When all of these $$24$$ four-digit numbers are put in order from smallest to largest, which one is in \\emph{eighth} position? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3569$$ "}], [{"aoVal": "B", "content": "$$5369$$ "}], [{"aoVal": "C", "content": "$$5396$$ "}], [{"aoVal": "D", "content": "$$5639$$ "}], [{"aoVal": "E", "content": "$$5936$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["When put in order, the numbers are: $$3569$$, $$3596$$, $$3659$$, $$3695$$, $$3956$$, $$3965$$, $$5369$$, $$5396$$, $$5639$$, $$5693$$, $$\\ldots $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1427", "queId": "c2850df5b6554b018fa4b547356557e6", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A dataset of $9$ numbers has an average of $72$. After removing one of the numbers, the average of the remaining numbers becomes $78$. The number that gets removed is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Basic Concepts of Statistics"], "answer_analysis": ["$$9\\times72=648$$ $$78\\times8=624$$ $$648-624=24$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1431", "queId": "41a6137c21344f3e831e24cdac9d3ee9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Joann has a robot toy that can walk. The robot can only walk in straight line, and each step can only walk forward for $$1$$ cm or $$3$$ cm. If the robot walks $$4$$ steps forward, it can travel~\\uline{~~~~~~~~~~}~different distances. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$1+1+1+1=4$ $3+3+3+3=12$ $1+1+1+3=6$ $1+1+3+3=8$ $1+3+3+3=10$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1435", "queId": "2f519d73837942268a43d639a00bf2be", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, $$9$$, $$10$$, $$11$$, and $$12$$ are arranged in $3$ columns of $4$ numbers eadh so that the sum of the numbers in each column is the same. The sum of the numbers in each column is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["It\\textquotesingle s just like a magic square! The sum of all $$12$$ numbers is $$78$$. Hence, the answer is $$78\\div3 = 26$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1436", "queId": "1d3ec9e3fd7346be99b1ee542c0c0f17", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Math Town is hosting a triathlon competition (a combination of swimming, cycling, and running). The competition starts at $$9:30$$ A.M.. It takes the winner $$25$$ minutes to swim, $$1$$ hour $$10$$ minutes to cycle, and $$35$$ minutes to run. At what time does the winner complete the competition? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11:30$$ A.M. "}], [{"aoVal": "B", "content": "$$10:40$$ A.M. "}], [{"aoVal": "C", "content": "$$11:40$$ A.M. "}], [{"aoVal": "D", "content": "$$11:50$$ A.M. "}], [{"aoVal": "E", "content": "$$11:40$$ P.M. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["It takes $25+35=60$ min, which is equal to $1$ hour to swim and run. It takes $1$ h + $1$ h $10$ min = $2$ h $10$ min in total. Thus, the end time is $9:30+$$2$ h $10$ min$=11:40$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1440", "queId": "2abe574009cc4f8c8f52c19f82bbf3de", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Joann and Sana are practicing writing stories. Joann writes $6$ stories each day, and she writes $2$ more than that of Sana each day. How many stories do they write in total in one week? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$28$$ "}], [{"aoVal": "C", "content": "$$42$$ "}], [{"aoVal": "D", "content": "$$70$$ "}], [{"aoVal": "E", "content": "$$98$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$$6-2=4$$ $$6+4=10$$ $$7\\times 10=70$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1441", "queId": "8f7c27a619214f5fb14b9e526ed6e554", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A win, a loss and a draw are three outcomes of a football game: a win scores $$2$$ points, a draw scores $$1$$ point for each of two teams and a loss scores $$0$$ points. Now, $15$ teams run a single round-robin tournament. How many scores in total will all the $15$ teams get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$150$$ "}], [{"aoVal": "B", "content": "$$420$$ "}], [{"aoVal": "C", "content": "$$105$$ "}], [{"aoVal": "D", "content": "$$225$$ "}], [{"aoVal": "E", "content": "$$210$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$15\\times14\\div2\\times2=210$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1444", "queId": "21bf9f93ec02471c8f27775f464e16a0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "On a fine morning, a rabbit, a dog, a cat, and a duck went out to look for food. The rabbit said: \"If I get food, the dog will also get food.\" The dog said: \"If I get food, the cat will also get food.\" The cat said: \"If I get food, the duck will also get food.\" That evening, they found that all of them were telling the truth but only two of them did get food.~\\uline{~~~~~~~~~~}~and~\\uline{~~~~~~~~~~}~didn\\textquotesingle t get any food. ", "answer_option_list": [[{"aoVal": "A", "content": "The rabbit; the dog "}], [{"aoVal": "B", "content": "The dog; the cat "}], [{"aoVal": "C", "content": "The cat; the duck "}], [{"aoVal": "D", "content": "The cat; the rabbit "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["We can infer that if the rabbit gets food, then all of the other three would get food; if the dog gets food, then both of the cat and duck would get food. Therefore, only when the rabbit, and the dog don\\textquotesingle t get food, the cat and the duck would get food. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1445", "queId": "14bd41ec17884c6eb89863b6732ded60", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Seattle is $3$ hours behind New York. For example, when Seattle is $6$ AM, New York is $9$ AM. One day, Rosie took a flight from Seattle to New York. The flight took $$5$$ hours to reach New York, and the time was $9:40$ PM in New York when Rosie arrived. What was the time in Seattle when Rosie departed? ", "answer_option_list": [[{"aoVal": "A", "content": "$3:40$ PM "}], [{"aoVal": "B", "content": "$3:20$ PM "}], [{"aoVal": "C", "content": "$2:40$ PM "}], [{"aoVal": "D", "content": "$1:40$ PM "}], [{"aoVal": "E", "content": "$1:20$ PM "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["It\\textquotesingle s $9:40$ PM in New York, which means it\\textquotesingle s $6:40$ PM in Seattle. The plane departed at $6:40$-$5$ hours=$1:40$ PM. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1446", "queId": "38869b24001448c0b04c1830fbee4d90", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Fiona spent $$1$$ h $45$ min at the library. At the library, she spent $$30$$ min looking for reading materials. She spent the rest of the time reading them. How many minutes did Fiona spend reading? (adapted from 2011 Math kangaroo Problems, Level 3-4 , Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ min "}], [{"aoVal": "B", "content": "$$35$$ min "}], [{"aoVal": "C", "content": "$$75$$ min "}], [{"aoVal": "D", "content": "$$55$$ min "}], [{"aoVal": "E", "content": "$$65$$ min "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Time spent reading $$\\rm =1h45min-30min$$ $$\\rm =1h15min$$ $$\\rm =60min+ 15min$$ $$\\rm =75min$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1447", "queId": "10d1ffb3ab824082947c19e52983ba11", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Four friends, Edwin, Fred, Gary and Howard, were playing together when one of them broke a vase. The teacher asked,~\"Who is the culprit?\" \\textbf{Both Edwin and Howard said, \"Not me.\"} \\textbf{Fred said, \"Howard broke the vase.\"} \\textbf{Gary said, \"Fred is the culprit.\"} If only one of four boys was lying, who broke the vase? ", "answer_option_list": [[{"aoVal": "A", "content": "Edwin "}], [{"aoVal": "B", "content": "Howard "}], [{"aoVal": "C", "content": "Fred "}], [{"aoVal": "D", "content": "Gary "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Either Fred or Howard must be lying since what they said is conflicting. Since only one person was lying, Gary was telling the truth, which means Fred broke the vase. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1449", "queId": "a2132529f9e74821999fe242a6633bb1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Teacher Anderson has pens with three different colours, $$12$$ black, $$8$$ red and $$10$$ green. He put all of these pens in his pencil case. If he close his eyes and randomly pick a pen, at least how many pen he must pick to guarantee he get a red pen?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$22$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["To guarantee he get a red pen, the worse cases scenario is he picked all the green and black pens. Which is $$12+10=22$$. Then, the next pen must be the red. Thus, $$22+1=23$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1460", "queId": "58c9fdd68fe547bca3e0ec8ee1a04bf0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sophia's average score on six tests is $$82$$. Her average score on the $$7^{}\\text{th}$$ and $$8^{}\\text{th}$$ test is $$98$$. What is her average score on all eight tests? ", "answer_option_list": [[{"aoVal": "A", "content": "$$86$$ "}], [{"aoVal": "B", "content": "$$88$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$94$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Sophia\\textquotesingle s total score on the first six tests is $$6\\times82=492$$. Her total score on all eight tests is $$492+2\\times98=688$$, and her average score is $$688\\div8=86$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1461", "queId": "4f93489a6c1d44fa8e93c83f63b99903", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In my suitcase I have $$5$$ sweaters and $$6$$ pairs of pants. If I make an outfit of a sweater and a pair of pants, how many different outfits can I select? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$25$$ "}], [{"aoVal": "D", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["I have $$5$$ sweaters and $$6$$ pairs of pants. For each sweater, there are $$6$$ pairs of pants with which that sweater can be paired. There are $$5$$ sweaters, so there are $$5\\times6=30$$ different possible outfits. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1462", "queId": "58cade1f23f84cfdaf10502245c5b1b4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The time on a $$12$$-hour circular clock is $$11:00$$ A.M. When the \\emph{minute} hand goes around $$3$$ times, the time will be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$11:03$$ A.M. "}], [{"aoVal": "B", "content": "$$11:30$$ A.M. "}], [{"aoVal": "C", "content": "$$1:00$$ P.M. "}], [{"aoVal": "D", "content": "$$2:00$$ P.M. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["It takes $$3$$ hours for the \\emph{minute} hand to go around $$3$$ times, so the time will be $$2$$ P.M. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1466", "queId": "1509e9bf5500411aa92e6817da9eef2e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many ways are there to rearrange the letters in the word \\textquotesingle BEAUTY\\textquotesingle{} if the vowels are never together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$144$$ "}], [{"aoVal": "D", "content": "$$480$$ "}], [{"aoVal": "E", "content": "$$720$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$3\\times2\\times1=6$ $4\\times3\\times2=24$ $24\\times6=144$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1468", "queId": "2aed4afd23dc463cb5a65074b4a858a2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Four friends, Edwin, Fred, Gary and Howard, were playing together when one of them broke a vase. The teacher asked: \"Who is the culprit?\" Both Edwin and Howard said, \"Not me.\" Fred said, \"Howard broke the vase.\" Gary said, \"Fred is the culprit.\" If only one of four boys was lying, who broke the vase? ", "answer_option_list": [[{"aoVal": "A", "content": "Edwin "}], [{"aoVal": "B", "content": "Fred "}], [{"aoVal": "C", "content": "Gary "}], [{"aoVal": "D", "content": "Howard "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis"], "answer_analysis": ["Either Fred or Howard must be lying since what they said did not tally. Since only one person was lying, Gary was telling the truth i.e, Fred broke the vase. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1474", "queId": "19424fafba5745258fe6e0b1621cd02f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Eight pupils stand in a row to take a photo. Four of them insist on standing together. How many different ways are there to arrange them? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$120$$ "}], [{"aoVal": "C", "content": "$$576$$ "}], [{"aoVal": "D", "content": "$$2880$$ "}], [{"aoVal": "E", "content": "$$14400$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$8-4+1=5$ $5\\times4\\times3\\times2\\times1=120$ $4\\times3\\times2\\times1=24$ $120\\times24=2880$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1480", "queId": "41d870c768404e87a180fd836a93732b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two different numbers are randomly selected from the set $-2, -1, 0, 3, 4, 5$~and multiplied together. What is the probability that the product is $0$? ($2016$ AMC $8$ Problem, Question \\#$13$) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{6}$ "}], [{"aoVal": "B", "content": "$\\frac{1}{5}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{4}$ "}], [{"aoVal": "D", "content": "$\\frac{1}{3}$ "}], [{"aoVal": "E", "content": "$\\frac{1}{2}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The product can only be $0$ if one of the numbers is $0$. Once we choose $0$, there are $5$ ways of choosing the second number, and there are $15$ ways of choosing $2$ numbers randomly. Thus $\\frac{5}{15} = \\frac{1}{3}$. The answer is $D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1481", "queId": "66b9e3e4c1224fcca6d2f9216ce33271", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Four students asked their teacher, Mr. Carter, to line up with them to take a picture. ①If Mr. Carter does not want to stand on either ends, how many different ways can they line up for the picture? ②If Mr. Carter insists on standing on one of the $2$ ends, how many different ways can they line up for the picture? ", "answer_option_list": [[{"aoVal": "A", "content": "$72$ , $24$ "}], [{"aoVal": "B", "content": "$96$ , $24$ "}], [{"aoVal": "C", "content": "$72$ , $48$ "}], [{"aoVal": "D", "content": "$96$ , $48$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems"], "answer_analysis": ["①$$3\\times 4\\times 3\\times 2\\times 1=72$$ , ②$$2\\times 4\\times 3\\times 2\\times 1=48$$ . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1485", "queId": "15506ace06dc42c38384c462a87d3e64", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Molly, Dolly, Sally, Elly and Kelly are sitting on a park bench. Molly is not sitting on the far right and Dolly is not sitting on the far left. Sally is not sitting at either end. Kelly is not sitting next to Sally and Sally is not sitting next to Dolly. Elly is sitting to the right of Dolly but not necessarily next to her. Who is sitting at the far right end? ", "answer_option_list": [[{"aoVal": "A", "content": "Molly　 "}], [{"aoVal": "B", "content": "Dolly　 "}], [{"aoVal": "C", "content": "Sally　 "}], [{"aoVal": "D", "content": "Kelly　 "}], [{"aoVal": "E", "content": "Elly　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The question tells us that Sally is not sitting at either end. This leaves three possible positions for Sally, which we will call positions $$2$$, $$3$$ and $$4$$ from the left-hand end. Were Sally to sit in place $$2$$, neither Dolly nor Kelly could sit in places $$1$$ or $$3$$ as they cannot sit next to Sally and, since Elly must sit to the right of Dolly, there would be three people to fit into places $$4$$ and $$5$$ which is impossible. Similarly, were Sally to sit in place $$3$$, Dolly could not sit in place $$2$$ or $$4$$ and the question also tells us she cannot sit in place $$1$$ so Dolly would have to sit in place $$5$$ making it impossible for Elly to sit to the right of Dolly. However, were Sally to sit in place $$4$$, Dolly could sit in place $$2$$, Kelly in place $$1$$, Molly (who cannot sit in place $$5$$) in place $$3$$ leaving Elly to sit in place $$5$$ at the right-hand end. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1487", "queId": "1194be3e98bf4a57b03946c13d43f212", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The faces of each of two fair dice are numbered $1$, $2$, $3$, $5$, $7$, and $8$. When the two dice are tossed, what is the probability that their sum will be an even number? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{4}{9}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "C", "content": "$\\dfrac{5}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{3}{5}$ "}], [{"aoVal": "E", "content": "$\\dfrac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["There are two cases in which the sum can be an even number: both numbers are even and both numbers are odd. This results in only one case where the sum of the numbers are odd (one odd and one even in any order). We can solve for how many ways the $2$ numbers add up to an odd number and subtract the answer from $1$. How to solve the problem: The probability of getting an odd number first is $\\dfrac{4}{6}=\\dfrac{2}{3}$. In order to make the sum odd, we must select an even number next. The probability of getting an even number is $\\dfrac{2}{6}=\\dfrac{1}{3}$. Now we multiply the two fractions: $\\dfrac{2}{3}\\times\\dfrac{1}{3}=\\dfrac{2}{9}$. However, this is not the answer because we could pick an even number first then an odd number. The equation is the same except switched, and by the Communitive Property of Multiplication, it does not matter if the equations are switched. Thus we do $\\dfrac{2}{9}\\times2=\\dfrac{4}{9}$. This is the probability of getting an odd-number sum. In order to get the probability of getting an even number we do $1-\\dfrac{4}{9}=\\left (\\text{C}\\right )\\dfrac{5}{9}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1490", "queId": "828a960283bf45d5ab7a869505d1ee8a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eight pupils from Victory Primary School take a Mathematics test, but none of the pupils wrote his/her name on the test. The tests are therefore handed back to the pupils at random. In how many ways can exactly $5$ of the $8$ pupils get the correct test back? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$56$$ "}], [{"aoVal": "D", "content": "$$112$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"], "answer_analysis": ["If exactly $5$ pupils get the correct test, then exactly $3$ pupils must get the wrong test. No. of ways to choose $5$ pupils to get the correct test is $$\\frac{8 \\times 7 \\times 6 \\times 5 \\times 4}{5 \\times 4 \\times 3 \\times 2 \\times 1}-56.$$ To make sure that the other $3$ pupils get the wrong tests, the correct number is $2$. Hence, the total no, of ways $=56 \\times2=112$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1491", "queId": "66c640732a1446f8b4dad3d8744e6b60", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the angle between the hour hand and the minute hand at seven o\\textquotesingle clock?~ ~ ． ", "answer_option_list": [[{"aoVal": "A", "content": "$50^{}\\circ $ "}], [{"aoVal": "B", "content": "$120^{}\\circ $ "}], [{"aoVal": "C", "content": "$135^{}\\circ $ "}], [{"aoVal": "D", "content": "$150^{}\\circ $ "}], [{"aoVal": "E", "content": "$165^{}\\circ $ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Reading the Clock"], "answer_analysis": ["The smaller angle is $\\frac 5{12}$ of a full circle. A full circle has $360$ degrees, so the angle is $\\frac 5{12}\\times 360^{}\\circ =150^{}\\circ $. So, the answer is $\\rm D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1495", "queId": "198eff5c69114ce884a8cbec48e5b72e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A fair $6-$sided die is rolled twice. What is the probability that the sum of the two rolls\\textquotesingle{} outcomes is a perfect square? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{27}$ "}], [{"aoVal": "B", "content": "$\\dfrac{7}{9}$ "}], [{"aoVal": "C", "content": "$\\dfrac{7}{36}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{9}$ "}], [{"aoVal": "E", "content": "$\\dfrac{5}{18}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers"], "answer_analysis": ["There are $7$ out of $36$ outcomes are perfect squares: $1+3$, $2+2$, $3+1$, $3+6$, $4+5$, $5+4$, $6+3$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1496", "queId": "22384723f6d44875a9d57c536cb949fa", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many two-digit numbers are there where the ones digit is greater than the tens~ digit?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$26$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["$$8+7+6+5+4+3+2+1=36$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1499", "queId": "ab7155b238924018ac1b8872fe7198eb", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In how many ways can the letters in $BEEKBBPERPP$ be rearranged so that two or more $E$s do not appear together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$49200$$ "}], [{"aoVal": "B", "content": "$$94080$$ "}], [{"aoVal": "C", "content": "$$564480$$ "}], [{"aoVal": "D", "content": "$$1800$$ "}], [{"aoVal": "E", "content": "$$98400$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["There are $3$ $E$s in total now with other $8$ letters remaining. But pay attention to $B$ and $P$: there are $3$ $B$s and $3$ $P$ here. There are $\\_8P\\_5 \\div \\_3P\\_3$ ways for us to arrange the $8$ letters\\textquotesingle{} positions. Then, we can put the $3$ $E$s in the $9$ intervals. So the answer is $\\_8P\\_5 \\div \\_3P\\_3 \\times \\_9C\\_3=94080$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1501", "queId": "6b70de5c92f84217ae66e29987625519", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$150$$ students went to a $$\\text{CCA}$$ fair and all of them at least tried out one activity. $$85$$ students tried out Sports activity. $$77$$ students tried out Art activity. How many students tried out both Sport activity and Art activities? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$85+77-150=12$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1505", "queId": "1209f5e86827424f9e34aac645fcac31", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Maria went to the market at $$9:35$$ a.m. She spent $$1.5$$ hours at the market, and she took an hour to reach home. What time did she reach home? ", "answer_option_list": [[{"aoVal": "A", "content": "$11:05$ am. "}], [{"aoVal": "B", "content": "$12:05$ am. "}], [{"aoVal": "C", "content": "$11:45$ am. "}], [{"aoVal": "D", "content": "$11:55$ am. "}], [{"aoVal": "E", "content": "$12:00$ am. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$9:35+1:30+1=12:05$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1507", "queId": "15c706325c3e4d159799b40bcc65ba78", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$9+99+999+9999+99999=$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$111109$$ "}], [{"aoVal": "B", "content": "$$111119$$ "}], [{"aoVal": "C", "content": "$$111100$$ "}], [{"aoVal": "D", "content": "$$111105$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["$9+99+999+9999+99999=10+100+1000+10000+100000-5=111105$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1509", "queId": "3d75f56e1e0447acaa184dd990e73a09", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the average of $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, and $$9$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Using Formulas"], "answer_analysis": ["The average is the middle number, $$5$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1511", "queId": "345c493c39f948be8430c91b1b7490a7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Pat and Lee counted leaves on two plants. Pat\\textquotesingle s got a $$1$$-digit number. Lee got a $$3$$-digit number. If the difference between their numbers was $$91$$, what was the sum of their numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$109$$ "}], [{"aoVal": "C", "content": "$$191$$ "}], [{"aoVal": "D", "content": "$$200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle"], "answer_analysis": ["Pat and Lee counted leaves on two plants. Pat\\textquotesingle s got a $$1$$-digit number. Lee got a $$3$$-digit number. If the dīfference of the numbers was $$91$$, the numbers were $$100$$ and $$9$$, and the sum is $$109$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1520", "queId": "46a5c0c7f9034dd48ffc4c59736cb30b", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "How many whole numbers between $$1$$ and $$1000$$ do not contain the digit $$1$$? ($2009$ AMC $8$ Problems, Question \\#$22$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$512$$ "}], [{"aoVal": "B", "content": "$$648$$ "}], [{"aoVal": "C", "content": "$$720$$ "}], [{"aoVal": "D", "content": "$$728$$ "}], [{"aoVal": "E", "content": "$$800$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["One-digit number: $9-1=8$ Two-digit number: $8\\times9=72$ Three-digit number: $8\\times9\\times9=648$ So, there are $8+72+648=728$ numbers that meet the requirements. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1521", "queId": "19f895820c764ca6b019a9ca5da7e2fa", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "The product of the formula \"$486\\times$~\\uline{~~~~~~~~~~}~$5$ = $7$~\\uline{~~~~~~~~~~}~$90$\" is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$7190$$ "}], [{"aoVal": "B", "content": "$$7290$$ "}], [{"aoVal": "C", "content": "$$7390$$ "}], [{"aoVal": "D", "content": "$$7490$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (horizontal forms)"], "answer_analysis": ["$486\\times 15 = 7290$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1522", "queId": "15fed02bffce4a0abb413342397401f4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Three girls and two boys were dancing. They danced in pairs so that each girl danced with each boy for exactly one minute. At any time, there was only one pair on the dance floor. For how many minutes did they dance? (2021 Math Kangaroo Problem, Level 1-2, Question \\#21) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication->Matching Objects"], "answer_analysis": ["In total, there are $2+2+2=6$ different pairs. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1524", "queId": "8fa56af22f2349d3922d1e7a6f573ab3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "~$19+37+81=$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$130$$ "}], [{"aoVal": "B", "content": "$$137$$ "}], [{"aoVal": "C", "content": "$$138$$ "}], [{"aoVal": "D", "content": "$$129$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["$19+37+81=19+81+37=100+37=137$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1526", "queId": "98ea89280094466fb896465acb7357a5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A cuboid has a length of $2\\textasciitilde cm$, breadth of $4\\textasciitilde cm$ and a height of $8\\textasciitilde cm$. A cube has the same volume. Determine the side length of the cube. ", "answer_option_list": [[{"aoVal": "A", "content": "$3\\textasciitilde cm$ "}], [{"aoVal": "B", "content": "$4\\textasciitilde cm$ "}], [{"aoVal": "C", "content": "$5\\textasciitilde cm$ "}], [{"aoVal": "D", "content": "$6\\textasciitilde cm$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle"], "answer_analysis": ["Volume of cube $=2\\times4\\times8=64\\textasciitilde cm^{3}$ Side length of cube $=$$\\sqrt[3]{64}$$=4\\textasciitilde cm$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1528", "queId": "160d25d6a50f4c74a3ca8f2f8f889255", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$25\\times 30\\times 6=$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$5800$$ "}], [{"aoVal": "B", "content": "$$4500$$ "}], [{"aoVal": "C", "content": "$$4300$$ "}], [{"aoVal": "D", "content": "$$4750$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["$$Nil$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1530", "queId": "d08c8b7ff1fc4f8588800ece33aa8405", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "In Carl\\textquotesingle s pencil case there are nine pencils. At least one of the pencils is blue. In any group of four pencils, at least two have the same colour. In any group of five pencils, at most three have the same colour. How many pencils are blue? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "More information needed "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The information that in any group of four pencils, at least two have the same colour, tells us that there at most three different coloured pencils in Carl\\textquotesingle s pencil case. The information that in any group of five pencils, at most three have the same colour, tells us that there are at most three pencils of any single colour in the pencil case. Hence there are three pencils of each of the three different colours and so Carl\\textquotesingle s pencil case contains three blue pencils. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1534", "queId": "1a2ac73100ce4743b86be9755a52dc3f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eddie is ordering lunch at a fast food restaurant that has sandwiches and burgers on the lunch menu, along with coffee, milk, and tea as drink options. If Eddie chooses one food and one drink from the lunch menu, he hasdifferent ways to order lunch. ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"], "answer_analysis": ["$$2\\times 3=6$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1537", "queId": "66edd9443b81485587e2824db888141f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Suzie flips a fair coin $6$ times. The probability that Suzie flips $3$ heads in a row but not $4$ heads in a row is given by $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. $m+n=$~\\uline{~~~~~~~~~~}~. $\\textasciitilde$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$19$$ "}], [{"aoVal": "E", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["Consider the distribution of the three consecutive heads. We have four cases: 1110xx, 01110x, x01110, xx0111. Since case 1 and case4, case 2 and case 3 are the same, we only need to think about case 1 and case 2. The probability of case 1: $(\\dfrac{1}{2})^{4}=\\frac{1}{16}$. The probability of case 2: $(\\dfrac{1}{2})^{5}=\\frac{1}{32}$. The sum of the probabilities of 4 cases is $2\\times(\\frac{1}{16}+\\frac{1}{32})=\\frac{3}{16}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1538", "queId": "2b81f56ab7d941eeb7b7bcbc4f5f1ad5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate:~$4+5+6+\\cdots +19+20=$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$192$$ "}], [{"aoVal": "B", "content": "$$196$$ "}], [{"aoVal": "C", "content": "$$200$$ "}], [{"aoVal": "D", "content": "$$204$$ "}], [{"aoVal": "E", "content": "$$208$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$(4+20)\\times17\\div2=204$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1541", "queId": "5db2b86e09d04404a5a93012bdf2bcc8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In Tim\\textquotesingle s class, there are $$20$$ students who can swim, $$25$$ students who can play basketball, and $$10$$ students who can do both. If everyone in the class plays at least one sport, how many students are there in Tim\\textquotesingle s class?~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["$$20+25-10=35$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1543", "queId": "1a47984902454f2e81f29a50aa8dcc8f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Dexter sprinted for the first $600\\textasciitilde m$ of a race in $160\\textasciitilde s$ and jogged the remaining $\\frac{2}{5}$ of the race in $240\\textasciitilde s$. What was his average speed? ", "answer_option_list": [[{"aoVal": "A", "content": "$2.5\\textasciitilde m/s$ "}], [{"aoVal": "B", "content": "$5\\textasciitilde m/s$ "}], [{"aoVal": "C", "content": "$2\\textasciitilde m/s$ "}], [{"aoVal": "D", "content": "$0.4\\textasciitilde m/s$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle"], "answer_analysis": ["Average speed $=\\frac{Total distance}{Total Time}=\\frac{1000\\textasciitilde m}{400\\textasciitilde s}=2.5\\textasciitilde m/s$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1545", "queId": "5db9d87e4de24a34b7b2782d4397e7ed", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "April wants to split $$6$$ identical sweets into $$2$$ identical containers. How many different ways can she do so if a container can be empty? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["$$6=0+6$$ $$6=1+5$$ $$6=2+4$$ $$6=3+3$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1548", "queId": "1e87a6f10166422590055d9dd0faa9df", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many two-digit numbers are there where the ones digit is greater than the tens~ digit?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$26$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["$$8+7+6+5+4+3+2+1=36$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1550", "queId": "2736492b500848269c99e861833e77a6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Tiffany uses $3$ identical red gems, $6$ identical blue gems, and $9$ identical pearls to make a necklace. If any two gems cannot be adjacent, how many ways does she have to make the necklace? (After flipping or rotating, if two neckleces can be the same, then count them as $1$ way.) ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["The $9$ pearls should be put in each of the two gems. Thus, just consider the combination of gems: if all red gems are together, she has $1$ way; if two red gems are together, she has $3$ ways; if all the red gems are not together, the blue gems can be put $1-2-3$, $1-1-4$ or $2-2-2$, so there are $3$ ways. There are $7$ ways. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1556", "queId": "27406d2891c74876845206828df01851", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of two whole numbers is $$30$$. What is the least possible value of their sum? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$31$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Problems of Extreme Value with Fixed Products"], "answer_analysis": ["The product of two whole numbers is $$30$$. If the numbers are $$5$$ and $$6$$, their sum is $$5+6=11$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1557", "queId": "5492c26b0d0a465d9a5b59e7c1a9e536", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amos is taller than Eugene. Leo is shorter than James but taller than Eugene. James is shorter than Amos. is the tallest andis the shortest. ", "answer_option_list": [[{"aoVal": "A", "content": "Amos, James "}], [{"aoVal": "B", "content": "James, Eugene "}], [{"aoVal": "C", "content": "James, Leo "}], [{"aoVal": "D", "content": "Amos, Eugene "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["From clue $$2$$, James is taller than Leo and Leo is taller than Eugene. From clue $$3$$, Amos is taller than James. Rank from tallest to shortest: \\textbf{Amos}, James, Leo, \\textbf{Eugene}. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1559", "queId": "2bb4ee4c28de4ac4978153c8ce363882", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A meal was priced at $\\textbackslash$80$. The shop offered Jane the meal at a $40\\textbackslash\\%$ discount. After service charges of $10\\textbackslash\\%$, how much did Jane pay for her meal? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\textbackslash$48$ "}], [{"aoVal": "B", "content": "$\\textbackslash$88$ "}], [{"aoVal": "C", "content": "$\\textbackslash$35.20$ "}], [{"aoVal": "D", "content": "$\\textbackslash$52.80$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle"], "answer_analysis": ["Price after discount $=\\textbackslash$80\\times(100\\textbackslash\\%-40\\textbackslash\\%)=\\textbackslash$48$ Price after service charges $=\\textbackslash$48\\times110\\textbackslash\\%=\\textbackslash$52.80$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1566", "queId": "22fc29d7be164157b1b826e309b5b2e2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy, Bill and Celine are friends with different ages. Only one of the following statements is true. $$\\rm I$$. Bill is the oldest. $$\\rm II$$. Amy is not the oldest. $$\\rm III$$. Celine is not the youngest. Rank the friends from oldest to youngest. ", "answer_option_list": [[{"aoVal": "A", "content": "Bill, Amy, Celine "}], [{"aoVal": "B", "content": "Amy, Bill, Celine "}], [{"aoVal": "C", "content": "Celine, Amy, Bill "}], [{"aoVal": "D", "content": "Celine, Bill, Amy "}], [{"aoVal": "E", "content": "Amy, Celine, Bill "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["If Bill is the oldest, then Amy is not the oldest, and both statements $$\\rm I$$ and $$\\rm II$$ are true, so statement $$\\rm I$$ is not the true one. If Amy is not the oldest, and we know Bill cannot be the oldest, then Celine is the oldest. This would mean she is not the youngest, and both statements $$\\rm II$$ and $$\\rm III$$ are true, so statement $$\\rm II$$ is not the true one. Therefore, statement $$\\rm III$$ is the true statement, and both $$\\rm I$$ and $$\\rm II$$ are false. From this, Amy is the oldest, Celine is in the middle, and Bill is the youngest. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1567", "queId": "9da6fccd5d7c46ac920031ceebd5b866", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Express $$\\frac{7}{8}$$ as a decimal. ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.725$$ "}], [{"aoVal": "B", "content": "$$0.785$$ "}], [{"aoVal": "C", "content": "$$0.825$$ "}], [{"aoVal": "D", "content": "$$0.875$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules", "Overseas In-curriculum->Knowledge Point->Knowing Numbers->Decimals->Converting Between Fractions and Decimals->Converting Fractions to Decimals"], "answer_analysis": ["Perform long division. $7\\div8=0.875$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1568", "queId": "6705c414205b424a9575a3f6bf86ff8a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many minutes is it from $$22:45$$ today to $$00:35$$ tomorrow? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90 $$ "}], [{"aoVal": "B", "content": "$$ 100 $$ "}], [{"aoVal": "C", "content": "$$ 110 $$ "}], [{"aoVal": "D", "content": "$$120 $$ "}], [{"aoVal": "E", "content": "$$130$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["It is $$75$$ minutes from $$22:45$$ to midnight and then another $$35$$ minutes from midnight until $$00:35$$. So the required number of minutes is $$75 + 35 = 110$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1572", "queId": "1ab1a1575a38447299682886540a2baa", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many of the following statements are correct? Statement $1$: The probability of a certain event to happen is $$1$$. Statement $2$: Indefinite events include impossible events. Statement $3$: The probability of an impossible event to happen is $$0$$. Statement $4$: The probability of an indefinite event to happen is between $$0$$ and $$1$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Impossible events are definite events. $$\\text{Statement 2}$$ is wrong. $$\\text{Statement 1}$$, $$\\text{Statement 3}$$, and $$\\text{Statement 4}$$ are right. Thus, the answer is $$\\text{D}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1576", "queId": "1ab9073e2c8f4e4e95cbf3d80c638a88", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$38$$ students in the class. Each student is in either math club or music club or both. Given that among students in this class, $$26$$ students are in the math club, and $$18$$ students are in the music club, there are~\\uline{~~~~~~~~~~}~students in the math club only and not in the music club. ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$19$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$26+18-38=6$$, $$26-6=20$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1578", "queId": "c75b143de0a249769a802eb010ea57b8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of the smallest $4$-digit number and the largest $1$-digit number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$109$$ "}], [{"aoVal": "C", "content": "$$999$$ "}], [{"aoVal": "D", "content": "$$1009$$ "}], [{"aoVal": "E", "content": "$$9999$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$9+1000=1009$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1579", "queId": "3dd195b54ee647e3b0582f566e631227", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There are some pieces of candy on a table. You are challenged by your friend to play the following game: The two players take turns taking some candy. Every turn, you can take away either $$1$$, $$2$$, $$3$$, $$4$$ or $$5$$ pieces from the table. The person who takes away the final piece of candy from the table wins. If you go second, how many pieces of candy should be on the table before the game starts such that you can ensure victory? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Only $$18$$ is one of the multiples of $$5+1$$, and the second player can ensure victory. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1580", "queId": "304c78f2d1664d75a8d94f02948b37ce", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many of the following statements are current? Statement $1$: The probability of an indefinite event to happen is between $$0$$ and $$1$$. Statement $2$: The probability of an impossible event to happen is $$0$$. Statement $3$: The probability of a certain event to happen is $$1$$. Statement $4$: Indefinite events include impossible events. ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Impossible events are definite events. $$\\text{Statement 4}$$ is wrong. $$\\text{Statement 1}$$, $$\\text{Statement 2}$$, and $$\\text{Statement 3}$$ are right. Thus, the answer is $$\\text{D}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1582", "queId": "d53e329cb40d46fb8583c10a5464bc0a", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Between them, the two four-digit integers $$M$$ and $$N$$ contain all ten digits from $$1$$ to $$8$$. What is the least possible difference between $$M$$ and $$N$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$123$$ "}], [{"aoVal": "B", "content": "$$247$$ "}], [{"aoVal": "C", "content": "$$427$$ "}], [{"aoVal": "D", "content": "$$472$$ "}], [{"aoVal": "E", "content": "$$742$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value in Enumeration Problems"], "answer_analysis": ["The first digits of the two numbers will need to be as close as possible to each other. Since they cannot be equal, they will have to differ by $$1$$; say they are $$n$$ and $$n + 1$$. The difference between the two numbers will then be minimised by making the four digits after $$n + 1$$ as small as possible and the four digits after $$n$$ as large as possible. The smallest four-digit number available is $$123$$ and the largest is $$876$$. So we need to make $$n= 4$$ and then the required diference is $$5123 - 4876 = 247$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1585", "queId": "593ad6ab1b4b4c7aa94b43d7dc9de025", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eddie reads at least one chapter of a book with $$16$$ chapters each day. If he is asked to read a different number of chapters each day, this book can be finished reading for at most~\\uline{~~~~~~~~~~}~days. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"], "answer_analysis": ["$$16=1+2+3+4+6$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1587", "queId": "990883c520024355a82e294e65a222d5", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A chess singles tournament had $10$ players. Each player played with every other player only once. $2$ points are earned for winning a game, $0$ points are earned for losing a game, and $1$ point is earned by each player in a tie. After the tournament, the judge finds that the sum of these $10$ players\\textquotesingle{} points is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$180$$ "}], [{"aoVal": "B", "content": "$$100$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["There are $$10$$ players, so there are $$10\\times9\\div2=45$$ games in total. The sum of the points of two players in each game must be $2$. Thus, the sum of all points earned by $10$ players in $45$ games is $2\\times45=90$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1590", "queId": "1eef58703ef840aca99d77cba17a1232", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Hilla can make $9$ burgers every hour. In a day, she makes burgers for $6$ hours. How many burgers can she make? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$72$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$54$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["$6\\times9=54$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1595", "queId": "34e18200ccc94f538e6eec3df0880ba4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Only $$1$$ of the $$3$$ boys Abel, Ben and Charles can swim. Abel says, \"I can swim.\" Ben says, \"I cannot swim.\" Charles says, \"Abel cannot swim.\" Only $$1$$ boy is telling the truth. Who can swim? ", "answer_option_list": [[{"aoVal": "A", "content": "Abel "}], [{"aoVal": "B", "content": "Ben "}], [{"aoVal": "C", "content": "Charles "}], [{"aoVal": "D", "content": "more information needed "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Only $$1$$ of the $$3$$ boys can swim. Only $$1$$ of the $$3$$ boys is telling the truth! Since Abel and Cain contradict each other, there must be one who is telling the truth! If Abel is true, Ben is lying and Ben can swim. Then we have $$2$$ boys (Abel and Ben) who can swim. Contradiction. Hence, Cain is true. Abel is lying and so is Ben. Then, Ben can swim. Abel cannot swim and we are not sure if Cain can swim. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1598", "queId": "d9e385fcc1f4411d8d5cbbb56e2c16c3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Abby, Bret, Carl, and Dana are sitting in a row of four seats numbered $$1$$ to $$4$$. Joe looks at them and says: \"Bret is next to Carl.\" \"Abby is between Bret and Carl.\" However, all of Joe\\textquotesingle s statements are false. Bret is actually sitting in the seat $$3$$. Who is sitting in seat the $$2$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "Abby "}], [{"aoVal": "B", "content": "Bret "}], [{"aoVal": "C", "content": "Carl "}], [{"aoVal": "D", "content": "Dana "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["We know that Carl does not sit next to Bret, so he must sit in seat $$1$$. Since Abby is not between Bret and Carl, she must sit in seat $$4$$. Finally, Dana has to take the last seat available, which is $$2$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1602", "queId": "2348d3ed80f0430db07814eb49059cf2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In numbers 30 to 90, there are some two-digit numbers in which the sum of the tens digit and the ones digit is 13. How many of such numbers are there?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["49, 58, 67, 76, 85 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1604", "queId": "307019b435fa4c3fb617b6c72a1ae02b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A top hat contains $$3$$ red chips and $$2$$ green chips. Chips are drawn randomly, one at a time without replacement, until all $$3$$ of the reds are drawn or until both green chips are drawn. What is the probability that the $$3$$ reds are drawn? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3}{10}$$ "}], [{"aoVal": "B", "content": "$$\\frac{2}{5}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "D", "content": "$$\\frac{3}{5}$$ "}], [{"aoVal": "E", "content": "$$\\frac{7}{10}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability"], "answer_analysis": ["There are two ways of ending the game, either you picked out all the red chips or you picked out all the green chips. We can pick out $3$ red chips, $3$ red chips and $1$ green chip, $2$ green chips, $2$ green chips and $1$ red chip, and $2$ green chips and $2$ red chips. Because order is important in this problem, there are $1+4+1+3+6=15$ ways to pick out the chip. But we noticed that if you pick out the three red chips before you pick out the green chip, the game ends. So we need to subtract cases like that to get the total number of ways a game could end, which $15-5=10$. Out of the $10$ ways to end the game, $4$ of them ends with a green chip. The answer is $\\frac{4}{10}=\\frac{2}{5}$, or $(\\mathbf{B}) \\frac{2}{5}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1607", "queId": "30745a2d2ec5416f9de7435ca7b477a4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ali, Barb, and Cal were all born on April $$1$$, in different years. This coming April $$1$$, if I add all their ages together, I\\textquotesingle ll get $$9$$. On that day, Ali\\textquotesingle s age could not be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Ali, Barb, and Cal \\emph{were} all born on April $$1$$, in \\emph{different} years. This coming Apr $$1$$, if I add all their ages, I\\textquotesingle ll get $$9$$. Since the youngest possible ages are $$1$$ and $$2$$, the oldest possible age is $$6$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1608", "queId": "3972f893d1ee46548e5263dcefee3d7d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sophia's average score on six tests is $$82$$. Her average scores on the $$7^{}\\text{th}$$ and $$8^{}\\text{th}$$ tests is $$98$$. What is her average score on all eight tests? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$86$$ "}], [{"aoVal": "B", "content": "$$88$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$94$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Sophia\\textquotesingle s total score on the first six tests is $$6\\times82=492$$. Her total score on all eight tests is $$492+2\\times98=688$$, and her average score is $$688\\div8=86$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1609", "queId": "1f1df9e818064915906918e1d35d7c0d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$10$$ boys in Pat\\textquotesingle s math class. If there are twice as many girls as boys in the class, how many girls are there in the class? ", "answer_option_list": [[{"aoVal": "A", "content": "$$50$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["girls = $10\\times2=20$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1613", "queId": "27ae9ac7c26e4fc5929f456a790b2611", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are three boxes labeled $$A$$, $$B$$, and $$C$$. Box $$A$$ contains $$1$$ red ball and $$4$$ white balls. Box $$B$$ contains $$2$$ red balls and $$3$$ white balls. Box $$C$$ contains $$3$$ red balls. All the balls are the same except for the color. Oscar randomly selects one box and then randomly selects one ball from the selected box. What is the probability that he selects a red ball? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{6}{13}$$ "}], [{"aoVal": "B", "content": "$$\\frac{2}{5}$$ "}], [{"aoVal": "C", "content": "$$\\frac{8}{13}$$ "}], [{"aoVal": "D", "content": "$$\\frac{8}{15}$$ "}], [{"aoVal": "E", "content": "$$\\frac{11}{15}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$\\frac{1}{3}\\times \\frac{1}{5}+\\frac{1}{3}\\times \\frac{2}{5}+\\frac{1}{3}=\\frac{8}{15}$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1614", "queId": "2c0e0ff33b394d04939f900ffd4069e7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Matt had to deliver flyers to all houses numbered from 25 to 57. How many houses got th flyers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$31$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$34$$ "}], [{"aoVal": "E", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["L - F +1 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1617", "queId": "9db9f389feed49da9466ee914232281b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following expression doesn\\textquotesingle t mean the sum of 6 + 6 + 6 + 6 + 6? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6+6+6+6+6$$ "}], [{"aoVal": "B", "content": "$$5+6$$ "}], [{"aoVal": "C", "content": "$$5\\times 6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["By the meaning of multiplication, $$5\\times 6$$ means the sum of five $$6$$\\textquotesingle s. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1621", "queId": "2363fce3f68a40fea59c731f165c7aa0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many thousands of seconds are there in $$365$$ days? ", "answer_option_list": [[{"aoVal": "A", "content": "$$31536$$ "}], [{"aoVal": "B", "content": "$$525600$$ "}], [{"aoVal": "C", "content": "$$1892160$$ "}], [{"aoVal": "D", "content": "$$3536000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$365$$ days have $$365\\times24\\times60\\times60\\div1000=31536$$ thousand seconds． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1622", "queId": "2365ee15594a41aba5678ac2435010b5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There is a box contains $7$ chips numbered $1$, $2$, $3$, $4$, $5$, $6$, and $7$. A chip is drawn randomly from the box. What is the probability that the number on the chip is an even number? (adapted from 2015 AMC 8 Problem, Question \\#7) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac17$ "}], [{"aoVal": "B", "content": "$\\frac37$ "}], [{"aoVal": "C", "content": "$\\frac57$ "}], [{"aoVal": "D", "content": "$\\frac47$ "}], [{"aoVal": "E", "content": "$\\frac67$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$2$, $4$, and $6$ are even numbers. Thus, the probability is $\\frac37$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1623", "queId": "50325552e3904b0282a3ff972b178cca", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of the following outcomes is most likely? ", "answer_option_list": [[{"aoVal": "A", "content": "all $4$ are boys "}], [{"aoVal": "B", "content": "all $4$ are girls "}], [{"aoVal": "C", "content": "$2$ are girls and $2$ are boys "}], [{"aoVal": "D", "content": "$3$ are of one gender and $1$ is of the other gender "}], [{"aoVal": "E", "content": "all of these outcomes are equally likely "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["Nil "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1625", "queId": "9916d162cdb74e5bb9a3b52b5e6011f0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following statements is a certain event? ", "answer_option_list": [[{"aoVal": "A", "content": "$3$ is a factor of $98765$. "}], [{"aoVal": "B", "content": "The sum of the interior angles of a triangle is $180$°. "}], [{"aoVal": "C", "content": "The age difference between Michael and Candy will increase in $10$ years. "}], [{"aoVal": "D", "content": "Choose a $3$-digit number and it can be divided by $9$ without any remainder. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$A$ is an impossible event. $C$ is an impossible event. $D$ is a random event. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1628", "queId": "1b416ed35aec4c8eaae1050204f876ab", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eddie reads at least one chapter of a $$15-$$chapter book each day. If he is asked to read a different number of chapters each day, this book can be read for at most~\\uline{~~~~~~~~~~}~days. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"], "answer_analysis": ["$$15=1+2+3+4+5$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1631", "queId": "398a037a8d4840c58952677dcfd35257", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Seven girls and three boys are standing in a line randomly. What is the probability that three boys are next to each other? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{15}$ "}], [{"aoVal": "B", "content": "$\\dfrac{2}{15}$ "}], [{"aoVal": "C", "content": "$\\dfrac{1}{5}$ "}], [{"aoVal": "D", "content": "$\\dfrac{4}{15}$ "}], [{"aoVal": "E", "content": "$\\dfrac{1}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["$\\dfrac{A\\_8^{8}\\times A\\_3^{3}}{A\\_{10}^{10}}=\\dfrac{6}{90}=\\dfrac{1}{15}$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1632", "queId": "b4e3317cfb8b4449a3a5d4fe5aae6904", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "What is the value of the following sum? $$902+804+700+609+508+403+307+201+106$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$4450$$ "}], [{"aoVal": "B", "content": "$$4540$$ "}], [{"aoVal": "C", "content": "$$4500$$ "}], [{"aoVal": "D", "content": "$$4505$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["simple math calculation "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1635", "queId": "8fe026582403482ca9b5d36f7d7a5087", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A candy store sells some assorted candies. Each bag of assorted candies is made up of $2$ kilograms of toffee and $3$ kilograms of fruit drops. The price of toffee is $\\textbackslash$6$ per kg, and the price of fruit drops is $\\textbackslash$1$ per kg. How much is the cost of the assorted candies per kilogram? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\textbackslash$2$$ "}], [{"aoVal": "B", "content": "$$\\textbackslash$3$$ "}], [{"aoVal": "C", "content": "$$\\textbackslash$5$$ "}], [{"aoVal": "D", "content": "$$\\textbackslash$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The assorted candy weighs $2+3=5$ kg and is priced at $2\\times6+3\\times1=\\textbackslash$15$ in total. Therefore, each kilogram of the assorted candy is priced at $15\\div5=3$ dollars. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1636", "queId": "abaa0a6e489c46c5bd6a1de0b6cc0d3f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many positive integers from $1$ to $100$ do not have $2,3$ or $5$ as its factors? ", "answer_option_list": [[{"aoVal": "A", "content": "$$23$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1639", "queId": "7e47fcd395f94abda3db528bf96663ef", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Elson finished reading a storybook last week. He read an average of $19$ pages per day for the first four days of the week. He read an average of $25$ pages per day from Friday to Saturday. He did not read on Sunday. How many pages on average did Elson read per day throughout the entire week? ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$17$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$(19\\times4+25\\times2)\\div7=18$ pages. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1641", "queId": "4731ba56e521440f9160d5d0679428c3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $6$ more red fish than yellow fish in Joann\\textquotesingle s aquarium. Joann buys $8$ new red fish and $3$ new yellow fish. How many more red fish than yellow fish are in the aquarium now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$8-3=5$ $6+5=11$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1644", "queId": "be2edf07b2f44cc2bf7bfbc0b43cb4f1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Three children have $$10$$ balloons in total, and each of them has a different number of balloons. Joann has the most balloons, and at least how many balloons should she have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Splitting Whole Numbers"], "answer_analysis": ["$10=1+2+7=1+3+6=1+4+5=2+3+5$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1645", "queId": "42b39fadca61484aa4552c3b10fd8352", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Molly, Dolly, Sally, Elly and Kelly are sitting on a park bench. Molly is not sitting on the far right and Dolly is not sitting on the far left. Sally is not sitting at either end. Kelly is not sitting next to Sally and Sally is not sitting next to Dolly. Elly is sitting to the right of Dolly but not necessarily next to her. Who is sitting at the far right end? ", "answer_option_list": [[{"aoVal": "A", "content": "Molly　 "}], [{"aoVal": "B", "content": "Dolly　 "}], [{"aoVal": "C", "content": "Sally　 "}], [{"aoVal": "D", "content": "Kelly　 "}], [{"aoVal": "E", "content": "Elly　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions"], "answer_analysis": ["The question tells us that Sally is not sitting at either end. This leaves three possible positions for Sally, which we will call positions $$2$$, $$3$$ and $$4$$ from the left-hand end. Were Sally to sit in place $$2$$, neither Dolly nor Kelly could sit in places $$1$$ or $$3$$ as they cannot sit next to Sally and, since Elly must sit to the right of Dolly, there would be three people to fit into places $$4$$ and $$5$$ which is impossible. Similarly, were Sally to sit in place $$3$$, Dolly could not sit in place $$2$$ or $$4$$ and the question also tells us she cannot sit in place $$1$$ so Dolly would have to sit in place $$5$$ making it impossible for Elly to sit to the right of Dolly. However, were Sally to sit in place $$4$$, Dolly could sit in place $$2$$, Kelly in place $$1$$, Molly (who cannot sit in place $$5$$) in place $$3$$ leaving Elly to sit in place $$5$$ at the right-hand end. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1647", "queId": "5053a7942b514916bbea8bbd86d3475b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$20$$ red balls, $$2$$ black balls, and 1 white ball in a cloth bag. They are of identical shape, size and quality except for color. Take out 1 ball at random. Among the following statements, which one is true? ", "answer_option_list": [[{"aoVal": "A", "content": "The probability of taking out a black ball is the smallest. "}], [{"aoVal": "B", "content": "It\\textquotesingle s impossible to take out a white ball. "}], [{"aoVal": "C", "content": "The probability of taking out a red ball is larger. "}], [{"aoVal": "D", "content": "A red ball is surely to be taken out. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The number of red balls in the bag is the most compared with other colored balls. If we take out one ball at random, the probability of taking out a red ball is larger. So $$\\text{C}$$ is the answer. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1657", "queId": "674a40172e3f47be898041cd1f36a5b6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Joshua took a $$3$$ hours $$20$$ minutes train ride from Town $$X$$ to Town $$Y$$. The train departed at $$7:55$$ am, but stopped for $30$ minutes due to heavy rain during his trip. When did Joshua arrive in Town $$Y$$? (2009 Math kangaroo Problems, Level 3-4 , Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$11:15$ "}], [{"aoVal": "B", "content": "$10:45$ "}], [{"aoVal": "C", "content": "$10:55$ "}], [{"aoVal": "D", "content": "$11:45$ "}], [{"aoVal": "E", "content": "$10:35$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$7:55+ 3$ hours $$20$$ minutes=$11:15$ $11:15$+$30$ minutes=$11:45$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1659", "queId": "5e1ca765d89240a3bd326cca23dc8d84", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A whole number has two digits. The product of the digits of this number is 15. The sum of digits of this number is: ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["3 + 5 = 8 "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1663", "queId": "39cd74a1141f4ee3b8f79370143e4479", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Abe holds $1$ green and $1$ red jelly bean in his hand. Bob holds $1$ green, $1$ yellow, and $2$ red jelly beans in his hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match? ($2013$ AMC $8$ Problem, Question \\# $14$) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{4}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "C", "content": "$\\dfrac{3}{8}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "E", "content": "$\\dfrac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["The probability of both show a green bean is $\\dfrac{1}{2}\\times \\dfrac{1}{4}=\\dfrac{1}{8}$. The probability of both show a red bean is $\\dfrac{1}{2}\\times \\dfrac{2}{4}=\\dfrac{1}{4}$. Therefore, the probability is $\\dfrac{1}{4}+\\dfrac{1}{8}=\\boxed {\\left (\\text{C}\\right )\\dfrac{3}{8}}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1667", "queId": "23f9ae16f74c4a4fbbaf7a92242a10c0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$230\\times9 =$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2070$$ "}], [{"aoVal": "B", "content": "$$1980$$ "}], [{"aoVal": "C", "content": "$$2130$$ "}], [{"aoVal": "D", "content": "$$2240$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"], "answer_analysis": ["$$230$$x(10-1) =230x10-230x1 =2300-230 =2070 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1668", "queId": "283df565a5014b5a88c62e62616d38ce", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many whole numbers between $$5000$$ and $$6000$$ consist of four different digits that decrease from left to right? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$69$$ "}], [{"aoVal": "D", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Finding the Shortest Path by Number Notation->Finding the Shortest Path by Number Notation (with specific points or areas)"], "answer_analysis": ["The only such numbers are $$5432$$, $$5431$$, $$5430$$, $$5421$$, $$5420$$, $$5410$$, $$5321$$, $$5320$$, $$5310$$, and $$5210$$. In all, there are $$10$$ such numbers. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1671", "queId": "82fc23b75f2946c692af29fa152cc7b8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$151$$ traffic ambassadors lined up neatly in a straight line (at equal distances from each other) on a highway to promote traffic laws. After completing their task, at which position of the highway should they assemble in order to minimise their total walking distance from their respective positions to the assembly area? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$75^{}\\text{th}$$ traffic ambassador\\textquotesingle s position "}], [{"aoVal": "B", "content": "$$76^{}\\text{th}$$ traffic ambassador\\textquotesingle s position "}], [{"aoVal": "C", "content": "Between the $$75^{}\\text{th}$$ and $$76^{}\\text{th}$$ traffic ambassadors\\textquotesingle~positions "}], [{"aoVal": "D", "content": "Any position on the highway "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["There are an odd number of positions, the assembly area should be in the mid-point, $$\\left( 151+1 \\right)\\div 2=76$$, that is, the $$76^{}\\text{th}$$ traffic ambassador\\textquotesingle s position "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1672", "queId": "f12c124690ca46559a23667e9e0a469b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "One morning, a rabbit, a dog, a cat, and a duck went looking for food outside. The rabbit says: \"If I get food, the dog will also get food.\" The dog says: \"If I get food, the cat will also get food.\" The cat says: \"If I get food, the duck will also get food.\" In the evening, they find that all of them tell the truth but only two of them get food.~\\uline{~~~~~~~~~~}~and~\\uline{~~~~~~~~~~}~don\\textquotesingle t get food. ", "answer_option_list": [[{"aoVal": "A", "content": "The rabbit; the dog "}], [{"aoVal": "B", "content": "The dog; the cat "}], [{"aoVal": "C", "content": "The cat; the duck "}], [{"aoVal": "D", "content": "The cat; the rabbit "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["We can infer that if the rabbit gets food, then all of the other three would get food; if the dog gets food, then both of the cat and duck would get food. Therefore, only when the rabbit and the dog don\\textquotesingle t get food, the cat and the duck would get food. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1676", "queId": "62c81205c9d94e5a910a7e889508aa0e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sam\\textquotesingle s exam was meant to begin at $$13:45$$ but started $$17$$ minutes late. At what time did it begin?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$13:28$$ "}], [{"aoVal": "B", "content": "$$13:38$$ "}], [{"aoVal": "C", "content": "$$13:56$$ "}], [{"aoVal": "D", "content": "$$14:02$$ "}], [{"aoVal": "E", "content": "$$14:06$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["Seventeen minutes after $$13:45$$ is $$14:02$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1679", "queId": "357e06dfd883445ea9c7707e1d9d3c6c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$24$$ four-digit numbers which is formed using each of the digits $$3$$, $$4$$, $$5$$ and $$6$$ once only. When all of these $$24$$ four-digit numbers are put in order from smallest to largest, which one is in the seventh position? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3546$$ "}], [{"aoVal": "B", "content": "$$3645$$ "}], [{"aoVal": "C", "content": "$$4356$$ "}], [{"aoVal": "D", "content": "$$4536$$ "}], [{"aoVal": "E", "content": "$$5346$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["$3456, 3465, 3546, 3564, 3546, 3564$ $\\underline{4356}, 4365, 4536, 4563, 4635, 4653$ $5346, 5364, 5436, 5463, 5634, 5643$ $6345, 6354, 6435, 6453, 6534, 6543$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1680", "queId": "be4176ea62284e0f8c306760f0f6fd4f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jack enters the classroom and sees all the $6$ classmates in the classroom. How many students are there in the classroom now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "It cannot be determined. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$$6+1=7$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1681", "queId": "39fa9ae6649a44578070833ab7ef9d48", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In how many different ways can six identical coins be distributed among Al, Bo, and Carl so that each gets at least $$1$$ oin? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The only possible distributions (Al, Bo, Carl) are these ten: $$(1,1,4)$$, $$(1,2,3)$$, $$(1,3,2)$$, $$(1,4,1)$$, $$(2,1,3)$$, $$(2,2,2)$$, $$(2,3,1)$$, $$(3,1,2)$$, $$(3,2,1)$$, and $$(4,1,1)$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1683", "queId": "2433f1ce1d74454a83f1d7d9c13ff39e", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "If $$a⊕b= \\frac{1}{ \\dfrac{1}{a}+ \\dfrac{1}{b}}$$, then what is the value of $$ (1\\times2)⊕(2\\times3)⊕(3 \\times4)⊕\\ldots⊕(2013\\times2014)$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac {2013}{2014}$$ "}], [{"aoVal": "B", "content": "$$\\frac{2014}{2013}$$ "}], [{"aoVal": "C", "content": "$$\\frac{2014}{2015}$$ "}], [{"aoVal": "D", "content": "$$\\frac{2015}{2014}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Notice that $$x\\_{1}⊕x\\_{2}⊕\\ldots⊕x\\_{n}={{(\\sum\\nolimits\\_{i=1}^{n}{x\\_{i}^{-1}})}^{-1}}$$, $$\\sum\\nolimits\\_{i=1}^{n}{\\frac{1}{i(i+1)}}=\\sum\\nolimits\\_{i=1}^{n}{(\\frac{1}{1}}-\\frac{1}{i+1})=1-\\frac{1}{n+1}=\\frac{1}{n+1}$$ and so $$(1\\times 2)\\oplus (2\\times 3)\\oplus (3\\times 4)\\oplus \\cdots \\oplus (2013\\times 2014)={{(\\frac{2013}{2014})}^{-1}}=\\frac{2014}{2013}$$, This is the reason behind the pattern. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1684", "queId": "39fbf643f5bb4f00822616bd37e2438b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the angle between the hour hand and the minute hand at seven o\\textquotesingle clock?~ ~ ．(Only consider angles less than 180^{}\\circ) ", "answer_option_list": [[{"aoVal": "A", "content": "$50^{}\\circ $ "}], [{"aoVal": "B", "content": "$120^{}\\circ $ "}], [{"aoVal": "C", "content": "$135^{}\\circ $ "}], [{"aoVal": "D", "content": "$150^{}\\circ $ "}], [{"aoVal": "E", "content": "$165^{}\\circ $ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Reading the Clock"], "answer_analysis": ["The smaller angle is $\\frac 5{12}$ of a full circle. A full circle has $360$ degrees, so the angle is $\\frac 5{12}\\times 360^{}\\circ =150^{}\\circ $. So, the answer is $\\rm D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1685", "queId": "87aa3bb8e7d34e189e17dcdd165316c7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If we throw two $6-$sided dice of the same shape and size, which statements among the following options is an impossible event? ", "answer_option_list": [[{"aoVal": "A", "content": "The sum of dots is $$12$$. "}], [{"aoVal": "B", "content": "The product is a prime number. "}], [{"aoVal": "C", "content": "The sum of dots is larger than $$1$$ but smaller than $$3$$. "}], [{"aoVal": "D", "content": "The product of is $40$. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["So $$\\text{D}$$ is the answer. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1692", "queId": "3a06acae6d3e47d6b367cc69d386d382", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "The time twelve thousand and twelve hours after $$7$$ A.M. is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ A.M. "}], [{"aoVal": "B", "content": "$$7$$ P.M. "}], [{"aoVal": "C", "content": "$$7$$ A.M. "}], [{"aoVal": "D", "content": "$$7$$ P.M. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["Divide $$12012\\div24$$ to get remainder $$12$$. $$12$$ hours after $$7$$ A.M. is $$7$$ P.M. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1699", "queId": "245bf38d9b6a4d2fb44c0db8201e5aa5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$18$$ boys in Pat\\textquotesingle s math class. If there are twice as many girls as boys in the class, how many girls are there in the class? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$54$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["girls = $18\\times2=36$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1702", "queId": "35a60dfffc8c4d21bb3ee59cee37d7e9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Kevin has 3 regular dice. Each dice has numbers from 1 to 6. Which of the following could not be the sum of the numbers on top of the 3 dice? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$22$$ "}], [{"aoVal": "E", "content": "All the above numbers are possible sum "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["maximum is 6+6+6 = 18. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1703", "queId": "87b6269e455443ecac4605226e3c0771", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Veronica rolls three six-sided dice. The product of the three numbers is $$90$$. What is the sum of the three numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$90$$ "}], [{"aoVal": "E", "content": "more information is needed "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Given that the numbers on a die are $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ and $$6$$, to achieve a product of $$90$$, one of the numbers must be $$5$$ and the other two must have a product of $$18$$. Thus the numbers can only be $$3$$, $$5$$ and $$6$$ , whose sum is $$14$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1706", "queId": "3a1e941c19a746a98feed2461f1a0cd6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mike and Sara are looking for a place to eat lunch. They know there are nine Chinese restaurants, three Mexican restaurants, and two fast food restaurants nearby. How many different choices do they have in total to eat one meal? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$54$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["They can only choose one place, so it can only be Chinese, Mexican, or fast food. Therefore, we can add each one up to get $$9+3+2 = 14$$. ~ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1707", "queId": "6c14b8de695c48ae90a0617802524347", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Mary had equal number of green, yellow and red tokens. She used some of those tokens to make a pile. You can see all used tokens in the figure. She still has five tokens which are not on the pile. How many yellow tokens did she have have at the beginning? insert pic ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures->Counting Solid Figures"], "answer_analysis": ["The used tokens are 5 red tokens at the bottom, 4 green tokens and 4 yellow tokens. Now we distribute the unused 5 tokens to the 3 colors such that each color has the same number of tokens. Firstly, we need 1 more green token and 1 more yellow token to make all colors equal in number of tokens. We are left with 3 tokens, and we will equally distribute these tokens to the colors, i.e. each color will have 1 more token. Hence, the unused tokens are 1 red, 2 green and 2 yellow. There are 4+2 = 6 yellow tokens in total. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1708", "queId": "4318c317eda64578a34f69e6355509d7", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Josip has 4 toys - a car, a doll, a ball and a ship. He wants to put them on a line on a shelf. The ship has to be next to the car and the doll has to be next to the car. In how many ways can he arrange them so all the conditions would be fulfilled? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["The car is in the middle of the ship and the doll. There are 2 ways to arrange the three toys, i.e. door-call-ship and ship-car-doll. The last toy, the ball, can be placed on either of the 2 ends. Therefore, there are 2 x 2 = 4 ways to arrange the toys. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1710", "queId": "c78c3c59ee61497bbda755ce2fd68dd3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a toy store, cars are available in 5 different colours: blue, white, yellow, black and red. A car has either 2 or 4 doors. How many different version of the car are available? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["5 * 2 = 10 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1712", "queId": "6c1720a33e2e4554bbd467c0594fb8d7", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "A box contains $5$ red balls and $3$ white balls that are identical in all aspects except color. One ball is drawn at random from the box and then replaced. The box is then thoroughly shaken so that the balls are arranged at random again and a second ball is drawn randomly from the box. What is the probability of drawing white ball on both draws? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{5}{8}$$ "}], [{"aoVal": "B", "content": "$$\\frac{3}{8}$$ "}], [{"aoVal": "C", "content": "$$\\frac{25}{64}$$ "}], [{"aoVal": "D", "content": "$$\\frac{9}{64}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$D$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1721", "queId": "b070c18da2bd43158736190bd4e7702e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $6$ stairs, and you can walk for one or three staris each time. There are~\\uline{~~~~~~~~~~}~different ways to walk the $6$ stairs. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$$\\left( 1,1,1,1,1,1 \\right)$$；$$\\left( 3,1,1,1 \\right)$$；$$\\left( 1,3,1,1 \\right)$$；$$\\left( 1,1,3,1 \\right)$$；$$\\left( 1,1,1,3 \\right)$$；$$\\left( 3,3 \\right)$$． "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1722", "queId": "31679dc093494643b6e794adbadac9dc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$17$$ balls in a bag. Each ball has a number from $$1$$ to $$17$$ on it. We randomly pick a ball from the bag. What is the smallest number of balls we have to pick in order to be sure that we have at least one pair of balls with a sum equal to $$18$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Among these numbers, there are $$8$$ pairs of numbers can get the sum of $$18$$($$1+17=2+16=3+15=4+14=5+13=6+12=7+11=$$$$8+10$$), and $$9$$ is useless. So in the worst case, after we choose $$9$$, we need $$8+1=9$$ more numbers to make sure a pair appears. Thus, the answer is $$1+8+1=10$$. Copyrighted material used with permission from Math Kangaroo in USA, NFP Inc. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1727", "queId": "94bf0d44b07d4a5da9f148d4a28a50d5", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The faces of each of two fair dice are numbered $1$, $2$, $3$, $5$, $7$, and $8$. When the two dice are tossed, what is the probability that their sum will be an even number? (2019 AMC 8 Problems, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{4}{9}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "C", "content": "$\\dfrac{5}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{3}{5}$ "}], [{"aoVal": "E", "content": "$\\dfrac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["We have a 2 dice with 2 evens and 4 odds on both dice. For the sum to be even, the 2 rolls can be 2 odds or 2 evens. Ways to roll 2 odds (Case 1 ): The total number of ways to obtain 2 odds on 2 rolls is $4 * 4=16$, as there are 4 possible odds on the first roll and 4 possible odds on the second roll. Ways to roll 2 evens (Case 2 ): Similarly, we have $2 * 2=4$ ways to obtain 2 evens. Probability is $\\frac{20}{36}=\\frac{5}{9}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1728", "queId": "433c38c0d5df4ef3aeea022889e4d797", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Three kids line up to play games. In how many different ways can they form the line? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems"], "answer_analysis": ["There are $3\\times 2\\times 1=6$ different ways for three kids to line up. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1729", "queId": "94c020c6757e4b91946b6f6f46d75188", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, $$9$$, $$10$$, $$11$$, and $$12$$ are arranged in $3$ columns of $4$ numbers each so that the sum of the numbers in each column is the same. The sum of the numbers in each column is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Using Formulas"], "answer_analysis": ["It\\textquotesingle s just like a magic square! The sum of all $$12$$ numbers is $$78$$. Hence, the answer is $$78\\div3 = 26$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1733", "queId": "94c1c4d5f9814db0ab7ef45d30059df0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Mother has $$12$$ identical peaches. She wants to place them into $$3$$ identical baskets. How many ways can she place the peaches if the number of peaches in each basket cannot be zero and must be different from one other? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["Order does not matter as peaches and baskets are identical. But we need to have different number of peaches in each basket and none of the baskets can be empty. $$12=1+2+9$$ $$12=1+3+8$$ $$12=1+4+7$$ $$12=1+5+6$$ $$12=2+3+7$$ $$12=2+4+6$$ $$12=3+4+5$$ There are $$7$$ ways she can place the peaches. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1734", "queId": "28f00d1d506146e1897a8e14e321820b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Fill in the blank:~\\uline{~~~~~~~~~~}~is $2$ tens $8$ ones less than $5$ tens $5$ ones. ", "answer_option_list": [[{"aoVal": "A", "content": "$$27$$ "}], [{"aoVal": "B", "content": "$$37$$ "}], [{"aoVal": "C", "content": "$$73$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["$55 - 28 = 27$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1736", "queId": "35f1b35f04b14e8c9f52a608da0d0982", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Una rolls 6 standard 6 -sided dice simultaneously and calculates the product of the 6 numbers obtained. What is the probability that the product is divisible by 4 ? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{3}{4}$ "}], [{"aoVal": "B", "content": "$\\frac{57}{64}$ "}], [{"aoVal": "C", "content": "$\\frac{59}{64}$ "}], [{"aoVal": "D", "content": "$\\frac{187}{192}$ "}], [{"aoVal": "E", "content": "$\\frac{63}{64}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["We will use complementary counting to find the probability that the product is not divisible by 4 . Then, we can find the probability that we want by subtracting this from 1 . We split this into 2 cases. Case 1: The product is not divisible by 2. We need every number to be odd, and since the chance we roll an odd number is $\\frac{1}{2}$, our probability is $\\left(\\frac{1}{2}\\right)^{6}=\\frac{1}{64}$ Case 2: The product is divisible by 2 , but not by 4 . We need 5 numbers to be odd, and one to be divisible by 2 , but not by 4 . There is a $\\frac{1}{2}$ chance that an odd number is rolled, a $\\frac{1}{3}$ chance that we roll a number satisfying the second condition (only 2 and 6 work), and 6 ways to choose the order in which the even number appears. Our probability is $\\left(\\frac{1}{2}\\right)^{5}\\left(\\frac{1}{3}\\right) \\cdot 6=\\frac{1}{16}$. Therefore, the probability the product is not divisible by 4 is $\\frac{1}{64}+\\frac{1}{16}=\\frac{5}{64}$. Our answer is $1-\\frac{5}{64}=$ (C) $\\frac{59}{64}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1737", "queId": "318d3edaa35e404cbab437bb3c94d092", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A data set consists of~~(not distinct) positive integers: 1,7,5,2,5 and x. The average (arithmetic mean) of the~~numbers equals a value in the data set. What is the sum of all positive values of x? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$26$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$36$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$10+22+4=36$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1739", "queId": "2903d72e734d4f0e9e62c5a5d63d3bbc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If the average of two numbers is $$7$$, the numbers could be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ and $$4$$ "}], [{"aoVal": "B", "content": "$$1$$ and $$8$$ "}], [{"aoVal": "C", "content": "$$2$$ and $$14$$ "}], [{"aoVal": "D", "content": "$$6$$ and $$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["If the average of two numbers is $$7$$, their sum is $$2\\times7 = 14$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1742", "queId": "2911b7803f38479387146347299c7015", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Five balls are arranged around a circle. Chris chooses two adjacent balls at random and interchanges them. Then Silva does the same, with her choice of adjacent balls to interchange being independent of Chris\\textquotesingle s. What is the expected number of balls that occupy their original positions after these two successive transpositions? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1.6$$ "}], [{"aoVal": "B", "content": "$$1.8$$ "}], [{"aoVal": "C", "content": "$$2.0$$ "}], [{"aoVal": "D", "content": "$$2.2$$ "}], [{"aoVal": "E", "content": "$$2.4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["After the first swap, we do casework on the next swap. Case 1: Silva swaps the two balls that were just swapped There is only one way for Silva to do this, and it leaves $5$ balls occupying their original position. Case 2: Silva swaps one ball that has just been swapped with one that hasn\\textquotesingle t swapped There are two ways for Silva to do this, and it leaves $2$ balls occupying their original positions. Case 3 : Silva swaps two balls that have not been swapped There are two ways for Silva to do this, and it leaves $1$ ball occupying their original positions. Our answer is the average of all $5$ possible swaps, so we get $$ \\frac{5+2 \\cdot 2+2 \\cdot 1}{5}=\\frac{11}{5}=2.2$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1745", "queId": "70d7ac798f4f41389bd5c17998c880b4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The average mass of $$2$$ bags of flour is $$1.72 \\text{kg}$$. The mass of one of the bag of flour is $$1.68 \\text{kg}$$. What is the mass of the other bag of flour? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1.76kg$$ "}], [{"aoVal": "B", "content": "$$3.44kg$$ "}], [{"aoVal": "C", "content": "$$1.68kg$$ "}], [{"aoVal": "D", "content": "$$1.72kg$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$1.72\\times2=3.44$$ $$3.44 -1.68 = 1.76$$ The mass of the other bag of flour is $$1.76\\text{kg}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1746", "queId": "55688aaa8c5f420ea67ba8fc384dc356", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two different numbers are randomly selected from the set $-5, -3, -1, 3, 5$~and multiplied together. What is the probability that the product is a negative number?~ ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{5}{6}$ "}], [{"aoVal": "B", "content": "$\\frac{2}{5}$ "}], [{"aoVal": "C", "content": "$\\frac{3}{4}$ "}], [{"aoVal": "D", "content": "$\\frac{1}{2}$ "}], [{"aoVal": "E", "content": "$\\frac{3}{5}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$\\frac25\\times\\frac34+\\frac35\\times\\frac24=\\frac{3}{5}$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1748", "queId": "436055da612d46c0b1618ec271daea71", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Jack built a cube using 27 small cubes which are colored either black or white (see figure). No two of the small cubes which are colored in the same color have a common face. How many white cubes did Jack use? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures->Counting Solid Figures"], "answer_analysis": ["14 grey cubes and 13 white cubes. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1750", "queId": "be5f463b40014193af975ac5d1bbdd12", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I donate a ＄$$100$$ bill, $$2$$＄$$50$$ bills, $$3$$＄$$20$$ bills, $$4$$＄$$10$$ bills, and $$5$$＄$$5$$ bills. If $$5$$ people divide my money equally, each person receives． ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$37$$ "}], [{"aoVal": "B", "content": "＄$$65$$ "}], [{"aoVal": "C", "content": "＄$$70$$ "}], [{"aoVal": "D", "content": "＄$$75$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["I donate a total of ＄$$100+2\\times $$＄$$50+3\\times $$＄$$20+4\\times $$＄$$10+5\\times $$＄$$5=$$＄$$325$$. Each person receives ＄$$325 \\div5 =$$＄$$65$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1751", "queId": "67ac8ca30a5f4a5e8b15e0efc265972c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Find the number of two-digit positive integers whose digits total $7$. (2004 AMC 8 Problem, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["The numbers are $16,25,34,43,52,61,70$ which gives us a total of $(\\text{B}) 7$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1752", "queId": "9e09133b4ff0440291ebe9f67bbd206b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Rabbit Borya likes cabbages and carrots very much. In a day he eats either 9 carrots, or 2 cabbages, or 1 cabbage and 4 carrots. During one week Borya has eaten 30 carrots. How mnay cabbages has he eaten during this week? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Borya ate 30 carrots in a week, which is a number divisible by 3. On the days that he ate 9 carrots, the total number of carrots is also divisible by 3. Hence, the total number of carrots he ate on days that he ate 4 carrots must also be divisible by 3, meaning the number of days he ate 4 carrots is divisible by 3. If there were no days he ate 4 carrots, he ate 9 carrots in 30/9 days, which is impossible. If there were 6 days he ate 4 carrots, he was left with only 30-6 x 4 = 6 carrots to eat on other days, which is also impossible. therefore, he ate 4 carrots on 3 days, meaning there are \\_\\_\\_ 2 days he ate 9 carrots. There were 3 days Borya ate 1 cabbage, and 7 \\_ days he ate 2 cabbages. He ate a total of 3 + 2~ x 2 = 7 cabbages in a week. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1753", "queId": "3612e2e1b770400ebd328622a8ff2c2e", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "What is the average (mean) of all $$5-$$digit numbers that can be formed by using each of the digits $$1$$, $$3$$, $$5$$, $$7$$, and $$8$$ exactly once? ($$2005$$ AMC $$10B$$ Problem, Question \\#$$20$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$48000$$ "}], [{"aoVal": "B", "content": "$$49999.5$$ "}], [{"aoVal": "C", "content": "$$53332.8$$ "}], [{"aoVal": "D", "content": "$$55555$$ "}], [{"aoVal": "E", "content": "$$56432.8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Method $$1$$: We first look at how many times each number will appear in each slot. If we fix a number in a slot, then there are $$4!=24$$ ways to arrange the other numbers, so each number appears in each spot $$24$$ times. Therefore, the sum of all such numbers is $$24\\times (1+3+5+7+8)\\times (11111)=24\\times24\\times11111=6399936$$. Since there are $$5!=120$$ such numbers, we divide $$6399936\\div120$$~ to get $$53332.8$$. Method $$2$$: We can first solve for the mean for the digits $$1$$, $$3$$, $$5$$, $$7$$, and $$9$$ since each is $$2$$ away from each other. The mean of the numbers than can be solved using these digits is $$55555$$. The total amount of numbers that can be formed using these digits is $$5!=120$$. The sum of these numbers is $$55555(120)=6666600$$. Now we can find out the total value that was gained by replacing the $$8$$ with a $$9$$. We can start by calculating the gain when the $$8$$ was in the ones digit. Since there are $$4!=24$$ numbers with the $$8$$ in the ones digit and $$1$$ was gain from each of them, $$24$$ is the number gained. Then, we repeat this with the tens, hundreds, thousands, and ten thousands place, leading to a total of $$24+240+2400+24000+240000=266664$$ as the total amount that was gained. Subtract this amount from the sum of the digits using the~ $$9$$ instead of the $$8$$ to get $$6666600-266664=6399936$$. Finally, we divide this by $$120$$ to get the average $$\\frac{6399936}{120}=53332.8$$. Method $$3$$: The average value of the digits is $$\\frac{(1 + 3 + 5 + 7 + 8)}{5} = 4.8$$. Values occur in every place so $$4.8 \\times 11111 = 53332.8$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1755", "queId": "b9bd53e0d7154a31963c1d8e20dba6c4", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Timi has $8$ paintings: $3$ of them are drawing landscape, and $5$ of them are drawing figure. Among the $5$ figure paintings, there are $3$ drawing the whole family of Timi, and the other $2$ are drawing himself. Now, Timi wants to put those painting in a line. The $3$ landscape paintings cannot be adjacent. How many ways can he do this? ", "answer_option_list": [[{"aoVal": "A", "content": "$$288$$ "}], [{"aoVal": "B", "content": "$$72$$ "}], [{"aoVal": "C", "content": "$$144$$ "}], [{"aoVal": "D", "content": "$$96$$ "}], [{"aoVal": "E", "content": "$$252$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["$\\_2P\\_2\\times \\_3P\\_3 \\times \\_2P\\_2 \\times \\_3P\\_3=144$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1756", "queId": "59fbc19381244b308666096671fabb30", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many digits are there from $8$ to $78$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$70$$ "}], [{"aoVal": "B", "content": "$$71$$ "}], [{"aoVal": "C", "content": "$$138$$ "}], [{"aoVal": "D", "content": "$$140$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$8$ to $9 = 2$ digits $10$ to $78: 78 - 10 + 1 = 69$ numbers, $69 \\times 2 = 138$ digits $138 + 2 = 140$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1760", "queId": "b5250d41a03e44538b083c7bc79626ae", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$124$$ teams participating in a volleyball match held in the Boston. Using the single elimination method, how many games will be played in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$62$$ "}], [{"aoVal": "C", "content": "$$124$$ "}], [{"aoVal": "D", "content": "$$248$$ "}], [{"aoVal": "E", "content": "$$123$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition"], "answer_analysis": ["Single elimination tournament: $$124-1=123$$ games "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1761", "queId": "2525995aace248febca9bbcf8181eed7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2016 P2 Q6 Uncle John has a farm. His wife and his two sons are staying with him in the farm. They raise 10 cows and 20 chickens. How many total legs are there in the farm? ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$80$$ "}], [{"aoVal": "C", "content": "$$86$$ "}], [{"aoVal": "D", "content": "$$88$$ "}], [{"aoVal": "E", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["10 x 4 + 20 x 2 + 2 + 2 + 4 = 88. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1762", "queId": "70e6cf4eaab940eab0ae38b0668ca08d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Abby, Bret, Carl, and Dana are seated in a row of four seats numbered $$1$$ to $$4$$. Joe looks at them and says: ``Bret is next to Carl.\" \"Abby is between Bret and Carl.\" However, all of Joe\\textquotesingle s statements are false. Bret is actually sitting in seat $$3$$. Who is sitting in seat $$2$$? ", "answer_option_list": [[{"aoVal": "A", "content": "Abby "}], [{"aoVal": "B", "content": "Bret "}], [{"aoVal": "C", "content": "Carl "}], [{"aoVal": "D", "content": "Dana "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing"], "answer_analysis": ["We know that Carl does not sit next to Bret, so he must sit in seat $$1$$. Since Abby is not between Bret and Carl, she must sit in seat $$4$$. Finally, Dana has to take the last seat available, which is $$2$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1763", "queId": "43798c9abe88493c9e310873429ea390", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is $132$ . (2016 AMC 8 Problem, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["We can write the two digit number in the form of $10 a+b$; reverse of $10 a+b$ is $10 b+a$. The sum of those numbers is: $$ \\begin{gathered} (10 a+b)+(10 b+a)=132 \\textbackslash\\textbackslash{} 11 a+11 b=132 \\textbackslash\\textbackslash{} a+b=12 \\end{gathered} $$ We can use brute force to find order pairs $(a, b)$ such that $a+b=12$. Since $a$ and $b$ are both digits, both $a$ and $b$ have to be integers less than 10 . Thus our ordered pairs are $(3,9) ;(4,8) ;(5,7) ;(6,6) ;(7,5) ;(8,4) ;(9,3)$ or $(\\text{B}) 7$ ordered pairs. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1765", "queId": "8b9bd294693f4de888ec98e0ad2fed12", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ms. Osborne asks each student in her class to draw a rectangle with integral side lengths and a perimeter of $$50$$ units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles? ", "answer_option_list": [[{"aoVal": "A", "content": "$$76$$ "}], [{"aoVal": "B", "content": "$$120$$ "}], [{"aoVal": "C", "content": "$$128$$ "}], [{"aoVal": "D", "content": "$$132$$ "}], [{"aoVal": "E", "content": "$$136$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Geometry Modules->Objects with Straight Sides->Knowing Graphs"], "answer_analysis": ["As we know, the sum of the length and width is $$25$$. The largest area is $$13\\times12=156$$ and the smallest area is $$24\\times1=24$$, so the difference is $$156-24=132$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1767", "queId": "2d891671aff94c0ba31d6d85250c68c4", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won $$4$$ games, Ines won $$3$$ games, Janet won $$2$$ games, Kendra won $$2$$ games and Lara won $2$ games, how many games did Monica (the sixth player) win? ($$2006 \\text{ AMC } 8$$ Problem, Question \\#$$20$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["There are $$6$$ players, so there are $$6\\times5\\div2=15$$ games in total. By now, $$4+3+2+2+2=13$$ games have been finished (there is one winner in each game), so Monica needs to win $$15-13=2$$ games. Therefore, the answer is $$\\rm C$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1768", "queId": "2d8bf1c480d74fa19cf9b15144874312", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Each of $$300$$ students belongs to exactly $$2$$ of the $$5$$ school clubs. What is the average number of students in each club? ", "answer_option_list": [[{"aoVal": "A", "content": "$$50$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$120$$ "}], [{"aoVal": "D", "content": "$$150$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Since $$300$$ students belong to $$2$$ clubs each, there are $$600$$ club memberships. The average membership of the $$5$$ clubs is $$600\\div 5 = 120$$ students. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1770", "queId": "e36587c6c7b040799bc2e3c5fc7c5d12", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many terms are there in the arithmetic sequence~$2,\\textbackslash{} 5,\\textbackslash{} 8,\\textbackslash{} 11,\\textbackslash{} 14\\cdots \\textbackslash{} 95,\\textbackslash{} 98$$?$terms. ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$33$$ "}], [{"aoVal": "E", "content": "$$34$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$(98-2)\\div3+1=33$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1771", "queId": "abf1b845320044be82c69848e0b93524", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Three friends, Ms Raja, Ms Omar and Ms Beatty all live in the same street. They are a doctor, an engineer and a musician in some order. The youngest one, the doctor, does not have a brother. Ms Beatty is older than the engineer and is married to Ms Omar\\textquotesingle s brother. What are the names, in order, of the doctor and the engineer? ", "answer_option_list": [[{"aoVal": "A", "content": "Raja and Omar "}], [{"aoVal": "B", "content": "Omar and Beatty "}], [{"aoVal": "C", "content": "Beatty and Omar "}], [{"aoVal": "D", "content": "Raja and Beatty "}], [{"aoVal": "E", "content": "Omar and Raja "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing"], "answer_analysis": ["The doctor is the youngest and does not have a brother. Since Ms Omar has a brother and Ms Beatty is older than the engineer, the doctor is Ms Raja. Also, since Ms Beatty is older than the engineer she cannot be the engineer. Hence the engineer is Ms Omar. Therefore the doctor and the engineer in order are Raja and Omar. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1773", "queId": "903ded1863604801aeb335109b598651", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There were $20$ ducks, pigs, and sheep in total in Sam\\textquotesingle s farm. After Sam bought some new sheep, the number of sheep has doubled. There are $27$ ducks, pigs, and sheep in total. Originally, how many ducks and pigs were there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$27-20=7$ $7+7=14$ $27-14=13$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1775", "queId": "ecaa01c33c7a4e54a9c62bbaeca39a71", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A fair $6$-sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{6}$ "}], [{"aoVal": "B", "content": "$\\dfrac{5}{12}$ "}], [{"aoVal": "C", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "D", "content": "$\\dfrac{7}{12}$ "}], [{"aoVal": "E", "content": "$\\dfrac{5}{6}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["There are $6\\cdot 6=36$ ways to roll the two dice, and $6$ of them result in two of the same number. Out of the remaining $36-6=30$ ways, the number of rolls where the first dice is greater than the second should be the same as the number of rolls where the second dice is greater than the first. In other words, there are $\\dfrac{30}{2}=15$ ways the first roll can be greater than the second. The probability the first number is greater than or equal to the second number is $\\dfrac{15+6}{36}=\\dfrac{21}{36}=\\boxed {\\left (\\text{D}\\right )\\dfrac{7}{12}}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1777", "queId": "9e19e5df8abc4b57ba8d85a90910de5c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the angle between the hour hand and the minute hand at seven o\\textquotesingle clock?． ", "answer_option_list": [[{"aoVal": "A", "content": "$50^{}\\circ $ "}], [{"aoVal": "B", "content": "$120^{}\\circ $ "}], [{"aoVal": "C", "content": "$135^{}\\circ $ "}], [{"aoVal": "D", "content": "$150^{}\\circ $ "}], [{"aoVal": "E", "content": "$165^{}\\circ $ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The smaller angle is $\\frac 5{12}$ of a full circle. A full circle has $360$ degrees, so the angle is $\\frac 5{12}\\times 360^{}\\circ =150^{}\\circ $. So, the answer is $\\rm D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1778", "queId": "5a182ddaf3584def8a28471480816fb3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many whole numbers between $$5000$$ and $$6000$$ consist of four different digits that decrease from left to right? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$69$$ "}], [{"aoVal": "D", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The only such numbers are $$5432$$, $$5431$$, $$5430$$, $$5421$$, $$5420$$, $$5410$$, $$5321$$, $$5320$$, $$5310$$, and $$5210$$. In all, there are $$10$$ such numbers. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1779", "queId": "5ea921c71b6843c9926a5855741695a3", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Frieda the frog begins a sequence of hops on a $3 \\times 3$ grid of squares, moving one square on each hop and choosing at random the direction of each hop-up, down, left, or right. She does not hop diagonally. When the direction of a hop would take Frieda off the grid, she \"wraps around\" and jumps to the opposite edge. For example if Frieda begins in the center square and makes two hops \"up\", the first hop would place her in the top row middle square, and the second hop would cause Frieda to jump to the opposite edge, landing in the bottom row middle square. Suppose Frieda starts from the center square, makes at most four hops at random, and stops hopping if she lands on a corner square. What is the probability that she reaches a corner square on one of the four hops? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{9}{16}$ "}], [{"aoVal": "B", "content": "$\\frac{5}{8}$ "}], [{"aoVal": "C", "content": "$\\frac{3}{4}$ "}], [{"aoVal": "D", "content": "$\\frac{25}{32}$ "}], [{"aoVal": "E", "content": "$\\frac{13}{16}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["We will use complementary counting. First, the frog can go left with probability $\\frac{1}{4}$. We observe symmetry, so our final answer will be multiplied by 4 for the 4 directions, and since $4 \\cdot \\frac{1}{4}=1$, we will ignore the leading probability. From the left, she either goes left to another edge $\\left(\\frac{1}{4}\\right)$ or back to the center $\\left(\\frac{1}{4}\\right)$. Time for some casework. Case 1: She goes back to the center. Now, she can go in any 4 directions, and then has 2 options from that edge. This gives $\\frac{1}{2}$. -End case 1 Case 2: She goes to another edge (rightmost). Subcase 1: She goes back to the left edge. She now has 2 places to go, giving $\\frac{1}{2}$ Subcase 2: She goes to the center. Now any move works. $\\frac{1}{4} \\cdot \\frac{1}{2}+\\frac{1}{4} \\cdot 1=\\frac{1}{8}+\\frac{1}{4}=\\frac{3}{8}$ for this case. -End case 2 She goes back to the center in Case 1 with probability $\\frac{1}{4}$, and to the right edge with probability $\\frac{1}{4}$ So, our answer is $\\frac{1}{4} \\cdot \\frac{1}{2}+\\frac{1}{4} \\cdot \\frac{3}{8}=\\frac{1}{4}\\left(\\frac{1}{2}+\\frac{3}{8}\\right)=\\frac{1}{4} \\cdot \\frac{7}{8}=\\frac{7}{32}$ But, don\\textquotesingle t forget complementary counting. So, we get $1-\\frac{7}{32}=\\frac{25}{32} \\Longrightarrow D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1784", "queId": "559db01df85746308c15885b6063e3c3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sam\\textquotesingle s exam was meant to begin at $$13:45$$ but started $$17$$ minutes late. At what time did it begin?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$13:38$$ "}], [{"aoVal": "B", "content": "$$13:56$$ "}], [{"aoVal": "C", "content": "$$14:02$$ "}], [{"aoVal": "D", "content": "$$14:06$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["Seventeen minutes after $$13:45$$ is $$14:02$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1785", "queId": "e80d5adfd7834fe0831120d9364615c2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2014 P2 Q6 A shop sells sweets where every 3 sweet wrappers can be excanged for one more sweet. Ali has enough money to buy only 7 sweets. What is the biggest number of sweets that he can get from the shop? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["7 = 3 + 3 + 1 + (1) + (1) + (1) = 10 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1786", "queId": "3f2debe2bbf84634999aabf6179615de", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "One day, Pip asks his parents: \"What day is it today?\" His mother says: \"Today is Monday.\" His father says: \"Today is Tuesday.\" Which of the following is true? ", "answer_option_list": [[{"aoVal": "A", "content": "One of these two sentences is definitely wrong and the other one is correct. "}], [{"aoVal": "B", "content": "It is possible that both of Pip\\textquotesingle s parents are wrong. "}], [{"aoVal": "C", "content": "It is possible that both of Pip\\textquotesingle s parents are right. "}], [{"aoVal": "D", "content": "If Pip\\textquotesingle s mother is wrong, then his father must be right "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["\"Today is Monday\" is not the opposite of \"Today is Tuesday\".i.e. they can both be false. \"Today is Monday\" is the direct opposite of \"Today is not Monday\". One must be true and the other must be false. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1787", "queId": "904d2efadea04dafbbf833c3346904a9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Five students are lining up to take a picture. If Jessica is standing in the middle, and Ian is standing on either end, how many ways can the students line up? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$6$ "}], [{"aoVal": "B", "content": "$8$ "}], [{"aoVal": "C", "content": "$10$ "}], [{"aoVal": "D", "content": "$12$ "}], [{"aoVal": "E", "content": "$14$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$2\\times3\\times2\\times1=12$$ ways. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1788", "queId": "3211a6e1de4f43da89d9b02db1e1983a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A sergeant stands too long in the sun and gets confused. His troops are lined up facing north. Then he gives the order to \"Right Turn $90^{}\\circ$\" $$70$$ times, and his troops do so. In which direction are the troops facing at the end? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$north "}], [{"aoVal": "B", "content": "$$$$east "}], [{"aoVal": "C", "content": "$$$$south "}], [{"aoVal": "D", "content": "$$$$west "}], [{"aoVal": "E", "content": "$$$$west-south-west "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Directions and Coordinates->Directions"], "answer_analysis": ["After every $$4$$ \"Right turns\" the troops will be facing north again; so after $$68$$ turns they are facing north, after $$69$$ turns east, and after $$70$$ turns south. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1791", "queId": "6c6d443982e749b6b231f6357043c04a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Hansel wants to buy 2 dice of different colours. If the available colours in a store are red, blue, green, yellow, pink and white, how many different combinations of 2 dice are there in the store? (Example: 1 combination is yellow and white) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["RB, RG, RY, RP, RW BG, BY, BP, BW GY, GP, GW, YP, YW, PW "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1792", "queId": "e36f6864cf5b45538f5271f3ee2ae513", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "There is a cuboid with a dimension of $3\\times4\\times5$. Now paint all the surfaces red and cut it into many $1\\times1\\times1$ cubes. How many cubes that have two faces painted red are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Coloring Problems"], "answer_analysis": ["Remove the two cubes in both ends, and then we can get: $[(3-2)+(4-2)+(5-2)]\\times4=24$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1796", "queId": "29add6104d624851b8f8dc4e36b4b25a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sophia's average score on six tests is $$82$$. Her average scores on the $$7^{}\\text{th}$$ and $$8^{}\\text{th}$$ tests is $$98$$. What is her average score on all eight tests? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$86$$ "}], [{"aoVal": "B", "content": "$$88$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$94$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)"], "answer_analysis": ["Sophia\\textquotesingle s total score on the first six tests is $$6\\times82=492$$. Her total score on all eight tests is $$492+2\\times98=688$$, and her average score is $$688\\div8=86$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1799", "queId": "8806e80664d943e885d3c855067ffc24", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Nina and four of her friends are lining up to take a picture. If Nina has to be in the middle, how many different ways can the five friends line up? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems"], "answer_analysis": ["Since Nina has to be in the middle, then there are four friends who can line up in different ways. We can write the equation as $$4\\times3\\times2\\times1=24$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1801", "queId": "5135af6fb15744dbabf339397c68abd6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Each of Basil\\textquotesingle s friends added the number of the day and the number of the month of their birthdays and obtained $$35$$. Their birthdays all fall on different days. What is the greatest possible number of friends that Basil has? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Their birthdays could fall on $$5/30$$, $$6/29$$, $$7/28$$, $$8/27$$, $$9/26$$, $$10/25$$, $$11/24$$ and $$12/23$$ to meet the greatest possible number. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1804", "queId": "5a425a8e304c4a58985e71b2bbe3db8f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $20$ cards numbered from $1$ to $20$, respectively. What is the probability of taking out a card with a prime number? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{3}{10}$ "}], [{"aoVal": "B", "content": "$\\dfrac{7}{20}$ "}], [{"aoVal": "C", "content": "$\\dfrac{2}{5}$ "}], [{"aoVal": "D", "content": "$\\dfrac{9}{20}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["There are $8$ prime numbers in total. So, answer $= \\frac{8}{20} = \\frac{2}{5}$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1807", "queId": "6c83bf009df34c81adcf13177f3b6ee5", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "SASMO 2015 P2 Q7 Study the figures made with matchsticks below. How many matchsticks are needed to make figure 5? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$33$$ "}], [{"aoVal": "C", "content": "$$39$$ "}], [{"aoVal": "D", "content": "$$45$$ "}], [{"aoVal": "E", "content": "$$51$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures->Classifying and Enumerating->Counting Regular Figures->Counting Triangles"], "answer_analysis": ["Figure 1 = 1 triangle = 3 matchsticks Figure 2 = (1+2) triangle = 3 x 3 = 9 matchsticss. Figure 3 = (1+2+3) triangle = 6 x 3 = 18 matchsticks. Figure 4 = Figure 5 = (1+2+3+4+5) triangle = 15 x 3 = 45 matchsticks. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1810", "queId": "43dd6e1255844ac1a3fd8cefa4d0a14a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Among the natural numbers $1-75$: How many are divisible by $3$ or $5$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["All natural numbers divisible by $3$ in the range of $1-75$ are：$75\\div3=25$． All natural numbers divisible by $5$ in the range of $1-75$ are：$75\\div5=15$． The natural numbers divisible by 3 and 5 that are divisible by $15$：$75\\div15=5$． The natural numbers divisible by $3$ or $5$ are：$25+15-5=35$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1819", "queId": "b54a0a7bd7fa4a1fba3968a9f604e30a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Miruna had to multiply two $$2$$-digit numbers together, but she accidentally reversed the digits of both of them before multiplying and reached the answer $$209$$. Which of the following answers should she have got? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1001$$ "}], [{"aoVal": "B", "content": "$$1003$$ "}], [{"aoVal": "C", "content": "$$1005$$ "}], [{"aoVal": "D", "content": "$$1007$$ "}], [{"aoVal": "E", "content": "$$1009$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Splitting Whole Numbers"], "answer_analysis": ["The prime factors of $$209$$ are $$11$$ and $$19$$, so these must have been the reversed numbers that Miruna multiplied. The correct multiplication was $$11 \\times 91=1001$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1820", "queId": "43ef7192dbc840abbe82c2fa34a0cba5", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The product of three consecutive numbers is $$15600$$. What is their sum? ", "answer_option_list": [[{"aoVal": "A", "content": "$$75$$ "}], [{"aoVal": "B", "content": "$$78$$ "}], [{"aoVal": "C", "content": "$$81$$ "}], [{"aoVal": "D", "content": "$$84$$ "}], [{"aoVal": "E", "content": "$$87$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Splitting Whole Numbers"], "answer_analysis": ["Given that the product, $$15600$$, is a multiple of $$25$$, the three numbers between them must contribute two factors of $$5$$; since they are consecutive and there are only three of them, this can happen only if one number is itself a multiple of $$25$$. It is now worth observing that the product of three consecutive numbers is roughly the same as the cube of the middle of the three. Since $$20^{3}\\textless{} 15 600 \\textless{} 30^{3}$$, the middle number must lie between $$20$$ and $$30$$, hence one of the numbers must be $$25$$. The numbers can therefore be $$\\left\\textbackslash{ {23, 24, 25} \\right\\textbackslash}$$,~ $$\\left\\textbackslash{ {24, 25, 26} \\right\\textbackslash}$$ or $$\\left\\textbackslash{ {25, 26, 27} \\right\\textbackslash}$$. The product $$15600 =13 \\times1200$$, so it has factors both $$4$$ and $$13$$. The triple $$\\left\\textbackslash{ {25, 26, 27} \\right\\textbackslash}$$ has no factor of $$4$$, and $$\\left\\textbackslash{ {23, 24, 25} \\right\\textbackslash}$$ no factor of $$13$$. So, by elimination, the numbers are $$24$$, $$25$$ and $$26$$, and their total is $$75$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1824", "queId": "881e5b6785314bbe8e1f403d9b62e8df", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A fair $6$-sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number? ($2011$ AMC $8$ Problem, Question \\#$18$) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{6}$ "}], [{"aoVal": "B", "content": "$\\dfrac{5}{12}$ "}], [{"aoVal": "C", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "D", "content": "$\\dfrac{7}{12}$ "}], [{"aoVal": "E", "content": "$\\dfrac{5}{6}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $6\\times6=36$ ways to roll a die twice, and $6$ of them result in two of the same number. Out of the remaining $36-6=30$ ways, the number of rolls where the first time is greater than the second should be the same as the number of rolls where the second time is greater than the first. In other words, there are $\\dfrac{30}{2}=15$ ways the first roll can be greater than the second. The probability the first number is greater than or equal to the second number is $\\dfrac{15+6}{36}=\\dfrac{21}{36}=\\frac{7}{12}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1830", "queId": "b54e7c5761fa4231b5ff1f2d5f787381", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Wendy wrote all the whole numbers from $$13$$ to $$78$$ on her paper. How many times did she write all the digit \"$$3$$ on her paper? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$17$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["Ones: $$13, 23, 33, 43, 53, 63, 73$$ Tens: $$30, 31, 32, 33, 34, 35, 36, 37, 38, 39$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1833", "queId": "328cd57f7b924ac39b4e9e35a4ceee7c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$12 + 8 + 8 + 4 $ is the same as~\\uline{~~~~~~~~~~}~$\\times 4$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["$$12+8+8+4=32$$ $$32\\div4=8$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1834", "queId": "36e3ce4e3919466b9a4adb3f938d0251", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A school has 100 students and 5 teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are $50,20,20,5$, and 5 . Let $l$ be the average value obtained if a teacher is picked at random and the number of students in their class is noted. Let $s$ be the average value obtained if a student was picked at random and the number of students in their class, including the student, is noted. What is $t-s$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$-18.5$$ "}], [{"aoVal": "B", "content": "$$-13.5$$ "}], [{"aoVal": "C", "content": "$$0$$ "}], [{"aoVal": "D", "content": "$$13.5$$ "}], [{"aoVal": "E", "content": "$$18.5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The formula for expected values is $$ \\text { Expected Value }=\\sum(\\text { Outcome } \\cdot \\text { Probability }) . $$ We have $$ \\begin{aligned} t \\& =50 \\cdot \\frac{1}{5}+20 \\cdot \\frac{1}{5}+20 \\cdot \\frac{1}{5}+5 \\cdot \\frac{1}{5}+5 \\cdot \\frac{1}{5} \\textbackslash\\textbackslash{} \\& =(50+20+20+5+5) \\cdot \\frac{1}{5} \\textbackslash\\textbackslash{} \\& =100 \\cdot \\frac{1}{5} \\textbackslash\\textbackslash{} \\& =20, \\textbackslash\\textbackslash{} s \\& =50 \\cdot \\frac{50}{100}+20 \\cdot \\frac{20}{100}+20 \\cdot \\frac{20}{100}+5 \\cdot \\frac{5}{100}+5 \\cdot \\frac{5}{100} \\textbackslash\\textbackslash{} \\& =25+4+4+0.25+0.25 \\textbackslash\\textbackslash{} \\& =33.5 . \\end{aligned} $$ Therefore, the answer is $t-s=(\\mathbf{B})-13.5$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1835", "queId": "36e5bb4bc2be423d9333c1bc4e5c1d76", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Julia, Kasia, Susanna, and Helena have their birthdays on March $$1^{\\rm st}$$, May $$17^{\\rm th}$$, July $$20^{\\rm th}$$, and March $$20^{\\rm th}$$. Kasia and Susanna were born in the same month. Julia and Susanna were born on the same day of a month. Which of the girls was born on May $$17^{\\rm th}$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "Julia "}], [{"aoVal": "B", "content": "Kasia "}], [{"aoVal": "C", "content": "Susanna "}], [{"aoVal": "D", "content": "Helena "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Susanna: March 20\\textsuperscript{th} Kasia: March 1\\textsuperscript{st} Julia: July 20\\textsuperscript{th} Helena: May 17\\textsuperscript{th} "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1844", "queId": "714526c1c46e48e7a28685ba491517ca", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$7\\times 11\\times 13=$$ ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1001$$ "}], [{"aoVal": "B", "content": "$$1111$$ "}], [{"aoVal": "C", "content": "$$1221$$ "}], [{"aoVal": "D", "content": "$$1101$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["7x(10+1)x13 =(70+7)x13 =77x(10+3) =77x10+77x3 =770+231 =1001 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1846", "queId": "36fced2494b74a45a475cda4ab25cc2b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Abe has $1$ green and $1$ red jelly beans in his hand. Bob has $1$ green and $2$ yellow jelly beans in his hand. Each randomly picks a jelly bean to show to the other. What is the probability that the colours match? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "C", "content": "$\\dfrac{3}{4}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{6}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The probability that both show a green bean is $\\dfrac{1}{2}\\cdot \\dfrac{1}{3}=\\dfrac{1}{6}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1847", "queId": "3fafe26edbcf45dc911b588010cddd44", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two different numbers are randomly selected from the set $-5, -3, -1, 3, 5$~and multiplied together. What is the probability that the product is a negative number? (adapted from $2016$ AMC $8$ Problem, Question \\#$13$) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{5}{6}$ "}], [{"aoVal": "B", "content": "$\\frac{2}{5}$ "}], [{"aoVal": "C", "content": "$\\frac{3}{4}$ "}], [{"aoVal": "D", "content": "$\\frac{1}{2}$ "}], [{"aoVal": "E", "content": "$\\frac{3}{5}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$\\frac25\\times\\frac34+\\frac35\\times\\frac24=\\frac{3}{5}$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1848", "queId": "be9555649bea4303988fca913604c63b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Given that $x+2y=3$, $3^{}x\\cdot 9^{}y=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$27$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$81$$ "}], [{"aoVal": "E", "content": "$$243$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$3^{}x \\cdot 9^{}y=3^{x+2y}=3^{3}=27$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1851", "queId": "5a807ac12ec24905a5494005f5556bfe", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The total score of $8$ students is an even number. Each of $3$ of them gets an odd number score, and each of $4$ of them gets an even number score. Which of the following would be the possible score that the last student gets? ", "answer_option_list": [[{"aoVal": "A", "content": "$$66$$ "}], [{"aoVal": "B", "content": "$$70$$ "}], [{"aoVal": "C", "content": "$$74$$ "}], [{"aoVal": "D", "content": "$$77$$ "}], [{"aoVal": "E", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["The sum of $3$ odd numbers is an odd number. The sum of $4$ even numbers is an even number. The sum of an odd number and an even number is an odd number, so the total score of the $7$ students is an odd number. The total score of $8$ students is an even number, and the sum of $2$ odd numbers is an even number. Therefore, the score of the last one should be an odd number. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1855", "queId": "cc6f6541566c452490a87b3564e29f40", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A deck of cards contains a white card and two red cards. Take one card out randomly, record its colour, and put it back in the deck. Then, take another card out randomly. Compare the probability of the following situations. I. Both cards are of the same colour. II. Both cards are red. III. Two cards are of different colours. Which one has the highest probability? ", "answer_option_list": [[{"aoVal": "A", "content": "$$I$$ "}], [{"aoVal": "B", "content": "$$II$$ "}], [{"aoVal": "C", "content": "$$III$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["I. Both cards are in the same colour: $$ \\dfrac{5}{9}$$; II. Both cards are red: $$\\dfrac{4}{9}$$; III. Two cards are in different colours: $$\\dfrac{4}{9}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1857", "queId": "90843d76af6842838e41ed2dc89fe834", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Each of the 5 sides and the 5 diagonals of a regular pentagon are randomly and independently colored red or blue with equal probability. What is the probability that there will be a triangle whose vertices are among the vertices of the pentagon such that all of its sides have the same color? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{2}{3}$ "}], [{"aoVal": "B", "content": "$\\frac{105}{128}$ "}], [{"aoVal": "C", "content": "$\\frac{125}{128}$ "}], [{"aoVal": "D", "content": "$\\frac{253}{256}$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Instead of finding the probability of a same-colored triangle appearing, let us find the probability that one does not appear. After drawing the regular pentagon out, note the topmost vertex; it has 4 sides/diagonals emanating outward from it. We do casework on the color distribution of these sides/diagonals. Case 1: all 4 are colored one color. In that case, all of the remaining sides must be of the other color to not have a triangle where all three sides are of the same color. We can correspondingly fill out each color based on this constraint, but in this case you will always end up with a triangle where all three sides have the same color by inspection. Case $2: 3$ are one color and one is the other. Following the steps from the previous case, you can try filling out the colors, but will always arrive at a contradiction so this case does not work either. Case $3: 2$ are one color and 2 are of the other color. Using the same logic as previously, we can color the pentagon 2 different ways by inspection to satisfy the requirements. There are $\\left(\\begin{array}{l}4 \\textbackslash\\textbackslash{} 2\\end{array}\\right)$ ways to color the original sides/diagonals and 2 ways after that to color the remaining ones for a total of $6 \\cdot 2=12$ ways to color the pentagon so that no such triangle has the same color for all of its sides. These are all the cases, and there are a total of $2^{10}$ ways to color the pentagon. Therefore the answer is $1-\\frac{12}{1024}=1-\\frac{3}{256}=\\frac{253}{256}=D$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1861", "queId": "90859900398246a884296140a9866b58", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amos is taller than Eugene. Leo is shorter than James but taller than Eugene. James is shorter than Amos. is the tallest andis the shortest. ", "answer_option_list": [[{"aoVal": "A", "content": "Amos, James "}], [{"aoVal": "B", "content": "James, Eugene "}], [{"aoVal": "C", "content": "James, Leo "}], [{"aoVal": "D", "content": "Amos, Eugene "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["From clue $$2$$, James is taller than Leo and Leo is taller than Eugene. From clue $$3$$, Amos is taller than James. Rank from tallest to shortest: \\textbf{Amos}, James, Leo, \\textbf{Eugene}. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1862", "queId": "3fc6cbfa76dc4a95a60495e8d4f64e0f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many different positive integers at most can add up to $$80$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10+11+12 = 78$$, $$80 -- 78 = 2$$. Since all the numbers should be different, the remaining \\textquotesingle$$2$$\\textquotesingle{} cannot make up a new positive integer. It can only be added to the number(s) before. Therefore, there are at most $$12$$ different positive integers that can add up to $$80$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1863", "queId": "d5ab9226afbf420d8fe2f7e3d8f38cda", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following statements is not correct? ", "answer_option_list": [[{"aoVal": "A", "content": "Indefinite events include impossible events. "}], [{"aoVal": "B", "content": "The probability of an impossible event to happen is $$0$$. "}], [{"aoVal": "C", "content": "The probability of an indefinite event to happen is between $$0$$ and $$1$$. "}], [{"aoVal": "D", "content": "The probability of a certain event to happen is $$1$$. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Impossible events are definite events. $$\\text{B}$$, $$\\text{C}$$, and $$\\text{D}$$ are right. Thus, the answer is $$\\text{A}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1864", "queId": "4d16926a519a4b2a89a2ce3d0d3037bb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A bag contains four pieces of paper, each labeled with one of the digits $$1$$, $$2$$, $$3$$ or $$4$$, with no repeats. Three of these pieces are drawn, one at a time without replacement, to construct a three-digit number. What is the probability that the three-digit number is a multiple of $$3$$? ($$2007$$ AMC $$8$$ Problem, Question \\#$$24$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{4}$$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "D", "content": "$$\\frac{2}{3}$$ "}], [{"aoVal": "E", "content": "$$\\frac{3}{4}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["The combinations of digits that give multiples of $$3$$ are $$(1$$, $$2$$, $$3)$$ and $$(2$$, $$3$$, $$4)$$. For each of them, there are $3\\times2\\times1=6$ possibilities. Thus, there are $6+6=12$ possibilities in total. The number of ways to choose three digits out of four is $$4\\times3\\times2=24$$. Therefore, the probability is $$\\frac{12}{24}=\\frac12$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1866", "queId": "3720b430820c42fd845a485ce0513699", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many two-digit numbers are there where the ones digit is greater than the tens digit?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$26$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["$$8+7+6+5+4+3+2+1=36$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1868", "queId": "5f1c36fc8aa24bbb91f4f668d51ce46f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There is a ball in a box. Three kids are guessing the colour of the ball. Val says: \"The ball is white.\" John says: \"The ball is blue.\" Elvis says: \"I agree with Val.\" Then, they open the box and find only one of them guessed right. The ball is . ", "answer_option_list": [[{"aoVal": "A", "content": "white "}], [{"aoVal": "B", "content": "Blue "}], [{"aoVal": "C", "content": "Uncertain "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis"], "answer_analysis": ["Val\\textquotesingle s point and Elvis\\textquotesingle{} points are identical, so both of them guessed incorrectly. Therefore, John guessed correctly. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1870", "queId": "8bf0c901100f4df9921ef80bc9aa2f06", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A number is formed by writing $2022$ consecutively for $3$ times. Which of the following statements is correct? ", "answer_option_list": [[{"aoVal": "A", "content": "The number is a multiple of $3$, $6$ and $9$. "}], [{"aoVal": "B", "content": "The number is a multiple of $3$ and $6$ but not a multiple of $9$. "}], [{"aoVal": "C", "content": "The number is a multiple of $3$ and $9$ but not a multiple of $6$. "}], [{"aoVal": "D", "content": "The number is a multiple of $3$ but not a multiple of $6$. "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["The sum of the digits of 202220222022 is 2 x 9 = 18. Hence this number is divisible by 3 and 9. As its last digit is 2, it is also divisible by 6. The answer is \\textbf{Option A.} "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1872", "queId": "372febe1d77e44779f823b72285e9e55", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The average height of June, Ali and Linda is $$160\\text{cm}$$. Ali is $$166 \\text{cm}$$ tall. June and Linda are as tall as each other. What is Linda\\textquotesingle s height? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\rm~~154 cm$$ "}], [{"aoVal": "B", "content": "$$\\rm~~157 cm$$ "}], [{"aoVal": "C", "content": "$$\\rm~~162 cm$$ "}], [{"aoVal": "D", "content": "$$\\rm~~164 cm$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The total height is $160\\times 3 = 480\\text{cm}$ and hence the height of both June and Linda is $480-166=314\\text{cm}$. Therefore the height of Linda is $314 \\div 2 = 157\\text{cm}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1873", "queId": "4d2ab60fe61d41cd90306c9d3ac14aa5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2014 P2 Q8 Find the number A such that the following statement is true: 7 x A = 3 x 8 + 4 x 8 ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["7A = 24 + 32 7A = 56 A = 8 "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1877", "queId": "ac37c638e4b44d5581ab51ec6279ebb9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the probability of choosing a composite number from $0\\sim10$? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac12$ "}], [{"aoVal": "B", "content": "$\\frac5{11}$ "}], [{"aoVal": "C", "content": "$\\frac3{10}$ "}], [{"aoVal": "D", "content": "$\\frac25$ "}], [{"aoVal": "E", "content": "$\\frac{6}{11}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $11$ numbers in total. Among them, $4,6, 8, 9,$ and $10$ are composite numbers. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1878", "queId": "5aad067b35ef49a993a680e7cdf5f7cc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$30$$ pupils in my class. $$20$$ pupils like Maths and $$18$$ pupils like English. Twice as many pupils like both subjects as like neither of them. How many pupils like only Maths? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["Let the number of pupils who like neither subject be $$x$$. Hence the number who like both subjects is $$2x$$. Therefore the number of pupils who like only Maths is $$20−2x$$ and the number who like only English is $$18−2x$$. Since there are $$30$$ pupils in my class, we have $$\\left( 20-2x \\right)+2x+\\left( 18-2x \\right)+x=30$$ and hence $$38−x = 30$$. This has solution $$x = 8$$ and hence the number of pupils who like only Maths is $$20-2\\times 8=4$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1880", "queId": "4d429ac74b03437a854b11a6acc6377b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amos is taller than Eugene. Leo is shorter than James but taller than Eugene. James is shorter than Amos. is the tallest andis the shortest. ", "answer_option_list": [[{"aoVal": "A", "content": "Amos, James "}], [{"aoVal": "B", "content": "James, Eugene "}], [{"aoVal": "C", "content": "James, Leo "}], [{"aoVal": "D", "content": "Amos, Eugene "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing"], "answer_analysis": ["From tallest to shortest: \\textbf{Amos}, James, Leo, \\textbf{Eugene}. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1882", "queId": "5f3e5f54885147cbb77d123c1011d0cb", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The faces of each of two fair dice are numbered $1$, $2$, $3$, $5$, $7$, and $8$. When the two dice are tossed, what is the probability that their sum will be an even number? (2019 AMC 8 Problems, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{4}{9}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "C", "content": "$\\dfrac{5}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{3}{5}$ "}], [{"aoVal": "E", "content": "$\\dfrac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["We have a $2$ dice with $2$ evens and $4$ odds on both dice. For the sum to be even, the $2$ rolls can be $2$ odds or $2$ evens. Ways to roll $2$ odds: The total number of ways to obtain $2$ odds on $2$ rolls is $4 * 4=16$, as there are $4$ possible odds on the first roll and $4$ possible odds on the second roll. Ways to roll $2$ evens: Similarly, we have $2 * 2=4$ ways to obtain $2$ evens. The probability is $\\frac{20}{36}=\\frac{5}{9}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1883", "queId": "375ec214b88e4e52857810cbb82ec91b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many digits are there from $5$ to $118$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$114$$ "}], [{"aoVal": "B", "content": "$$204$$ "}], [{"aoVal": "C", "content": "$$239$$ "}], [{"aoVal": "D", "content": "$$242$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$5 - 9: 9 - 5 + 1 = 5$ $10 - 99: 99 - 10 + 1 = 90$ $100 - 118: 118 - 100 + 1 = 19$ $5\\times1 + 90\\times2 + 19\\times3 = 5 + 180 + 57 = 242$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1884", "queId": "3bb5487fc7e549b6881a25b8bcc090c5", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Calculate the value of $$7 + 16 + 34 + 45 + 50 - 6 - 15 - 4 - 7$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$70$$ "}], [{"aoVal": "B", "content": "$$120$$ "}], [{"aoVal": "C", "content": "$$127$$ "}], [{"aoVal": "D", "content": "$$124$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["$$7-7 + 16-6 + 34-4 + 45-15 +50$$ $$= 0+10+30+30+50$$ $$= 120$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1886", "queId": "4d4f6174062f4fc685eca0e271bc7fd4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the UK it is now $$11$$ am. The time in San Francisco is $$8$$ hours behind the UK. What time do the clocks now show in San Francisco? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ am "}], [{"aoVal": "B", "content": "$$4$$ am "}], [{"aoVal": "C", "content": "$$5$$ am "}], [{"aoVal": "D", "content": "$$11$$ am "}], [{"aoVal": "E", "content": "$$7$$ pm "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Eight hours behind $$11$$ am is $$3$$ am. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1890", "queId": "48dec6f093ed42d58db5f970b6a29abe", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Nick wants to bake a cake that consists of only $$1$$ flavour and $$1$$ topping. He gets to choose from $$3$$ different flavours and $$3$$ different toppings. How many different kinds of cake can he make? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["$$3\\times3=9$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1891", "queId": "ba0df020f4914f85a0b1e2f19155c87e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two different numbers are randomly selected from the set $-2, -1, 0, 3, 4, 5$~and multiplied together. What is the probability that the product is $0$? ($2016$ AMC $8$ Problem, Question \\#$13$) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{6}$ "}], [{"aoVal": "B", "content": "$\\frac{1}{5}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{4}$ "}], [{"aoVal": "D", "content": "$\\frac{1}{3}$ "}], [{"aoVal": "E", "content": "$\\frac{1}{2}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The product can only be $0$ if one of the numbers is $0$. Once we choose $0$, there are $5$ ways of choosing the second number, and there are 15 ways of choosing $2$ numbers randomly. Thus $\\frac{5}{15} = \\frac{1}{3}$. The answer is $D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1894", "queId": "56531441bf5a4ce4972bbc0e02bb3bc5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sophia's average score on six tests is $$82$$. Her average score on the $$7^{}\\text{th}$$ and $$8^{}\\text{th}$$ test is $$98$$. What is her average score on all eight tests? ", "answer_option_list": [[{"aoVal": "A", "content": "$$86$$ "}], [{"aoVal": "B", "content": "$$88$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$94$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)"], "answer_analysis": ["Sophia\\textquotesingle s total score on the first six tests is $$6\\times82=492$$. Her total score on all eight tests is $$492+2\\times98=688$$, and her average score is $$688\\div8=86$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1896", "queId": "d5c239259ce341c388dd6def140749ef", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many distinguishable arrangements are there of $1$ blue tile, $2$ green tiles, and $3$ yellow tiles in row from left to right? (Tiles of the same color are indistinguishable) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$\\frac{6!}{3!\\times2!}=60$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1899", "queId": "6cfaf4c58c9941ab97ee2d689a1b3aa7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are different ways for a librarian, lending six books to three students, given that each student gets a book. ", "answer_option_list": [[{"aoVal": "A", "content": "$$120$$ "}], [{"aoVal": "B", "content": "$$100$$ "}], [{"aoVal": "C", "content": "$$96$$ "}], [{"aoVal": "D", "content": "$$72$$ "}], [{"aoVal": "E", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The first student has six choices of books; the second has five; and the third has four. By the Rule of product, there is a total of $$6\\times5\\times4=120$$ways. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1900", "queId": "3be83c3539e34482adf2910d2a162f21", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Use a simple method to compute the following. $$25\\times38$$=． ", "answer_option_list": [[{"aoVal": "A", "content": "$$960$$ "}], [{"aoVal": "B", "content": "$$950$$ "}], [{"aoVal": "C", "content": "$$940$$ "}], [{"aoVal": "D", "content": "$$930$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["25x38 =25x(30+8) =25x30+25x8 =750+200 =950 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1904", "queId": "5ae62eda88cc4e72bee25c8bdf4f7ae8", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "Moon and Archie played chess competitively. Both of them had same levels of skill. They agreed to play seven games, and the one that win four games first would be the ultimate winner. Now, they have already played three games, and Moon won two games while Archie won one game. What is the probability that Mon be the ultimately winner? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3}{8}$$ "}], [{"aoVal": "B", "content": "$$\\frac{11}{16}$$ "}], [{"aoVal": "C", "content": "$$\\frac{3}{16}$$ "}], [{"aoVal": "D", "content": "$$\\frac{7}{16}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$\\rm B$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1905", "queId": "4d80a5456a214c48a187fe0826c90cce", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "One day, Pip asks his parents: \"What day is it today?\" His mother says: \"Today is Monday.\" His father says: \"Today is Tuesday.\" From the options below, \\textbf{Pip agrees with B}. Do you agree with Pip? ", "answer_option_list": [[{"aoVal": "A", "content": "One of these two sentences is definitely wrong and the other one is correct. "}], [{"aoVal": "B", "content": "It is possible that both of Pip\\textquotesingle s parents are wrong. "}], [{"aoVal": "C", "content": "It is possible that both of Pip\\textquotesingle s parents are right. "}], [{"aoVal": "D", "content": "If Pip\\textquotesingle s mother is wrong, then his father must be right. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing"], "answer_analysis": ["\"Today is Monday\" is not the opposite of \"Today is Tuesday\".i.e. they can both be false. \"Today is Monday\" is the direct opposite of \"Today is not Monday\". One must be true and the other must be false. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1908", "queId": "5aeec78699d442a7bc4efa2a6d03e635", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Abe holds $1$ green and $1$ red jelly bean in his hand. Bob holds $1$ green, $1$ yellow, and $2$ red jelly beans in his hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match? (2013 AMC 8 Problem, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{4}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "C", "content": "$\\dfrac{3}{8}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "E", "content": "$\\dfrac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["The probability that both show a green bean is $\\dfrac{1}{2}\\times\\dfrac{1}{4}=\\dfrac{1}{8}$. The probability that both show a red bean is $\\dfrac{1}{2}\\times \\dfrac{2}{4}=\\dfrac{1}{4}$. Therefore the probability is $\\frac{1}{4}+\\frac{1}{8}=\\frac{3}{8}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1910", "queId": "facfe16f2d0c4dee86ae66aac2c9384d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two tiles numbered $1$ and $2$ are turned face down, respectively. One tile is turned up at random, and throw a die to get a number from $1$ to $6$. What is the probability that the product of the numbers on the tile and the die is greater than or equal to $12$? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac {1}{2}$ "}], [{"aoVal": "B", "content": "$\\frac {1}{6}$ "}], [{"aoVal": "C", "content": "$\\frac {1}{3}$ "}], [{"aoVal": "D", "content": "$\\frac {1}{4}$ "}], [{"aoVal": "E", "content": "$\\frac {1}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $12$ different combinations. The product of two numbers is greater than $12$ will be $2\\times6$. Thus, the probability is $\\frac 1{12}$ . "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1917", "queId": "7ac651da1f0f4f66b63cd1030372704e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the value of the following sum? $$299 + 297 + 295 + 296 + 298$$ ", "answer_option_list": [[{"aoVal": "A", "content": "1494 "}], [{"aoVal": "B", "content": "1490 "}], [{"aoVal": "C", "content": "1485 "}], [{"aoVal": "D", "content": "1484 "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["$$299 + 297 + 295 + 296 + 298$$ = $300 - 1 + 300 - 3 + 300 - 5 + 300 - 4 + 500 - 2$~ = $1485$~ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1919", "queId": "44d34ac72aeb4ab0b8826f2e5d00c186", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$29$$ students in a certain class. $$12$$ of the students have a sister and $$18$$ of the students have a brother. In this class, only Tania, Barbara, and Anna do not have any siblings. How many students from this class have both a brother and a sister? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$None "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["$(12+18)-(29-3)=4$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1922", "queId": "4933e763c25641f4aab461d66a3b5c89", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eddie finished reading a story book last week. He read an average of $19$ pages per day for the first six days of the week and $26$ pages on the last day. How many pages on average did Eddie read per day? ", "answer_option_list": [[{"aoVal": "A", "content": "$$26$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)"], "answer_analysis": ["$(19\\times6+26)\\div7=140\\div7=20$ pages. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1923", "queId": "4da737d544b74deba23cdd83b2d08358", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Julia, Kasia, Zuzanna, and Helena have their birthdays on March $$1^{\\rm st}$$, May $$17^{\\rm th}$$, July $$20^{\\rm th}$$, and March $$20^{\\rm th}$$. Kasia and Zuzanna were born in the same month. Julia and Zuzanna were born on the same day of a month. Which of the girls was born on May $$17^{\\rm th}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "Julia "}], [{"aoVal": "B", "content": "Kasia "}], [{"aoVal": "C", "content": "Zuzanna "}], [{"aoVal": "D", "content": "Helena "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Given that Kasia and Zuzanna were born in the same month, their birth month must be March. Given that Julia and Zuzanna were born on the same day of a month, they must be born on the $$20^{\\rm th}$$. Hence, Zuzanna was born on March $$20$$; Kasia was born on March $$1$$; and Julia was born on July $$20$$. Helena is therefore the one born on May $$17$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1924", "queId": "4da7bffb7fbc48b98b8b471435da8871", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A cat divides $$24$$ fish into $$4$$ groups, and each group has at least $$1$$ fish. There are at most~\\uline{~~~~~~~~~~}~fish in the group that has most of the fish. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$ 1 + 1+1 + 21 = 24$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1927", "queId": "407d23699db043908c97fcdb4be0149f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the smallest possible sum of two positive integers with a product of $$100$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$52$$ "}], [{"aoVal": "C", "content": "$$29$$ "}], [{"aoVal": "D", "content": "$$25$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Since the product of the two positive integers is $$100$$, the possible pairs of integers are $$\\left( 1,100 \\right)$$, $$\\left( 2,50 \\right)$$, $$\\left( 4,25 \\right)$$, $$\\left( 5,20 \\right)$$, $$\\left( 10,10 \\right)$$, the smaller the difference, the smaller the sum, so the smallest sum is $$10+10=20$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1928", "queId": "99fc0ffce9ba453597236a382a82ace9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The diagram shows some cubes of the same size stacked at a corner of a room. How many cubes are there altogether? (Note: The floor is horizontal and the two walls are vertical. There are no gaps or holes behind the visible cubes). ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "$$28$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["Count layer by layer. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1935", "queId": "9a01a0e72b634b66ae70360ab8eefa7c", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In how many ways can the letters in $CPCCKBY$ be rearranged so that $C$ cannot be put in both ends and two or more $C$s do not appear together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$64$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["There are $3$ $C$s in total now with other $4$ letters remaining. There are $\\_4P\\_4$ ways for us to arrange the $4$ letters\\textquotesingle{} positions. So the answer is $\\_4P\\_4=24$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1936", "queId": "c3693b7489db4021b489244fff6dde2d", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A drawer contains ten identical yellow socks, eight identical blue socks and one hundred identical pink socks. Amrita picks socks from the drawer without looking. What is the smallest number of socks she must pick to be sure that she has at least two pairs of matching socks? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems"], "answer_analysis": ["Consider the worst case scenario: first 3 are drawn, all of different colors, when the fourth is drawn, no matter which color is drawn, a pair of the same color will definitely be matched. Continue to draw the fifth one. The worst case is that the last color socks are drawn again, and at this point there are three socks of the same color and one sock of each of the other two colors. If you continue to draw the sixth one, no matter which color you draw, you will be able to form two pairs of socks of the same color. So the answer is to draw 6 times. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1937", "queId": "68a2baebd2f0430b9342dbcf2f4d794d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a box, there are $10$ balls of which $4$ are red, $3$ are black and $3$ are white. What is the probability of picking up $3$ balls randomly such that there are $2$ red balls and $1$ balck ball? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac12$ "}], [{"aoVal": "B", "content": "$\\frac13$ "}], [{"aoVal": "C", "content": "$\\frac1{12}$ "}], [{"aoVal": "D", "content": "$\\dfrac{3}{20}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["$\\dfrac{\\_4C\\_2 \\times~~\\_3C\\_1}{\\_{10}C\\_3}=\\dfrac{6\\times3}{120}=\\dfrac{3}{20}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1938", "queId": "ecf1a314406a4af99af6eea197e8d791", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many triangles of all sizes can be seen in the picture below? [insert pic] ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures->Classifying and Enumerating->Counting Regular Figures->Counting Triangles"], "answer_analysis": ["[insert pic] "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1939", "queId": "3c41bcd640814682ba1c21e5bd0ef636", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Let $(a, b, c, d)$ be integers where they are not necessarily different. If each one of them is in the set ($0$, $1$, $2$, $3$), what is the probability that $a \\cdot d-b \\cdot c$ is odd? (For example, ($0$, $3$, $1$, $1$) meet the condition, because $0 \\cdot 1-3 \\cdot 1=-3$ is odd.) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac3{16}$ "}], [{"aoVal": "B", "content": "$\\frac14$ "}], [{"aoVal": "C", "content": "$\\frac38$ "}], [{"aoVal": "D", "content": "$\\frac12$ "}], [{"aoVal": "E", "content": "$\\frac34$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["In order for $a \\cdot d-b \\cdot c$ to be odd, we need to consider the parity. We must have (even)-(odd) or (odd)-(even). There are $2\\times2+2\\times4=12$ ways to pick numbers to obtain an even product. There are $2 \\cdot 2=4$ ways to obtain an odd product. Therefore, the total amount of ways to make $a \\cdot d-b \\cdot c$ odd is $2 \\cdot(12 \\cdot 4)=96.$ Thus, the answer is $\\frac{96}{256}=\\frac38$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1940", "queId": "7f6b374388654c678e41ec85da5b5167", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A positive integer divisor of $12 !$ is chosen at random. The probability that the divisor chosen is a perfect square can be expressed as $\\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. What is $m+n$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The prime factorization of $12 !$ is $2^{10} \\cdot 3^{5} \\cdot 5^{2} \\cdot 7 \\cdot 11$. This yields a total of $11 \\cdot 6 \\cdot 3 \\cdot 2 \\cdot 2$ divisors of $12 !$. In order to produce a perfect square divisor, there must be an even exponent for each number in the prime factorization. Note that 7 and 11 can not be in the prime factorization of a perfect square because there is only one of each in $12 !$. Thus, there are $6 \\cdot 3 \\cdot 2$ perfect squares. (For $2$ , you can choose $0,2,4,6,8,$ or $10$, etc. The probability that the divisor chosen is a perfect square is $$ \\frac{6 \\cdot 3 \\cdot 2}{11 \\cdot 6 \\cdot 3 \\cdot 2 \\cdot 2}=\\frac{1}{22} \\Longrightarrow \\frac{m}{n}=\\frac{1}{22} \\Longrightarrow m+n=1+22=\\text { (E) } 23 $$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1944", "queId": "523a0ded6b794fa8afbce0e8195941e9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My average score on $$8$$ math tests is $$90$$. If my average score on the first $$5$$ tests was $$87$$, what was my average score on the last $$3$$ tests? ", "answer_option_list": [[{"aoVal": "A", "content": "$$96$$ "}], [{"aoVal": "B", "content": "$$95$$ "}], [{"aoVal": "C", "content": "$$94$$ "}], [{"aoVal": "D", "content": "$$93$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["I scored a total of $$720$$ on all $$8$$ tests. The total of $$435$$ on the first $$5$$ tests leaves a total of $$285$$ for the last $$3$$ tests, so the average is $$285\\div3 = 95$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1945", "queId": "e3b528cbf5a1456f842d31461835bb55", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A pair of fair 6 -sided dice is rolled $n$ times. What is the least value of $n$ such that the probability that the sum of the numbers face up on a roll equals 7 at least once is greater than $\\frac{1}{2}$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Rolling a pair of fair 6 -sided dice, the probability of getting a sum of 7 is $\\frac{1}{6}$ : Regardless what the first die shows, the second die has exactly one outcome to make the sum 7 . We consider the complement: The probability of not getting a sum of 7 is $1-\\frac{1}{6}=\\frac{5}{6}$. Rolling the pair of dice $n$ times, the probability of getting a sum of 7 at least once is $1-\\left(\\frac{5}{6}\\right)^{}n$. Therefore, we have $1-\\left(\\frac{5}{6}\\right)^{}n\\textgreater\\frac{1}{2}$, or $$ \\left(\\frac{5}{6}\\right)^{}n\\textless\\frac{1}{2} $$ Since $\\left(\\frac{5}{6}\\right)^{4}\\textless\\frac{1}{2}\\textless\\left(\\frac{5}{6}\\right)^{3}$, the least integer $n$ satisfying the inequality is (C) 4 . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1947", "queId": "bed7c3fff239400596e81c3ec5aadc31", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$20$$ red balls, $$2$$ black balls, and $$1$$ white ball in a bag. They are of identical shape, size and quality except for colour. Take out $$1$$ ball without looking. Among the following statements, which one is true? ", "answer_option_list": [[{"aoVal": "A", "content": "The ball taken out must be a black ball. "}], [{"aoVal": "B", "content": "It is impossible that a white ball will be taken out. "}], [{"aoVal": "C", "content": "It is very likely that a red ball will be taken out. "}], [{"aoVal": "D", "content": "It is certain that a red ball will be taken out. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The number of red balls in the bag is the most compared with other coloured balls. If we take out one ball at random, the probability of taking out a red ball is larger. So $$\\text{C}$$ is the answer. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1951", "queId": "c371d59488d54b85a308c0243d7f7ee4", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There are some pieces of candy on a table.You are challenged by your friend to play the following game: you both have to altemate moves, and in each move, you can take away either $$1$$, $$2$$, $$3$$,~ $$4$$ or $$5$$ pieces from the table. The person who takes away the final piece from the table wins. If you go second, how many pieces of candy should be on the table before the game starts such that you can ensure victory? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["Only $$18$$ is one of the multiples of $$5+1$$, and the second player can ensure victory. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1953", "queId": "71d2aec22a124398a56b054090982f2e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Elsa is looking for some two-digit numbers. The difference between the digits in the tens place and the ones place is 5. How many of such numbers are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["16, 27, 38, 49, 50, 61, 72, 83, 94 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1954", "queId": "6d455825ec26493290a27e4670dae1ff", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The faces of two identical fair dice are numbered $1$, $2$, $3$, $5$, $7$, and $8$. When the two dice are tossed, what is the probability that their sum will be an even number? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{4}{9}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "C", "content": "$\\dfrac{5}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{3}{5}$ "}], [{"aoVal": "E", "content": "$\\dfrac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["There are two cases in which the sum can be an even number: both numbers are even and both numbers are odd. This results in only one case where the sum of the numbers are odd (one odd and one even in any order). We can solve for how many ways the $2$ numbers add up to an odd number and subtract the answer from $1$. How to solve the problem: The probability of getting an odd number first is $\\dfrac{4}{6}=\\dfrac{2}{3}$. In order to make the sum odd, we must select an even number next. The probability of getting an even number is $\\dfrac{2}{6}=\\dfrac{1}{3}$. Now we multiply the two fractions: $\\dfrac{2}{3}\\times\\dfrac{1}{3}=\\dfrac{2}{9}$. However, this is not the answer because we could pick an even number first then an odd number. The equation is the same except switched, and by the Communitive Property of Multiplication, it does not matter if the equations are switched. Thus we do $\\dfrac{2}{9}\\times2=\\dfrac{4}{9}$. This is the probability of getting an odd-number sum. In order to get the probability of getting an even number we do $1-\\dfrac{4}{9}=\\left (\\text{C}\\right )\\dfrac{5}{9}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1957", "queId": "4de9c00fe8654795bad33d49f4f74ebc", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There are many red balls, yellow balls, and blue balls of identical shape in a bag. Many students are playing a game in which each of them can take $$2$$ balls from the bag without observing the color of the balls. (After each student takes the balls, they should put them back in the bag.) The teacher finds that no matter how the students take the balls, there are always at least $$2$$ students who take the same balls. (For example, student $$A$$ and student $$B$$ both get one red ball and one yellow ball.) There would be at least~\\uline{~~~~~~~~~~}~students playing the game. ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["There are $$6$$ possible cases when taking $$2$$ balls from the box. In the worst case, each of the first $$6$$ students takes different balls to the others. When the $${{7}^{\\text{th}}}$$ student takes the balls, he/she would definitely take the same balls with someone among the first $$6$$ students. $$6+1=7$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1959", "queId": "71dcaa51999e400487a9888e170f33a7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A city has a bicycle hire scheme where it is possible to hire a bicycle for short journeys. Last year I hired a bicycle $$60$$ times and rode for $$13$$ hours altogether. For how long on average did I hire the bicycle on each ride? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ minutes "}], [{"aoVal": "B", "content": "$$23$$ minutes "}], [{"aoVal": "C", "content": "$$39$$ minutes "}], [{"aoVal": "D", "content": "$$47$$ minutes "}], [{"aoVal": "E", "content": "$$73$$ minutes "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The rider travels for $$13$$ hours over $$60$$ rides, which is anaverage time of $$\\frac{13}{60}$$ of an hour per ride, hence $$13$$ minutes. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1961", "queId": "766643659f1a47928fee3628051a090a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Let $(a, b, c, d)$ be an ordered quadruple of not necessarily distinct integers, each one of them is in the set ($0$, $1$, $2$, $3$). What is the probability that $a \\cdot d-b \\cdot c$ is odd? (For example, ($0$, $3$, $1$, $1$) meet the condition, because $0 \\cdot 1-3 \\cdot 1=-3$ is odd.) (Adapted from 2020 AMC 10A Problem, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac3{16}$ "}], [{"aoVal": "B", "content": "$\\frac14$ "}], [{"aoVal": "C", "content": "$\\frac38$ "}], [{"aoVal": "D", "content": "$\\frac12$ "}], [{"aoVal": "E", "content": "$\\frac34$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["In order for $a \\cdot d-b \\cdot c$ to be odd, we need to consider the parity. We must have (even)-(odd) or (odd)-(even). There are $2\\times2+2\\times4=12$ ways to pick numbers to obtain an even product. There are $2 \\cdot 2=4$ ways to obtain an odd product. Therefore, the total amount of ways to make $a \\cdot d-b \\cdot c$ odd is $2 \\cdot(12 \\cdot 4)=96.$ Thus, the answer is $\\frac{96}{256}=\\frac38$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1962", "queId": "7f886e8d429e44f4bafbd85630747019", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$124$$ children attended a fair. $$87$$ of them tried out sports events. $$65$$ of them tried out art activities. How many children tried out both sport events and art activities? ", "answer_option_list": [[{"aoVal": "A", "content": "$$22$$ "}], [{"aoVal": "B", "content": "$$28$$ "}], [{"aoVal": "C", "content": "$$37$$ "}], [{"aoVal": "D", "content": "$$59$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["Nil "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1966", "queId": "7f8d7b08b9b147259bd74bea73ddfb83", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "What is the value of the following sum? $$902+804+700+609+508+403+307+201+106$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$4450$$ "}], [{"aoVal": "B", "content": "$$4540$$ "}], [{"aoVal": "C", "content": "$$4500$$ "}], [{"aoVal": "D", "content": "$$4505$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["simple math calculation "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1967", "queId": "40e1fb4527294322a9284700c2273266", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Professor Chang has nine language books lined up on a bookshelf: two different Arabic books, three different German books, and four different Spanish books. How many ways are there to arrange the nine books on the shelf keeping the Arabic books together and keeping the Spanish books together? ($2018$ AMC $8$ Problem, Question \\#$16$) $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ \\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}$\\textasciitilde$ \\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}$\\textasciitilde$ \\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}$\\textasciitilde$ \\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}$\\textasciitilde$ \\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}$\\textasciitilde$ \\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}$\\textasciitilde$\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt} \\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}$\\textasciitilde$ \\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}$\\textasciitilde$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$1440$$ "}], [{"aoVal": "B", "content": "$$2880$$ "}], [{"aoVal": "C", "content": "$$5760$$ "}], [{"aoVal": "D", "content": "$$182440$$ "}], [{"aoVal": "E", "content": "$$362880$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["Since the two Arabic books and four Spanish books have to be kept together, respectively, we can treat them both as just one book. That means we\\textquotesingle re trying to find the number of ways you can arrange one Arabic book, one Spanish book, and three German books, which is just $\\_5P\\_5$. Now we multiply this product by $\\_2P\\_2\\times \\_4P\\_4$~because there are $\\_2P\\_2$~ways to arrange just two Arabic books, and $\\_4P\\_4$~ways to arrange just four Spanish books. Multiplying all these together, we have the answer $C$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1977", "queId": "68e87c4827ac44b0949bfd3a06d736fa", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy, Bill, and Celine are friends with different ages. Exactly one of the following statements is true. $$\\rm I$$. Bill is the oldest. $$\\rm II$$. Amy is not the oldest. $$\\rm III$$. Celine is not the youngest. Rank the friends from oldest to youngest. ($$2004$$ AMC $$8$$ Problem, Question \\#$$13$$) ", "answer_option_list": [[{"aoVal": "A", "content": "Bill, Amy, Celine "}], [{"aoVal": "B", "content": "Amy, Bill, Celine "}], [{"aoVal": "C", "content": "Celine, Amy, Bill "}], [{"aoVal": "D", "content": "Celine, Bill, Amy "}], [{"aoVal": "E", "content": "Amy, Celine, Bill "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions"], "answer_analysis": ["If Bill is the oldest, then Amy is not the oldest, and both statements $$\\rm I$$ and $$\\rm II$$ are true, so statement $$\\rm I$$ is not the true one. If Amy is not the oldest, and we know Bill cannot be the oldest, then Celine is the oldest. This would mean she is not the youngest, and both statements $$\\rm II$$ and $$\\rm III$$ are true, so statement $$\\rm II$$ is not the true one. Therefore, statement $$\\rm III$$ is the true statement, and both $$\\rm I$$ and $$\\rm II$$ are false. From this, Amy is the oldest, Celine is in the middle, and lastly Bill is the youngest. This order is $$\\rm E$$: Amy, Celine, Bill. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1982", "queId": "8c6d2d28d0d742ff957972d8113e3aa9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There is a three-digit number \\textquotesingle$$502$$\\textquotesingle. John writes a digit before this number to make it a new four-digit number. If he writes a~\\uline{~~~~~~~~~~}~, the new four-digit number would be as small as possible. ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value in Enumeration Problems"], "answer_analysis": ["Note that the digit \\textquotesingle$$0$$\\textquotesingle{} could not be the highest digit of a four-digit number. Therefore, the smallest number is $$1502$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1983", "queId": "646b5dcd458049cd9a5031dfd08ab1a1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The average of the \\emph{different~}prime factors of $$2009$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2009$$ "}], [{"aoVal": "B", "content": "$$147$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$2009=7^{2}\\times 41$$, and the average of $$7$$ and $$41$$ is $$(7+41)\\div 2=24$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1984", "queId": "49b43f5480d0426a98710992fff6720a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the expression $$1□2□3□4$$ each $$□$$ is to be replaced by either $$+$$ or $$\\times$$. What is the largest value of all the expressions that can be obtained in this way? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["If $$m$$ and $$n$$ are positive integers, then $$mn{}\\textgreater m+n$$ unless at least one of $$m$$ or $$n$$ is equal to $$1$$, or $$m=n=2$$. So, to maximise the expression, we need to place multiplication signs between $$2$$ and $$3$$ and between $$3$$ and $$4$$. However, we need to place an addition sign between $$1$$ and $$2$$ because $$1+2\\times3\\times4=25$$, whereas $$1\\times2\\times3\\times4=24$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1990", "queId": "68f8806c2c6341d1bbca84a559277ee5", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There are $$12$$ gold coins with exactly the same appearance, including $$11$$ real coins and $$1$$ fake coin. The weight of the fake coin is different from that of the real coin, and whether the fake coin is lighter or heavier than the real coin is unknown. How many times at least do you need to weigh the coins using a balance to ensure that you can find the fake coin? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"], "answer_analysis": ["In the first weighing with the balance, put coins $$1$$, $$2$$, $$3$$, and $$4$$ on one end of the balance and coins $$5$$, $$6$$, $$7$$, and $$8$$ on the other end of the balance. The balance has two situations: balanced or not. Analyze the situation of the balance: if balanced, the fake coin is among the remaining $$4$$ coins. In the second weighing with the balance, randomly take $$3$$ coins from coin $$1$$ to coin $$8$$ and put them on the left end of the balance and randomly take $$3$$ coins from coin $$9$$ to coin $$12$$ and put them on the right end of the balance (such as $$9$$, $$10$$, $$11$$). The balance also has two situations: balanced or not. If balanced, coin $$12$$ is the coin of different weight. In the third weighing with the balance, comparing No. $$12$$ coin with any other coin, whether the coin is lighter or heavier can be known. If not, it can be known that the coin of different weight is among the three coins $$9$$, $$10$$, and $$11$$, and that whether it is lighter or heavier than other coins can be known. In the third weighing with the balance, randomly take two of the coins (such as $$9$$ and $$10$$) and put them on the both ends of the balance. If balanced, the remaining coin (coin $$11$$) is the one we are looking for; if not, based on the previous judgement that whether the coin is lighter or heavier, it can be determined that which one of the coins on the balance is what we are looking for. Analyze the first imbalanced situation as follows: There are two situations: the right end weighs more or the left end weighs more. Assume the left end weighs more (which is the same for the situation that the right end weighs more.) In the second weighing with the balance, take off $$3$$ coins randomly from the left end (such as $$1$$, $$2$$, and $$3$$) and move $$3$$ coins from the right end to the left end (such as $$5$$, $$6$$, and $$7$$), then take $$3$$ coins randomly from the $$4$$ coins left in the first weighing (such as $$9$$, $$10$$, and $$11$$) to the right end, and there sees $$3$$ situations for the balance: ① the left end weighs more, ② the two ends strike a balance, ③ the right end weighs more. Analyze the situations one by one as follows: ① If the left end weighs more, the coin we are looking for must be coin $$4$$ or coin $$8$$. In the third time weighing with the balance, take one of the coins (such as coin $$4$$) and put it on the left end of the balance. Randomly take one of the remaining $$10$$ coins and put it on the right end. There are also $$3$$ situations. $$a$$: If balanced, coin $$8$$ is the one we are looking for. Based on the result of using the balance for the second time, it is known that the coin weighs less than other coins. $$b$$: If the left end weighs more, coin $$4$$ is the one we are looking for and it weighs more than other coins. $$c$$: If the right end weighs more, coin $$4$$ is the one we are looking for and it weighs less than other coins. ② If the two ends strike a balance, the coin we are looking for is among the three coins ($$1$$, $$2$$, and $$3$$) taken from the left end. Since the left end weighs more in the first weighing, it is known that the coin weighs more than other coins. The following analysis is the same as previous one and will not be repeated. ③ If the right end weighs more, the coin we are looking for is among the three coins ($$5$$, $$6$$, and $$7$$) moved from the right end to the left end. Based on the results of weighing in the first two times (the left end weighs more in the first weighing and the right end weighs more in the second weighing), it is known that the coin weighs less than other coins. The following analysis is the same. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1992", "queId": "9ecbace59af947a98efd30d6bfee7ea7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two tiles numbered $3$ and $4$ are turned face down, respectively. One tile is turned up at random, and throw a die to get a number from $1$ to $6$. What is the probability that the product of the numbers on the tile and the die is greater than or equal to $20$? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac {1}{2}$ "}], [{"aoVal": "B", "content": "$\\frac {1}{6}$ "}], [{"aoVal": "C", "content": "$\\frac {1}{3}$ "}], [{"aoVal": "D", "content": "$\\frac {1}{4}$ "}], [{"aoVal": "E", "content": "$\\frac {1}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $12$ different combinations. The product of two numbers is greater than $20$ will be $4\\times5$ and $4\\times6$. Thus, the probability is $\\frac 2{12}$ = $\\frac 16$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1994", "queId": "6d81a975109845e4934429b0cc7046b8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A cat divides $$24$$ fish into $$4$$ groups, and each group has at least $$1$$ fish. There are fish in the group that has the largest number of fish. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$ 1 + 1+1 + 21 = 24$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1995", "queId": "570eb928590149698c21fc49298a6c6d", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In how many ways can the letters in $CPCCKBY$ be rearranged so that two or more $C$s do not appear together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$240$$ "}], [{"aoVal": "B", "content": "$$180$$ "}], [{"aoVal": "C", "content": "$$64$$ "}], [{"aoVal": "D", "content": "$$96$$ "}], [{"aoVal": "E", "content": "$$140$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["There are $3$ $C$s in total now with other $4$ letters remaining. There are $\\_4P\\_4$ ways for us to arrange the $4$ letters\\textquotesingle{} positions. So the answer is $\\_4P\\_4\\times \\_5C\\_3 =240$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "1999", "queId": "9ed17d75563e441c814518084540e20b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The digits $1$, $2$, and $3$ can make~\\uline{~~~~~~~~~~}~three-digit numbers. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$3\\times 3\\times 3=27$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2000", "queId": "7b23b5f388c545f69d2b555359d14191", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In my suitcase I have $$5$$ sweaters and $$6$$ pairs of pants. If I make an outfit of a sweater and a pair of pants, how many different outfits can I select? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$25$$ "}], [{"aoVal": "D", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"], "answer_analysis": ["I have $$5$$ sweaters and $$6$$ pairs of pants. For each sweater, there are $$6$$ pairs of pants with which that sweater can be paired. There are $$5$$ sweaters, so there are $$5\\times6=30$$ different possible outfits. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2005", "queId": "b1310fe0d45644e9ad14be2f08a29483", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There were $20$ ducks, pigs, and sheep in total in Sam\\textquotesingle s farm. After Sam bought some new sheep, the number of sheep has doubled. There are $27$ ducks, pigs, and sheep in total. Originally, how many ducks and pigs were there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$27-20=7$ $7+7=14$ $20-14=6$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2006", "queId": "52bb2baf096f4f3b9ec44611e5990ba6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two tiles numbered $5$ and $6$ are turned face down, respectively. One tile is turned up at random, and throw a die to get a number from $1$ to $6$. What is the probability that the product of the numbers on the tile and the die is smaller than or equal to $8$? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac {1}{2}$ "}], [{"aoVal": "B", "content": "$\\frac {1}{3}$ "}], [{"aoVal": "C", "content": "$\\frac {1}{4}$ "}], [{"aoVal": "D", "content": "$\\frac {1}{5}$ "}], [{"aoVal": "E", "content": "$\\frac {1}{6}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $2\\times6=12$ different combinations. The product of two numbers is smaller than $8$ will be $5\\times1$ and $6\\times1$. Thus, the probability is $\\frac 2{12}$ = $\\frac 16$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2007", "queId": "69140399bc1b4dd0b5816fa5caa15f02", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In how many ways can the letters in $AAABCDA$ be rearranged so that two or more $A$s do not appear together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["There are $4$ $A$s in total, which have $3$ intervals leaving for the other $3$ letters. Thus, the answer is $\\_3P\\_3=6$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2008", "queId": "572ce9654d2b4febb024d7a99b93c8a7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If Keyue fished every day from July $$17$$ through July $$31$$ (within the same year), she fished fordays． ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Total number of days $$=31-17 +1= 15$$ days. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2009", "queId": "52c6207fa8804709aa84e9ba5922057a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a toy store, cars are available in $5$ different colours: blue, white, yellow, black and red. A car has either $2$ or $4$ doors. How many different version of the car are available? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["$$5 \\times 2 = 10$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2010", "queId": "722695fd536f4365979931cf749ce274", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Two distinct numbers from $$1$$ to $$100$$ inclusive will form a pair if the sum of these two is a multiple of $$5$$. How many different pairs are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$50$$ "}], [{"aoVal": "B", "content": "$$150$$ "}], [{"aoVal": "C", "content": "$$800$$ "}], [{"aoVal": "D", "content": "$$990$$ "}], [{"aoVal": "E", "content": "$$1200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2016", "queId": "602bba30d0134c36b4b5fa456a5d9f69", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Today is Amy\\textquotesingle s birthday! She takes photos with her four close friends. All of them stand in a line and they make Amy stand in the middle. There are~\\uline{~~~~~~~~~~}~different ways for them to form the line. ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"], "answer_analysis": ["$$4 \\times 3 \\times 1 \\times 2 \\times 1 = 24$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2019", "queId": "b5d7a074e1b948c6896bb247fe89b5d1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$24$$ four-digit numbers which is formed using each of the digits $$3$$, $$5$$, $$6$$ and $$9$$ once only. When all of these $$24$$ four-digit numbers are put in order from smallest to largest, which one is in the eighth position? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3569$$ "}], [{"aoVal": "B", "content": "$$5369$$ "}], [{"aoVal": "C", "content": "$$5396$$ "}], [{"aoVal": "D", "content": "$$5639$$ "}], [{"aoVal": "E", "content": "$$5936$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["When put in order, the numbers are: $$3569$$, $$3596$$, $$3659$$, $$3695$$, $$3956$$, $$3965$$, $$5369$$, $$5396$$, $$5639$$, $$5693$$, $$\\ldots $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2023", "queId": "723cc96ad7154d2188e6b67f31124584", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The maximum number of intersection points of $$4$$ different circles is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math->Dotted Line Arrangement"], "answer_analysis": ["Each pair has $$2$$ intersection points. The $$6$$ pairs have $$12$$ such points. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2024", "queId": "64bccbe63c3e42898ca4ea00630a6410", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In how many ways can the digits in $3433256337$ be rearranged so that two or more $3$s do not appear together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1800$$ "}], [{"aoVal": "B", "content": "$$1200$$ "}], [{"aoVal": "C", "content": "$$1000$$ "}], [{"aoVal": "D", "content": "$$720$$ "}], [{"aoVal": "E", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["There are $5$ $3$s in total now with other $5$ digits remaining. There are $\\_5P\\_5$ ways for us to arrange the $5$ letters\\textquotesingle{} positions. Then, we can put the $5$ $3$s in the $6$ intervals. So the answer is $\\_5P\\_5 \\times \\_6C\\_5=720$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2026", "queId": "6dbca5ce7ad249f5b7cf84af074885e6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A cup costs ￡$$8$$. Which of the following payment is not correct?． ", "answer_option_list": [[{"aoVal": "A", "content": "One £5 note and three~£1 coins "}], [{"aoVal": "B", "content": "Eight £1 coins "}], [{"aoVal": "C", "content": "One £5 note and four 50p coins "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2028", "queId": "d1746f9d6b9b43fbb265766b43c04a10", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Elvis is packing shirts for a trip. He just randomly grabs $3$ shirts from his closet without observing them. The closet contains $10$ shirts: $5$ striped, $3$ plaid, and $2$ pure-colored ones. What is the probability that he chooses $2$ striped shirts and $1$ pure-colored shirt? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac12$ "}], [{"aoVal": "B", "content": "$\\frac13$ "}], [{"aoVal": "C", "content": "$\\frac1{12}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{6}$ "}], [{"aoVal": "E", "content": "$\\frac14$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["$\\dfrac{\\_5C\\_2 \\times~~\\_2C\\_1}{\\_{10}C\\_3}=\\dfrac{10\\times2}{120}=\\dfrac{2}{12}=\\dfrac{1}{6}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2030", "queId": "95cdd421cf914fb2839aaf1ae4abfebc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "We can formdifferent two-digit numbers with the numbers $$1$$, $$3$$ and $$0$$.（without using the same number two times like $$33$$ ） ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Dictionary Ordering"], "answer_analysis": ["$$13$$、$$10$$、$$31$$、$$30$$， notice that $$0$$ cannot be in the first place, so only $$4$$ numbers can be formed． So the answer is $$\\text{B}$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2033", "queId": "8906b1ae01284acfb9aab9fe3fdc2507", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many four-digit numbers can be made using the digits $1-8$ without repeating digits? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1680$$ "}], [{"aoVal": "B", "content": "$$4096$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$256$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$8\\times 7\\times 6\\times 5=1680$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2036", "queId": "daaf67385813407c9cb3c81d4135f4b2", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Eight cards are numbered from $$1$$ to $$8$$. The cards are placed in two boxes $$P$$ and $$Q$$ so that the sum of the numbers on the three cards in box $$P$$ is equal to the sum of the numbers on the five cards in box $$Q$$. Which of the following statements must be true? ", "answer_option_list": [[{"aoVal": "A", "content": "The card numbered $$1$$ is not in box $$Q$$ "}], [{"aoVal": "B", "content": "Four cards in box $$Q$$ have even numbers on "}], [{"aoVal": "C", "content": "The card numbered $$5$$ is in box $$Q$$ "}], [{"aoVal": "D", "content": "The card numbered $$2$$ is in box $$Q$$ "}], [{"aoVal": "E", "content": "Exactly three cards in box $$Q$$ have odd numbers on "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions"], "answer_analysis": ["Note first that the sum of the numbers on the eight cards is $$36$$. Therefore the sum of the numbers on the cards in each of the boxes is $$18$$. There are only three cards in box $$P$$ and hence the possible combinations for the numbers on the cards in box $$P$$ are $$\\left( 8,7,3 \\right)$$, $$\\left( 8,6,4 \\right)$$ and $$\\left( 7,6,5 \\right)$$ with the corresponding combinations for box $$Q$$ being $$\\left( 6,5,4,2,1 \\right)$$, $$\\left( 7,5,3,2,1 \\right)$$ and $$\\left( 8,4,3,2,1 \\right)$$. The only statement which is true for all three possible combinations for box $$Q$$ is that the card numbered $$2$$ is in box $$Q$$. Hence the only statement which must be true is statement $$\\rm D$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2037", "queId": "4a492e681fdd4f10ae76b995e71e7aca", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy has $$7$$ gray balls, $$4$$ white balls and $$3$$ black balls in a bag. What is the least number of balls she has to take out of the bag with her eyes closed to be sure that she takes at least two balls of each color? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems"], "answer_analysis": ["$$7+4+2=13$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2038", "queId": "ccdfb184585d41d9ab03251044d3c8c3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Abe holds 1 green and 1 red jelly bean in his hand. Bob holds 1 green, 1 yellow, and 2 red jelly beans in his hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match? (2013 AMC 8 Problem, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{4}$ "}], [{"aoVal": "B", "content": "$\\frac{1}{3}$ "}], [{"aoVal": "C", "content": "$\\frac{3}{8}$ "}], [{"aoVal": "D", "content": "$\\frac{1}{2}$ "}], [{"aoVal": "E", "content": "$\\frac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The probability that both show a green bean is $\\frac{1}{2} \\cdot \\frac{1}{4}=\\frac{1}{8}$. The probability that both show a red bean is $\\frac{1}{2} \\cdot \\frac{2}{4}=\\frac{1}{4}$. Therefore the probability is $\\frac{1}{4}+\\frac{1}{8}=\\left(\\right.$ C) $\\frac{3}{8}$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2042", "queId": "76e10088bf4347549d0a37705c6f7e7d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A box contains $11$ cards, numbered from $1$ to $11$. One card is selected randomly from the box. What is the probability that the number on the selected card is greater than $7$? (adapted from 2017 AMC 8 Problem, Question \\#10) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac1{11}$ "}], [{"aoVal": "B", "content": "$\\frac4{11}$ "}], [{"aoVal": "C", "content": "$\\frac7{11}$ "}], [{"aoVal": "D", "content": "$\\frac{10}{11}$ "}], [{"aoVal": "E", "content": "$\\frac2{11}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $4$ numbers greater than $7$. Thus, the probability is $\\frac4{11}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2043", "queId": "891311e0a4b84fd190e4dd478b1bd475", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A dinner set in a restaurant is free to choose a main course, a salad and a drink. Today, the restaurant offers five main courses, three salads, and six drinks for customers to choose. How many different sets can be matched? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$14$ "}], [{"aoVal": "B", "content": "$30$ "}], [{"aoVal": "C", "content": "$48$ "}], [{"aoVal": "D", "content": "$80$ "}], [{"aoVal": "E", "content": "$90$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["$5\\times3\\times6=90$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2046", "queId": "578ca784e36c446f8189a58f4e558d67", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Throw two dice of the same quality and size. The six sides of each die are marked with number of dots from $$1$$ to $$6$$. Among the following options,~\\uline{~~~~~~~~~~}~is an impossible event. ", "answer_option_list": [[{"aoVal": "A", "content": "The sum of dots is $$12$$. "}], [{"aoVal": "B", "content": "The sum of dots is smaller than $$3$$. "}], [{"aoVal": "C", "content": "The sum of dots is larger than $$4$$ but smaller than $$8$$. "}], [{"aoVal": "D", "content": "The sum of dots is $$13$$. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The maximum sum is $$6+6=12$$, so \"the sum of dots is $$13$$\" is an impossible event; so $$\\text{D}$$ is the answer. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2047", "queId": "4ec22e8dd77d442ab99de50da721383c", "competition_source_list": ["2020年希望杯二年级竞赛模拟第30题", "其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $13$ kids in line. They are numbered following the pattern: $1$, $2$, $3$, $4$, $5$, $1$, $2$, $3$, $4$, $5$, and so on. How many kids are numbered with odd numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$13\\div5=2R3$ There are $3$ odd numbers in each cycle. $3\\times2+2=8$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2049", "queId": "fb10de2c5de84ca493e6be29d9ac1fde", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A palindromic number is a number that reads the same when the order of its digits is reversed. What is the difference between the largest and smallest five-digit palindromic numbers that are both multiples of $$45$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9180$$ "}], [{"aoVal": "B", "content": "$$9090$$ "}], [{"aoVal": "C", "content": "$$9000$$ "}], [{"aoVal": "D", "content": "$$8910$$ "}], [{"aoVal": "E", "content": "$$8190$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value in Enumeration Problems"], "answer_analysis": ["For a number to be a multiple of $$45$$ it must be a multiple of $$5$$ and also of $$9$$. In order to be a multiple of $$5$$, a number\\textquotesingle s units digit must be $$0$$ or $$5$$. However, the units digit of a palindromic number cannot be $$0$$, so it may be deduced that any palindromic number which is a multiple of $$45$$ both starts and ends in the digit $$5$$. In order to make the desired number as large as possible, its second digit should be $$9$$ and for it to be as small as possible its second digit should be $$0$$. So, if possible, the numbers required are of the form \\textquotesingle$$59x95$$\\textquotesingle{} and \\textquotesingle$$50y05$$\\textquotesingle{} . In addition, both numbers are to be multiples of $$9$$ which means the sum of the digits of both must be a multiple of $$9$$. For this to be the case, $$x=8$$ and $$y=8$$ , giving digit sums of $$36$$ and $$18$$ respectively. So the two required palindromic numbers are $$59895$$ and $$50805$$. Their difference is $$9090$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2051", "queId": "9f0bb2300e844df3a5ab129451d44027", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are 70 beads.~ $$A$$ and $$B$$ take turns taking beads from the pile ($$A$$ goes first). Each person can take between 1 and 4 beads per turn. The person who takes the last bead loses. If $$A$$ wants to win, how many beads should he take on the first turn? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$A$$ can\\textquotesingle t win "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Math Game->Sudoku"], "answer_analysis": ["$$(70-1)\\div (1+4)=17\\cdots 1$$ $$A$$ takes one bead first, and then regardless of how many beads $$B$$ takes, as long as the sum of $$A$$ and $$B$$ is 5, $$A$$ will win. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2053", "queId": "72740173941e4d1e83c51eef19ddbc26", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is $$6$$ ones and $$15$$ thousandths? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.615$$ "}], [{"aoVal": "B", "content": "$$6.0015$$ "}], [{"aoVal": "C", "content": "$$6.015$$ "}], [{"aoVal": "D", "content": "$$6.105$$ "}], [{"aoVal": "E", "content": "$$6.15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$$6$$ ones $=6$ $$15$$ thousandths $=$ $1$ hundredth and $5$ thousandths $=0.015$ $\\textasciitilde$ Total $=6.015$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2055", "queId": "579d3e203de64f3f8aa9228e449180e2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$20$$ students in a class standing in a line for recess. Mike is the $$7$$\\textsuperscript{th} counting from front to back. How many students are behind Mike? What is his position counting backwards? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$, $$13$$ "}], [{"aoVal": "B", "content": "$$13$$, $$14$$ "}], [{"aoVal": "C", "content": "$$13$$, $$12$$ "}], [{"aoVal": "D", "content": "$$14$$, $$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems"], "answer_analysis": ["The number of students behind Mike plus the position of Mike equals the total number of students in the class. So there are $$13$$ students behind Mike: $$20-7=13$$. However Mike is not included in these $$13$$ students, which means Mike is the $$14$$\\textsuperscript{th} student counting from back to front. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2058", "queId": "8926df07bc694a279f5202e74f414806", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sophia's average score on six tests is $$82$$. Her average scores on the $$7^{}\\text{th}$$ and $$8^{}\\text{th}$$ tests is $$98$$. Sophia then took another test and the average score of all $9$ tests is $87$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$86$$ "}], [{"aoVal": "B", "content": "$$88$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$94$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Sophia\\textquotesingle s total score on the first six tests is $$6\\times82=492$$. Her total score on all eight tests is $$492+2\\times98=688$$, and her average score is $$688\\div8=86$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2059", "queId": "727dd6fedd1448d4b362de3c0b5d3216", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In an opaque bag, there are $5$ red balls, $5$ white balls, and $5$ yellow balls. The balls are the same except for their colours. Take out one ball from the bag. What is the probability that you take out a yellow ball? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "C", "content": "$\\dfrac{1}{4}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["$\\dfrac{5}{15}=\\dfrac{1}{3}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2067", "queId": "b170a81b6eba4b29a2327c1c89e60e4f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Maria had $$28$$ dreams last month. If $$16$$ of them involved monkeys, $$15$$ involved squirrels, and $$4$$ involved no animals, then at least how many dreams involved both monkeys and squirrels? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Maria had $$28$$ dreams last month, $$24$$ of which involved animals. Since $$16+ 15 =31$$ involved moneys or squirrels, then at least $$31 - 24 = 7$$ dreams involved both monkeys and squirrels. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2071", "queId": "651b5c7e517c41b5856c7aa645eda6fb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$\\frac{7}{9}$, $\\frac{5}{4}$ Subtract the sum from the difference of the above two fractions. ", "answer_option_list": [[{"aoVal": "A", "content": "$2\\frac{1}{2}$ "}], [{"aoVal": "B", "content": "$\\frac{17}{36}$ "}], [{"aoVal": "C", "content": "$\\frac{73}{36}$ "}], [{"aoVal": "D", "content": "$\\frac{14}{9}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle"], "answer_analysis": ["Sum $=\\frac{5}{4}+\\frac{7}{9}=\\frac{73}{36}$ Difference $=\\frac{5}{4}-\\frac{7}{9}=\\frac{17}{36}$ Difference (Sum and difference) $=\\frac{73}{36}-\\frac{17}{36}=\\frac{56}{36}=\\frac{14}{9}=1\\frac{5}{9}$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2073", "queId": "6995a76f7281441daecf55f18cafe426", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two dice are thrown. What is the probability that the product of the two numbers is a multiple of $5 ?$ (2001 AMC 8 Problem, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{36}$ "}], [{"aoVal": "B", "content": "$\\frac{1}{18}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{6}$ "}], [{"aoVal": "D", "content": "$\\frac{11}{36}$ "}], [{"aoVal": "E", "content": "$\\frac{1}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["This is equivalent to asking for the probability that at least one of the numbers is a multiple of 5 , since if one of the numbers is a multiple of 5 , then the product with it and another integer is also a multiple of 5 , and if a number is a multiple of 5 , then since 5 is prime, one of the factors must also have a factor of 5 , and 5 is the only multiple of 5 on a die, so one of the numbers rolled must be a 5 . To find the probability of rolling at least one 5 , we can find the probability of not rolling a 5 and subtract that from 1, since you either roll a 5 or not roll a 5 . The probability of not rolling a 5 on either dice is $\\left(\\frac{5}{6}\\right)\\left(\\frac{5}{6}\\right)=\\frac{25}{36}$. Therefore, the probability of rolling at least one five, and thus rolling two numbers whose product is a multiple of 5 , is $1-\\frac{25}{36}=\\frac{11}{36}, \\text{D}$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2076", "queId": "5c33efb416cd462d89c2be2f757e18b6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Louis chooses a whole number from $$1$$ to $$30$$ at random. What is the probability that the number he chooses is a prime number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3}{10}$$. "}], [{"aoVal": "B", "content": "$$\\frac{2}{5}$$. "}], [{"aoVal": "C", "content": "$$\\frac{1}{6}$$. "}], [{"aoVal": "D", "content": "$$\\frac{13}{30}$$. "}], [{"aoVal": "E", "content": "$$\\frac{1}{3}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["Prime numbers from $$1$$ to $$30$$: $$2$$, $$3$$, $$5$$, $$7$$, $$11$$, $$13$$, $$17$$, $$19$$, $$23$$, $$29$$ Thus, there are $$10$$ prime numbers from $$1$$ to $$30$$. Therefore, the probability that the number she chooses is a prime number is $$\\frac{10}{30}=\\frac{1}{3}$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2078", "queId": "6e1b0cbbbc304d89b2272499075b022f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of two whole numbers is $$30$$. What is the least possible value of their sum? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$31$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The product of two whole numbers is $$30$$. If the numbers are $$5$$ and $$6$$, their sum is $$5+6=11$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2079", "queId": "699f8849ad564ba3a5f1d0be04821892", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "A box contains $5$ red balls and $3$ white balls that are identical in all aspects except color. One ball is drawn at random from the box and then replaced. The box is then thoroughly shaken so that the balls are arranged at random again and a second ball is drawn randomly from the box. What is the probability of drawing white ball for both time? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{5}{8}$$ "}], [{"aoVal": "B", "content": "$$\\frac{3}{8}$$ "}], [{"aoVal": "C", "content": "$$\\frac{25}{64}$$ "}], [{"aoVal": "D", "content": "$$\\frac{9}{64}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$D$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2081", "queId": "5375cf6df31c46019eb965d98fc7ce54", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many numbers are there between $$0 \\sim 50$$ that do not consist of digit \\textquotesingle$$6$$\\textquotesingle?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["$$6, 16, 26, 36, 46$$ $$50$$ numbers minus $$5$$ numbers -\\/-\\textgreater{} $$45$$ numbers "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2082", "queId": "69a2d4d040234693a62e92391c32b12b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many $$4$$-digit numbers greater than $$1000$$ are there that use the four digits of $$2012$$? ($$2012$$ AMC $$8$$ Problems, Question \\#$10$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["There are $3$ numbers that can be formed between $1000$ and $1999$, and $3\\times2\\times1=6$ numbers that can be formed with $2$ in the first place. So the answer is $3+6=9$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2086", "queId": "5c4deb95f6144c019c74dde6c4a12e62", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Ali, Bonnie, Carlo, and Dianna are going to drive together to a nearby theme park. The car they are using has 4 seats: 1 Driver seat, 1 front passenger seat, and 2 back passenger seat. Bonnie and Carlo are the only ones who know how to drive the car. How many possible seating arrangements are there? (2003 AMC 8 Problem, Question \\#16) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are only 2 people who can go in the driver\\textquotesingle s seat-Bonnie and Carlo. Any of the 3 remaining people can go in the front passenger seat. There are 2 people who can go in the first back passenger seat, and the remaining person must go in the last seat. Thus, there are $2 \\cdot 3 \\cdot 2$ or 12 ways. The answer is then (D) 12 . "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2088", "queId": "60c5d02a494a4f0bafe8df11cb7fd491", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the digits of $$1993$$ is $$1+9+9+3$$, or $$22$$. At some time in the future, the sum of the digits of a year will be $$33$$. This will \\emph{first} occur in the century. ", "answer_option_list": [[{"aoVal": "A", "content": "$$21\\text{st}$$ "}], [{"aoVal": "B", "content": "$$60\\text{th}$$ "}], [{"aoVal": "C", "content": "$$70\\text{th}$$ "}], [{"aoVal": "D", "content": "$$80\\text{th}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Splitting Whole Numbers"], "answer_analysis": ["The sum of the digits of $$1993$$ is $$1+9+9+3$$, or $$22$$. At some time in the future, the sum of the digits of a year will be $$33$$. Since $$9+9+9 = 27$$, this will \\emph{first} occur in $$6999$$, the $$70\\text{th}$$ century. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2090", "queId": "60c9f38655d64dccba2ff23f8bb5822b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ms. Osborne asks each student in her class to draw a rectangle with integral side lengths and a perimeter of $$50$$ units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles? ", "answer_option_list": [[{"aoVal": "A", "content": "$$76$$ "}], [{"aoVal": "B", "content": "$$120$$ "}], [{"aoVal": "C", "content": "$$128$$ "}], [{"aoVal": "D", "content": "$$132$$ "}], [{"aoVal": "E", "content": "$$136$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Geometry Modules->Objects with Straight Sides->Knowing Graphs"], "answer_analysis": ["As we know, the sum of the length and width is $$25$$. The largest area is $$13\\times12=156$$ and the smallest area is $$24\\times1=24$$, so the difference is $$156-24=132$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2092", "queId": "c87329ff9e974460bf34e979fa0ebbe1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Harriet tells Topaz that she is thinking of three positive integers, not necessarily all different. She tells her that the product of her three integers is $$36$$. She also tells her the sum of her three integers. However, Topaz still cannot work out what the three integers are. What is the sum of Harriet\\textquotesingle s three integers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The possible groups of three integers with product $$36$$ are $$(1,1,36)$$, $$(1,2,18)$$, $$(1,3,12)$$, $$(1,4,9)$$, $$(1,6,6)$$, $$(2,2,9)$$, $$(2,3,6)$$ and $$(3,3,4)$$ with sums $$38$$, $$21$$, $$16$$, $$14$$, $$13$$, $$13$$, $$11$$ and $$10$$ respectively. The only value for the sum that occurs twice is $$13$$. Hence, since Topaz does not know what the three integers chosen are, the sum of Harriet\\textquotesingle s three integers is $$13$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2093", "queId": "a8621f87be1c4768ae4ed142fce037f1", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "There are some two-digit numbers. The sum of the digits in the tens place and the ones place is 7. How many such numbers are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["16,25,34,43,52,61,70 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2100", "queId": "60dde909c7e4475cb1652e40e6b54bf3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There is a two-digit number. The product of its digits is $$18$$. The sum of the digits is $$11$$. The difference of the digits of this number is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$17$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$3\\times6=18$, $3+6=9$ $2\\times9=18$, $9+2=11$ Thus, the two digits of the number is $9$ and $2$. The difference is $9-2=7$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2103", "queId": "7743df7759a04ef8a291d7bf91fa9967", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The clock is showing $$11\\text{am}$$ now. When the hour hand has turned through $$165{}^{}\\circ$$, what time will it be? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11.30\\text{pm}$$ "}], [{"aoVal": "B", "content": "$$12.30\\text{pm}$$ "}], [{"aoVal": "C", "content": "$$4.30\\text{pm}$$ "}], [{"aoVal": "D", "content": "$$5.30\\text{pm}$$ "}], [{"aoVal": "E", "content": "$$11.30\\text{pm}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Each hour, the hour hand turns $$30{}^{}\\circ$$, so it will take $$5\\frac{1}{2}$$ hours to turn $$165{}^{}\\circ$$; the time will therefore be $$4.30\\text{pm}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2104", "queId": "58101dacb8e9498b92a770273fe0757f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a particular game, each of 4 players rolls a standard 6 -sided die. The winner is the player who rolls the highest number. If there is a tie for the highest roll, those involved in the tie will roll again and this process will continue until one player wins. Hugo is one of the players in this game. What is the probability that Hugo\\textquotesingle s first roll was a 5 , given that he won the game? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{61}{216}$ "}], [{"aoVal": "B", "content": "$\\frac{367}{1296}$ "}], [{"aoVal": "C", "content": "$\\frac{41}{144}$ "}], [{"aoVal": "D", "content": "$\\frac{185}{648}$ "}], [{"aoVal": "E", "content": "$\\frac{11}{36}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Since we know that Hugo wins, we know that he rolled the highest number in the first round. The probability that his first roll is a 5 is just the probability that the highest roll in the first round is 5 . Let $P(x)$ indicate the probability that event $x$ occurs. We find that $P($ No one rolls a 6$)-P($ No one rolls a 5 or 6$)=P($ The highest roll is a 5$)$, so $$ \\begin{gathered} P(\\text { No one rolls a } 6)=\\left(\\frac{5}{6}\\right)^{4}, \\textbackslash\\textbackslash{} P(\\text { No one rolls a } 5 \\text { or } 6)=\\left(\\frac{2}{3}\\right)^{4}, \\textbackslash\\textbackslash{} P(\\text { The highest roll is a } 5)=\\left(\\frac{5}{6}\\right)^{4}-\\left(\\frac{4}{6}\\right)^{4}=\\frac{5^{4}-4^{4}}{6^{4}}=\\frac{369}{1296}=(\\text { C }) \\frac{41}{144} \\text {. } \\end{gathered} $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2107", "queId": "d1a9c72503b6476792b1f275c92a6cdf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Miley had some keychains at first. She gave $$\\frac{6}{7}$$ of them to her friends. Her mother then gave her another $$8$$ keychains. She had $$15$$ keychains in the end. How many keychains did Miley give to her friends in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$42$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$49$$ "}], [{"aoVal": "D", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Word Problems Involving Fractions and Percentages->Finding a Whole Given a Part and the Percentage", "Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$\\frac{1}{7}$ of her keychains $=15-8=7$ $\\textasciitilde$ Given to friends $=\\frac{6}{7}$ of her keychains $=7\\times6$ $=42$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2109", "queId": "9ab786af5fa74339b1cf2dccecfc7c20", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Martin uses the five digits $$0$$, $$1$$, $$3$$, $$7$$, $$9$$ to make some numbers (each digit can only be used once). How many different three-digit numbers can be made? ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$4\\times4\\times3=48$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2111", "queId": "9f4751b3e5094b408eb824495672f140", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ann sleeps just $$8$$ hrs. each day, so in $$10$$ days, she\\textquotesingle s \\emph{awake~}~\\uline{~~~~~~~~~~}~hrs. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10\\times 16$$ "}], [{"aoVal": "B", "content": "$$8\\times 10$$ "}], [{"aoVal": "C", "content": "$$8\\times 24$$ "}], [{"aoVal": "D", "content": "$$16\\times 24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Ann\\textquotesingle s awake $$16$$ hours each day. In $$10$$ days, that\\textquotesingle s $$(10\\times 16)$$ hours. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2115", "queId": "d647d744a27e420a8b31473488fcd782", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A bag contains 4 red chips, 2 blue chips, and 3 white chips. If one chip is drawn at random, what is the probability that the chip will not be red? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac29$ "}], [{"aoVal": "B", "content": "$\\dfrac49$ "}], [{"aoVal": "C", "content": "$\\dfrac59$ "}], [{"aoVal": "D", "content": "$\\dfrac69$ "}], [{"aoVal": "E", "content": "$\\dfrac79$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$1-\\dfrac49=\\dfrac59$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2118", "queId": "84e206a1459a4819ac356c7eb7560d41", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In how many ways can the letters in $CPCCKBY$ be rearranged so that two or more $C$s are not adjacent to each other? ", "answer_option_list": [[{"aoVal": "A", "content": "$$240$$ "}], [{"aoVal": "B", "content": "$$180$$ "}], [{"aoVal": "C", "content": "$$64$$ "}], [{"aoVal": "D", "content": "$$96$$ "}], [{"aoVal": "E", "content": "$$140$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["There are $3$ $C$s in total now with other $4$ letters remaining. There are $\\_4P\\_4$ ways for us to arrange the remaining $4$ letters\\textquotesingle{} positions. So the answer is $\\_4P\\_4\\times \\_5C\\_3 =240$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2120", "queId": "806785f7d466437ca7e6866796b7f5fa", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a particular game, each of $4$ players rolls a standard $6$-sided die. The winner is the player who rolls the highest number. If there is a tie for the highest roll, those involved in the tie will roll again and this process will continue until one player wins. Hugo is one of the players in this game. What is the probability that Hugo\\textquotesingle s first roll was a $5$, given that he won the game? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{61}{216}$ "}], [{"aoVal": "B", "content": "$\\frac{367}{1296}$ "}], [{"aoVal": "C", "content": "$\\frac{41}{144}$ "}], [{"aoVal": "D", "content": "$\\frac{185}{648}$ "}], [{"aoVal": "E", "content": "$\\frac{11}{36}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Since we know that Hugo wins, we know that he rolled the highest number in the first round. The probability that his first roll is a $5$ is just the probability that the highest roll in the first round is $5$. Let $P(x)$ indicate the probability that event $x$ occurs. We find that $P$ (No one rolls a $6$)-$P$ (No one rolls a $5$ or $6$)$=P$ (The highest roll is a $5$), so $$ \\begin{gathered} P(\\text {No one rolls a } 6)=\\left(\\frac{5}{6}\\right)^{4}, \\textbackslash\\textbackslash{} P(\\text {No one rolls a } 5 \\text { or } 6)=\\left(\\frac{2}{3}\\right)^{4}, \\textbackslash\\textbackslash{} P(\\text {The highest roll is a } 5)=\\left(\\frac{5}{6}\\right)^{4}-\\left(\\frac{4}{6}\\right)^{4}=\\frac{5^{4}-4^{4}}{6^{4}}=\\frac{369}{1296}=(\\text {C}) \\frac{41}{144} \\text {. } \\end{gathered} $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2121", "queId": "58312ccd76fb42d2b1eb110755407a98", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many two-digit numbers are there where the tens digit is greater than the ones digit? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$26$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$36$$ "}], [{"aoVal": "E", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$1+2+3+4+5+6+7+8+9=45$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2122", "queId": "cd19fc4a3d1441c4bb8e417013270bb9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many three-digit numbers are there that have the sum of their digits equal to $5$? (For example, $122$ is such a number, because $1+2+2=5$.)． ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$25$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Splitting Whole Numbers"], "answer_analysis": ["Method 1: $104, 113, 122, 131, 140$; $203, 212, 221, 230$; $302, 311, 320$; $401, 410$; $500$ $5+4+3+2+1=15$ Method 2:$5=0+0+5=0+1+4=0+2+3=1+1+3=1+2+2$ When the three-digit number is formed by $0$, $0$, $5$, it can only be $500$, therefore $1$ number; when the three-digit number is formed by $0$, $1$, $4$, it can be $104$, $140$, $401$ or $410$, therefore $4$ numbers; when the three-digit number is formed by $0$, $2$, $3$, it can be $203$, $230$, $302$, or $320$, therefore $4$ numbers； when the three-digit number is formed by $1$, $1$, $3$, it can be $113$, $131$, or $311$, therefore $3$ numbers; when the three-digit number is formed by $1$, $2$, $2$, it can be $122$, $212$, or $221$, therefore $3$ numbers; in total there are $1+4+4+3+3=15$ numbers that meet the requirement of the question. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2123", "queId": "657d735b686c4620b6d9d7438d18b2e4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$97+101+102+104+105=$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$500$$ "}], [{"aoVal": "B", "content": "$$505$$ "}], [{"aoVal": "C", "content": "$$507$$ "}], [{"aoVal": "D", "content": "$$509$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["$97+101+102+104+105=100\\times5-3+1+2+4+5=509$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2127", "queId": "d64ff40f731b4ebd9bb745d809566848", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Four students asked their teacher, Mr. Carter, to line up with them to take a picture. ①If Mr. Carter does not want to stand on an end, how many different ways can they line up for the picture? ②If Mr. Carter insists on standing on an end, how many different ways can they line up for the picture? ", "answer_option_list": [[{"aoVal": "A", "content": "$72$ , $24$ "}], [{"aoVal": "B", "content": "$96$ , $24$ "}], [{"aoVal": "C", "content": "$72$ , $48$ "}], [{"aoVal": "D", "content": "$96$ , $48$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["①$$3\\times 4\\times 3\\times 2\\times 1=72$$ , ②$$2\\times 4\\times 3\\times 2\\times 1=48$$ . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2128", "queId": "6e7280985ee54081910ebe04359fbb13", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Adele has $1$ blue and $1$ red marble in her hand. Bobby has $1$ blue, $1$ yellow, and $2$ red marbles in his hand. Each of them randomly picks a marble to show the other. What is the probability that the colors are the same? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{4}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "C", "content": "$\\dfrac{3}{8}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "E", "content": "$\\dfrac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["The probability that both show a blue marble is $\\dfrac{1}{2}\\times \\dfrac{1}{4}=\\dfrac{1}{8}$. The probability that both show a red marble is $\\dfrac{1}{2}\\times \\dfrac{2}{4}=\\dfrac{1}{4}$. Therefore, the probability is $\\dfrac{1}{4}+\\dfrac{1}{8}=\\dfrac{3}{8}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2129", "queId": "c88bf42018ec43668199866dcc7e9863", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following statements is wrong ? ", "answer_option_list": [[{"aoVal": "A", "content": "The probability of a certain event to happen is $$1$$. "}], [{"aoVal": "B", "content": "The probability of an impossible event to happen is $$0$$. "}], [{"aoVal": "C", "content": "The probability of an indefinite event to happen is between $$0$$ and $$1$$. "}], [{"aoVal": "D", "content": "Indefinite events include impossible events. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Impossible events are definite events. So $$\\text{D}$$ is wrong. $$\\text{A}$$, $$\\text{B}$$, and $$\\text{C}$$ are right. So the answer is $$\\text{D}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2133", "queId": "d656f85fee634ebbb6cc9299423884f3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Abby, Bret, Carl, and Dana are seated in a row of four seats numbered \\#$$1$$ to \\#$$4$$. Joe looks at them and says: ``Bret is next to Carl.\" \"Abby is between Bret and Carl.\" However, each one of Joe's statements is false. Bret is actually sitting in seat \\#$$3$$. Who is sitting in seat \\#$$2$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "Abby "}], [{"aoVal": "B", "content": "Bret "}], [{"aoVal": "C", "content": "Carl "}], [{"aoVal": "D", "content": "Dana "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["We know that Carl does not sit next to Bret, so he must sit in seat \\#$$1$$. Since Abby is not between Bret and Carl, she must sit in seat \\#$$4$$. Finally, Dana has to take the last seat available, which is \\#$$2$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2137", "queId": "ad19a5fb2d804590ac67a57ddd3dbe65", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Bruno Mars is packing $3$ shirts for a trip. He just randomly grabs $3$ shirts from his closet without observing them. The closet contains $10$ shirts: $5$ striped, $3$ plaid, and $2$ solid-colored ones. What is the probability that he chooses $2$ striped shirts and $1$ solid-colored shirt? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac12$ "}], [{"aoVal": "B", "content": "$\\frac13$ "}], [{"aoVal": "C", "content": "$\\frac1{12}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{6}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["$\\dfrac{\\_5C\\_2 \\times~~\\_2C\\_1}{\\_{10}C\\_3}=\\dfrac{10\\times2}{120}=\\dfrac{2}{12}=\\dfrac{1}{6}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2138", "queId": "bf698ab4e913450a8c0f545a2539a74c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eddie is ordering lunch at a fast food restaurant with the following menu. Mains: Sandwich, Burger, Pizza Sides: Chicken Wings, Salad Drinks: Coffee, Tea, Coke If Eddie chooses to buy one main, one side, and one drink, how many different ways can he order lunch? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"], "answer_analysis": ["$$3\\times2\\times 3=18$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2139", "queId": "df83ea7bcb5340059bd2fa78ac02eaeb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A conductor wanted to make a trio consisting of a violinist, a pianist, and a drummer. He had to choose one of two violinists, one of two pianists, and one of two drummers. How many possible combinations did he have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$2\\times2\\times2=8$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2141", "queId": "daf13be3f95e49049c1326279bb220b3", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The room numbers of a hotel are all three-digit numbers. The first digit represents the floor and the last two digits represent the room number. The hotel has rooms on five floors, numbered $$1$$ to $$5$$. It has $$35$$ rooms on each floor, numbered $$n01$$ to $$n35$$ where $$n$$ is the number of the floor. In numbering all the rooms, how many times will the digit $$2$$ be used? ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$65$$ "}], [{"aoVal": "C", "content": "$$95$$ "}], [{"aoVal": "D", "content": "$$100$$ "}], [{"aoVal": "E", "content": "$$105$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["Each floor has $$35$$ rooms. On every floor except floor $$2$$, the digit $$2$$ will be used for rooms \\textquotesingle$$n02$$\\textquotesingle, \\textquotesingle$$n12$$\\textquotesingle, \\textquotesingle$$n20$$\\textquotesingle{} to \\textquotesingle$$n29$$\\textquotesingle{} (including \\textquotesingle$$n22$$\\textquotesingle) and \\textquotesingle$$n32$$\\textquotesingle. Hence the digit $$2$$ will be used $$14$$ times on each floor except floor $$2$$. On floor $$2$$, the digit $$2$$ will be used an extra $$35$$ times as the first digit of the room number. Therefore the total number of times the digit $$2$$ will be used is $$5\\times14+35 = 105$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2151", "queId": "6e9e0cb019ee47d8a27d7832a5175286", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the angle between the hour hand and the minute hand at seven o\\textquotesingle clock?~ ~ ．(Only consider angles less than 180°) ", "answer_option_list": [[{"aoVal": "A", "content": "$50^{}\\circ $ "}], [{"aoVal": "B", "content": "$120^{}\\circ $ "}], [{"aoVal": "C", "content": "$135^{}\\circ $ "}], [{"aoVal": "D", "content": "$150^{}\\circ $ "}], [{"aoVal": "E", "content": "$165^{}\\circ $ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Reading the Clock"], "answer_analysis": ["The smaller angle is $\\frac 5{12}$ of a full circle. A full circle has $360$ degrees, so the angle is $\\frac 5{12}\\times 360^{}\\circ =150^{}\\circ $. So, the answer is $\\rm D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2157", "queId": "5ce915eac011416d812b4a0e92c09eaa", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many numbers are there between $$0 \\sim 50$$ that do not consist of digit \\textquotesingle$$6$$\\textquotesingle?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$42$$ "}], [{"aoVal": "B", "content": "$$43$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$46$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["$$6, 16, 26, 36, 46$$ $$51$$ numbers minus $$5$$ numbers -\\/-\\textgreater{} $$45$$ numbers "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2163", "queId": "7c2ac3a1a6db4eeca578a2237ceddd9b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A top hat contains $$3$$ red chips and $$2$$ green chips. Chips are drawn randomly, one at a time without replacement, until all $$3$$ of the reds are drawn or until both green chips are drawn. What is the probability that the $$3$$ reds are drawn? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\dfrac{3}{10}$$ "}], [{"aoVal": "B", "content": "$$\\dfrac{2}{5}$$ "}], [{"aoVal": "C", "content": "$$\\dfrac{1}{2}$$ "}], [{"aoVal": "D", "content": "$$\\dfrac{3}{5}$$ "}], [{"aoVal": "E", "content": "$$\\dfrac{7}{10}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["There are two ways of ending the game, either you picked out all the red chips or you picked out all the green chips. We can pick out $$3$$ red chips, $$3$$ red chips, and $$1$$ green chip, $$2$$ green chips, $$2$$ green chips and $$1$$ red chip, and $$2$$ green chips, and $$2$$ red chips.Because order is important in this problem, there are $$1+4+1+3+6=15$$ ways to pick out the chip. But we noticed that if you pick out the three red chips before you pick out the green chip, the game ends. So we need to subtract cases like that to get the total number of ways a game could end, which $$15-5=10$$. Out of the $$10$$ ways to end the game, $$4$$ of them ends with a red chip. The answer is $$\\dfrac{4}{10}=\\dfrac{2}{5}$$, or $$\\boxed { (\\text{B})\\dfrac{2}{5}}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2167", "queId": "8d6873a4b87544b2b4d0ac0819c07636", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There is a box containing~$7$ chips numbered $1$, $2$, $3$, $4$, $5$, $6$, and $7$. A chip is drawn randomly from the box. What is the probability that the number on the chip is an even number? (adapted from 2015 AMC 8 Problem, Question \\#7) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac17$ "}], [{"aoVal": "B", "content": "$\\frac37$ "}], [{"aoVal": "C", "content": "$\\frac57$ "}], [{"aoVal": "D", "content": "$\\frac47$ "}], [{"aoVal": "E", "content": "$\\frac67$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$2$, $4$, and $6$ are even numbers. Thus, the probability is $\\frac37$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2174", "queId": "db0facc52ac44da8ac3e887235e1e4e8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When three line segments with the lengths of $3$, $$4$$, and $$7$$ are used to form a triangle, it is called a/an~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "Random event "}], [{"aoVal": "B", "content": "Certain event "}], [{"aoVal": "C", "content": "Impossible event "}], [{"aoVal": "D", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["∵$$3+4=7$$, ∴ Three line segments measuring $$3$$, $$4$$, and $$7$$ cannot form a triangle, ∴ Using three line segments measuring $$3$$, $$4$$, and $$7$$ to form a triangle is an impossible event. So $$\\text{C}$$ is the answer. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2180", "queId": "89dd8d5253a74c10b1241cc67630ff0c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Josh started playing soccer at $$14 : 35$$. He stopped playing at $$16 : 05$$. How much time did he spend playing soccer?~\\uline{~~~~~~~~~~}~$$\\text{h}$$~\\uline{~~~~~~~~~~}~$$\\min $$ ", "answer_option_list": [[{"aoVal": "A", "content": "1，25 "}], [{"aoVal": "B", "content": "1，30 "}], [{"aoVal": "C", "content": "2，25 "}], [{"aoVal": "D", "content": "2，30 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["1h 30min "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2181", "queId": "9fa93fc1e90a41a3b6055c885642de92", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many three-digit whole numbers have a ones digit equal to the sum of the hundreds digit and the tens digit? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["If the ones digit is $$2$$, the $$2$$ numbers are $$202$$ and $$112$$. For each ones digit, the number of possible numbers is the same as the ones digit. In all, there are $$1+2+3+\\cdots+8+9 =45$$ numbers. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2183", "queId": "c8c795265b754f13986d23b6586f7b0d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Four friends, Edwin, Fred, Gary and Howard, were playing together when one of them broke a vase. The teacher asked: \"Who is the culprit?\" Both Edwin and Howard said, \"Not me.\" Fred said, \"Howard broke the vase.\" Gary said, \"Fred is the culprit.\" If only one of four boys was lying, broke the vase. ", "answer_option_list": [[{"aoVal": "A", "content": "Edwin "}], [{"aoVal": "B", "content": "Fred "}], [{"aoVal": "C", "content": "Gary "}], [{"aoVal": "D", "content": "Howard "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis"], "answer_analysis": ["Either Fred or Howard must be lying since what they said did not tally. Since only one person was lying, Gary was telling the truth i.e, Fred broke the vase. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2189", "queId": "d1f686ef16ca48ba9a0f00c49e8ff656", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many minutes is it from $$22:45$$ today to $$00:35$$ tomorrow? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90 $$ "}], [{"aoVal": "B", "content": "$$ 100 $$ "}], [{"aoVal": "C", "content": "$$ 110 $$ "}], [{"aoVal": "D", "content": "$$120 $$ "}], [{"aoVal": "E", "content": "$$130$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["It is $$75$$ minutes from $$22:45$$ to midnight and then another $$35$$ minutes from midnight until $$00:35$$. So the required number of minutes is $$75 + 35 = 110$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2194", "queId": "73905b841a9649ac8bbcec9874f81f2d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The code is a two-digit number. The ones digit is 6 more than the tens digit. How many possible codes are there in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers->Complex Forming Numbers (with special requirements)"], "answer_analysis": ["17, 28, 39 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2195", "queId": "7806712561014f5fa9fe8bbd8286cb47", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If the correct time now is $$1:15$$ P.M., and if my clock stopped running three and one-half hours ago, when did it stop running? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8:45$$ A.M. "}], [{"aoVal": "B", "content": "$$9:45$$ A.M. "}], [{"aoVal": "C", "content": "$$10:45$$ A.M. "}], [{"aoVal": "D", "content": "$$4:45$$ P.M. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["One hour ago the time was $$12:15$$ P.M.; two hours ago the time was $$11:15$$ A.M.; three hours ago the time was $$10:15$$ A.M. Three and one-half hours ago the time was $$9:45$$ A.M. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2200", "queId": "ad764c1774b64d9594a68468dd22a75e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "One morning, a rabbit, a dog, a cat, and a duck went looking for food outside. The rabbit says: \"If I get food, the dog will also get food.\" The dog says: \"If I get food, the cat will also get food.\" The cat says \"If I get food, the duck will also get food.\" In the evening, they find that all of them tell the truth but only two of them get food.~\\uline{~~~~~~~~~~}~and~\\uline{~~~~~~~~~~}~don\\textquotesingle t get food. ", "answer_option_list": [[{"aoVal": "A", "content": "The rabbit; the dog "}], [{"aoVal": "B", "content": "The dog; the cat "}], [{"aoVal": "C", "content": "The cat; the duck "}], [{"aoVal": "D", "content": "The cat; the rabbit "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["We can infer that if the rabbit gets food, then all of the other three would get food; if the dog gets food, then both of the cat and duck would get food. Therefore, only when the rabbit and the dog don\\textquotesingle t get food, the cat and the duck would get food. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2201", "queId": "c8dca7e381b04ac0a8d5945151f22517", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A magazine printed photos of three celebrities along with three photos of the celebrities as babies. The baby pictures did not identify the celebrities. Readers were asked to match each celebrity with the correct baby pictures. What is the probability that a reader guessing at random will match all three correctly? (2014 AMC 8 Problems, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{9}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{6}$ "}], [{"aoVal": "C", "content": "$\\dfrac{1}{4}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "E", "content": "$\\dfrac{1}{2}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability"], "answer_analysis": ["There are $3 \\times 2 \\times 1 = 6$ ways assign the pictures to each of the celebrities. There is one favorable outcome where all of them are matched correctly, so the answer is (B) $\\frac{1}{6}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2202", "queId": "bb1d4016e3284296aed97a8de5afeab0", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Nini has $$6$$ identical balls and she wants to place them into $$3$$ identical baskets. How many different ways can she do so? (The baskets cannot be empty.) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["Since the balls and baskets are all identical, the order does not matter. $$6=1+1+4$$ $$6=1+2+3$$ $$6=2+2+2$$ So, there are $3$ ways to place them. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2203", "queId": "9b49579e6d2c424aaa9b70ecd2ab48e0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The numbers from $1$ to $40$ are written on $40$ pieces of paper, respectively, and put into a box. A piece of paper is chosen at random. Find the probability of choosing a number greater than $20$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{4}$$ "}], [{"aoVal": "D", "content": "$$\\frac{2}{5}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["Half the numbers from $1$ to $40$ are greater than $20$, Thus, the probability of choosing numbers greater than $20$ is $\\dfrac{1}{2}$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2207", "queId": "a4641f22178b43d0a0194b665b0f637f", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "How many different cubes are there with three faces coloured red and three faces coloured blue? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["Consider the case where two opposite faces are coloured red. Whichever of the four remaining faces is also coloured red, the resulting arrangement is equivalent under rotation to a cube with top, bottom and front faces coloured red. Hence, there is only one distinct colouring of a cube consisting of three red and three blue faces with two opposite faces coloured red. Now consider the case where no two opposite faces are coloured red. This is only possible when the three red faces share a common vertex and, however these faces are arranged, the resulting arrangement is equivalent under rotation to a cube with top, front and right-hand faces coloured red. Hence there is also only one distinct colouring of a cube consisting of three red and three blue faces in which no two opposite faces are coloured red. Therefore there are exactly two different colourings of the cube as described in the question. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2212", "queId": "9fdc914f04ec482996088dc787cacdb5", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Molly, Dolly, Sally, Elly and Kelly are sitting on a park bench. Molly is not sitting on the far right and Dolly is not sitting on the far left. Sally is not sitting at either end. Kelly is not sitting next to Sally and Sally is not sitting next to Dolly. Elly is sitting to the right of Dolly but not necessarily next to her. Who is sitting at the far right end? ", "answer_option_list": [[{"aoVal": "A", "content": "Molly　 "}], [{"aoVal": "B", "content": "Dolly　 "}], [{"aoVal": "C", "content": "Sally　 "}], [{"aoVal": "D", "content": "Kelly　 "}], [{"aoVal": "E", "content": "Elly　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The question tells us that Sally is not sitting at either end. This leaves three possible positions for Sally, which we will call positions $$2$$, $$3$$ and $$4$$ from the left-hand end. Were Sally to sit in place $$2$$, neither Dolly nor Kelly could sit in places $$1$$ or $$3$$ as they cannot sit next to Sally and, since Elly must sit to the right of Dolly, there would be three people to fit into places $$4$$ and $$5$$ which is impossible. Similarly, were Sally to sit in place $$3$$, Dolly could not sit in place $$2$$ or $$4$$ and the question also tells us she cannot sit in place $$1$$ so Dolly would have to sit in place $$5$$ making it impossible for Elly to sit to the right of Dolly. However, were Sally to sit in place $$4$$, Dolly could sit in place $$2$$, Kelly in place $$1$$, Molly (who cannot sit in place $$5$$) in place $$3$$ leaving Elly to sit in place $$5$$ at the right-hand end. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2213", "queId": "a4692e728ca74fa89f4d817c332dc301", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Professor Chang has nine different language books lined up on a bookshelf: two Arabic, three German, and four Spanish. How many ways are there to arrange the nine books on the shelf keeping the Arabic books together and keeping the Spanish books together? ($2018$ AMC $8$ Problem, Question \\#$16$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1440$$ "}], [{"aoVal": "B", "content": "$$2880$$ "}], [{"aoVal": "C", "content": "$$5760$$ "}], [{"aoVal": "D", "content": "$$182440$$ "}], [{"aoVal": "E", "content": "$$362880$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["Since the two Arabic books and four Spanish books have to be kept together, respectively, we can treat them both as just one book. That means we\\textquotesingle re trying to find the number of ways that you can arrange one Arabic book, one Spanish book, and three German books, which is just $\\_5P\\_5$. Now we multiply this product by $\\_2P\\_2\\times \\_4P\\_4$~because there are $\\_2P\\_2$~ways to arrange just two Arabic books, and $\\_4P\\_4$~ways to arrange just four Spanish books. Multiplying all these together, we have the answer $C$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2214", "queId": "9fddf3d1f270438fa43cc5d45beb0c2e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A school has $100$ students and $5$ teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are $50,20,20,5$, and $5$. Let $l$ be the average value obtained if a teacher is picked at random and the number of students in their class is noted. Let $s$ be the average value obtained if a student was picked at random and the number of students in their class, including the student, is noted. What is $t-s$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$-18.5$$ "}], [{"aoVal": "B", "content": "$$-13.5$$ "}], [{"aoVal": "C", "content": "$$0$$ "}], [{"aoVal": "D", "content": "$$13.5$$ "}], [{"aoVal": "E", "content": "$$18.5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The formula for expected values is $$ \\text { Expected Value }=\\sum(\\text { Outcome } \\cdot \\text { Probability }). $$ We have $$ \\begin{aligned} t \\& =50 \\cdot \\frac{1}{5}+20 \\cdot \\frac{1}{5}+20 \\cdot \\frac{1}{5}+5 \\cdot \\frac{1}{5}+5 \\cdot \\frac{1}{5} \\textbackslash\\textbackslash{} \\& =(50+20+20+5+5) \\cdot \\frac{1}{5} \\textbackslash\\textbackslash{} \\& =100 \\cdot \\frac{1}{5} \\textbackslash\\textbackslash{} \\& =20, \\textbackslash\\textbackslash{} s \\& =50 \\cdot \\frac{50}{100}+20 \\cdot \\frac{20}{100}+20 \\cdot \\frac{20}{100}+5 \\cdot \\frac{5}{100}+5 \\cdot \\frac{5}{100} \\textbackslash\\textbackslash{} \\& =25+4+4+0.25+0.25 \\textbackslash\\textbackslash{} \\& =33.5 . \\end{aligned} $$ Therefore, the answer is $t-s=(\\mathbf{B})-13.5$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2218", "queId": "7839b24bb467458aa0809a466600eb70", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Several distinct positive integers no larger than $$10$$ are listed in a row. After inspecting the row of numbers, Mark concluded with astonishment that in each pair of adjacent numbers one is a divisor of the other. At most how many numbers are in the list? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"], "answer_analysis": ["$$6$$, $$3$$, $$9$$, $$1$$, $$4$$, $$8$$, $$2$$, $$10$$, $$5$$. Only $$7$$, which is a prime number and doesn\\textquotesingle t have multiples except itself among $$1$$\\textasciitilde$$10$$, doesn\\textquotesingle t appear. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2219", "queId": "cd7666425f8d4f10800912af7030c656", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A fair $6$-sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{6}$ "}], [{"aoVal": "B", "content": "$\\dfrac{5}{12}$ "}], [{"aoVal": "C", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "D", "content": "$\\dfrac{7}{12}$ "}], [{"aoVal": "E", "content": "$\\dfrac{5}{6}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["There are $6\\cdot 6=36$ ways to roll the two dice, and $6$ of them result in two of the same number. Out of the remaining $36-6=30$ ways, the number of rolls where the first dice is greater than the second should be the same as the number of rolls where the second dice is greater than the first. In other words, there are $\\dfrac{30}{2}=15$ ways the first roll can be greater than the second. The probability the first number is greater than or equal to the second number is $\\dfrac{15+6}{36}=\\dfrac{21}{36}=\\boxed {\\left (\\text{D}\\right )\\dfrac{7}{12}}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2220", "queId": "8dc6d6b00f0049bc983f596785f89524", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the expression $$1□2□3□4$$ each $$□$$ is to be replaced by either $$+$$ or $$\\times$$. What is the largest value of all the expressions that can be obtained in this way? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["If $$m$$ and $$n$$ are positive integers, then $$mn{}\\textgreater m+n$$ unless at least one of $$m$$ or $$n$$ is equal to $$1$$, or $$m=n=2$$. So, to maximise the expression, we need to place multiplication signs between $$2$$ and $$3$$ and between $$3$$ and $$4$$. However, we need to place an addition sign between $$1$$ and $$2$$ because $$1+2\\times3\\times4=25$$, whereas $$1\\times2\\times3\\times4=24$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2223", "queId": "8135fde73e00422b9ee6032a564936be", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$10$$ boys in Pat\\textquotesingle s math class. If there are twice as many girls as boys in the class, how many grilss are there in the class? ", "answer_option_list": [[{"aoVal": "A", "content": "$$50$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["girls = $10\\times2=20$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2224", "queId": "bfca59bacb8a4e6e992c82f9c1733d9f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many different $3-$digit numbers are there with the sum of digits as $15$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$69$$ "}], [{"aoVal": "B", "content": "$$78$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$51$$ "}], [{"aoVal": "E", "content": "$$49$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["To divide $15+1+1=17$ into three groups, there are $\\_{16}C\\_{2}=120$ ways in total. But, since all digits cannot be larger than $9$, except the situations that don\\textquotesingle t meet the requirements, there are $120-\\_7C\\_2-\\_6C\\_2\\times 2=69$ numbers that match the condition. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2225", "queId": "78477d0289164adfad44b77d45459c5b", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Gregor, the mathematician, forms two numbers with the digits $$0$$, $$1$$, $$2$$, $$3$$, $$4$$, and $$5$$. Both numbers have three digits, and each digit is used only once. He adds these two numbers. What is the greatest sum Gregor can get? (adapted from 2012 Math Kangaroo Problem, Level 3 - 4, Question \\#19) ", "answer_option_list": [[{"aoVal": "A", "content": "$$753$$ "}], [{"aoVal": "B", "content": "$$861$$ "}], [{"aoVal": "C", "content": "$$951$$ "}], [{"aoVal": "D", "content": "$$1086$$ "}], [{"aoVal": "E", "content": "$$1110$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers"], "answer_analysis": ["If we want to get the sum as large as possible, the hundred digits for both numbers should be as large as possible. Therefore, they should be $$5$$ and $$4$$. The sum of the hundreds digits is $$9$$. For the same reason, the sum of the tens digits should be $$3+2=5$$ and the sum of the ones digits should be $$1 + 0 = 1$$. Therefore, $$\\rm C$$ is the correct answer. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2229", "queId": "c8f5ab72dee64ba29bd237beab8c4d82", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$10$$ cards in a box, which numbered $$1$$, $$3$$, $$4$$, $$6$$, $$7$$, $$11$$, $$15$$, $$16$$, $$18$$, and $$20$$, respectively. Cathy picks a card from the box randomly. What is the probability the number on the card that Cathy picks is a multiple of $3$? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac 1{10}$ "}], [{"aoVal": "B", "content": "$\\frac 3{10}$ "}], [{"aoVal": "C", "content": "$\\frac 2{5}$ "}], [{"aoVal": "D", "content": "$\\frac 1{2}$ "}], [{"aoVal": "E", "content": "$\\frac 3{5}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["$3, 6, 15,$ and $18$ are multiples of $3$. Thus, the probability is $\\frac 2{5}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2230", "queId": "73df234c360c46889db15ddef2154564", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$29$$ students in a certain class. $$12$$ of the students have a sister and $$18$$ of the students have a brother. In this class, only Tania, Barbara, and Anna do not have any siblings. How many students from this class have both a brother and a sister? ($$2003$$ Math Kangaroo Problems, Level $$3-4$$, Question \\#$$17$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$None "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["$(12+18)-(29-3)=4$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2233", "queId": "b6afd547783243b39f95efd2947832a8", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In how many ways can the digits in $3433256337$ be rearranged so that two or more $3$s are not adjacent to each other? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1800$$ "}], [{"aoVal": "B", "content": "$$1200$$ "}], [{"aoVal": "C", "content": "$$1000$$ "}], [{"aoVal": "D", "content": "$$720$$ "}], [{"aoVal": "E", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["There are $5$ $3$s in total. There are $\\_5P\\_5$ ways for us to arrange the other $5$ letters\\textquotesingle{} positions. Then, we can put the five $3$s in the $6$ intervals. So the answer is $\\_5P\\_5 \\times \\_6C\\_5=720$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2238", "queId": "8df2e70b7aa744e7b89c7f95f186fc31", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$31$$ children stand in a row from the shortest to the tallest. The last child is $$131$$ cm height. Tom stands the $${{10}^{\\text{th}}}$$ place counting from the first. No two children have the same height. What is the maximum height of Tom? (The height of all the children are whole numbers.) ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ cm "}], [{"aoVal": "B", "content": "$$105$$ cm "}], [{"aoVal": "C", "content": "$$110$$ cm "}], [{"aoVal": "D", "content": "$$111$$ cm "}], [{"aoVal": "E", "content": "$$125$$ cm "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Extreme Value in Inclusion-Exclusion for Multi-sets"], "answer_analysis": ["$$131-21=110$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2239", "queId": "8a5a81e305b44d33adcaf64875f66995", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In Bill\\textquotesingle s class, every student can play either piano, or violin, or both. $24$ of his classmates can play piano, and the number of students that can play violin is half of that of playing piano. If there are $4$ students who can play both, how many students are there in the class? ", "answer_option_list": [[{"aoVal": "A", "content": "$$68$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$38$$ "}], [{"aoVal": "D", "content": "$$34$$ "}], [{"aoVal": "E", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle"], "answer_analysis": ["$24+24\\div2-4=32$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2240", "queId": "787f25f5874a4360b53a9bdd25c1370f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Four students asked their teacher, Mr. Carter, to line up with them to take a picture. ①If Mr. Carter does not want to stand on either end, how many different ways can they line up for the picture? ②If Mr. Carter insists on standing on one of the $2$ ends, how many different ways can they line up for the picture? ", "answer_option_list": [[{"aoVal": "A", "content": "$72$ , $24$ "}], [{"aoVal": "B", "content": "$96$ , $24$ "}], [{"aoVal": "C", "content": "$72$ , $48$ "}], [{"aoVal": "D", "content": "$96$ , $48$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems"], "answer_analysis": ["①$$3\\times 4\\times 3\\times 2\\times 1=72$$ , ②$$2\\times 4\\times 3\\times 2\\times 1=48$$ . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2242", "queId": "8e011fec98824c37ad4ce316baf6ca30", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$13\\times 21+26\\times 23+39\\times 11=$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$130$$ "}], [{"aoVal": "B", "content": "$$1300$$ "}], [{"aoVal": "C", "content": "$$260$$ "}], [{"aoVal": "D", "content": "$$2600$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"], "answer_analysis": ["$$=13\\times(21+46+33)=1300$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2244", "queId": "97060e7e21a4450faeae9a6584af0c4e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are 70 beads.~ $$A$$ and $$B$$ take turns taking beads from the pile ($$A$$ goes first). Each person can take between 1 and 4 beads per turn. The person who takes the last bead loses. If $$A$$ wants to win, how many beads should he take on the first turn? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$A$$ can\\textquotesingle t win "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$(70-1)\\div (1+4)=13\\cdots 4$$ $$A$$ takes four bead first, and then regardless of how many beads $$B$$ takes, as long as the sum of $$A$$ and $$B$$ is 5, $$A$$ will win. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2245", "queId": "9707dc686ef940da95cade9459f8e225", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The password for a bankbook has six digits (digits can be $$0$$). Mr. Wang forgets the first digit. The probability that he can get the first digit right on his first try is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{6}$$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{9}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{10}$$ "}], [{"aoVal": "D", "content": "$$\\frac{1}{12}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Statistical Graphs"], "answer_analysis": ["∵ There are $$10$$ possible situations. However, there\\textquotesingle s only one time for him to get the first digit right at the first try. ∴ The probability that he can get the first digit right at the first try is $$\\frac{1}{10}$$. So $$\\text{D}$$ is the answer. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2247", "queId": "cd96f1c6dd6d462f806f9b15f9a82883", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Kevin has $3$ regular dice. Each dice has numbers from $1$ to $6$. Which of the following could not be the sum of the numbers on top of the $3$ dice? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$22$$ "}], [{"aoVal": "E", "content": "All the above numbers are possible sum "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["maximum is 6+6+6 = 18. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2248", "queId": "8e06d0b667304217bb98a69538beedab", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$56+127+34+73=$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$190$$ "}], [{"aoVal": "B", "content": "$$290$$ "}], [{"aoVal": "C", "content": "$$390$$ "}], [{"aoVal": "D", "content": "$$490$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["$56+127+34+73=(56+34)+(127+73)=90+200=290$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2250", "queId": "7d052e0439c54d9e8156534f4eb7c59a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A film on TV lasts $$2$$ hours and $$28$$ minutes, and finishes at $$11.18 \\text{p}.\\text{m}.$$ At what time does it start? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8.10\\text{p}.\\text{m}.$$ "}], [{"aoVal": "B", "content": "$$8.50\\text{p}.\\text{m}.$$ "}], [{"aoVal": "C", "content": "$$9.10\\text{p}.\\text{m}.$$ "}], [{"aoVal": "D", "content": "$$9.50\\text{p}.\\text{m}.$$ "}], [{"aoVal": "E", "content": "$$1.46\\text{p}.\\text{m}.$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$$8.50\\text{p}.\\text{m}.$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2252", "queId": "81801030bcb94e30aab60c5616e8ae9d", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In a regular hexagonal prism, how many pairs of parallel edges can you find? ", "answer_option_list": [[{"aoVal": "A", "content": "$$33$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$\\_4C\\_2\\times3+\\_6C\\_2=33$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2254", "queId": "7d09e14d04f4403387b0797a4f9d0896", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of all the even numbers between $30$ and $40$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$72$$ "}], [{"aoVal": "B", "content": "$$108$$ "}], [{"aoVal": "C", "content": "$$140$$ "}], [{"aoVal": "D", "content": "$$144$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["Even number between 30 and 40: 32,34,36,38 $$32+34+36+38=140$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2256", "queId": "a4ae5374837f43c1b17864e66398bb5a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many of the following statements are wrongt? Statement $1$: The probability of a certain event to happen is $$1$$. Statement $2$: Indefinite events include impossible events. Statement $3$: The probability of an impossible event to happen is $$0$$. Statement $4$: The probability of an indefinite event to happen is between $$0$$ and $$1$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Impossible events are definite events. $$\\text{Statement 2}$$ is wrong. $$\\text{Statement 1}$$, $$\\text{Statement 3}$$, and $$\\text{Statement 4}$$ are right. Thus, the answer is $$\\text{D}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2257", "queId": "d6c9e498579440029124ccff90582e18", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A drawer contains ten identical yellow socks, eight identical blue socks and four identical pink socks. Amrita picks socks from the drawer without looking. What is the smallest number of socks she must pick to be sure that she has at least two pairs of matching socks? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems"], "answer_analysis": ["Two matching pairs of socks could be obtained by choosing four socks, but this is not certain. For instance, two of one colour, one of a second colour and one of a third colour could be drawn. Combinations of five chosen socks would give two matching pairs unless three socks of one colour, one of a second colour and one of a third colour were chosen. When this is the case, drawing a sixth sock would guarantee that there would be two matching pairs as there would now be either four socks of one colour plus two other socks or three socks of one colour, two of a second colour plus one of a third colour. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2262", "queId": "78be18a696b54de0bd4c3361c47a299f", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Peter bought a carpet 36dm wide and 60dm long. The figure shows part of this carpet. As seen, the carpet has a small squares contianing either a sun or a moon. You can count that along the width there are nine squares. When the carpet is fully unrolled, how many moons will be seen? [Insert pic] ", "answer_option_list": [[{"aoVal": "A", "content": "$$68$$ "}], [{"aoVal": "B", "content": "$$67$$ "}], [{"aoVal": "C", "content": "$$65$$ "}], [{"aoVal": "D", "content": "$$63$$ "}], [{"aoVal": "E", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures->Classifying and Enumerating->Counting Figures Formed by Grid Points"], "answer_analysis": ["Each small square is 36/9 = 4 dm on a side. there are 60/4 = 15 squares along the length. Both dimensions, 15 and 9, are odd. Also the corners are suns, so there is one more sun than there are moons. Thus, there are a total of (15 x 9 - 1)/2 = 67 moons in the carpet when fully rolled. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2264", "queId": "9bb76f7860dd436f9fb8c8e7eda7ff4e", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There are $$12$$ gold coins with exactly the same appearance, including $$11$$ real coins and $$1$$ fake coin. The weight of the fake coin is different from that of the real coin, and whether the fake coin is lighter or heavier than the real coin is unknown. How many times at least do you need to weigh the coins using a balance before finding the fake coin?. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["In the first weighing with the balance, put coins $$1$$, $$2$$, $$3$$, and $$4$$ on one end of the balance and coins $$5$$, $$6$$, $$7$$, and $$8$$ on the other end of the balance. The balance has two situations: balanced or not. Analyze the situation of the balance: if balanced, the fake coin is among the remaining $$4$$ coins. In the second weighing with the balance, randomly take $$3$$ coins from coin $$1$$ to coin $$8$$ and put them on the left end of the balance and randomly take $$3$$ coins from coin $$9$$ to coin $$12$$ and put them on the right end of the balance (such as $$9$$, $$10$$, $$11$$). The balance also has two situations: balanced or not. If balanced, coin $$12$$ is the coin of different weight. In the third weighing with the balance, comparing No. $$12$$ coin with any other coin, whether the coin is lighter or heavier can be known. If not, it can be known that the coin of different weight is among the three coins $$9$$, $$10$$, and $$11$$, and that whether it is lighter or heavier than other coins can be known. In the third weighing with the balance, randomly take two of the coins (such as $$9$$ and $$10$$) and put them on the both ends of the balance. If balanced, the remaining coin (coin $$11$$) is the one we are looking for; if not, based on the previous judgement that whether the coin is lighter or heavier, it can be determined that which one of the coins on the balance is what we are looking for. Analyze the first imbalanced situation as follows: There are two situations: the right end weighs more or the left end weighs more. Assume the left end weighs more (which is the same for the situation that the right end weighs more.) In the second weighing with the balance, take off $$3$$ coins randomly from the left end (such as $$1$$, $$2$$, and $$3$$) and move $$3$$ coins from the right end to the left end (such as $$5$$, $$6$$, and $$7$$), then take $$3$$ coins randomly from the $$4$$ coins left in the first weighing (such as $$9$$, $$10$$, and $$11$$) to the right end, and there sees $$3$$ situations for the balance: ① the left end weighs more, ② the two ends strike a balance, ③ the right end weighs more. Analyze the situations one by one as follows: ① If the left end weighs more, the coin we are looking for must be coin $$4$$ or coin $$8$$. In the third time weighing with the balance, take one of the coins (such as coin $$4$$) and put it on the left end of the balance. Randomly take one of the remaining $$10$$ coins and put it on the right end. There also sees $$3$$ situations. $$a$$: If balanced, coin $$8$$ is the one we are looking for. Based on the result of using the balance for the second time, it is known that the coin weighs less than other coins. $$b$$: If the left end weighs more, coin $$4$$ is the one we are looking for and it weighs more than other coins. $$c$$: If the right end weighs more, coin $$4$$ is the one we are looking for and it weighs less than other coins. ② If the two ends strike a balance, the coin we are looking for is among the three coins ($$1$$, $$2$$, and $$3$$) taken from the left end. Since the left end weighs more in the first weighing, it is known that the coin weighs more than other coins. The following analysis is the same as previous one and will not be repeated. ③ If the right end weighs more, the coin we are looking for is among the three coins ($$5$$, $$6$$, and $$7$$) moved from the right end to the left end. Based on the results of weighing in the first two times (the left end weighs more in the first weighing and the right end weighs more in the second weighing), it is known that the coin weighs less than other coins. The following analysis is the same. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2266", "queId": "81b15b7870c54aa9894e9c77f1bada85", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A top hat contains $$3$$ red chips and $$2$$ green chips. Chips are drawn randomly, one at a time without replacement, until all $$3$$ of the reds are drawn or until both green chips are drawn. What is the probability that the $$3$$ reds are drawn? (2016 AMC 8 Problems, Question \\#21) ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3}{10}$$ "}], [{"aoVal": "B", "content": "$$\\frac{2}{5}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "D", "content": "$$\\frac{3}{5}$$ "}], [{"aoVal": "E", "content": "$$\\frac{7}{10}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability"], "answer_analysis": ["There are two ways of ending the game, either you picked out all the red chips or you picked out all the green chips. We can pick out $3$ red chips, $3$ red chips and $1$ green chip, $2$ green chips, $2$ green chips and $1$ red chip, and $2$ green chips and $2$ red chips. Because order is important in this problem, there are $1+4+1+3+6=15$ ways to pick out the chip. But we noticed that if you pick out the three red chips before you pick out the green chip, the game ends. So we need to subtract cases like that to get the total number of ways a game could end, which $15-5=10$. Out of the $10$ ways to end the game, $4$ of them ends with a green chip. The answer is $\\frac{4}{10}=\\frac{2}{5}$, or $(\\mathbf{B}) \\frac{2}{5}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2268", "queId": "92bf4864c32d4e089857f171c93afce4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many minutes is it from $$22:45$$ today to $$00:35$$ tomorrow? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90 $$ "}], [{"aoVal": "B", "content": "$$ 100 $$ "}], [{"aoVal": "C", "content": "$$ 110 $$ "}], [{"aoVal": "D", "content": "$$120 $$ "}], [{"aoVal": "E", "content": "$$130$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["It is $$75$$ minutes from $$22:45$$ to midnight and then another $$35$$ minutes from midnight until $$00:35$$. So the required number of minutes is $$75 + 35 = 110$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2269", "queId": "c92da52e8baa43ee93674526f1313219", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A box contains blue marbles. Another two boxes contain only white marbles. Label on Box $$\\rm A$$: white marbles Label on Box $$\\rm B$$: blue marbles Label on Box $$\\rm C$$: Box $$\\rm B$$ contains blue marbles Which box contains blue marbles if two of the above labels are wrong? ", "answer_option_list": [[{"aoVal": "A", "content": "Box A "}], [{"aoVal": "B", "content": "Box B "}], [{"aoVal": "C", "content": "Box C "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis"], "answer_analysis": ["If Box $$\\rm A$$ has the wrong label, it contains blue marbles. This indicates that Box $$\\rm B$$ has the wrong label too, because only one box has blue marbles. It also means that Box $$\\rm C$$ has the wrong label. We will then have a scenario of three wrong labels, so Box $$\\rm A$$ cannot be the one having the wrong label. If Box $$\\rm A$$ has the right label, Box $$\\rm B$$ and Box $$\\rm C$$ will have the wrong labels. Box $$\\rm A\\rightarrow$$ white marbles Box $$\\rm B\\rightarrow$$ white marbles Box $$\\rm C\\rightarrow$$ blue marbles Box $$\\rm C$$ contains blue marbles. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2273", "queId": "e93689fd72a04d6aa73015316c7700ae", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Each of the 5 sides and the 5 diagonals of a regular pentagon are randomly and independently colored red or blue with equal probability. What is the probability that there will be a triangle whose vertices are among the vertices of the pentagon such that all of its sides have the same color? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{2}{3}$ "}], [{"aoVal": "B", "content": "$\\frac{105}{128}$ "}], [{"aoVal": "C", "content": "$\\frac{125}{128}$ "}], [{"aoVal": "D", "content": "$\\frac{253}{256}$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Instead of finding the probability of a same-colored triangle appearing, let us find the probability that one does not appear. After drawing the regular pentagon out, note the topmost vertex; it has $4$ sides/diagonals emanating outward from it. We do casework on the color distribution of these sides/diagonals. Case 1: all $4$ are colored one color. In that case, all of the remaining sides must be of the other color to not have a triangle where all three sides are of the same color. We can correspondingly fill out each color based on this constraint, but in this case you will always end up with a triangle where all three sides have the same color by inspection. Case $2$: $3$ are one color and one is the other. Following the steps from the previous case, you can try filling out the colors, but will always arrive at a contradiction so this case does not work either. Case $3$: $2$ are one color and $2$ are of the other color. Using the same logic as previously, we can color the pentagon $2$ different ways by inspection to satisfy the requirements. There are $\\left(\\begin{array}{l}4 \\textbackslash\\textbackslash{} 2\\end{array}\\right)$ ways to color the original sides/diagonals and 2 ways after that to color the remaining ones for a total of $6 \\cdot 2=12$ ways to color the pentagon so that no such triangle has the same color for all of its sides. These are all the cases, and there are a total of $2^{10}$ ways to color the pentagon. Therefore the answer is $1-\\frac{12}{1024}=1-\\frac{3}{256}=\\frac{253}{256}=D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2274", "queId": "e49df06486544a86a809fd0f082b1b7c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In my hometown, city streets are numbered with odd numbers in increasing order from south to north and with even numbers in increasing order from west to east. In what direction must I travel if I want to go directly from $$241\\text{st}$$ Street to $$225\\text{th}$$ Street? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$north "}], [{"aoVal": "B", "content": "$$$$south "}], [{"aoVal": "C", "content": "$$$$east "}], [{"aoVal": "D", "content": "$$$$west "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Directions and Coordinates->Directions"], "answer_analysis": ["In my hometown, city streets are numbered with odd numbers in increasing order from south to north. I must travel from north to south to go directly from $$241\\text{st}$$ Street to $$225\\text{th}$$ Street.~ When I travel from north to south, I travel south. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2275", "queId": "b6f351859db742cc8373892b74f48f51", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Anna went to travel by bike. She started at $8$ am. But she had to stop for $15$ minutes on the way and arrived at $12$ am. How long did Anna ride her bicycle? (adapted from 2011 Math kangaroo Problems, Level 3-4 , Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$3$ hours $$45$$ min "}], [{"aoVal": "B", "content": "$3$ hours $$35$$ min "}], [{"aoVal": "C", "content": "$2$ hours $$45$$ min "}], [{"aoVal": "D", "content": "$3$ hours $$25$$ min "}], [{"aoVal": "E", "content": "$3$ hours $$45$$ min "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$$12:00-8:00=4$$ h $4$h- $15$min =$3$ h $45$min "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2277", "queId": "b26dac281b974552897d16efa880dc23", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Peter rolls two standard six-sided dice at the same time. What is the probability that the sum of both rolls is a prime number less than $6$? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{7}{36}$. "}], [{"aoVal": "B", "content": "$\\dfrac{1}{6}$. "}], [{"aoVal": "C", "content": "$\\dfrac{5}{36}$. "}], [{"aoVal": "D", "content": "$\\dfrac{1}{9}$. "}], [{"aoVal": "E", "content": "$\\dfrac{5}{12}$. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["There are $7$ out of $36$ outcomes which are prime numbers under $6$: $1+1$, $1+2$, $1+4$, $2+1$, $2+3$, $3+2$, $4+1$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2278", "queId": "78ea81008c2b4cf79bd932b8d0ce58d8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Abe has $1$ green and $1$ red jelly bean in his hand. Bob has $1$ green and $2$ yellow jelly beans in his hand. Each randomly picks a jelly bean to show to the other. What is the probability that the colours match? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "C", "content": "$\\dfrac{3}{4}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{6}$ "}], [{"aoVal": "E", "content": "$\\frac{1}{9}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The probability that both show a green bean is $\\dfrac{1}{2}\\cdot \\dfrac{1}{3}=\\dfrac{1}{6}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2280", "queId": "b6fb81ab751842238043bc15bf8f5f62", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Mary, Nancy, and Peter are playing archery. They have $$7$$ identical arrows in total. Each of them must shoot at least once. How many different ways can they shoot the arrows? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["There are 3 different people here, so order does matter. Each of them must shoot at least once: $$7=1+1+5$$ $$7=1+2+4$$ $$7=1+3+3$$ $$7=1+4+2$$ $$7=1+5+1$$ $\\textasciitilde$ $$7=2+1+4$$ $$7=2+2+3$$ $$7=2+3+2$$ $$7=2+4+1$$ $\\cdots$ And so on. If we keep listing, total will be: $$5+4+3+2+1=15$$ ways "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2281", "queId": "e93dd156683445918d5efba1b79271a0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $2$ black balls and $3$ white balls in an opaque bag. They are of identical shape, size and quality except for color. Under the condition that the balls cannot be seen, take out $3$ balls from the bag at a time randomly. Among the following events, the certain one is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "Among the $3$ balls taken out, at least $1$ is white. "}], [{"aoVal": "B", "content": "Among the $3$ balls taken out, at least $1$ is black. "}], [{"aoVal": "C", "content": "Among the $3$ balls taken out, at least $2$ are black. "}], [{"aoVal": "D", "content": "Among the $3$ balls taken out, at least $2$ are white. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$\\text{A}$$ is a certain event. $$\\text{B}$$ is a random event, so it\\textquotesingle s wrong. $$\\text{C}$$ is a random event, so it\\textquotesingle s wrong. $$\\text{D}$$ is a random event, so it\\textquotesingle s wrong. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2284", "queId": "c4a8a47fb8364bf2a7c21ca356a2b148", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "During Black Friday, a store earned a revenue of $80000$ dollars in one week. How much money can the store earn in a year, approximately, considering there are $52$ weeks in a year? ", "answer_option_list": [[{"aoVal": "A", "content": "4.16 million dollars "}], [{"aoVal": "B", "content": "4.17 million dollars "}], [{"aoVal": "C", "content": "4.18 million dollars "}], [{"aoVal": "D", "content": "unable to determine "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The sample is biased becuase Black Friday is a promotion which allowed the store to earn way much more than they usually earn. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2285", "queId": "92e0e9a53ae442d199ea1f56926df954", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Four friends, Edwin, Fred, Gary and Howard, were playing together when one of them broke a vase. The teacher asked: \"Who is the culprit?\" Both Edwin and Howard said, \"Not me.\" Fred said, \"Howard broke the vase.\" Gary said, \"Fred is the culprit.\" If only one of four boys was lying,~\\uline{~~~~~~~~~~}~broke the vase. ", "answer_option_list": [[{"aoVal": "A", "content": "Edwin "}], [{"aoVal": "B", "content": "Fred "}], [{"aoVal": "C", "content": "Gary "}], [{"aoVal": "D", "content": "Howard "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Either Fred or Howard must be lying since what they said did not tally. Since only one person was lying, Gary was telling the truth i.e, Fred broke the vase. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2287", "queId": "a4e9f13f98054b7da541931c70eb783e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2015 P2 Q2 For the number sentence below, what is the answer? $$15+15+15+15+15+15+15+15+15+15+15+15+15+15+15$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$210$$ "}], [{"aoVal": "B", "content": "$$215$$ "}], [{"aoVal": "C", "content": "$$220$$ "}], [{"aoVal": "D", "content": "$$225$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["7 x 30 + 15 = 210 + 15 = 225 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2292", "queId": "a4f076952a3b400fab68f7e0276001a4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$2$$ beds and $$4$$ chairs have a total mass of $$240$$$$\\text{kg}$$. $$1$$ bed weighs as much as $$6$$ chairs. Find the mass of $$1$$ chair. ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ $$\\text{kg}$$ "}], [{"aoVal": "B", "content": "$$15$$ $$\\text{kg}$$ "}], [{"aoVal": "C", "content": "$$24$$ $$\\text{kg}$$ "}], [{"aoVal": "D", "content": "$$30$$ $$\\text{kg}$$ "}]], "knowledge_point_routes": ["Overseas In-curriculum->Knowledge Point->Algebra-> Numbers, Letters and Equations->Equivalent Substitution->Direct Substitution", "Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$$240\\div16=15\\text{kg}$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2294", "queId": "c02f0d0143d946ed8b24afa50b84dd48", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A box contains seven cards, each with a different integer from $$1$$ to $$7$$ written on it. Avani takes three cards from the box and then Niamh takes two cards, leaving two cards in the box. Avani looks at her cards and then tells Niamh \"I know the sum of the numbers on your cards is even.\" What is the sum of the numbers on Avani\\textquotesingle s cards? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["To obtain an even number when adding two integers, both integers must be even or both integers must be odd. Therefore the four integers remaining once Avani has removed her three integers must all be odd or all be even or there would be a possibility that the sum of Niamh\\textquotesingle s two integers could be odd. Since there were four odd integers and three even integers on the cards in the box initially, the integers on the cards remaining once Avani has removed her cards are all odd. Therefore the cards Avani removed had the three even integers $$2$$, $$4$$ and $$6$$ written on them which have sum $$12$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2297", "queId": "f71fb69843fe470db8cd1eb8b3d74d31", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Maria had $$28$$ dreams last month. If $$16$$ of them involved monkeys, $$15$$ involved squirrels, and $$4$$ involved no animals, then at least how many dreams involved both monkeys and squirrels? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Maria had $$28$$ dreams last month, $$24$$ of which involved animals. Since $$16+ 15 =31$$ involved moneys or squirrels, then at least $$31 - 24 = 7$$ dreams involved both monkeys and squirrels. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2298", "queId": "b71537b50ca84e93ad633bbeea57a953", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Nine chairs are in a straight line and numbered $$1$$ to $$9$$ from left to right. Five girls and four boys sit in the chairs so that no girl is next to another girl. A boy could be sitting in the chair with which number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["The girls must be in the odd-numbered seats; otherwise, two girls would be seated next to each other. This leaves only the even-numbered seats for the boys, so a boy is seated in seat $$4$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2299", "queId": "9779dd7f66c34a08938ee67dd57af11f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Fill in the blank:~\\uline{~~~~~~~~~~}~is 2 tens 8 ones less than 5 tens 5 ones. ", "answer_option_list": [[{"aoVal": "A", "content": "$$27$$ "}], [{"aoVal": "B", "content": "$$37$$ "}], [{"aoVal": "C", "content": "$$73$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["55 - 28 = 27 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2300", "queId": "9c05cda4ab74421595036a965f31bc9e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In Tim\\textquotesingle s class, there are $$20$$ students who can swim, $$25$$ students who can play basketball, and $$10$$ students who can do both. If everyone in the class plays at least one sport, how many students are there in Tim\\textquotesingle s class?~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$32$$ "}], [{"aoVal": "B", "content": "$$33$$ "}], [{"aoVal": "C", "content": "$$34$$ "}], [{"aoVal": "D", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$20+25-10=35$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2307", "queId": "9796c245051d418f92d4eee9e998c33c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Alice\\textquotesingle s average score on the first four assignments is $$89$$. She got $$94$$ on the fifth assignment. What is Alice\\textquotesingle s average score on all five assignments? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ "}], [{"aoVal": "B", "content": "$$91$$ "}], [{"aoVal": "C", "content": "$$92$$ "}], [{"aoVal": "D", "content": "$$93$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)"], "answer_analysis": ["$$89\\times4=356$$ $$356+94=450$$ $$450\\div5=90$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2311", "queId": "a0a592ed2df44c0cbb10e99c74e982b2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jack, Sarah, and Jimmy participated in a Maths competition. \\textbf{Jack says: \"I won the competition.\"} \\textbf{Sarah says: \"I didn\\textquotesingle t win the competition.\"} \\textbf{Jimmy says: \"Jack didn\\textquotesingle t win the competition.\"} Only one of them told the truth. Who won the Maths competition? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$Jack "}], [{"aoVal": "B", "content": "Sarah "}], [{"aoVal": "C", "content": "Jimmy "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["We can spot that Jack\\textquotesingle s statement and Jimmy\\textquotesingle s statement contradict each other, so one of them is telling the truth. Therefore, Sarah tells a lie. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2313", "queId": "c96cc632f57b4425b11279a8f2aa29e2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Maria had $$28$$ dreams last month. If $$16$$ of them involved monkeys, $$15$$ involved squirrels, and $$4$$ involved no animals, then at least how many dreams involved both monkeys and squirrels? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["Maria had $$28$$ dreams last month, $$24$$ of which involved animals. Since $$16+ 15 =31$$ involved moneys or squirrels, then at least $$31 - 24 = 7$$ dreams involved both monkeys and squirrels. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2318", "queId": "8eca05934a3e497da86abe0383d3f6ec", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Joann and Sana have $20$ dresses in total. Joann gives half of her dresses to Claire, and then she and Sana have $14$ dresses in total. How many dresses does Sana have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["Joann gives $20-14=6$ dresses to Claire. Joann has $6+6=12$ dresses originally. Sana has $20-12=8$ dresses. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2321", "queId": "9c3917ccb5d6457bb6192fb0e86e4002", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Vansen left for school at $6:30$ am. He took half an hour to walk from his house to school. Ron reached school $1$ hour later than Vansen. At what time did Ron reach school? (adapted from 2009 Math Kangaroo Problem, Level 3-4, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$7:00$ am. "}], [{"aoVal": "B", "content": "$8:00$ am. "}], [{"aoVal": "C", "content": "$8:45$ am. "}], [{"aoVal": "D", "content": "$9:00$ am. "}], [{"aoVal": "E", "content": "$10:00$ am. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["Half an hour after $6:30$ is $7:00$ $7+1=8$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2324", "queId": "bbd5c995868249a89d7d1c6ac3c392d4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a certain country, a part of the residents can speak English only, a part can speak French only and the rest can speak both languages. It is known that $$85\\textbackslash\\%$$ residents can speak English and $$75\\textbackslash\\%$$ can speak French. What percent of the residents of this country can speak both English and French? ($$2002$$ Math kangaroo Problem, Level $$7-8$$, Question \\#$$17$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$50\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$57\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$25\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$60\\textbackslash\\%$$ "}], [{"aoVal": "E", "content": "$$40\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["$85\\textbackslash\\%+75\\textbackslash\\%-100\\textbackslash\\%=60\\textbackslash\\%$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2326", "queId": "fbe3b83d7a0c42bb9511c5c95517d771", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Tim, an adventurer, found three treasure chests in the cave. Only one of the chests contains the treasure. The following clues are written on the three treasure chests respectively: \\textbf{Treasure chest A: \"The treasure is not in Treasure chest C!\"} \\textbf{Treasure chest B: \"The treasure is not here!\"} \\textbf{Treasure chest C: \"The treasure is here!\"} Given that only one sentence of the above three is true, which chest should Tim open to get the treasure? ", "answer_option_list": [[{"aoVal": "A", "content": "A "}], [{"aoVal": "B", "content": "B "}], [{"aoVal": "C", "content": "C "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis"], "answer_analysis": ["The clues on treasure chest A and C are conflicting, so either A or C is telling the truth. Thus, the clue on treasure chest B is a lie. Therefore, the treasure is in chest B. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2328", "queId": "b2d83d45a2ce435ea7e529e294e89be0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Eddie, Avril and Pip want to share 10 cakes. Eddie only wants to get 3 cakes. Avril and Pip want to get at least 1 cake. How many ways are there to share the cakes? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["$$Omitted.$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2332", "queId": "a55b24a987114aa5a2ee64e4f5a0418e", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "The correct information James can get from the statement \"there is a $11\\textbackslash\\%$ chance that it will rain tomorrow in Los Angeles\"~is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "It will rain $11\\textbackslash\\%$ of the time tomorrow in Los Angeles. "}], [{"aoVal": "B", "content": "It will rain in $11\\textbackslash\\%$ of the regions in Los Angeles tomorrow. "}], [{"aoVal": "C", "content": "It will definitely rain tomorrow in Los Angeles. "}], [{"aoVal": "D", "content": "The probability of raining in Los Angeles is high. "}], [{"aoVal": "E", "content": "The probability of raining in Los Angeles is low. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["It is less likely to rain tomorrow in Los Angeles. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2334", "queId": "dbc93a3b6a1e435596c5021d882a4db5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Mia has a date tomorrow. She has $2$ hats, $3$ dresses, and $3$ pairs of shoes. Now she wants to choose one dress and one pair of shoes. How many options does she have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["She does not need to choose a hat. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2335", "queId": "ce16f4810a404d9092b07c6bba10d330", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Amy picks some numbers as shown below: $13, 20, 14, 15, 19, 20, 20, 19, 19, 15, 19, 19, 20, 13, 15$. What is the difference between their mode and median? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$19$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["She picks two $13$s, one $14$, three $15$s, five $19$s, and four $20$s. The mode is $19.$ The median is $19.$ Thus, their difference should be $0.$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2337", "queId": "a0e9b31ab9bf41d081984672445be84e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many multiples of 6 are there between 14 and 100? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2340", "queId": "b776a11b77aa435c9f6cbdd3c7746604", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$30$$ pupils in my class. $$20$$ pupils like Maths and $$18$$ pupils like English. Twice as many pupils like both subjects as those that like neither of them. How many pupils like only Maths? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Let the number of pupils who like neither subject be $$x$$. Hence the number who like both subjects is $$2x$$. Therefore the number of pupils who like only Maths is $$20−2x$$ and the number who like only English is $$18−2x$$. Since there are $$30$$ pupils in my class, we have $$\\left( 20-2x \\right)+2x+\\left( 18-2x \\right)+x=30$$ and hence $$38−x = 30$$. This has solution $$x = 8$$ and hence the number of pupils who like only Maths is $$20-2\\times 8=4$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2342", "queId": "ae779cff3fa44d2fb7cccfd6f1c3b067", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Betty and Abby are playing a game. They take turns writing numbers from $$1$$ to $$52 $$ on a blackboard. Each person can only write $$1$$, $$2$$, $$3$$ or $$4$$ numbers at a time, and each number can only be written once. The person who has no more numbers to write loses. Should Betty go first or second in order to win? ", "answer_option_list": [[{"aoVal": "A", "content": "First "}], [{"aoVal": "B", "content": "Second "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$52$$ is not a multiple of $$4+1$$, so the first player will win the game. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2345", "queId": "fbfa878ceb284cbbae63e7cf308c78d5", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Ashley and Elvis are playing a game that requires them to drink a total of $$12$$ cups of coffee. They take turns drinking and each can drink either $$1$$ or $$2$$ cups at a time. The person who finishes the last cup of coffee wins this game. Should Elvis go first or second to ensure victory? ", "answer_option_list": [[{"aoVal": "A", "content": "Go first "}], [{"aoVal": "B", "content": "Go second "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["$$12$$ is a multiple of $$2+1$$, so, the second player should make the total number for each round to be $$3$$ to ensure victory. Therefore, Elvis should go second to ensure his vitory. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2346", "queId": "aa058978e30e457390bb16522b4f758a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the smallest possible sum of two positive integers whose product is $$240$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$34$$ "}], [{"aoVal": "E", "content": "$$38$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Since the product of the two positive integers is $$240$$, the possible pairs of integers are $$\\left( 1,240 \\right)$$, $$\\left( 2,120 \\right)$$, $$\\left( 3,80 \\right)$$, $$\\left( 4,60 \\right)$$, $$\\left( 5,48 \\right)$$, $$\\left( 6,40 \\right)$$, $$\\left( 8,30 \\right)$$, $$\\left( 10,24 \\right)$$, $$\\left( 12,20 \\right)$$ and $$\\left( 15,16 \\right)$$. The respective sums of these pairs are $$241$$, $$122$$, $$83$$, $$64$$, $$53$$, $$46$$, $$38$$, $$34$$, $$32$$ and $$31$$. Of these, the smallest value is $$31$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2348", "queId": "a5820d815e3542f39c45ae3f7cd2512b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2014 P2 Q9 Two $1 coins and ten 50c coins are randomly distributed among 4 children such that each child receives the same number of coins. What is the difference between the biggest amount and the smallest amount a child can receive? ", "answer_option_list": [[{"aoVal": "A", "content": "$$50c$$ "}], [{"aoVal": "B", "content": "$1 "}], [{"aoVal": "C", "content": "$1.50 "}], [{"aoVal": "D", "content": "$2 "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["There are a total of 2+10 = 12 coins. so each child receives 12/4 = 3 coins. Largest possible is $1 + $1 +50c= $2.50. smallest possible is 50c + 50c + 50c= $1.50 $2.50 - $1.50 = $1 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2354", "queId": "c9b1f3a248b44867a71ce86ded57cf1a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Maria had $$28$$ dreams last month. If $$16$$ of them involved monkeys, $$15$$ involved squirrels, and $$4$$ involved no animals, then at least how many dreams involved both monkeys and squirrels? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["Maria had $$28$$ dreams last month, $$24$$ of which involved animals. Since $$16+ 15 =31$$ involved moneys or squirrels, then at least $$31 - 24 = 7$$ dreams involved both monkeys and squirrels. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2357", "queId": "f76b6dbfbbfd4d34af39b0933c9af5fb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$6\\times6$ =~\\uline{~~~~~~~~~~}~groups of $4$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["6x6=36; $$36\\div4=9$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2359", "queId": "a12259d74b2940ecbb1e536d4f96c877", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy, Bill and Celine are friends with different ages. Exactly one of the following statements is true. $$\\rm I$$. Bill is the oldest. $$\\rm II$$. Amy is not the oldest. $$\\rm III$$. Celine is not the youngest. Rank the friends from oldest to youngest. ", "answer_option_list": [[{"aoVal": "A", "content": "Bill, Amy, Celine "}], [{"aoVal": "B", "content": "Amy, Bill, Celine "}], [{"aoVal": "C", "content": "Celine, Amy, Bill "}], [{"aoVal": "D", "content": "Celine, Bill, Amy "}], [{"aoVal": "E", "content": "Amy, Celine, Bill "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions"], "answer_analysis": ["If Bill is the oldest, then Amy is not the oldest, and both statements $$\\rm I$$ and $$\\rm II$$ are true, so statement $$\\rm I$$ is not the true one. If Amy is not the oldest, and we know Bill cannot be the oldest, then Celine is the oldest. This would mean she is not the youngest, and both statements $$\\rm II$$ and $$\\rm III$$ are true, so statement $$\\rm II$$ is not the true one. Therefore, statement $$\\rm III$$ is the true statement, and both $$\\rm I$$ and $$\\rm II$$ are false. From this, Amy is the oldest, Celine is in the middle, and lastly Bill is the youngest. This order is $$\\rm E$$. Amy, Celine, Bill. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2361", "queId": "a124f8e223ad47308b56e9dfe697cbfa", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$17$$ balls in a bag. Each ball has a number from $$1$$ to $$17$$ on it. We randomly pick a ball from the bag. What is the smallest number of balls we have to pick in order to be sure that we have at least one pair of balls with a sum equal to $$18$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$17$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems"], "answer_analysis": ["Among these numbers, there are $$8$$ pairs of numbers can get the sum of $$18$$($$1+17=2+16=3+15=4+14=5+13=6+12=7+11=$$$$8+10$$), and $$9$$ is useless. So in the worst case, after we choose $$9$$, we need $$8+1=9$$ more numbers to make sure a pair appears. Thus, the answer is $$1+8+1=10$$. Copyrighted material used with permission from Math Kangaroo in USA, NFP Inc. ($$2005$$ Math Kangaroo Problem, Level $$9-10$$, Question $$ \\textbackslash\\# $$$$15$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2363", "queId": "aeaa5ac24ae54bb698855a055f3d265a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Pip multiplies all the digits in the number $$145$$ to get $$20$$. What's the biggest three digit number whose digits multiply together to give $$30$$?~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$999$$ "}], [{"aoVal": "B", "content": "$$922$$ "}], [{"aoVal": "C", "content": "$$651$$ "}], [{"aoVal": "D", "content": "$$532$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations->Basic Operations of Combinations"], "answer_analysis": ["$$651$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2365", "queId": "a5b3e8f27d1d4344917251f9120b41f1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Vicky is ordering lunch at a fast food restaurant that has sandwiches and burgers on the lunch menu, along with coffee, milk, and tea as drink options. If Vicky chooses one food item and one drink item from the lunch menu, she has~\\uline{~~~~~~~~~~}~different ways to order lunch. ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$2\\times 3=6$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2366", "queId": "93d81ea6b4dc41f1855426d2ed7c8350", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the following events, the certain event is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "Ame will get $$100$$ points in the final math exam. "}], [{"aoVal": "B", "content": "Claire will eat breakfast tomorrow. "}], [{"aoVal": "C", "content": "The news is on when you open the TV. "}], [{"aoVal": "D", "content": "There are two red balls and one white ball in a bag. If two balls are taken out, one must be red. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$\\text{A}$$. \"Ame will get $100$ points in the final math exam\" is a random event. $$\\text{B}$$. \"Claire will eat breakfast tomorrow.\" is a random event. $$\\text{C}$$. \"The news is on when you open the TV\" is a random event. $$\\text{D}$$. There are two red balls and one white ball in a bag. If two balls are taken out, one must be red. It is a certain event. So $$\\text{D}$$ is the answer. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2374", "queId": "c5501eef7cec4125ac04849014b374e3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a two-digit number, the digit in the ones place is 3. The digit in the tens place is 3 more than the digit in the ones place. What is the number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$63$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$66$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"], "answer_analysis": ["NA "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2375", "queId": "bc4b07a56d4242418a4ac08dd38d6d05", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two tiles numbered $1$ and $2$ are turned face down, respectively. One tile is turned up at random, and throw a die to get a number from $1$ to $6$. What is the probability that the product of the numbers on the tile and the die is greater than or equal to $10$? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac {1}{2}$ "}], [{"aoVal": "B", "content": "$\\frac {1}{6}$ "}], [{"aoVal": "C", "content": "$\\frac {1}{3}$ "}], [{"aoVal": "D", "content": "$\\frac {1}{4}$ "}], [{"aoVal": "E", "content": "$\\frac {1}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $12$ different combinations. The product of two numbers is greater than or equal to $10$ will be $2\\times5$ and $2\\times6$. Thus, the probability is $\\frac 2{12}$ = $\\frac 16$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2381", "queId": "a5eb55733af14fc5be1a65ed43c0ac59", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The Dragonvale Middle School chess team consists of two boys and three girls. A photographer wants to take a picture of the team to appear in the local newspaper. She decides to have them sit in a row with a boy at each end and the three girls in the middle. How many such arrangements are possible? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Boy, Girl, Girl, Girl, Boy.There are $$2\\times 1=2$$ ways of arranging two boys; there are $$3\\times 2\\times 1=6\\textasciitilde$$ways of arranging $3$ girls. Therefore, there are $$2\\times 6=12$$ ways of arranging all students. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2382", "queId": "e9cd7929a30c4bb497735c00e81a5047", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Martina and Linda had $$68$$ seashells. After Martina gave $$8$$ seashells to Linda, they had an equal amount of seashells. How many seashells did Martina have at first? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$42$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$ 68\\div 2=34$$, $$34+8=42$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2383", "queId": "c569d2401d0f48f6858865b7262402a0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$60$$ pupils in Arnold\\textquotesingle s class. $$35$$ pupils like Maths and $$38$$ pupils like English. Twice as many pupils like both subjects as those that like neither of them. How many pupils like only Maths? ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$27$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Let the number of pupils who like neither subject be $$x$$. Hence the number who like both subjects is $$2x$$. Therefore the number of pupils who like only Maths is $$35−2x$$ and the number who like only English is $$38−2x$$. Since there are $$60$$ pupils in Arnold\\textquotesingle s class, we have: $$\\left( 35-2x \\right)+2x+\\left( 38-2x \\right)+x=60$$ and hence $$x = 13$$ and hence the number of pupils who like only Maths is $$35-(2\\times 13)=9$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2386", "queId": "a5f647926dbc420399f3d5a9c31e5e66", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Julia, Kasia, Zuzanna, and Helena have their birthdays on March $$1^{\\rm st}$$, May $$17^{\\rm th}$$, July $$20^{\\rm th}$$, and March $$20^{\\rm th}$$. Kasia and Zuzanna were born in the same month. Julia and Zuzanna were born on the same day of a month. Which of the girls was born on May $$17^{\\rm th}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "Julia "}], [{"aoVal": "B", "content": "Kasia "}], [{"aoVal": "C", "content": "Zuzanna "}], [{"aoVal": "D", "content": "Helena "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions"], "answer_analysis": ["Given that Kasia and Zuzanna were born in the same month, their birth month must be March. Given that Julia and Zuzanna were born on the same day of a month, they must be born on the $$20^{\\rm th}$$. Hence, Zuzanna was born on March $$20$$; Kasia was born on March $$1$$; and Julia was born on July $$20$$. Helena is therefore the one born on May $$17$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2387", "queId": "ce7df7e183e1440b858a6062bd5d3d6c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A box contains blue marbles. Another two boxes contain only white marbles. Label on Box $$\\rm A$$: white marbles Label on Box $$\\rm B$$: blue marbles Label on Box $$\\rm C$$: Box $$\\rm B$$ contains blue marbles Which box contains blue marbles if two of the above labels are wrong?． ", "answer_option_list": [[{"aoVal": "A", "content": "Box A "}], [{"aoVal": "B", "content": "Box B "}], [{"aoVal": "C", "content": "Box C "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis"], "answer_analysis": ["If two of the labels are wrong, \\textbf{one label is correct.} If the label on Box A is correct, Box A contains white marbles. The label on Box B is wrong, so Box B contains white marbles. The label on Box C is wrong, so Box B contains white marbles. Therefore, Box A and Box B contain white marbles, while \\textbf{Box C} contains blue marbles. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2394", "queId": "e0bfced69d294a35bdb29ccdd8aa58b9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Three kids line up to play games. How many different ways can they form the line? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems"], "answer_analysis": ["There are six different ways for three kids to line up. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2396", "queId": "bc8b0dd2a6fa4b168cd0772f89bc9a56", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "An elementary school is arranging students\\textquotesingle{} schedules. For the first class in the morning, it has to be Chinese or Maths or English. Students won\\textquotesingle t start the day with the same class for two days in a row. If Wednesday starts with Chinese, then Thursday can start with~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "Chinese or Maths "}], [{"aoVal": "B", "content": "Maths or English "}], [{"aoVal": "C", "content": "English or Chinese "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Tree Diagrams"], "answer_analysis": ["Students won\\textquotesingle t start the day with the same class for two days in a row. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2398", "queId": "a61d91c2f3554c36a848ff4b32e30423", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Granny has $$10$$ grandchildren. Alice is the oldest. One day, Granny notices that her grandchildren all have different ages. If the sum of her grandchildren\\textquotesingle s ages is $$180$$, what is the youngest age that Alice can be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$19$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$21$$ "}], [{"aoVal": "D", "content": "$$22$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"], "answer_analysis": ["Try to consider the problem of the youngest Alice in such way: make each grandchild has a similar age as possible, and the age of each grandchild should be different, that is, $$1 + 2 + 3 +\\cdots 9 + 10 = 55$$; then $$180 - 55 = 125$$, $$125 \\div 10 = 12\\cdots\\cdots5$$, and $$5$$ is left. If every child\\textquotesingle s age is added by $$12$$, then $$5$$ is left. Give the extra year to each of the $$5$$ children who are the oldest. In doing so, the minimum number of Alice\\textquotesingle s age is $$10+12+1=23$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2401", "queId": "ce9f35d71ed640a786178e2a7f43155e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\dfrac{1}{2}$$ of the pens in a box are red, $$\\dfrac{1}{4}$$ of the remainder are blue and the rest are green. What percentage of the pens in the box are green? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12.5\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$25\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$37.5\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$75\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Word Problems Involving Fractions and Percentages->Finding the Percentage Given a Part and a Whole", "Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["Remainder $=1-\\frac{1}{2}=\\frac{1}{2}$ Green $=1-\\frac{1}{4}=\\frac{3}{4}$ of remainder $=\\frac{3}{4}\\times\\frac{1}{2}$ of total $=\\frac{3}{8}$ of total $=\\frac{3}{8}\\times100\\textbackslash\\%=37.5\\textbackslash\\%$ of total "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2402", "queId": "cea2680dc2644c8ca9e12ed694d8df3b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Using the digits $$1$$, $$3$$, and $$9$$, we can form~\\uline{~~~~~~~~~~}~different 3-digit numbers without repeating digits. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Three-digit:$$139$$, $$193$$, $$319$$, $$391$$ , $$913$$, $$931$$ for a total of $$6$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2403", "queId": "cea3c62e291d457eb01dae8ca219c1b9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Four students asked their teacher, Mr Carter, to line up with them to take a picture. ① If Mr Carter does not want to stand on either end, how many different ways can they line up for the picture? ② If Mr Carter insists on standing on one of the $2$ ends, how many different ways can they line up for the picture? ", "answer_option_list": [[{"aoVal": "A", "content": "$72$ , $24$ "}], [{"aoVal": "B", "content": "$96$ , $24$ "}], [{"aoVal": "C", "content": "$72$ , $48$ "}], [{"aoVal": "D", "content": "$96$ , $48$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems"], "answer_analysis": ["①$$3\\times 4\\times 3\\times 2\\times 1=72$$ , ②$$2\\times 4\\times 3\\times 2\\times 1=48$$ . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2406", "queId": "c5a63070999b4b91a54935ddf8bbcc64", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When Pinocchio lies, his nose gets 6 cm longer. When he tells the truth, his nose gets 2 cm shorter. When his nose was 9cm long, he told three lies and made twotrue statments. How long was Pinnochio\\textquotesingle s nose afterwards? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$cm "}], [{"aoVal": "B", "content": "$$15$$cm "}], [{"aoVal": "C", "content": "$$19$$cm "}], [{"aoVal": "D", "content": "$$23$$cm "}], [{"aoVal": "E", "content": "$$31$$cm "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["9 + (3 x 6) - (2 x 2) = 23cm. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2407", "queId": "dc54ca8438214cde85383b78815ff4e7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Four boys each prepared $1$ gift for a party. How many ways can these $4$ gifts be \\textsubscript{} distributed among the $4$ kids so that no one receives his own gift? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$1$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration"], "answer_analysis": ["Let the boys be A, B,~C and D and their gifts be 1, 2, 3 and 4. List down all possible arrangements: (A2, B1, C4, D3), (A2, B3, C4, D1), (A2, B4, C1, D3), (A3, B1, C4, D2), (A3, B4, C2, D1), (A3, B4, C1, D2), (A4, B1, C2, D3), (A4, B3, C2, D1), (A4, B3, C1, D2) There are \\textbf{9} possible arrangements. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2409", "queId": "a63e9ccc9ebe41a8a22286a7f6b279ca", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many three-digit whole numbers have a ones digit equal to the sum of the hundreds digit and the tens digit? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["If the ones digit is $$2$$, the $$2$$ numbers are $$202$$ and $$112$$. For each ones digit, the number of possible numbers is the same as the ones digit. In all, there are $$1+2+3+\\cdots+8+9 =45$$ numbers. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2412", "queId": "bcb32ca7ba83490fa0745c83abd5f8c7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of all the digits in the number $2023$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$2+0+2+3=7$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2414", "queId": "af43aa09c7134446b78f5960fc214021", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "The correct information James can get from the statement ``there is a $11\\textbackslash\\%$ chance that it will rain tomorrow in Los Angeles'' is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "It will rain $11\\textbackslash\\%$ of the time tomorrow in Los Angeles. "}], [{"aoVal": "B", "content": "It will rain in $11\\textbackslash\\%$ of the regions in Los Angeles tomorrow. "}], [{"aoVal": "C", "content": "It will definitely rain tomorrow in Los Angeles. "}], [{"aoVal": "D", "content": "The probability of raining in Los Angeles is high. "}], [{"aoVal": "E", "content": "The probability of raining in Los Angeles is low. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["It is less likely to rain tomorrow in Los Angeles. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2415", "queId": "d7d60869cbeb41ebab2d03b0d102f2e2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ron\\textquotesingle s work day is half over at $$1:15$$ P.M. if he starts work at $$9:30$$ A.M., his work day ends at． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4:30$$ P.M. "}], [{"aoVal": "B", "content": "$$5:00$$ P.M. "}], [{"aoVal": "C", "content": "$$5:30$$ P.M. "}], [{"aoVal": "D", "content": "$$9:30$$ P.M. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["From $$9:30$$ A.M. until $$1:15$$ P.M. is $$3$$ hours and $$45$$ minutes. Add $$3$$ hours and $$45$$ minutes to $$1:15$$ P.M. to get $$5:00$$ P.M.. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2416", "queId": "e580d20ee3e447eeb3fea060defb06b3", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "What time is $$11999$$ hours after $$3$$ P.M.? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ A.M. "}], [{"aoVal": "B", "content": "$$2$$ P.M. "}], [{"aoVal": "C", "content": "$$4$$ A.M. "}], [{"aoVal": "D", "content": "$$4$$ P.M. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$12000$$ hours after $$3$$ P.M. is $$3$$ P.M. $$11999$$ hours after $$3$$ P.M is $$2$$ P.M. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2417", "queId": "a65eafe014e64617a3346747ac7d190b", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "Moon and Archie played chess competitively. Both of them are of the same level in terms of skill. They agreed to play in a best-of-seven games, where the one who wins four games first would be the ultimate winner. They have already played three games, with Moon winning two games and Archie winning just one game. What is the probability that Moon will be the ultimate winner? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3}{8}$$ "}], [{"aoVal": "B", "content": "$$\\frac{11}{16}$$ "}], [{"aoVal": "C", "content": "$$\\frac{3}{16}$$ "}], [{"aoVal": "D", "content": "$$\\frac{7}{16}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$\\rm B$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2418", "queId": "eea371b244b34ad7842f480d2f34b255", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ms. Osborne asks each student in her class to draw a rectangle with integral side lengths and a perimeter of $$50$$ units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles? ", "answer_option_list": [[{"aoVal": "A", "content": "$$76$$ "}], [{"aoVal": "B", "content": "$$120$$ "}], [{"aoVal": "C", "content": "$$128$$ "}], [{"aoVal": "D", "content": "$$132$$ "}], [{"aoVal": "E", "content": "$$136$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"], "answer_analysis": ["As we know, the sum of the length and width is $$25$$. The largest area is $$13\\times12=156$$ and the smallest area is $$24\\times1=24$$, so the difference is $$156-24=132$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2419", "queId": "dc6dcb8d42a748ae8d20fbb83b097956", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Sandy, Sam, and Steve are observing a cat in the distance. The cat is eating something but it\\textquotesingle s hard to tell what it is. Sandy says:\"The cat is eating fish.\" Sam says:\"I agree with Sandy!\" Steve says: \"The cat is eating meat.\" Then they come closer and realize only one of them guessed right. The cat is eating . ", "answer_option_list": [[{"aoVal": "A", "content": "　meat "}], [{"aoVal": "B", "content": "　fish "}], [{"aoVal": "C", "content": "　Not certain "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["We can directly find that Sandy\\textquotesingle s point and Sam\\textquotesingle s point are identical,so both of them tell lies.Therefore, Steve tells the truth. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2422", "queId": "b84b8086106340249e6b7cd7a9ba4b42", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Today is Tuesday, and Cindy eats cakes today. She will eat cakes again after $5$ days. What day will it be? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Friday "}], [{"aoVal": "D", "content": "Thursday "}], [{"aoVal": "E", "content": "Wednesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures"], "answer_analysis": ["Today is Tuesday, and $5$ days later will be Sunday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2428", "queId": "f34ccda45217476381bb9ca89f85248f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "One day, Pip asks his parents: \"What day is it today?\" His mother says: \"Today is Monday.\" His father says: \"Today is Tuesday.\" From the options below, which one do you agree with? ", "answer_option_list": [[{"aoVal": "A", "content": "One of these two sentences is definitely wrong and the other one is correct. "}], [{"aoVal": "B", "content": "It is possible that both of Pip\\textquotesingle s parents are wrong. "}], [{"aoVal": "C", "content": "It is possible that both of Pip\\textquotesingle s parents are right. "}], [{"aoVal": "D", "content": "If Pip\\textquotesingle s mother is wrong, then his father must be right "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing"], "answer_analysis": ["\"Today is Monday\" is not the opposite of \"Today is Tuesday\".i.e. they can both be false. \"Today is Monday\" is the direct opposite of \"Today is not Monday\". One must be true and the other must be false. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2433", "queId": "d37cad20ddaa4cefb601bb3dbc0c4276", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many different three-digit numbers can we make using the digits $$2$$, $$4$$, and $$6$$? (Each digit can be used only once.) ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations->Basic Operations of Combinations"], "answer_analysis": ["$246, 264, 426, 462, 624, 642$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2435", "queId": "b879e45163ce4a22b695ad1d9c34da20", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is $$542$$ hundredths? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.0542$$ "}], [{"aoVal": "B", "content": "$$0.542$$ "}], [{"aoVal": "C", "content": "$$5.42$$ "}], [{"aoVal": "D", "content": "$$54.02$$ "}], [{"aoVal": "E", "content": "$$54.2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$$542$$ hundredths $=5$ ones, $4$ tenths and $2$ hundredths $=5.42$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2436", "queId": "fc9caa5fc3334cfa9b37b390a55ae5e0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two tiles numbered $1$ and $2$ are turned face down, respectively. One tile is turned up at random, and throw a die to get a number from $1$ to $6$. What is the probability that the product of the numbers on the tile and the die is greater than or equal to $12$? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac {1}{2}$ "}], [{"aoVal": "B", "content": "$\\frac {1}{6}$ "}], [{"aoVal": "C", "content": "$\\frac {1}{3}$ "}], [{"aoVal": "D", "content": "$\\frac {1}{4}$ "}], [{"aoVal": "E", "content": "$\\frac {1}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $12$ different combinations. The product of two numbers is greater than $12$ will be $2\\times6$. Thus, the probability is $\\frac 1{12}$ . "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2439", "queId": "ab21b4645a044e75aa66f47bd474ad08", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many two-digit numbers are there where the ones digit is greater than the tens digit?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$26$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$8+7+6+5+4+3+2+1=36$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2442", "queId": "ab251de94f1a4ce0a1a7a702241294c8", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many different four-digit numbers can be formed by rearranging the four digits in $2004$?~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$81$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["0 shouldn\\textquotesingle t be put in the highest digit. There are two 0s The solutions are: 2400, 2040, 2004, 4200, 4020, 4002. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2444", "queId": "ab2c17c6c6494a07b392bc009fd7a8c4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When Coco the Caterpillar is not sleeping, he eats $$5$$ grams of leaves per hour. Yesterday he slept $$20$$ hours. How many grams of leaves did he eat yesterday? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["Yesterday he did not sleep for $$24 - 20 = 4$$ hours, so he ate $$4 \\times 5 = 20$$ grams of leaves. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2446", "queId": "dca8ee477c0c4f62be97c544e454b510", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eight pupils from Victory Primary School take a Mathematics test, but none of the pupils wrote his/her name on the test. The tests are therefore handed back to the pupils at random. In how many ways can exactly $5$ of the $8$ pupils get the correct test back? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$56$$ "}], [{"aoVal": "D", "content": "$$112$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"], "answer_analysis": ["If exactly $5$ pupils get the correct test, then exactly $3$ pupils must get the wrong test. No. of ways to choose $5$ pupils to get the correct test is $$\\frac{8 \\times 7 \\times 6 \\times 5 \\times 4}{5 \\times 4 \\times 3 \\times 2 \\times 1}-56.$$ To make sure that the other $3$ pupils get the wrong tests, the correct number is $2$. Hence, the total no, of ways $=56 \\times2=112$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2448", "queId": "dcad7eb7c4a34404823f2c333ad628d4", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In how many ways can the letters in $BEEKBBPER$ be rearranged so that two or more $E$s do not appear together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4200$$ "}], [{"aoVal": "B", "content": "$$900$$ "}], [{"aoVal": "C", "content": "$$800$$ "}], [{"aoVal": "D", "content": "$$720$$ "}], [{"aoVal": "E", "content": "$$700$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["There are $3$ $E$s in total now with other $6$ letters remaining. But pay attention to $B$: there are $3$ $B$s here. There are $\\_6P\\_3$ ways for us to arrange the $6$ letters\\textquotesingle{} positions. Then, we can put the $3$ $E$s in the $7$ intervals. So the answer is $\\_6P\\_3 \\times \\_7C\\_3=4200$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2451", "queId": "bd20e4135a1843e2a7cc3bf68b67d32b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Pip multiplies all the digits in the number $$145$$ to get $$20$$. How many three digit numbers are there whose digits multiply to give $$20$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations->Basic Operations of Combinations"], "answer_analysis": ["$$145, 154, 415, 451, 514, 541, 225, 252, 522$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2452", "queId": "cf1e8441163d46f992fac984ca91d12f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ranson holds $3$ white and $9$ purple jelly beans in his hand. Nancy holds $2$ white, $5$ yellow, and $2$ purple jelly beans in her hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match? (adapted from $2013$ AMC $8$ Problem, Question \\# $14$) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{6}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "C", "content": "$\\dfrac{2}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "E", "content": "$\\dfrac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["The probability that both show a white bean is $\\dfrac{3}{12}\\times \\dfrac{2}{9}=\\dfrac{1}{18}$. The probability that both show a purple bean is $\\dfrac{9}{12}\\times \\dfrac{2}{9}=\\dfrac{1}{6}$. Therefore, the probability is $\\dfrac{1}{18}+\\dfrac{1}{6}=\\frac29$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2454", "queId": "cf23660aa74b4175a1af0dd2f69671a4", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "Linda picks $3$ different numbers from $$1-15$$. To make the sum of the three numbers divisible by $3$, how many different groups are there for Linda to pick? ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$910$$ "}], [{"aoVal": "C", "content": "$$91$$ "}], [{"aoVal": "D", "content": "$$155$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["Group $A$: $$1$$, $$4$$, $$7$$, $$10$$, $13$; Group $B$: $$2$$, $$5$$, $$8$$, $$11$$, $$14$$; Group $C$: $$3$$, $$6$$, $$9$$, $$12$$, $$15$$. Linda can choose three numbers from the same group, or choose each number from a different group to get the sum she needs. There are $3\\times\\_5C\\_3+5\\times5\\times5=155$ groups. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2455", "queId": "eef21b75d2494366bb82308b1151deb8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$5$$ dancers. Every $$2$$ dancers will have a dance. How many dances would they have in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$25$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$4+3+2+1=10$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2461", "queId": "d3b94fd0e3644f609ae3840c205b2115", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If your average score on your first six mathematics tests was $84$ and your average score on your first seven mathematics tests was $85$, then your score on the seventh test was ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$86$$ "}], [{"aoVal": "B", "content": "$$88$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$91$$ "}], [{"aoVal": "E", "content": "$$92$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)"], "answer_analysis": ["The total score of the first six tests was $84\\times6=504$, and the total score of the first seven tests was $85\\times7=595$. Therefore, the score of the seventh test equals to the difference: $595-504=91$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2472", "queId": "c6527faea2834d1196949ba2dba9a447", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Take out $$4$$ digits from $101112131415$ to make the rest of the digits into a new $8-$digit number without changing the order of digits. The least possible value of the new number is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10111111$$ "}], [{"aoVal": "B", "content": "$$10111110$$ "}], [{"aoVal": "C", "content": "$$10111100$$ "}], [{"aoVal": "D", "content": "$$10111011$$ "}], [{"aoVal": "E", "content": "$$10111112$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["To make it the least, you should make the digit in the first place as small as possible. Thus the $$2$$, $$3$$, $4$ and $$5$$ should be taken out. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2473", "queId": "fcef3f4c348346119f05bbbe0cb3458f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many two-digit numbers have digits whose sum is a perfect square? (2006 AMC 8 Problem, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$19$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["There is 1 integer whose digits sum to $1: 10$. There are 4 integers whose digits sum to $4: 13,22,31$, and 40 . There are 9 integers whose digits sum to $9: 18,27,36,45,54,63,72,81$, and 90 . There are 3 integers whose digits sum to $16: 79,88$, and 97 . Two digits cannot sum to 25 or any greater square since the greatest sum of digits of a twodigit number is $9+9=18$ Thus, the answer is $1+4+9+3=$ (C)17. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2474", "queId": "c6562aa5cfcd403faee3b5e3f12d0904", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Three students go apple-picking. Eddie picks $30$ apples, Avril picks $27$ apples, and Mike picks $33$ apples. How many apples does each of them pick on average? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ "}], [{"aoVal": "B", "content": "$$45$$ "}], [{"aoVal": "C", "content": "$$31$$ "}], [{"aoVal": "D", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["They pick $30+27+33=90$ apples in total. Therefore, on average, each of them picks $90\\div3=30$ apples. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2476", "queId": "bd5e640710994bc08a5ab9b8c4b46b1f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many two-digit numbers are there where the ones digit is greater than the tens~ digit?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$26$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["$$8+7+6+5+4+3+2+1=36$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2478", "queId": "fcfd4633aa54404eb36925fdd3fcaef5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2014 P2 Q1 What is 2014 + 2 x 0 x 1 x 4 equal to? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2014$$ "}], [{"aoVal": "B", "content": "$$2016$$ "}], [{"aoVal": "C", "content": "$$2021$$ "}], [{"aoVal": "D", "content": "$$2022$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"], "answer_analysis": ["anything x 0 = 0 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2479", "queId": "c1e5322370724acab3745a635ce09e1f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There is a ball in a box and three kids are guessing what colour it is. Val says: \"The ball is~red.\" John says: \"The ball is~green.\" Elvis says: \"I agree with~John.\" They open the box and find only one of them guessed right. What colour is the ball? ", "answer_option_list": [[{"aoVal": "A", "content": "red "}], [{"aoVal": "B", "content": "green "}], [{"aoVal": "C", "content": "Uncertain "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing"], "answer_analysis": ["We can spot that John\\textquotesingle s guess and Elvis\\textquotesingle{} guess are the same, so both of them must be wrong. Therefore, Val guessed it right. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2484", "queId": "b4763e9384324301b0d20a819a1de17a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Each of the 20 balls is tossed independently and at random into one of the 5 bins. Let $p$ be the probability that some bin ends up with 3 balls, another with 5 balls, and the other three with 4 balls each. Let $q$ be the probability that every bin ends up with 4 balls. What is $\\frac{p}{q}$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Solution 1: For simplicity purposes, we assume that the balls and the bins are both distinguishable. Recall that there are $5^{20}$ ways to distribute $20$ balls into $5$ bins. We have $$ p=\\frac{5 \\cdot 4 \\cdot\\left(\\begin{array}{c} 20 \\textbackslash\\textbackslash{} 3,5,4,4,4 \\end{array}\\right)}{5^{20}} \\text { and } q=\\frac{\\left(\\begin{array}{c} 20 \\textbackslash\\textbackslash{} 4,4,4,4,4 \\end{array}\\right)}{5^{20}} \\text {. } $$ Therefore, the answer is $$ \\frac{p}{q}=\\frac{5 \\cdot 4 \\cdot\\left(\\begin{array}{c} 20 \\textbackslash\\textbackslash{} 3,5,4,4,4 \\end{array}\\right)}{\\left(\\begin{array}{c} 20 \\textbackslash\\textbackslash{} 4,4,4,4,4 \\end{array}\\right)}=\\frac{5 \\cdot 4 \\cdot \\frac{20 !}{3 ! \\cdot 5 ! \\cdot 4 ! \\cdot 4 ! \\cdot 4 !}}{\\frac{20 !}{4 ! \\cdot 4 ! \\cdot 4 ! \\cdot 4 ! \\cdot 4 !}}=\\frac{5 \\cdot 4 \\cdot(4 ! \\cdot 4 ! \\cdot 4 ! \\cdot 4 ! \\cdot 4 !)}{3 ! \\cdot 5 ! \\cdot 4 ! \\cdot 4 ! \\cdot 4 !}=\\frac{5 \\cdot 4 \\cdot 4}{5}=(\\mathbf{E}) 16 . $$ Solution 2: For simplicity purposes, we assume that the balls and the bins are both distinguishable. Let $q=\\frac{x}{a}$, where $a$ is the total number of combinations and $x$ is the number of cases where every bin ends up with 4 balls. We can take 1 ball from one bin and place it in another bin so that some bin ends up with 3 balls, another with 5 balls, and the other three with 4 balls each. Note that one configuration of $4$-$4$-$4$-$4$-$4$ corresponds to $5 \\cdot 4 \\cdot 4=80$ configurations of $3$-$5$-$4$-$4$-$4$. On the other hand, one configuration of $3$-$5$-$4$-$4$-$4$ corresponds to 5 configurations of $4$-$4$-$4$-$4$-$4$. Therefore, we have $$ p=\\frac{80}{5} \\cdot \\frac{x}{a}=16 \\cdot \\frac{x}{a}, $$ from which $\\frac{p}{q}=$ (E) 16 . "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2485", "queId": "fd0d8d6173de4a41adf8252c46bde370", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Yuki and Claire are looking for a place to eat dinner. They know there are four Chinese restaurants, three French restaurants, and two Peruvian restaurants nearby. There are~\\uline{~~~~~~~~~~}~different choices in total for them to eat one meal in one place. ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["They can only choose one place, so it can only be either Chinese, French, or Peruvian restaurants. Therefore, we can add each one up to get $$4+3+2 = 9$$.~ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2487", "queId": "eabeb8c5c5fe40779c651eb626f9426e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $12$ black balls, $27$ red balls, and $11$ blue balls in an opaque box. The balls are the same except for their colors. Bob adds several red balls in the box and mixes the balls. Now, if the probability of taking out a black ball is $\\frac15$, how many red balls does Bob add? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$\\frac15=\\frac{12}{60}$, which means there are $60$ balls in total. Thus, Bob adds $60-12-27-11=10$ red balls. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2491", "queId": "c20cb81f61c64476aaee692c0191796b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$10$$ players in a chess tournament. If each game is played by $$2$$ players, and each player plays every other player exactly once, what is the total number of games played in the tournament? ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition"], "answer_analysis": ["There are $10$ players and each player plays $9$ games, so there are $10 \\times 9 \\div 2 = 45$ games in total. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2492", "queId": "e63d6b2dd6754002a17adb214e6604b9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Among $$30$$ children, there are at least~\\uline{~~~~~~~~~~}~children born in the same month. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["There are $$12$$ months. Thus, $$30\\div 12=2R6$$ and hence $$2+1=3$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2493", "queId": "d417d5dca1e34d569125b63827cc8532", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If the sum of $$9$$ numbers is $$1998$$, then their average is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$9+1998$$ "}], [{"aoVal": "B", "content": "$$9\\times 1998$$ "}], [{"aoVal": "C", "content": "$$1998\\div 9$$ "}], [{"aoVal": "D", "content": "$$9\\div 1998$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The average of any $$9$$ numbers is their sum divided by $$9$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2496", "queId": "eadab1d59ac24d1e9ae00cde0a91c8d5", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In the Coin Game, you toss three coins at the same time. You win only if the 3 coins are all showing heads, or if the 3 coins are all showing tails. If you play the game once only, what is the probability of winning? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{6}$ "}], [{"aoVal": "B", "content": "$\\frac{1}{3}$ "}], [{"aoVal": "C", "content": "$\\frac{2}{27}$ "}], [{"aoVal": "D", "content": "$\\frac{2}{3}$ "}], [{"aoVal": "E", "content": "$\\frac{1}{4}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Typical Probability Problems->Tossing Coins"], "answer_analysis": ["When tossing a single coin, there are two possible outcomes, a head (H) or a tail (T). When tossing 2 coins, there are $$2 \\times 2 = 4 $$possible outcomes. These are HH, HT, TH, and TT. When tossing 3 coins, there are $$2 \\times 2 \\times 2 = 8 $$possible outcomes. These are HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. Of these 8 possible outcomes, there are 2 winning outcomes, HHH and TTT. Thus, the probability of winning the Coin Game is $\\frac{1}{4}$ . Answer: E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2500", "queId": "ef70ffef212f4a8f81175aa644b19a19", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many different four-digit numbers can be formed by rearranging the four digits in $2021$?~(Adapted from $2004$ AMC $8$ Problem, Question \\#2) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"], "answer_analysis": ["When the thousand digit is $2$, there are $\\_3P\\_3=6$ ways. When the thousand digit is $1$, there are $\\_3C\\_1=3$ ways. So the answer is $3+6=9$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2504", "queId": "d435b88f8f31478fa6111cff560271c7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Paula shoots arrows at the following target. When she misses, she obtains zero points. Paula shoots two arrows and adds the number of points. Which of the following sums cannot be her score? ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$70$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$90$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["A is possible as 30+30 = 60 B is possible as 70+0+0 = 70 C is possible as 30 + 50 = 80 E is ossible as 30 + 70 = 100. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2508", "queId": "e1d7d09be42f49949fdfce15b31d1210", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many different natural numbers can be formed with the numbers $$1$$, $$2$$, $$3$$?（without using the same number two times like $$33$$） ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Dictionary Ordering"], "answer_analysis": ["Classify the number first by the digits and then enumerate． One-digit number：$$1$$、$$2$$、$$3$$， Two-digit number：$$12$$、$$13$$、$$21$$、$$23$$、$$31$$、$$32$$； Three-digit number：$$123$$、$$132$$、$$213$$、$$231$$、$$312$$、$$321$$； So totally $$3+6+6=15$$ different natural numbers can be formed． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2509", "queId": "e6692e2ba24646fa8c2161e8572310c1", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Three kids $$A$$、$$B$$、$$C$$ are playing the game \"pass the ball\". If it starts with $$A$$, he can pass the ball to~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$A$$ or $$B$$ or $$C$$ "}], [{"aoVal": "B", "content": "$$B$$ or $$C$$ "}], [{"aoVal": "C", "content": "$$A$$ or $$C$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Tree Diagrams"], "answer_analysis": ["A cannot pass the ball back to himself. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2511", "queId": "f8c6d87d8300475dafe4573626ecfd6f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "An acronym is a word formed from the first one or more letters of each word in a group of words. If \"UFO\"is an acronym for \"unidentified flying object,\" then for how many of the following word groups could MATH be an acronym? $$\\text{I}$$. Multiply All Those Hundreds $$\\text{II}$$. MArtians Take Hostages $$\\text{III}$$. MATthew Hides $$\\text{IV}$$. Minutes After The Hour ", "answer_option_list": [[{"aoVal": "A", "content": "one　 "}], [{"aoVal": "B", "content": "two　 "}], [{"aoVal": "C", "content": "three　 "}], [{"aoVal": "D", "content": "four　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions"], "answer_analysis": ["For $$\\text{I}$$ and $$\\text{IV}$$, use first letter of each word; for $$\\text{II}$$, use first two letters of first word and first letter of other words; and for $$\\text{III}$$, use first three letters of first word and first letter of second word. MATH could be an acronym for all four word groups. $$\\text{I}$$. Multiply All Those Hundreds $$\\text{II}$$. MArtians Take Hostages $$\\text{III}$$. MATthew Hides $$\\text{IV}$$. Minutes After The Hour "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2517", "queId": "e68631c9420a403eb5bed8bc4ce61599", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$10$$ players in a chess tournament. If each game is played by $$2$$ players, and each player plays every other player exactly once, what is the total number of games played in the tournament? ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["There are $10$ players and each player plays $9$ games, so there are $10 \\times 9 \\div 2 = 45$ games in total. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2519", "queId": "efa5efe78a404b5e81d42cef66fe920b", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Gregor forms two numbers with digits $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, and $$6$$. Both numbers have three digits, and each digit is used only once. He adds these two numbers. What is the greatest sum Gregor can get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$975$$ "}], [{"aoVal": "B", "content": "$$999$$ "}], [{"aoVal": "C", "content": "$$1083$$ "}], [{"aoVal": "D", "content": "$$1173$$ "}], [{"aoVal": "E", "content": "$$1221$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers"], "answer_analysis": ["If we want to get the sum as large as possible, the hundred digits for both numbers should be as large as possible. Therefore, they should be $$6$$ and $$5$$. The sum of the hundreds digits is $$11$$. For the same reason, the sum of the tens digits should be $$3+4=7$$ and the sum of the ones digits should be $$2 + 1 = 3$$. Therefore, $$\\rm D$$ is the correct answer. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2524", "queId": "d47a71fa532d410fb495431263d2fe77", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A fair $6$-sided die is rolled once. What is the probability that the number on the top is an odd number? (adapted from 2011 AMC 8 Problem, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac16$ "}], [{"aoVal": "B", "content": "$\\frac13$ "}], [{"aoVal": "C", "content": "$\\frac12$ "}], [{"aoVal": "D", "content": "$\\frac23$ "}], [{"aoVal": "E", "content": "$\\frac56$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["There are $3$ odd numbers out of $6$, so the probability is $\\frac36=\\frac12$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2526", "queId": "d90a8963a65b4431a2b9f5d3afbb089b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many two-digit numbers are there where the ones digit is greater than the tens digit? (2008 Math Kangaroo Problem, Level 3-4, Question \\#21) ", "answer_option_list": [[{"aoVal": "A", "content": "$$26$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["$$8+7+6+5+4+3+2+1=36$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2530", "queId": "d92127155ba2428bac61aae5756fa92a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy, Bill and Celine are friends with different ages. $$\\rm I$$. Bill is the oldest. $$\\rm II$$. Amy is not the oldest. $$\\rm III$$. Celine is not the youngest. Rank the friends from youngest to oldest. ", "answer_option_list": [[{"aoVal": "A", "content": "Bill, Amy, Celine "}], [{"aoVal": "B", "content": "Amy, Bill, Celine "}], [{"aoVal": "C", "content": "Celine, Amy, Bill "}], [{"aoVal": "D", "content": "Celine, Bill, Amy "}], [{"aoVal": "E", "content": "Amy, Celine, Bill "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions"], "answer_analysis": ["If Bill is the oldest, then Amy is not the oldest, and both statements $$\\rm I$$ and $$\\rm II$$ are true, so statement $$\\rm I$$ is not the true one. If Amy is not the oldest, and we know Bill cannot be the oldest, then Celine is the oldest. This would mean she is not the youngest, and both statements $$\\rm II$$ and $$\\rm III$$ are true, so statement $$\\rm II$$ is not the true one. Therefore, statement $$\\rm III$$ is the true statement, and both $$\\rm I$$ and $$\\rm II$$ are false. From this, Amy is the oldest, Celine is in the middle, and lastly Bill is the youngest. This order is $$\\rm E$$. Amy, Celine, Bill. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2534", "queId": "d025e59893d246d6b42f72bb2b139be0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$30$$ children going to Adventure Park took part in at least one of two events. $$15$$ of them took part in the \"moving bridge\" contest, and $$20$$ of them went down the zip-wire. How many children from Adventure Park took part in both events? ($$2013$$ Math Kangaroo Problems, Level $$3-4$$, Question \\#$$14$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets"], "answer_analysis": ["$15+20-30=5$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2537", "queId": "f92c2e0062c94f90b5de6ce08f77136e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The faces of each of two fair dice are numbered $1$, $2$, $3$, $5$, $7$, and $8$. When the two dice are tossed, what is the probability that their sum will be an even number? (2019 AMC 8 Problems, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{4}{9}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{2}$ "}], [{"aoVal": "C", "content": "$\\dfrac{5}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{3}{5}$ "}], [{"aoVal": "E", "content": "$\\dfrac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["We have a 2 die with 2 evens and 4 odds on both dies. For the sum to be even, the 2 rolls be 2 odds or 2 evens. Ways to roll 2 odds (Case 1 ): The total number of ways to obtain 2 odds on 2 rolls is $4 * 4=16$, as there are 4 possible odds on the first roll and 4 possible odds on the second roll. Ways to roll 2 evens (Case 2 ): Similarly, we have $2 * 2=4$ ways to obtain 2 evens. Probability is $\\frac{20}{36}=\\frac{5}{9}$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2538", "queId": "f48d47fdc56c4bf696a9f1930c0cc651", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many different four-digit odd numbers can be made by using digits $$1$$, $$2$$, $$3$$, $$4$$, and $$5$$ (without digits be repeated)? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$72$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers"], "answer_analysis": ["Rule of product: $$3\\times 4\\times 3\\times 2=72$$; therefore we can choose D. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2539", "queId": "f930f04b14ea48798ce974aee4142547", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many ways are there of making a total of 10 using three different positive numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$1$$ "}], [{"aoVal": "E", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Splitting Whole Numbers"], "answer_analysis": ["$$1+2+7=10$$， $$1+3+6=10$$， $$1+4+5=10$$， $$2+3+5=10$$． So the answer is $$\\text{A}$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2540", "queId": "e6efaac23bf74e2c9aebef6ef6381f64", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A conductor wanted to make a trio consisting of a fiddler, a pianist, and a drummer. He had to choose one of two fiddlers, one of two pianists, and one of two drummers. He decided to try each of the possible trios. How many attempts did he have to make? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"], "answer_analysis": ["$$2\\times2\\times2=8$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2541", "queId": "d9572184f9db488c9fd3385df1a4f731", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Eve brings $$12$$ pieces of candy, Alice brings $$9$$ pieces of candy and Irene doesn\\textquotesingle t bring any candy. They put all the pieces of candy together on a table and divide them equally among themselves. How many pieces of candy does each of the girls get? (2012 Math Kangaroo Problem, Levels 1-2, Question \\#15） ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["They have $12+9=21$ pieces of candy in total. $21\\div3=7$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2543", "queId": "d95d1f305f804593b5f612f66cf11261", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Given that only one of the following statement is corect, which one is correct? ($$1$$) All of the statements below are correct. ($$2$$) None of the statement below is corect. ($$3$$) One of the statements above is corect. ($$4$$) All the statements above are correct. ($$5$$) None of the statement above is corect. ", "answer_option_list": [[{"aoVal": "A", "content": "(1) "}], [{"aoVal": "B", "content": "(2) "}], [{"aoVal": "C", "content": "(3) "}], [{"aoVal": "D", "content": "(4) "}], [{"aoVal": "E", "content": "(5) "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning using Hypothesis"], "answer_analysis": ["Suppose ($$1$$) is correct, then ($$2$$) must be wrong which contradicts that only one statement is correct. Suppose ($$2$$) is correct, then ($$5$$) is correct which contradicts that only one statement is correct. Suppose ($$3$$) is correct, it also contradicts that only one statement is correct. Suppose ($$4$$) is correct, it also contradicts that only one statement is correct. Hence ($$5$$) is the correct statement. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2544", "queId": "e271e8538b984252b78fc49194c8bf83", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The farmer has a fish, a cat, and a dog. He wants to take them cross the river by boat, and he can only take one animal each time. When the farmer is away, the cat cannot be put with the fish or the dog, or they will fight. The boat makes one trip from one side of the river to the other side, so it takes~\\uline{~~~~~~~~~~}~trips in total to carry all the animals and farmers cross the river. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["We can use $A$ to represent the side of the river where the farmer is at the beginning, and use $B$ to represent the other side. The first time, take the cat from $A$ to $B$. The second time, the farmer go back to $A$. The third time, take the fish from $A$ to $B$. The fourth time, take the cat from $B$ to $A$. The fifth time, take the dog from $A$ to $B$. The sixth time, the farmer go back to $A$. The seventh time, take the cat from $A$ to $B$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2548", "queId": "d4ec3b8cda7148c0a16cc37e42785c43", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Two dice are thrown. What is the probability that the product of the two numbers is a multiple of $$5$$? ($$2001$$ AMC $$8$$ Problem, Question \\#$$ 18$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{36}$$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{18}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{6}$$ "}], [{"aoVal": "D", "content": "$$\\frac{11}{36}$$ "}], [{"aoVal": "E", "content": "$$\\frac{1}{3}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"], "answer_analysis": ["$$5$$ is the only multiple of $$5$$ on a die, so one of the numbers rolled must be a $$5$$. To find the probability of rolling at least one $$5$$, we can find the probability of not rolling a $$5$$ and subtract that from $$1$$, since you either roll a $$5$$ or not roll a $$5$$. The probability of not rolling a $$5$$ on either dice is $$\\left( \\frac{5}{6} \\right)\\times\\left( \\frac{5}{6} \\right)=\\frac{25}{36}$$. Therefore, the probability of rolling at least one five, and thus rolling two numbers whose product is a multiple of $$5$$, is $$1-\\frac{25}{36}=\\frac{11}{36}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2551", "queId": "fe14ff795f714e9795b2ec756be29b35", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Mom has $190$ coins in total and wants to give them to Sana as the pocket money. She gives Sana $30$ coins for the first month, and $40$ coins for each of the following months. How many months in total can Sana get the pocket money? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules"], "answer_analysis": ["$190-30=160$ $40+40+40+40=160$ $4+1=5$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2554", "queId": "f98009c9471f4e868f9580e0dd2a76e3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A top hat contains $$3$$ red chips and $$2$$ green chips. Chips are drawn randomly, one at a time without replacement, until all $$3$$ of the reds are drawn or until both green chips are drawn. What is the probability that the $$3$$ reds are drawn? (2016 AMC 8 Problems, Question \\#21) ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3}{10}$$ "}], [{"aoVal": "B", "content": "$$\\frac{2}{5}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "D", "content": "$$\\frac{3}{5}$$ "}], [{"aoVal": "E", "content": "$$\\frac{7}{10}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability"], "answer_analysis": ["There are two ways of ending the game, either you picked out all the red chips or you picked out all the green chips. We can pick out 3 red chips, 3 red chips and 1 green chip, 2 green chips, 2 green chips and 1 red chip, and 2 green chips and 2 red chips. Because order is important in this problem, there are $1+4+1+3+6=15$ ways to pick out the chip. But we noticed that if you pick out the three red chips before you pick out the green chip, the game ends. So we need to subtract cases like that to get the total number of ways a game could end, which $15-5=10$. Out of the 10 ways to end the game, 4 of them ends with a green chip. The answer is $\\frac{4}{10}=\\frac{2}{5}$, or $(\\mathbf{B}) \\frac{2}{5}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2555", "queId": "fe1b1d8608f44dee933e5311baf20726", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My train leaves Southampton and arrives in Birmingham at $$08:48$$ that morning, the duration of the whole journey is $$52$$ minutes, what time does the train leave Southampton? ", "answer_option_list": [[{"aoVal": "A", "content": "$$09:40$$ "}], [{"aoVal": "B", "content": "$$09:30$$ "}], [{"aoVal": "C", "content": "$$07:56$$ "}], [{"aoVal": "D", "content": "$$07:04$$ "}], [{"aoVal": "E", "content": "$$07:40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["The departure time is $$52$$ minutes forward from $$8:48$$. You can push it forward $$48$$ minutes, which is $$8:00$$, and then push it forward $$4$$ minutes, which is $$7:56$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2561", "queId": "de29deaa143a4ba6abcf1ac368fea1c3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the following events, the certain event is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "Toss two identical coins and both land on heads. "}], [{"aoVal": "B", "content": "Throw a fair die and number of the dot shown is $$3$$. "}], [{"aoVal": "C", "content": "Sun sets in the west. "}], [{"aoVal": "D", "content": "It must rain in cloudy days. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["$$\\text{A}$$. Throw a coin randomly. It has a $$50\\textbackslash\\%$$ chance of landing head up and a $$50\\textbackslash\\%$$ chance of landing tail up. $$\\text{B}$$. Throw a die, and number of the dot shown may be any number from $$1$$ to $$6$$. $$\\text{C}$$. Sun sets in the west. $$\\text{D}$$. It may not rain in cloudy days. So $$\\text{C}$$ is the answer. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2562", "queId": "ebea7be40d6142feb0c9c5fdf985ecbe", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The correct understanding of the statement \"there is a $$75\\textbackslash\\%$$ chance that it will rain tomorrow in New York City\" is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "It will rain $$75\\textbackslash\\% $$ of the time tomorrow in New York City. "}], [{"aoVal": "B", "content": "It will rain in $$75\\textbackslash\\%$$ of the regions in New York City tomorrow. "}], [{"aoVal": "C", "content": "It will definitely rain tomorrow in New York City. "}], [{"aoVal": "D", "content": "The probability of raining in New York City tomorrow is high. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["The statement that \"there is a $$75\\textbackslash\\% $$ chance that it will rain tomorrow in New York City\"~shows that it is more likely to rain tomorrow in New York city. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2566", "queId": "f51b0f1a42494b45aaa7fd06da6f9ca7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The digits $1$, $2$, and $3$ can make~\\uline{~~~~~~~~~~}~three-digit numbers without repeating digits. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers"], "answer_analysis": ["$$3\\times 2\\times 1=6$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2570", "queId": "f9c27828896246399f96388ff729aea5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If a turkey facing north turns $$225^{}\\circ $$ clockwise, it will then face． ", "answer_option_list": [[{"aoVal": "A", "content": "southwest　 "}], [{"aoVal": "B", "content": "southeast　 "}], [{"aoVal": "C", "content": "northwest　 "}], [{"aoVal": "D", "content": "northeast　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Directions and Coordinates->Directions"], "answer_analysis": ["Since $$225^{}\\circ =180^{}\\circ +45^{}\\circ $$, the bird turns $$45^{}\\circ $$ past south. That\\textquotesingle s southwest. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2571", "queId": "fe67caa7ac0b4ae18768267a16e4b232", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$17$$ balls in a bag. Each ball has a number from $$1$$ to $$17$$ on it. We randomly pick a ball from the bag. What is the smallest number of balls we have to pick in order to be sure that we have at least one pair of balls with a sum equal to $$18$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$17$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Among these numbers, there are $$8$$ pairs of numbers can get the sum of $$18$$($$1+17=2+16=3+15=4+14=5+13=6+12=7+11=$$$$8+10$$), and $$9$$ is useless. So in the worst case, after we choose $$9$$, we need $$8+1=9$$ more numbers to make sure a pair appears. Thus, the answer is $$1+8+1=10$$. Copyrighted material used with permission from Math Kangaroo in USA, NFP Inc. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2572", "queId": "f0a0dc9591534f4f9f34f325d05b3a94", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$71+82+93+104+195=$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$500$$ "}], [{"aoVal": "B", "content": "$$540$$ "}], [{"aoVal": "C", "content": "$$545$$ "}], [{"aoVal": "D", "content": "$$550$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"], "answer_analysis": ["$$71+82+93+104+195=70+80+90+100+200+5=545$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2576", "queId": "fe883f6135a745e8a4fcf7f257bed7f0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The number of days in July plus the number in August is twice the number of days in． ", "answer_option_list": [[{"aoVal": "A", "content": "March　 "}], [{"aoVal": "B", "content": "April　 "}], [{"aoVal": "C", "content": "June　 "}], [{"aoVal": "D", "content": "November　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"], "answer_analysis": ["Together, July \\& August have $$62$$ days. That\\textquotesingle s twice the $$31$$ days in March. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2580", "queId": "00049e782a754907a240d3d50b2fa854", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Let $f$ be a linear function for which $f(3)-f(2)=5$. What is $f(8)-f(2)$? ( Adapted From 2003 AMC 12B Problems, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Let $f$ be a linear function with slope $m$. $$ \\begin{gathered} m=\\frac{f(3)-f(2)}{\\Delta x}=\\frac{5}{3-2}=5\\textbackslash\\textbackslash{} f(8)-f(2)=m \\Delta x=5(8-2)=30 \\Rightarrow(D) \\end{gathered}$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2595", "queId": "00935489274c4420be1bc9435e88e790", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the $$100\\rm th$$ number in the arithmetic sequence $$1$$, $$5$$, $$9$$, $$13$$, $$17$$, $$21$$, $$25$$, $$\\cdots$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$397$$ "}], [{"aoVal": "B", "content": "$$399$$ "}], [{"aoVal": "C", "content": "$$401$$ "}], [{"aoVal": "D", "content": "$$403$$ "}], [{"aoVal": "E", "content": "$$405$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$$1+(5-1)\\times 99=397$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2598", "queId": "04f4387433cd4a2ab0c0878bfbc44f73", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the correct ordering of the three numbers $$\\dfrac{5}{19}$$, $$\\dfrac{7}{21}$$, and $$\\dfrac{9}{23}$$, in increasing order? ($$2012$$ AMC $$8$$ Problem, Question \\#$$4$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\dfrac{9}{23}\\textless{} \\dfrac{7}{21}\\textless\\dfrac{5}{19}$$ "}], [{"aoVal": "B", "content": "$$\\dfrac{5}{19}\\textless{} \\dfrac{7}{21}\\textless{} \\dfrac{9}{23}$$ "}], [{"aoVal": "C", "content": "$$\\dfrac{9}{23}\\textless{} \\dfrac{5}{19}\\textless{} \\dfrac{7}{21}$$ "}], [{"aoVal": "D", "content": "$$\\dfrac{5}{19}\\textless{} \\dfrac{9}{23}\\textless{} \\dfrac{7}{21}$$ "}], [{"aoVal": "E", "content": "$$\\dfrac{7}{21}\\textless{} \\dfrac{5}{19}\\textless{} \\dfrac{9}{23}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["$$\\rm Method$$ $$1$$: The value of $$\\dfrac{7}{21}$$ is $$\\dfrac{1}{3}$$. Now we give all the fractions a common denominator. $$\\dfrac{5}{19} \\Rightarrow \\dfrac{345}{1311}$$, $$\\dfrac{1}{3} \\Rightarrow \\dfrac{437}{1311}$$, $$\\dfrac{9}{23} \\Rightarrow \\dfrac{513}{1311}$$. Ordering the fractions from least to greatest, we find that they are in the order listed. Therefore, $$\\frac{5}{19}\\textless{} \\frac{7}{21}\\textless{} \\frac{9}{23}$$. $$\\rm Method$$ $$2$$: Instead of finding the LCD, we can subtract each fraction from $$1$$ to get a common numerator. Thus, $$1- \\dfrac{5}{19}= \\dfrac{14}{19}$$, $$1- \\dfrac{7}{21}= \\dfrac{14}{21}$$, $$1- \\dfrac{9}{23}= \\dfrac{14}{23}$$. All three fraction have common numerator $$14$$. Now the order of the fractions is obvious . $$\\dfrac{14}{19}\\textgreater\\dfrac{14}{21}\\textgreater\\dfrac{14}{23}\\Rightarrow\\dfrac{5}{19}\\textless\\dfrac{7}{21}\\textless\\dfrac{9}{23}$$. Therefore, $$\\dfrac{5}{19}\\textless\\dfrac{7}{21}\\textless\\dfrac{9}{23}$$. $$\\rm Method$$ $$3$$: Change $$\\frac7{21}$$ into $$\\frac13$$, $$\\dfrac{1}{3} \\times \\dfrac{5}{5}=\\dfrac{5}{15}$$, $$\\dfrac{5}{15}\\textgreater\\dfrac{5}{19}$$, $$\\dfrac{7}{21}\\textgreater\\dfrac{5}{19}$$, and $$\\dfrac{1}{3} \\times \\dfrac{9}{9}=\\dfrac{9}{27}$$, $$\\dfrac{9}{27}\\textless\\dfrac{9}{23}$$, $$\\dfrac{7}{21} \\textless{} \\dfrac{9}{23}$$. Therefore, $$\\dfrac{5}{19}\\textless\\dfrac{7}{21}\\textless\\dfrac{9}{23}$$. $$\\rm Method$$ $$4$$: When $$\\dfrac{x}{y}\\textless1$$ and $$z\\textgreater0$$, $$\\dfrac{x+z}{y+z}\\textgreater\\dfrac{x}{y}$$. Hence, $$\\dfrac{5}{19}\\textless\\dfrac{7}{21}\\textless\\dfrac{9}{23}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2605", "queId": "00d427d0803742559e253f650218c578", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following statements is true? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4+7=3$$ "}], [{"aoVal": "B", "content": "$$3=4-7$$ "}], [{"aoVal": "C", "content": "$$3+4=7$$ "}], [{"aoVal": "D", "content": "$$4=7+3$$ "}], [{"aoVal": "E", "content": "$$3-7=4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$3+4=7$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2608", "queId": "129d4b2e469145a597227d9f2c2cc46f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alysha and Julia have some biscuits. Altogether they have $28$ biscuits. Alysha has $4$ more biscuits than Julia. How many biscuits does Alysha have? (Adapted from 2021 Math Kangaroo Problem, Level 3-4, Question \\#7) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$(28 + 4) \\div 2 = 16$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2610", "queId": "00e60ed4c40247a2926cd1687b4bfa6b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the simplest form of $5$ minutes$: 30 $ seconds? ", "answer_option_list": [[{"aoVal": "A", "content": "$5:30$ "}], [{"aoVal": "B", "content": "$1:6$ "}], [{"aoVal": "C", "content": "$6:1$ "}], [{"aoVal": "D", "content": "$10:1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["We need to make units same first. $5$ minutes equal to $300$ seconds. Now we could remove the same unit, second. We get $300:30$ and simplify it to $10:1$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2611", "queId": "00f9ce38963f4a39ab403073204edfc8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Let $f$ be a linear function for which $f(6)-f(2)=12$. What is $f(12)-f(2)$? ( 2003 AMC 12B Problems, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Let $f$ be a linear function with slope $m$. $$ \\begin{gathered} m=\\frac{f(6)-f(2)}{\\Delta x}=\\frac{12}{6-2}=3 \\textbackslash\\textbackslash{} f(12)-f(2)=m \\Delta x=3(12-2)=30 \\Rightarrow(D) \\end{gathered}$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2613", "queId": "0511f9f8e31b477babc3320144303d48", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of five consecutive integers is $$2015$$. What is the smallest of these integers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$401$$ "}], [{"aoVal": "B", "content": "$$403$$ "}], [{"aoVal": "C", "content": "$$405$$ "}], [{"aoVal": "D", "content": "$$407$$ "}], [{"aoVal": "E", "content": "$$409$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["Let the five consecutive integers be $$n-2$$, $$n-1$$, $$n$$, $$n + 1$$ and $$n + 2$$. These have a sum of $$5n$$. Hence $$5n=2015$$ and therefore $$n=403$$. Therefore, the smallest integer is $$403-2=401$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2614", "queId": "0512381b057e479dbf94705e0b819514", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Megan wonders how the size of her beagle Herbie compares with other beagles. Herbie is 40.6cm tall. Megan learned on the internet that beagle heights are approximately normally distributed with a mean of 38.5 cm and a standard deviation of 1.25 cm. What is the percentile rank of Herbie's height?} ", "answer_option_list": [[{"aoVal": "A", "content": "$$59$$ "}], [{"aoVal": "B", "content": "$$65$$ "}], [{"aoVal": "C", "content": "$$74$$ "}], [{"aoVal": "D", "content": "$$92$$ "}], [{"aoVal": "E", "content": "$$95$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{Z = $$\\frac{40.6-38.5}{1.25}$$=1.68 → percentile = 0.9535} "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2625", "queId": "2095b32ee5f44460899a8356bfe35756", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$(2+4+6+8+10)\\div (10+8+6+4+2)=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$$(2+4+6+8+10)\\div (10+8+6+4+2)=30\\div30=1$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2633", "queId": "053f1c87681145219c33bc6298527528", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Jack has eight chocolates. He gives Jimmy one, Luna two, and Tim three respectively. Then Jack\\textquotesingle s mother gives Jack two more. How many chocolates are left for Jack?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition and Subtraction of Whole Numbers->Questions Involving Addition and Subtraction"], "answer_analysis": ["The problem can be regarded as an equation $8$ is the number of chocolates Jack had, $1, 2, 3$ is the number of chocolates Jack gave out, and $2$ is the number of chocolates his mother gave Jack. So the remaining chocolate is $8-1-2-3+2=4$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2634", "queId": "01657c61596b4ee7a6e1cc20fd79dc3b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "One kind of computer can make $$4\\times {{10}^{9}}$$ operations per second.~ How many operations can it make in $$5\\times {{10}^{2}}$$ seconds? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4\\times {{10}^{11}}$$ "}], [{"aoVal": "B", "content": "$$2\\times {{10}^{11}}$$ "}], [{"aoVal": "C", "content": "$$2\\times {{10}^{12}}$$ "}], [{"aoVal": "D", "content": "$$20\\times {{10}^{18}}$$ "}], [{"aoVal": "E", "content": "$$2\\times {{10}^{19}}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas"], "answer_analysis": ["$$4\\times {{10}^{9}}\\times 5\\times {{10}^{2}}$$ $$=20\\times {{10}^{9}}+2$$ $$=2\\times {{10}^{1}}\\times {{10}^{11}}$$ $$=2\\times {{10}^{1+11}}$$ $$=2\\times {{10}^{12}}$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2640", "queId": "09a054124c5f4a9dad695cc544fade91", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$9+9+9+9 +9+9+9=9\\times$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$9+9+9+9 +9+9+9=$$ seven $$9$$\\textquotesingle s $$=9\\times7$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2642", "queId": "054d6ee9792341a0b399af02f1ee7d99", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$(3\\times 1)+(3\\times 2)+(3\\times 3)+(3\\times 4)=3\\times $$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$1+2+3+4$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$1\\times 2\\times 3\\times 4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$$3+6+9+12=30=3\\times 10=3\\times (1+2+3+4)$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2644", "queId": "5cfad257e51c4410a5230276c95df2d6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Lucas pays for $4$ pens and $3$ pencils. Bryan spends twice as much paying for $2$ pens and $16$ pencils. A pen is how many times as expensive as a pencil? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{3}{2}$ "}], [{"aoVal": "B", "content": "$\\frac{5}{3}$ "}], [{"aoVal": "C", "content": "$\\frac{7}{4}$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$\\frac{13}{4}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2647", "queId": "09a72333df58425d97ec486e15e0b665", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Abel and Bella are friends and they always want to sit next to each other. How many ways are there to arrange Abel, Bella and three of their acquaintances to sit in a row, while satisfying the condition? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$32$$ "}], [{"aoVal": "E", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2655", "queId": "664c084ab14747d1b7f9ca6705757d3d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$100$$ hundreds $$+10$$ tens $$+1$$ one $$=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$111$$ "}], [{"aoVal": "B", "content": "$$1101$$ "}], [{"aoVal": "C", "content": "$$1011$$ "}], [{"aoVal": "D", "content": "$$10101$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$$100\\times 100+10\\times 10+1\\times 1=10000+100+1=10101$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2663", "queId": "01cd3cca71b64f94b672e393ccb14e64", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When calculating $$16\\times 29$$, which of the following choices is correct? ", "answer_option_list": [[{"aoVal": "A", "content": "$$144$$ in the blue box represents $$9\\times 16$$. "}], [{"aoVal": "B", "content": "$$32$$ in the red box represents $$2\\times 16$$. "}], [{"aoVal": "C", "content": "The product is $$32+144 =176$$. "}], [{"aoVal": "D", "content": "There is no regrouping in the calculation. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$32$$ in the red box represents $$20 \\times 16 = 320$$, and the product should be $$320 +144 = 464$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2664", "queId": "61a7e86b3df9477d9c123468a2179516", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "David measured the length of his garden. It was $$15$$ metres to the nearest tenth of a metre. Between what limits was the actual length? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14.995\\leqslant $$ the actual length $$\\leqslant 15.005$$ "}], [{"aoVal": "B", "content": "$$14.9\\leqslant $$ the actual length $$\\textless~15.1$$ "}], [{"aoVal": "C", "content": "$$14.95\\leqslant $$ the actual length $$\\textless{} 15.05$$ "}], [{"aoVal": "D", "content": "$$14.99\\leqslant $$ the actual length $$\\leqslant 15.01$$ "}], [{"aoVal": "E", "content": "$$14.5\\textless$$ the actual length $$\\textless15.5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals->Finding Approximate Values"], "answer_analysis": ["14.9500000\\ldots{} 15.0499999\\ldots{} "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2668", "queId": "05864560662d4c2bba2d42debbe8ebc7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Let $$a\\square b=ab+a+b$$ for any integers $$a$$ and $$b$$. The solution of the equation $$3\\square 5=2\\square x$$ is: $x = $~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Unknowns Using the Given Operations"], "answer_analysis": ["$3\\square 5=2\\square x \\implies 15+3+5=2x+2+x$, hence $x=7$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2670", "queId": "0e33548a602e4755bafb988bf8e8f4fd", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $A=1+3+5+7+\\cdots +99$, and $B=2+4+6+\\cdots +100$, what is the value of $B-A$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$49$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$99$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$B-A=(2-1)+(4-3)+(6-5)+\\cdots +(100-99)=50$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2671", "queId": "12c44a952df14e27b0aa92c65b04770f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A certain game uses a set of cards containing odd numbers. There are one 1, three 3s, two 5s, one 7, and three 9s. The mean value of this deck is 5.4, with a standard deviation of 2.8. If someone purchased three more decks of these cards and combined~them into single large deck, what would the new mean and standard deviation be? ", "answer_option_list": [[{"aoVal": "A", "content": "Mean = 5.4; standard deviation = 2.8 "}], [{"aoVal": "B", "content": "Mean = 5.4; standard deviation = 2.95 "}], [{"aoVal": "C", "content": "Mean = 16.2; standard deviation = 2.90 "}], [{"aoVal": "D", "content": "Mean = 16.2; standard deviation = 8.4 "}], [{"aoVal": "E", "content": "Mean = 21.6standard deviation = 11.2 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The mean is a measure of center. While it can be affected by adding new values ,the purchase of second deck would merely add more cards with the same values .As a result ,the mean would not change .Eliminate (C), (D),and (E). The standard deviation is a measure of sprees. As above, unique values will cause the standard deviation to change. However, since the new decks are identic -call to the old, the standard deviation will not change. Eliminate (B). "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2673", "queId": "0e372079a0644fdfb30abec09691a34b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $A:B=2:3$, $B:C=3:4$, find $A:B:C$=~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$2:3:4$ "}], [{"aoVal": "B", "content": "$8:6:15$ "}], [{"aoVal": "C", "content": "$6:3:9$ "}], [{"aoVal": "D", "content": "$16:6:15$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$A:B=4:3$ $B:C=2:5$ $A:B:C=8:6:15$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2674", "queId": "3338ac51fbf14e61a6dc7193fb4e4285", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Boyuan bought $$3$$ types of candies. He bought $$5$$ times as many toffee as lollipop. He bought $$5$$ more chocolate bar than lollipop. If he has $$7$$ lollipop, how many candies did he bought in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$17$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$54$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["Lollipop: $$7$$ Toffee: $$7\\times5=35$$ Chocolate bar: $$7+5=12$$ Total: $$7+35+12=54$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2680", "queId": "02437b002cc54e51870cdf575ea50479", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Tom and Jerry found $\\frac{1}{2}$ of a steak in the kitchen. Tom ate $\\frac{1}{2}$ of the leftover steak and Jerry ate $\\frac{1}{4}$ of it. They decided to give the rest to their friend Spike. What portion of the original steak would Spike get? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{4}$ "}], [{"aoVal": "B", "content": "$\\frac{1}{8}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{16}$ "}], [{"aoVal": "D", "content": "$\\frac{1}{32}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$\\frac{1}{2}-\\frac{1}{2}\\times \\frac{1}{2}-\\frac{1}{2}\\times \\frac{1}{4}=\\frac{1}{8}$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2681", "queId": "09d091d59f8842d585d66a578a55994e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Free-response questions on the AP Statistics Exam are graded 4, 3, 2, 1, or~ 0. Question 2 on the exam was of moderate difficulty. The average score on question 2 was 2.05 with a standard deviation of 1. To the nearest tenth, what score was achieved by a student who was at the 90th percentile of all students on the test? You may assume that the scores on the question were approximately normally distributed. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3.5$$ "}], [{"aoVal": "B", "content": "$$3.3$$ "}], [{"aoVal": "C", "content": "$$2.9$$ "}], [{"aoVal": "D", "content": "$$3.7$$ "}], [{"aoVal": "E", "content": "$$3.1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["\\textbf{Z = 1.28} \\textbf{$$\\frac{x-2.05}{1}$$ = 1.28} \\textbf{x= 3.33} "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2683", "queId": "024e250c29ef4898b04ffc256f6a4065", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Josie and Holly share $$48$$ dollars between them. Josie has three times as much as Holly. How much does Holly have? ", "answer_option_list": [[{"aoVal": "A", "content": "$12$ dollars "}], [{"aoVal": "B", "content": "$24$ dollars "}], [{"aoVal": "C", "content": "$$36$$ dolllars "}], [{"aoVal": "D", "content": "$$40$$ dollars "}], [{"aoVal": "E", "content": "$$45$$ dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$48 \\div (3 + 1) = 12$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2688", "queId": "09d73a9e09604ff39357c34017117a36", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In an arithmetic sequence with $$13$$ terms, if the seventh term is $$20$$, what is the sum of all the terms? ", "answer_option_list": [[{"aoVal": "A", "content": "$130 "}], [{"aoVal": "B", "content": "$$260$$ "}], [{"aoVal": "C", "content": "$$300$$ "}], [{"aoVal": "D", "content": "$$360$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["Sum $$=$$ Middle Term $$\\times$$ Number of Terms, $$20 \\times 13 = 260$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2693", "queId": "028390a4050a457982a0a58301524291", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the value of $$123\\times (-129)+123\\times130$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$123$$ "}], [{"aoVal": "B", "content": "$$132$$ "}], [{"aoVal": "C", "content": "$$129$$ "}], [{"aoVal": "D", "content": "$$-123$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$$\\begin{eqnarray}\\&\\&123\\times (-129+130)\\textbackslash\\textbackslash{} \\&=\\&123\\times (130-129)\\textbackslash\\textbackslash{} \\&=\\&123\\times1\\textbackslash\\textbackslash{} \\&=\\&123.\\end{eqnarray}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2708", "queId": "585db4b84e5c4105830b3c6912597c6f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $A$ ◆$B=(A\\times A)-B$ , then $(3$◆$4)$ ◆$5$ ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["$(3$◆$4)=(3\\times 3)-4=5$ , and $(3$◆$4)$◆$5=5$◆$5=(5\\times5)-5=20$ . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2709", "queId": "02ce37d006f34e05a90f73cef5f475ed", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The ratio of the perimeter of a rectangle to the length of one of its sides is~$14:3$. If the area is 27 square inches, how many inches long is one of the longer sides? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$\\dfrac{2\\left( x+y\\right)}{x}=\\dfrac{14}{3}\\textbackslash{} \\textbackslash{} \\Rightarrow\\textbackslash{} \\textbackslash{} \\dfrac{x+y}{x}$~$=\\dfrac{7}{3}\\textbackslash{} \\textbackslash{} \\Rightarrow\\textbackslash{} \\textbackslash{} 1+\\dfrac{y}{x}=1+\\dfrac{4}{3}$ $\\Rightarrow\\textbackslash{} \\textbackslash{} \\dfrac{y}{x}=\\dfrac{4}{3}\\textbackslash{} \\textbackslash{} \\Rightarrow\\textbackslash{} \\textbackslash{} \\dfrac{y\\times y}{x\\times y}=\\dfrac{4}{3}$ The area is~$x\\times y=27\\textbackslash{} \\textbackslash{} \\Rightarrow\\textbackslash{} \\textbackslash{} \\dfrac{y\\times y}{27}=\\dfrac{4}{3}\\textbackslash{} \\textbackslash{} \\Rightarrow\\textbackslash{} \\textbackslash{} y\\times y=36\\textbackslash{} \\textbackslash{} \\Rightarrow\\textbackslash{} \\textbackslash{} y=6$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2713", "queId": "0e551479032a4f42b956dd36f77c42e5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $2021^{st}$ digit at the right of the decimal point in the decimal expression of $\\dfrac{6}{7}$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["$$\\frac{6}{7}=0.\\overline{857142}$$, it is a decimal which repeats in cycles of $6$ digits. Every $6$$^{th}$ digit goes back to $2$. The $2022$$$^{nd}$$ digit is $2$, so the $2021$$^{st}$ digit is $4$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2715", "queId": "09f7d5728f4f4f62bae910dd0c957efa", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two non-zero real numbers, $x$ and $y$, satisfy $x = 6-y$. Which of the following is a possible value of $$ \\frac{{{x}^{2}}}{x-y}+\\frac{{{y}^{2}}}{y-x}$$? (Adapted From 2000 AMC 12 Problems, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$-1$ "}], [{"aoVal": "B", "content": "$-\\frac{1}{2}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{2}$ "}], [{"aoVal": "D", "content": "$1$ "}], [{"aoVal": "E", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Note that $x = 6-y \\Rightarrow x+y = 6$. Then, $$ \\frac{{{x}^{2}}}{x-y}+\\frac{{{y}^{2}}}{y-x}=\\frac{{{x}^{2}}-{{y}^{2}}}{x-y}=\\frac{(x+y)(x-y)}{x-y}=x+y = 6$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2719", "queId": "03163ac6938145a59d51fa5d3b81c0a2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $ a◆b$ means $(a\\times b)+b$, then $2◆3$ has the value of~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["$2◆3=(2\\times3)+3=9$. So the answer is $\\rm B$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2720", "queId": "0620f153d4814df0befc6f3c8bbd7f84", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Each of two boxes contains three chips numbered $$1$$, $$2$$, and $$3$$. A chip is drawn randomly from each box and the numbers on the two chips are multiplied. What is the probability that their product is even? (2015 AMC 8 Problem, Question \\#7) ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{9}$$ "}], [{"aoVal": "B", "content": "$$\\frac{2}{9}$$ "}], [{"aoVal": "C", "content": "$$\\frac{4}{9}$$ "}], [{"aoVal": "D", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "E", "content": "$$\\frac{5}{9}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["We can instead calculate the probability that their product is odd, and subtract this from $$1$$. In order to get an odd product, we have to draw an odd number from each box. We have a $$\\frac23$$ probability of drawing an odd mumber from one box, so there is a $$\\left(\\frac{2}{3}\\right)^{2}= \\frac{4}{9}$$ probability of having an odd product. Thus, there is a $$1- \\frac{4}{9}= \\frac{5}{9}$$ probability of having an even product. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2722", "queId": "0a0b0945c44a48519c5f8a1e20f990c9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$8$$ watermelons cost as much as $$12$$ pears, then $$24$$ waternelons cost as much as pears. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Heuristics Skills-> Equivalent Substitution"], "answer_analysis": ["$$8$$ watermelons = $$12$$ pears $$8\\times3$$ watermelons = $24$ watermelons $$12\\times3$$ pears = $36$ pears "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2734", "queId": "0366bf821a1b48b4a00522f64209748c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "An object of mass m is traveling at constant speed v in acircular path of radius r. How much work is done by the centripetal force during one-half of a revolution? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\pi mv^{2}$ "}], [{"aoVal": "B", "content": "$$0$$ "}], [{"aoVal": "C", "content": "$\\pi mv^{2}r$ "}], [{"aoVal": "D", "content": "$2\\pi mv^{2}r$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables"], "answer_analysis": ["Since the centripetal force always points along a raduis toward the center of the od the circle, and the velocity of the object is always tangent to the circle (and thus perpendicular to the radius), the work done by the centripetal force is zero. Alternatively, since the object\\textquotesingle s speed remains constant, the Work-Energy Theorem tells you that no work is being performed. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2754", "queId": "0a304a6d281d4381b033cb4f04977c2c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When Xiao Dong did the subtraction equation, he saw the minuend as $$90$$ instead of $$75$$, and the difference he got was $$55$$. The correct result should be~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$75$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$55$$ "}], [{"aoVal": "D", "content": "$$35$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Wrong: $$90 - A = 55$$ -\\/-\\textgreater{} $$A=90-55=35$$ Correct: $$75 - 35 = 40$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2755", "queId": "067b05d0215a41e483c38a24adba8f29", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "The number of papers I have is $$4\\times 21$$ more than $6$ dogs. I have~\\uline{~ ~?~ ~ ~ ~}~dogs． ", "answer_option_list": [[{"aoVal": "A", "content": "$$54$$ "}], [{"aoVal": "B", "content": "$$78$$ "}], [{"aoVal": "C", "content": "$$84$$ "}], [{"aoVal": "D", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$4\\times 21+ 6 = 90$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2757", "queId": "04008c8172774622959efa193c286968", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "$$4\\times 9=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$16\\times 2$$ "}], [{"aoVal": "B", "content": "$$12\\times 3$$ "}], [{"aoVal": "C", "content": "$$7\\times 5$$ "}], [{"aoVal": "D", "content": "$$38\\times 1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$4\\times 9=36$$. $$\\text{A}$$: $$16\\times 2=32$$; $$\\text{B}$$: $$12\\times 3=36$$; $$\\text{C}$$: $$7\\times 5=35$$; $$\\text{D}$$: $$38\\times 1=38$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2758", "queId": "0a3d1ef1a19948c4a0e65c32ac9a313f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the remainder when $$987\\textasciitilde654\\textasciitilde321$$ is divided by $$100$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$42$$ "}], [{"aoVal": "C", "content": "$$65$$ "}], [{"aoVal": "D", "content": "$$98$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["If a number is divided by $$100$$, the remainder is the number\\textquotesingle s last $$2$$ digits. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2759", "queId": "040c02054bcc49f09cd13774d4401467", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$629+=1000 -174$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$197$$ "}], [{"aoVal": "B", "content": "$$371$$ "}], [{"aoVal": "C", "content": "$$826$$ "}], [{"aoVal": "D", "content": "$$1455$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$1000-174=826$$ $$826-629=197$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2762", "queId": "0696089424354015b1f3f3370af6094d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The distance between A and B is $$350$$km. Kin and Mary drive away from A and B respectively at $8$ a.m. and go towards each other at same time. Kin drives $$40$$km/h, and Mary drives $$50$$km/h. Mary rested for $$2$$ hours on her way and then continues driving. They will meet at~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ a.m. "}], [{"aoVal": "B", "content": "$$11$$ a.m. "}], [{"aoVal": "C", "content": "$$12$$ p.m. "}], [{"aoVal": "D", "content": "$$1$$ p.m. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$(350-80)$$$\\div$$$(40+50)=3$$hr $$8+2+3=13$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2764", "queId": "b91c4c823e014b3e874c67237fbdb874", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A list of $2018$ positive integers has a unique mode, which occurs exactly $10$ times. What is the least number of distinct values that can occur in the list? (2018 AMC 10B Problems, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$202$$ "}], [{"aoVal": "B", "content": "$$223$$ "}], [{"aoVal": "C", "content": "$$224$$ "}], [{"aoVal": "D", "content": "$$225$$ "}], [{"aoVal": "E", "content": "$$234$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["To minimize the number of distinct values, we want to maximize the number of times they appear. So, we could have $223$ numbers appear $9$ times, $1$ number appear once, and the mode appear $10$ times, giving us a total of $223+1+1=$ (D) $225$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2767", "queId": "04326f2b03834968a9b4fde46eac539a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is a solution of $$\\begin{cases}2x-4=0 \\textbackslash\\textbackslash{} 4x-y=7 \\end{cases}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "($x$,$y$)=($2$,$-1$) "}], [{"aoVal": "B", "content": "($x$,$y$)=($2$,$1$) "}], [{"aoVal": "C", "content": "($x$,$y$)=($-2$,$1$) "}], [{"aoVal": "D", "content": "($x$,$y$)=($-2$,$-1$) "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables"], "answer_analysis": ["$x=2$ $8-y=7$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2771", "queId": "d056ecb872d245c4b3d83f39858bd87a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A bakery sells cakes in three different sizes: small ($S$), medium ($M$), and large ($L$). The medium size costs $40\\textbackslash\\%$ more than the small size and contains $25\\textbackslash\\%$ less cake than the large size. The large size contains twice as much cake as the small size and costs $60\\textbackslash\\%$ more than the medium size. Rank the three sizes from best to worst buy in terms of cost per unit of cake. (Adapted From 2005 AMC 8 Problems, Question \\#22) ", "answer_option_list": [[{"aoVal": "A", "content": "$MSL$ "}], [{"aoVal": "B", "content": "$SML$ "}], [{"aoVal": "C", "content": "$LSM$ "}], [{"aoVal": "D", "content": "$SLM$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Suppose the small size costs $$$1$$ and the large size has $10$ grams of cake. The medium size then costs $$$1.40$$ and has $7.5$ grams of cake. The small size has $5$ grams of cake and the large size costs $$$2.24$$. The small, medium, and large size cost respectively, $0.200$, $0.187$, $0.224$ dollars per gram. The sizes from best to worst buy are $MSL$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2788", "queId": "86e5d81247be4bd0959526b764399924", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Find the value of the expression $100-98+96-94+92-90+\\cdots +8-6+4-2$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$80$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Grouping in Fast Addition and Subtraction of Whole Numbers"], "answer_analysis": ["$(100-98)+(96-94)+(92-90)+\\cdots +(8-6)+(4-2)=2\\times25=50$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2789", "queId": "06e912b7f45d451e9d5da59934c65c3b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If~$\\dfrac{y}{x-z}=\\dfrac{x+y}{z}=\\dfrac{x}{y}$~for three positive numbers x, y and z, all different, then what is the value of~$\\dfrac{x}{y}$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$\\dfrac{x}{y}=\\dfrac{y}{x-z}=\\dfrac{x+y}{z}\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\Rightarrow\\textbackslash{} \\textbackslash{} \\textbackslash{} \\dfrac{x}{y}=\\dfrac{x+y+(x+y)}{y+\\left( x-z\\right)+z}=\\dfrac{2x+2y}{x+y}=\\dfrac{2\\left( x+y\\right)}{x+y}=2.$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2790", "queId": "179ae86698124919a866205f7ad7d040", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$280$$ adults and $$445$$ children visited Universal Studios last week. $330$ visitors did not take the rollercoasters. How many visitors took the roller coaster last week? ", "answer_option_list": [[{"aoVal": "A", "content": "$$145$$ "}], [{"aoVal": "B", "content": "$$245$$ "}], [{"aoVal": "C", "content": "$$625$$ "}], [{"aoVal": "D", "content": "$$395$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$280+445=725$. $725-330=395$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2796", "queId": "33547e7a8d924d3ca7173edffa8d8fa8", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "What is the simplest form of $3\\dfrac{8}{12}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$3\\dfrac{3}{4}$ "}], [{"aoVal": "B", "content": "$\\frac{42}{12}$ "}], [{"aoVal": "C", "content": "$\\frac{10}{3}$ "}], [{"aoVal": "D", "content": "$3\\dfrac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions->Using Common Factors to Simplify Fractions"], "answer_analysis": ["Factors of $8$ are $1, 2, 4, 8$ and factors of $12$ are $1, 2, 3, 4, 6, 12$. The highest commom factor of $8$ and $12$ is $4$. Dividing $8$ and $12$ by $4$ respectively, we get $\\frac{8 \\div 4}{12 \\div 4}$=$\\frac{2}{3}$; Write the whole and the simplified fraction together, $3\\dfrac{2}{3}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2801", "queId": "20d438ded3a64303b527f3e0bb77b480", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "$$5\\textasciitilde\\text{m}+5\\textasciitilde\\text{cm}+5\\textasciitilde\\text{mm}=$$$$\\text{mm}$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$5055$$ "}], [{"aoVal": "B", "content": "$$5505$$ "}], [{"aoVal": "C", "content": "$$5550$$ "}], [{"aoVal": "D", "content": "$$55550$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Length"], "answer_analysis": ["$$5\\textasciitilde\\text{m}+5\\textasciitilde\\text{cm}+5\\textasciitilde\\text{mm}=5000\\textasciitilde\\text{mm}+50\\textasciitilde\\text{mm}+5\\textasciitilde\\text{mm}=5055\\textasciitilde\\text{mm}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2802", "queId": "5869be46b4b3426c9f8a226682f5e139", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "An automobile manufacturer wished to know which of two new paint colors were preferred on its newest line of vehicles. A~large simple random sample was taken from people throughout the USA who had purchased one of their vehicles in the~previous five years. What is the safest generalization of this survey? ", "answer_option_list": [[{"aoVal": "A", "content": "Only those people who took this particular survey "}], [{"aoVal": "B", "content": "All future customers of this automobile manufacturer "}], [{"aoVal": "C", "content": "All people who have purchased from that manufacturer in the previous five years "}], [{"aoVal": "D", "content": "Only those people who have purchased a vehicle in the previous five years "}], [{"aoVal": "E", "content": "All vehicle owners in the USA "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["A safe generalization will broaden the survey to a population that closely resembles the group of people surveyed. Since the sample was taken from purchasers of a single auto manufacturer over the past five years, the safest generalization is a population with these same qualities. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2806", "queId": "37fd4a4404ef459bb0ccc4b3b272c454", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "14. Consider the following system of equations: $$\\begin{cases} 5 x+7 y=8 \\textbackslash\\textbackslash{} 2 x+q y=r \\end{cases}$$, where $q$ and $r$ are constants. If $q$ and $r$ are chosen such that this system has infinitely many solutions $(x, y)$, find $q+r=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Indefinite Equations->System of Indefinite Equations"], "answer_analysis": ["For the system to have infinitely many solutions, the second equation must be a constant multiple of the first. Comparing the coefficients of $x$, the second equation must be $\\frac{2}{5}$ times the first equation. Therefore, $q+r=\\left(\\frac{2}{5}\\right)\\times (7)+\\left(\\frac{2}{5}\\right)\\times(8)=6$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2808", "queId": "744c86ea1b0a4f9c8b112383357309c3", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all of its side lengths are integers. The primeter of $\\triangle ABC$ with a side of length $12$ and a side length of $7$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "$$28$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+7\\textgreater12$. $P=s+7+12\\textgreater12+12$. Therefore, $P\\textgreater24+1=25$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2819", "queId": "d4fbf01bbfd345efae4e54b5c317011c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of the numbers that range from $$1$$ to $$100$$ when divide by $$3$$ give you a remainder of $$1$$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1700$$ "}], [{"aoVal": "B", "content": "$$1716$$ "}], [{"aoVal": "C", "content": "$$1717$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$$\\left( 1+100 \\right)\\times 34\\div 2=1717$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2820", "queId": "2eb9d36081b24ff6a193d89d44dca5ea", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A cup of boiling water ($212$\\textsuperscript{◦}F) is placed to cool in a room whose temper- ature remains constant at $68$\\textsuperscript{◦}F. Suppose the difference between the water temperature and the room temperature is halved every $5$ minutes. What is the water temperature, in degrees Fahrenheit, after $15$ minutes? ", "answer_option_list": [[{"aoVal": "A", "content": "$$77$$ "}], [{"aoVal": "B", "content": "$$86$$ "}], [{"aoVal": "C", "content": "$$92$$ "}], [{"aoVal": "D", "content": "$$98$$ "}], [{"aoVal": "E", "content": "$$104$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2823", "queId": "20dd6067a47643c799c96638adb3ee6d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the missing number in the box? $2:3=\\boxed{?}:9$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions"], "answer_analysis": ["$\\frac{2}{3}=\\frac{6}{9}$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2829", "queId": "0ab576840bac4994bc1d970e3aebd489", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "(the number of $$\\rm cm$$ in $$1\\rm m$$):(the number of $$\\rm m$$ in $$1\\rm km$$)$$=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$100:1000$$ "}], [{"aoVal": "B", "content": "$$1000:100$$ "}], [{"aoVal": "C", "content": "$$1:100$$ "}], [{"aoVal": "D", "content": "$$100:1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Length"], "answer_analysis": ["$$1\\rm m=100\\rm cm$$ and $$1\\rm km=1000m$$; the correct ratio is $$100:1000$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2841", "queId": "0ee20f1d2a594003a997e0dba4f9b8f0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The house number of a community consists of $5$ digits: $1, 2, 3, 6, 7$. Which number is not used if these $5$ digits are filled in the squares below to make the equation correct? Each number can only be filled in once. $$\\huge\\square -\\square =\\square +\\square $$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"], "answer_analysis": ["Pay attention to look at both sides of the formula. One side is addition, and the other side is subtraction. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2842", "queId": "33659f49907d4d1eb62de88bdfa326fc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Kangaroo came up with a new operation * for positive integers. He gave a few examples as shown below: $$2$$ * $$3$$$$=\\left( 2+1 \\right)\\times 3=9$$; $$4$$ * $$2$$$$=\\left( 4+3+2+1 \\right)\\times 2=20$$; $$3$$ * $$5$$$$=\\left( 3+2+1 \\right)\\times 5=30$$. What is the value of the expression $$6$$ * $$5$$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$105$$ "}], [{"aoVal": "D", "content": "$$210$$ "}], [{"aoVal": "E", "content": "$$315$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly->Ordinary Type"], "answer_analysis": ["$$6$$ * $$5 = (6+5+4+3+2+1) \\times 5 = 21\\times 5 = 105$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2843", "queId": "079c9da0836345b0b5538d76fc614903", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number y of service calls in a month at each location. Summary calculations give $$\\bar{}x$$ = 8.4, $$S\\_x$$ = 2.1, ȳ = 14.2, $$S\\_y$$ = 3.8, and r = 0.86. What is the slope of the least squares regression line of number of service calls on number of copiers?} ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.86$$ "}], [{"aoVal": "B", "content": "$$1.56$$ "}], [{"aoVal": "C", "content": "$$0.48$$ "}], [{"aoVal": "D", "content": "None of the above "}], [{"aoVal": "E", "content": "\\textbf{Can't tell from the information given} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$\\beta\\_1 =r \\frac{S\\_y}{S\\_x} = 0.86 * \\frac{3.8}{2.1} = 1.56$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2848", "queId": "0ada71cf35354155a5fe6a47f631fa27", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A firm had sales revenue of 1 million dollars last year. It spent 600,000 dollars on labor, 150,000 dollars on capital, and 200,000 dollars on materials. What was the firm\\textquotesingle s accounting profit? ", "answer_option_list": [[{"aoVal": "A", "content": "0 dollar "}], [{"aoVal": "B", "content": "50,000 dollars "}], [{"aoVal": "C", "content": "400,000 dollars "}], [{"aoVal": "D", "content": "650,000 dollars "}], [{"aoVal": "E", "content": "1,000,000 dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Accounting profit = total revenue - explicit cost "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2851", "queId": "07a8e85769834a1b948dce3fe9fd8562", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Nicolas is planning to send a package to his friend Anton, who is a stamp collector. To pay for the postage, Nicolas, would like to cover the package with a large number of stamps. Suppose he has a collection of $5$-cent, $10$-cent, and $25$-cent stamps, with exactly $20$ of each type. What is the greatest number of stamps Nicolas can use to make exactly $\\textbackslash$7.10$ in postage? ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$46$$ "}], [{"aoVal": "C", "content": "$$51$$ "}], [{"aoVal": "D", "content": "$$54$$ "}], [{"aoVal": "E", "content": "$$55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["E "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2859", "queId": "20f30d08be89451dac76540282ee3134", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{In a statistics course, a linear regression equation was computed to predict the final exam score from the score on the first test. The equation was y = 10 + .9x where y is the final exam score and x is the score on the first test. Carla scored 95 on the first test. What is the predicted value of her score on the final exam?} ", "answer_option_list": [[{"aoVal": "A", "content": "$$95$$ "}], [{"aoVal": "B", "content": "$$85.5$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$95.5$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{$$\\hat{y}$$= 10 + .9*95=95.5. The predicted final exam score is 95.5.} "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2862", "queId": "0aefedee11194fa393c700759834a3eb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A rectangular water tank is filled to a depth of $$70$$cm. It contains $$1050$$ litres of water. Some water is taken out of the tank. The water level drops by $$25$$cm. How much water is left in the tank? ", "answer_option_list": [[{"aoVal": "A", "content": "$$625\\rm L$$ "}], [{"aoVal": "B", "content": "$$375\\rm L$$ "}], [{"aoVal": "C", "content": "$$525\\rm L$$ "}], [{"aoVal": "D", "content": "$$270\\rm L$$ "}], [{"aoVal": "E", "content": "$$675\\rm L$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$$1050\\times \\frac {70-25}{70} = 675$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2888", "queId": "74563c2b07e34518971c31ae51dd2171", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$19.2\\div6\\times1.1=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$35.2$ "}], [{"aoVal": "B", "content": "$3.52$ "}], [{"aoVal": "C", "content": "$37.4$ "}], [{"aoVal": "D", "content": "$3.74$ "}], [{"aoVal": "E", "content": "$3.47$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals"], "answer_analysis": ["$$19.2\\div6\\times1.1$$ $$=3.2\\times1.1$$ $$=3.52$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2889", "queId": "136d4672f6bd474ea1f416effbaca508", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Pip and Bud buys some £$$10$$ books and £$$15$$ books together. If they spent £$$90$$ on the books, how many books have they bought at most in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Indefinite Equations"], "answer_analysis": ["Let $$x$$ be the number of £$$10$$ books and $$y$$ be the number of £$$15$$ books $$10x+15y=90$$, which has two positive integer solutions only. $$\\begin{cases} x=6 \\textbackslash\\textbackslash{} y=2 \\end{cases}$$, $$\\begin{cases} x=3 \\textbackslash\\textbackslash{} y=4 \\end{cases}$$ $$6+2=8$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2894", "queId": "0821752c889b46bcb475fda4b4db906e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For how many values of $a$ is it true that the line $y=x+a^{2}-a-3$ passes through the vertex of the parabola $y=x^{2}-6x+a^{2}$? (Adapted From 2005 AMC 12B Problem, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "infinitely many "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["We see that the vertex of the quadratic function $y=x^{2}-6x+a^{2}$ is $\\left(3, a^{2}-9\\right)$. If $\\left(2, a^{2}-1\\right)$ will be on the line $y=x+a^{2}-a-3$, $a^{2} -9=3+a^{2}-a-3$. Solve for $a$, there is one solution, $a=9$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2896", "queId": "1c75d885fbe34318a93ae2f18e40b65f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For how many values of $a$ is it true that the line $y=x+a$ passes through the vertex of the parabola $y=x^{2}+a^{2}$? (2005 AMC 12B Problem, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "infinitely many "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["We see that the vertex of the quadratic function $y=x^{2}+a^{2}$ is $\\left(0, a^{2}\\right)$. The $y$-intercept of the line $y=x+a$ is $(0, a)$. We want to find the values (if any) such that $a=a^{2}$. Solving for $a$, the only values that satisfy this are 0 and 1 , so the answer is $(\\text{C}) 2$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2900", "queId": "0b390db819814a4982ad79243b143626", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$(100 + 98 + 96 + \\cdots +2) -(99 + 97 + 95 + \\cdots + 1)=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$99$$ "}], [{"aoVal": "D", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$(100-99)+(98-97)+ \\cdots +(2-1) = 1+1+ \\cdots +1 = 50$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2907", "queId": "0843b6ad1da44afe8370c982940c49b3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "For the ratio of $$3:8$$, if the consequent increases by $$24$$, the antecedent should~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$+24$$ "}], [{"aoVal": "B", "content": "$$\\times 4$$ "}], [{"aoVal": "C", "content": "$$\\times 24$$ "}], [{"aoVal": "D", "content": "$$+4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["$$8+24=32=8\\times 4$$ So, $$3\\times 4=12$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2908", "queId": "0b429f1917194480897543d4a59d9081", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "What is the value of $$1+3+5+\\cdots +2017+2019-2-4-6-\\cdots -2016-2018$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$-1010$$ "}], [{"aoVal": "B", "content": "$$-1009$$ "}], [{"aoVal": "C", "content": "$$1008$$ "}], [{"aoVal": "D", "content": "$$1009$$ "}], [{"aoVal": "E", "content": "$$1010$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Grouping in Fast Addition and Subtraction of Whole Numbers"], "answer_analysis": ["Solution 1 Rearranging the terms, we get $$(1-2)+(3-4)+(5-6)+\\cdots (2017-2018)+2019$$, and our answer is $$-1009+2019=1010$$. Solution 2 We can rewrite the given expression as $$1+(3-2)+(5-4)+\\cdots +(2017-2016)+(2019-2018)=1+1+1+\\cdots +1$$. The number of $$1$$s is the same as the number of terms in $$1$$, $$3$$, $$5$$, $$7\\cdots $$, $$2017$$, $$2019$$. Thus the answer is $$1010$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2912", "queId": "587e928fe97f4f2299b2aa3a202f2312", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Seagram knows that $$1111\\times 2222=2468642$$ Which of the following answers should he decide is $$3333\\times 4444$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14811850$$ "}], [{"aoVal": "B", "content": "$$14811851$$ "}], [{"aoVal": "C", "content": "$$14811852$$ "}], [{"aoVal": "D", "content": "$$14811853$$ "}], [{"aoVal": "E", "content": "$$14811854$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["$$14811852$$ It should be noted that the units digit of the product of $$3333$$ and $$4444$$ will be the same as the units digit of the product of $$3$$ and $$4$$, namely $$2$$: this succinctly identifies the correct option as $$14811852$$. Alternatively, the calculation $$3333\\times 4444$$ will have an answer that is $$3\\times 2$$ times greater than $$1111\\times 2222$$. Now we can work out $$2468642\\times 6$$ exactly, which is indeed $$14811852$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2917", "queId": "53e05f29d1a347c497ba14c52e5c4b6a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "For each patient visiting a doctor\\textquotesingle s office, the nurse records the patient\\textquotesingle s body temperature. The plot above shows the temperatures of 28 patients for one particular day. Which of the following statements is true about the distribution of body temperatures? ", "answer_option_list": [[{"aoVal": "A", "content": "The distribution is skewed to the left. "}], [{"aoVal": "B", "content": "The median temperature could be 98.2$^{\\circ}F$ "}], [{"aoVal": "C", "content": "The median temperature could be 98.4$^{\\circ}F$ "}], [{"aoVal": "D", "content": "The minimum temperature is exactly 97.0$^{\\circ}F$ "}], [{"aoVal": "E", "content": "The distribution is normal. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The correct answer is (b).Since there are 28 patients, the median will be between the 14th and 15th data points, which puts it in the bar centered at 98.25°$F$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2918", "queId": "0b5f45370372467eb1aa83fbaa6f9386", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Points $(\\sqrt{\\pi}, a)$ and $(\\sqrt{\\pi}, b)$ are distinct points on the graph of $y^{2}+x^{4}=2 x^{2} y+1$. What is $\\textbar a-b\\textbar$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$\\frac{\\pi}{2}$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$\\sqrt{1+\\pi}$ "}], [{"aoVal": "E", "content": "$1+\\sqrt{\\pi}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["Since points on the graph make the equation true, substitute $\\sqrt{\\pi}$ in to the equation and then solve to find $a$ and $b$. $$ \\begin{aligned} \\&y^{2}+\\sqrt{\\pi}^{4}=2 \\sqrt{\\pi}^{2} y+1 \\textbackslash\\textbackslash{} \\&y^{2}+\\pi^{2}=2 \\pi y+1 \\textbackslash\\textbackslash{} \\&y^{2}-2 \\pi y+\\pi^{2}=1 \\textbackslash\\textbackslash{} \\&(y-\\pi)^{2}=1 \\textbackslash\\textbackslash{} \\&y-\\pi=\\pm 1 \\textbackslash\\textbackslash{} \\&y=\\pi+1 \\textbackslash\\textbackslash{} \\&y=\\pi-1 \\end{aligned} $$ There are only two solutions to the equation $(y-\\pi)^{2}=1$, so one of them is the value of $a$ and the other is $b$. The order does not matter because of the absolute value sign. $$ \\textbar(\\pi+1)-(\\pi-1)\\textbar=2 $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2921", "queId": "0f455be763e344b4bd9454a8426fe47f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Henry the donkey has a very long piece of pasta. He takes a number of bites of pasta, each time eating $3$ inches of pasta from the middle of one piece. In the end, he has $10$ pieces of pasta whose total length is $17$ inches. How long, in inches, was the piece of pasta he started with? ", "answer_option_list": [[{"aoVal": "A", "content": "$$34$$ "}], [{"aoVal": "B", "content": "$$38$$ "}], [{"aoVal": "C", "content": "$$41$$ "}], [{"aoVal": "D", "content": "$$44$$ "}], [{"aoVal": "E", "content": "$$47$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2924", "queId": "1390d466b6c1454a8e3d6401a19ee877", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A new operation $$⊕$$ is defined as $$a⊕b=\\frac{2}{a^{2}}+\\frac{1}{b}$$: Which of the equations below is/are correct? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2⊕4=4⊕2$$ "}], [{"aoVal": "B", "content": "$$3⊕6=6⊕3$$ "}], [{"aoVal": "C", "content": "$$4⊕8=8⊕4$$ "}], [{"aoVal": "D", "content": "$$1008⊕2016=2016⊕1008$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["method $$1$$: （$$1$$）$$\\frac{2}{2^{2}}+ \\frac{1}{4}= \\frac{2}{4}+ \\frac{1}{4}= \\frac{3}{4}$$， $$\\frac{2}{4^{2}}+ \\frac{1}{2}= \\frac{2}{16}+ \\frac{1}{2}= \\frac{10}{16}= \\frac{5}{8}$$. Rejected. （$$2$$）$$\\frac{2}{3^{2}}+ \\frac{1}{6}= \\frac{2}{9}+ \\frac{1}{6}= \\frac{4}{18}+ \\frac{3}{18}= \\frac{7}{18}$$,~ $$\\frac{2}{6^{2}}+ \\frac{1}{3}= \\frac{2}{36}+\\frac{1}{3}=\\frac{1}{18}+\\frac{1}{3}=\\frac{1}{18} +\\frac{6}{18}=\\frac{7}{18}$$. ($$3$$）$$\\frac{2}{4^{2}}+ \\frac{1}{8}= \\frac{2}{16}+ \\frac{1}{8}= \\frac{1}{4}$$, $$\\frac{2}{8^{2}}+ \\frac{1}{4}= \\frac{2}{64}+ \\frac{1}{4}= \\frac{1}{32}+ \\frac{8}{32}= \\frac{9}{32} \\neq \\frac{1}{4}.$$ ($$4$$)$$\\frac{2}{1008^{2}}+ \\frac{1}{2016}= \\frac{1}{252 \\times 2016}+ \\frac{1}{2016}= \\frac{253}{252 \\times 2016}.$$ $$\\frac{2}{2016^{2}}+ \\frac{1}{1008}= \\frac{1}{2016 \\times 1008}+ \\frac{1}{1008}= \\frac{2017}{2016 \\times 1008}.$$ $$1008⊕2016\\neq 2016⊕1008$$. method $$2$$: $$4$$ is twice of $$2$$, $$6$$ is twice of $$3$$, $$8$$ is twice of $$4 $$, $$2016$$ is twice of $$1008$$. Specifically, the question is asking when is $$k⊕2k=2k⊕k$$? $$\\frac{2}{k^{2}}+ \\frac{1}{2k}= \\frac{2}{\\left(2k\\right)^{2}}+ \\frac{1}{k} \\Rightarrow \\frac{2}{k^{2}}+ \\frac{1}{2k}= \\frac{1}{2k^{2}}+ \\frac{1}{k}$$ $$\\Rightarrow \\frac{4}{2k^{2}}+ \\frac{1}{2k}= \\frac{1}{2k^{2}}+ \\frac{2}{2k} \\Rightarrow \\frac{3}{2k^{2}}= \\frac{1}{2k}$$ $$\\Rightarrow \\frac{3}{k}=1 \\Rightarrow k=3$$ Hence, ($$2$$) is the only possible answer. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2928", "queId": "98a474c459014d438102dba3698796fd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$10+8\\times6-4\\div2=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$27$$ "}], [{"aoVal": "C", "content": "$$52$$ "}], [{"aoVal": "D", "content": "$$56$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$$10+8\\times6-4\\div2=10+48-2=56$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2932", "queId": "1c8ada2ec61445ba82b2291d1a6fd9df", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many even numbers are there? 2, 3, 5, 6, 7, 9, 10. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$Omitted.$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2933", "queId": "18034004d570491f90d707daac2dbbd2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{If I toss a fair coin 5000 times} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{and I get anything other than 2500 heads, then something is wrong with the way I flip coins.} "}], [{"aoVal": "B", "content": "\\textbf{the proportion of heads will be close to 0.5} "}], [{"aoVal": "C", "content": "\\textbf{a run of 10 heads in a row will increase the probability of getting a run of 10 tails in a row.} "}], [{"aoVal": "D", "content": "\\textbf{the proportion of heads in these tosses is a parameter} "}], [{"aoVal": "E", "content": "\\textbf{the proportion of heads will be close to 50.} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{Since this is a fair coin, the probability to get a head is always 0.5.} "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2939", "queId": "41630c2862554c5c85f4b2c25d56ba31", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "True or False: It is impossible for the $25$-th percentile to be equal to the median. ", "answer_option_list": [[{"aoVal": "A", "content": "True "}], [{"aoVal": "B", "content": "False "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["For example, consider a dataset with the following values: 0, 2, 2, 3, 3. The median of this dataset is $2$, and the $25$-th percentile is also $2$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2944", "queId": "ab44f50307df4917bfab956617b9070f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Find the value of the expression $100-98+96-94+92-90+\\cdots +8-6+4-2$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$80$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Grouping in Fast Addition and Subtraction of Whole Numbers"], "answer_analysis": ["$(100-98)+(96-94)+(92-90)+\\cdots +(8-6)+(4-2)=2\\times25=50$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2947", "queId": "53e5bd42ebef4159b929ae1aba9649c1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$98 + 99 + 100 + 101 + 102 =$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$497$$ "}], [{"aoVal": "B", "content": "$$498$$ "}], [{"aoVal": "C", "content": "$$499$$ "}], [{"aoVal": "D", "content": "$$500$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["Regrouping,$$ (98+102) + (99+101) + 100 = 500$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2952", "queId": "3389c8962aa946e6b224482fc0083542", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alex and Felicia each have cats as pets. Alex buys cat food in cylindrical cans that are 6 cm in diameter and 12 cm high. Felicia buys cat food in cylindrical cans that are 12 cm in diameter and 6 cm high. What is the ratio of the volume of one of Alex\\textquotesingle s cans to the volume of one of Felicia\\textquotesingle s cans? (2019 AMC 8, 9) ", "answer_option_list": [[{"aoVal": "A", "content": "$1:4$ "}], [{"aoVal": "B", "content": "$1:2$ "}], [{"aoVal": "C", "content": "$1:1$ "}], [{"aoVal": "D", "content": "$2:1$ "}], [{"aoVal": "E", "content": "$4:1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["Solution 1 Using the formula for the volume of a cylinder, we get Alex,~$\\pi108$, and Felicia,~$\\pi216$. We can quickly notice that~~cancels out on both sides, and that Alex\\textquotesingle s volume is~$\\dfrac{1}{2}$~~of Felicia\\textquotesingle s leaving~$\\dfrac{1}{2}=\\boxed{1:2}$~as the answer. Solution 2 Using the formula for the volume of a cylinder, we get that the volume of Alex\\textquotesingle s can is~$3^{2}\\cdot12\\cdot\\pi$, and that the volume of Felicia\\textquotesingle s can is~$6^{2}\\cdot6\\cdot\\pi$. Now, we divide the volume of Alex\\textquotesingle s can by the volume of Felicia\\textquotesingle s can, so we get~$\\dfrac{1}{2}$, which is$\\boxed{\\left( B\\right)\\textbackslash{} 1:2}.$ Solution 3 The ratio of the numbers is~$\\dfrac{1}{2}$. Looking closely at the formula~$r^{2}*h*\\pi$, we see that the~$r*h*\\pi$~will cancel, meaning that the ratio of them will be~$\\dfrac{1\\left( 2\\right)}{2\\left( 2\\right)}=\\boxed{\\left( B\\right)\\textbackslash{} 1:2}$ Solution 4 The second can is 2 size in each of 2 dimensions, and~$\\dfrac{1}{2}$~size in 1 dimension.~$\\dfrac{2^{2}}{2}=\\boxed{\\left( B\\right)\\textbackslash{} 1:2}$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2954", "queId": "08bf8bfac804495abd16f793baaf3ddc", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For certain real numbers $a, b$, and $c$, the polynomial $$ g(x)=x^{3}+a x^{2}+x+10 $$ has three distinct roots, and each root of $g(x)$ is also a root of the polynomial $$ f(x)=x^{4}+x^{3}+b x^{2}+100 x+c . $$ What is $f(1)$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$-9009$$ "}], [{"aoVal": "B", "content": "$$-8008$$ "}], [{"aoVal": "C", "content": "$$-7007$$ "}], [{"aoVal": "D", "content": "$$-6006$$ "}], [{"aoVal": "E", "content": "$$-5005$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Indefinite Equations->System of Indefinite Equations"], "answer_analysis": ["$f(x)$ must have four roots, three of which are roots of $g(x)$. Using the fact that every polynomial has a unique factorization into its roots, and since the leading coefficient of $f(x)$ and $g(x)$ are the same, we know that $$ f(x)=g(x)(x-r) $$ where $r \\in \\mathbb{C}$ is the fourth root of $f(x)$. Substituting $g(x)$ and expanding, we find that $$ \\begin{aligned} f(x) \\&=\\left(x^{3}+a x^{2}+x+10\\right)(x-r) \\textbackslash\\textbackslash{} \\&=x^{4}+(a-r) x^{3}+(1-a r) x^{2}+(10-r) x-10 r \\end{aligned} $$ Comparing coefficients with $f(x)$, we see that $$ \\begin{aligned} a-r \\&=1 \\textbackslash\\textbackslash{} 1-a r \\&=b \\textbackslash\\textbackslash{} 10-r \\&=100 \\textbackslash\\textbackslash{} -10 r \\&=c . \\end{aligned} $$ Let\\textquotesingle s solve for $a, b, c$, and $r$. Since $10-r=100, r=-90$, so $c=(-10)(-90)=900$. Since $a-r=1, a=-89$. Then, since $b=1-a r, b=-8009$. Thus, we know that $$ f(x)=x^{4}+x^{3}-8009 x^{2}+100 x+900 . $$ Taking $f(1)$, we find that $$ \\begin{aligned} f(1) \\&=1^{4}+1^{3}-8009(1)^{2}+100(1)+900 \\textbackslash\\textbackslash{} \\&=1+1-8009+100+900 \\textbackslash\\textbackslash{} \\&=(\\mathbf{C})-7007 . \\end{aligned} $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2957", "queId": "13aa5e3e4f334a3aa4e0e74969d2b2fd", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Find the value of $$\\left\\textbackslash{ \\frac{2018+1}{5} \\right\\textbackslash} + \\left\\textbackslash{ \\frac{2018+2}{5} \\right\\textbackslash} + \\cdots \\cdots + \\left\\textbackslash{ \\frac{2018+2017}{5} \\right\\textbackslash} + \\left\\textbackslash{ \\frac{2018+2018}{5} \\right\\textbackslash}$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$751$$ "}], [{"aoVal": "C", "content": "$$810$$ "}], [{"aoVal": "D", "content": "$$1009$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$807$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2958", "queId": "2126e2710ce04cef8ba870364020fdaa", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{According to data from the United States Elections Project, only 36 percent of eligible voters voted in the 2014 elections. For random samples of size 40, which of the following best describes the sampling distribution of pˆ, the sample proportion of people who voted in the 2014 elections?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{The sampling distribution is skewed to the left, with mean 0.36 and standard deviation 0.076.} "}], [{"aoVal": "B", "content": "\\textbf{The sampling distribution is skewed to the right, with mean 0.64 and standard deviation 0.006.~} "}], [{"aoVal": "C", "content": "\\textbf{The sampling distribution is approximately normal, with mean 0.36 and standard deviation 0.076.~} "}], [{"aoVal": "D", "content": "\\textbf{The sampling distribution is approximately normal, with mean 0.36 and standard deviation 0.006.~} "}], [{"aoVal": "E", "content": "\\textbf{The sampling distribution is approximately normal,with mean 0.64 and standard deviation 0.076.~} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{For a large n, the sampling distribution of $\\hat{p}$ is approximately normal distribution with $E(\\hat{p})=p$} \\textbf{$\\sigma\\_{\\hat{p}}=\\sqrt{\\frac{p(1-p)}{n}}$.~} \\textbf{$E(\\hat{p})=0.36$} \\textbf{$\\sigma\\_{\\hat{p}}=\\sqrt{\\frac{p(1-p)}{n}} = \\sqrt{\\frac{0.36*0.64}{40}}=0.07589$} "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2961", "queId": "2a52bb2fabfd45cd9b2e52905d064532", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many digits after the decimal does the product of $3.222$ and $4.22$ have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals"], "answer_analysis": ["Count the number of digits in each decimals, the product of the two decimals will have that many digits after the decimal point. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2964", "queId": "08e893436bc24c6097eb84b0ed6b3a5e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In your family, there are $$15$$ chairs, $$5$$ tables, and $$20$$ cups. What is the ratio of chairs to cups? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15:5$$ "}], [{"aoVal": "B", "content": "$$5:15$$ "}], [{"aoVal": "C", "content": "$$5:20$$ "}], [{"aoVal": "D", "content": "$$3:4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["There are $$15$$ chairs and $$20$$ cups. So the ratio of chairs to cups is $$15:20$$. The simplest form is $$3:4$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2974", "queId": "25c31620c166409d9fb27214b861119b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of the remainders of $$1234 \\div5$$ and $$6789 \\div 10$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["The remainders are $$4$$ and $$9$$. Their sum is $$4 +9= 13$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2976", "queId": "25c3b520648e44a8b43d3e197aa41eb8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If the 9-digit number $$2017122\\square2$$ can be divisible by $$4$$, then the number in $$\\square$$ can be ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["We check if it is divisible by $$4$$ by looking at the last two digits. $$72$$ is divisible by $$4$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2977", "queId": "ec3e931c41f3420a80d6992d94b84e57", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A box has fewer than $50$ cookies in it. The cookies can be divided evenly between $2, 3,$ or $4$ children. However, they cannot be divided evenly between $7$ children because $6$ more cookies would be needed. How many cookies are there in the box? (2021 Math Kangaroo Problem, Level 3-4, Question \\#20) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$36$$ "}], [{"aoVal": "E", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The cookies can be divided evenly between $2, 3,$ or $4$ children, which means the number of cookies can be divisible by $2, 3,$ and $4$ at the same time. The cookies cannot be divided evenly between $7$ children because $6$ more cookies would be needed, which means the number of cookies divided by $7$ with $1$ remaining. Thus, the right answer is $D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2983", "queId": "588ba0b26c254a45a0aef455f1ccf8bf", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The following are the weights (in pounds) of seven people: $100, 115, 135, 140, 180, 197, 230$. Find the $80$-th percentile. ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$135$$ "}], [{"aoVal": "C", "content": "$$197$$ "}], [{"aoVal": "D", "content": "$$230$$ "}], [{"aoVal": "E", "content": "$$185$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$np=7(0.8)=5.6 \\uparrow 6$ The $80$-th percentile is $197$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2984", "queId": "090824b5c85b45c3af7e450aa7789397", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Meena had $$96$$ coconuts. She sold $$\\frac{1}{3}$$ of them yesterday and $$\\frac{1}{2}$$ of them today. How many coconuts did she sell altogether? ", "answer_option_list": [[{"aoVal": "A", "content": "$$63$$ "}], [{"aoVal": "B", "content": "$$72$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$84$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules", "Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Word Problems Involving Fractions and Percentages->Finding a Whole Given a Part and the Percentage"], "answer_analysis": ["$$\\frac{1}{3}+\\frac{1}{2}=\\frac{5}{6}$$ $\\frac{5}{6}\\times96=80$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2994", "queId": "091acec720664c15b3c2da44698978c6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Mariam had ＄$$4y$$. After buying some cloth at ＄$$7$$ per metre, she had ＄$$y$$ left. How many metres of cloth did she buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3y}{7}$$ "}], [{"aoVal": "B", "content": "$$\\frac{5y}{7}$$ "}], [{"aoVal": "C", "content": "$21y$ "}], [{"aoVal": "D", "content": "$$35y$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["Amount of money she spent to buy the cloth $$\\rightarrow$$＄$$4y-$$＄$$y$$ $$=$$＄$$3y$$, Length of cloth she bought $$\\rightarrow$$＄$$3y\\div $$＄$$7/\\text{m}$$ $$= \\frac{3y}{7}\\text{m}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "2995", "queId": "0f931b5bb90746c8bcbbe42900113c52", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The mid points of the four sides of a rectangle are $(−3,0)$, $(2,0)$, $(5,4)$, and $(0, 4)$. What is the area of the rectangle? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$50$$ "}], [{"aoVal": "E", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3004", "queId": "3837cbbd0ce24bc3a9672bdce2914a8b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Pick two consecutive positive integers whose sum is less than $$100$$. Square both of those integers and then find the difference of the square numbers. Which of the following could be the difference? ($2007$ AMC $8$ Problem, Question \\#$19$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$64$$ "}], [{"aoVal": "C", "content": "$$79$$ "}], [{"aoVal": "D", "content": "$$96$$ "}], [{"aoVal": "E", "content": "$$131$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas-> Difference of Two Squares Formula"], "answer_analysis": ["Let\\textquotesingle s say that $x$ is the smaller of the two numbers. So the question is $$(x+1)+x\\textless100(x+1)^{2}-x^{2}=x^{2}+2x+1-x^{2}=2x+1$$. ~$$2x+1$$ is obviously odd, so the answer could be $$\\text{C}$$ or $$\\text{E}$$. $$2x+1=131$$ doesn\\textquotesingle t match with $$2x+1\\textless100$$, so the answer is $$79$$. Therefore, the answer is $$\\text{C}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3006", "queId": "339d23c6d10d423696ef81cebc0ee787", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Two integers are inserted into the list $3,3,8,11,28$ to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$56$$ "}], [{"aoVal": "B", "content": "$$57$$ "}], [{"aoVal": "C", "content": "$$58$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$61$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3010", "queId": "ab4a2fac752e41dda61332f79fdfc6ff", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $1986^{}\\text{th}$ digit at the right of the decimal point in the decimal expression of $\\dfrac{1}{7}$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"], "answer_analysis": ["$$\\frac{1}{7}=0.\\overline{142857}$$, it is a decimal which repeats in cycles of $6$. Every $6$\\textsuperscript{th}~digit is $7$. The $1986$\\textsuperscript{th} digit is $7$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3014", "queId": "1cbf29a1824f450f8d5a03ab34502b3d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are four more girls than boys in Mr. Tse\\textquotesingle s class of 28 students. What is the ratio of number of girls to the number of boys in her class? ", "answer_option_list": [[{"aoVal": "A", "content": "$4:3$ "}], [{"aoVal": "B", "content": "$3:2$ "}], [{"aoVal": "C", "content": "$7:4$ "}], [{"aoVal": "D", "content": "$2:1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["We can set up an equation with $x$ being the number of girls in the class. The number of boys in the class is equal to $x-4$. Since the total number of students is equal to 28 , we get $x+x-4=28$. Solving this equation, we get $x=16$. There are $16-4=12$ boys in our class, and our answer is $16: 12=$ (B) $4: 3$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3022", "queId": "e79a938986014ae0b8681a678f3871c1", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Cassandra is helping her mother to pack $$75$$ cupcakes. The boxes that her mother prepares can only fit $$7$$ cupcakes. She must ensure the box is full before she can use the next box. How many boxes she can fill up? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$68$$ "}], [{"aoVal": "E", "content": "$$70$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers"], "answer_analysis": ["$$75\\div7=10R5$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3025", "queId": "825baef83b3e42d9afae2f1ee4e3100f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $*abcd*=a\\times d+b\\times c$, then $*2543*=$~\\uline{~~~~~~~~~~}~. ($2004$ Math League.com contest problem, $8$\\textsuperscript{th} Grade, Question \\#$33$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["$*2543*=2\\times3+5\\times4=6+20=26$. So the answer is $\\rm C$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3029", "queId": "b92f825aa14a463c884b78ba09d73857", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Louis had $8$ sticks. He broke three of them into two pieces. How many sticks does he have now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$8 + 3 = 11$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3034", "queId": "33aa4abc98b3494aae488e50a499574b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "If $3^{}p+3^{4}=90$, $2^{}r+44=76$, and $5^{3}+6^{}s=1421$, what is the product of $p$, $r$, and $s$? (2013 AMC 8 Problem, Question \\#15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$27$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$70$$ "}], [{"aoVal": "E", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers"], "answer_analysis": ["Start with $3^{}p+3^{4}=90$. Then, change $3^{4}$ to $81$. Subtract from $81$ from both sides to get $3^{}p=9$ and see that $p$ is $2$. Now, solve for $r$. Since $2^{}r+44=76$, $2^{}r$ must equal $32$, so $r=5$. Now, solve for $s$. $5^{3}+6^{}s=1421$ can be simplified to $125+6^{}s=1421$, which simplifies further to $6^{}s=1296$. Therefore, $s=4$. $prs$ equals $2\\times5\\times4$ which equals $40$. So, the answer is $40$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3039", "queId": "c7222249cad54e39affd54dd8fc0ed22", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Hannah bought $$5$$ whole pizzas: $$1$$ for herself and $$1$$ for each of her $$4$$ students. Hannah sliced her pizza into $$5$$ equal parts and ate only $$3$$ slices. Student $$A$$ sliced his pizza into $$4$$ equal parts, but ate only $$3$$ slices. Student $$B$$ sliced his pizza into $$8$$ equal parts, but ate only $$7$$ slices. Student $$C$$ sliced her pizza into $$3$$ equal parts, but ate only $$2$$ slices. Student $$D$$ sliced her pizza into $$6$$ equal parts, but ate only $$3$$ slices. Who ate less pizza than Hannah? ", "answer_option_list": [[{"aoVal": "A", "content": "Student $$A$$ "}], [{"aoVal": "B", "content": "Student $$B$$ "}], [{"aoVal": "C", "content": "Student $$C$$ "}], [{"aoVal": "D", "content": "Student $$D$$ "}], [{"aoVal": "E", "content": "Nobody "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["All of them eat more than $$\\frac{1}{2}$$, except student $$D$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3042", "queId": "0fe9ea5733434bb3999766d2af02150f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When Koko the Koala is awake, he eats $84$ grams of leaves per hour. He was awake for $2$ hours yesterday and $10$ hours today. How many grams of leaves did he eat in total in the two days? (adapted from 2014 Math Kangaroo Problem, Level 3-4, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$840$$ "}], [{"aoVal": "B", "content": "$$168$$ "}], [{"aoVal": "C", "content": "$$672$$ "}], [{"aoVal": "D", "content": "$$1008$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$84 \\times (10 + 2) = 84 \\times 10 + 84 \\times 2 = 840 + 168 = 1008$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3047", "queId": "9d5b54d3ca0d4dfe980eac13b829b188", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is not an equivalent ratio of $$4:12$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1:3$$ "}], [{"aoVal": "B", "content": "$$2:6$$ "}], [{"aoVal": "C", "content": "$$8:36$$ "}], [{"aoVal": "D", "content": "$$32:96$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions"], "answer_analysis": ["Option A: $$1:3$$ $\\to$ $4:12$ Option B: $2:6$ $\\to$ $$1:3$$ $\\to$ $4:12$ Option C: $8:36$ $\\to$ $4:18$ Option D: $32:96$ $\\to$ $$1:3$$ $\\to$ $4:12$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3051", "queId": "0c521e91f13a48f9b0b8207028cee9b7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a math competition, each participant has a unique $5$-digit registration number of the form $\\overline{BBCAC}$, where $0 \\leq A \\textless{} B\\textless{} C \\leq 9$ and $B$ is the average of $A$ and $C$. What is the maximum number of participant that can join this competition? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3059", "queId": "384db7f8e417484398459f2da518902f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all its side lengths are integers. The primeter of $\\triangle ABC$ with a side of length $14$ and a side length of $8$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$26$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+8\\textgreater14$. Therefore, $P\\textgreater14+14$. The least integer value of $P$ is $29$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3060", "queId": "2f1912f582c94b3cb9fdf661a69a062b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are two positive integers, $$x$$ and $$y$$. $$x$$ equals to $$3^{2}$$, and $$y$$ is the base of $$5^{3}$$. What is the product of $$x$$ and $$y$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$15$ "}], [{"aoVal": "B", "content": "$45$ "}], [{"aoVal": "C", "content": "$90$ "}], [{"aoVal": "D", "content": "$1125$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers"], "answer_analysis": ["$$x=3^{2}=9$$ $$5$$ cubed is $$5^{3}$$. And the base is $$5$$. So, $$x\\cdot y=9\\times 5=45$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3061", "queId": "0c5c6aa8452b43919bde5a93ed8675f6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2016 P2 Q5 What number does () stands for? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns->Encryption and Decryption"], "answer_analysis": ["banana = 32-24= 8 A + 8 = 12 A = 4 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3063", "queId": "41857e581e2a46869b29dafc95600556", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all its side lengths are integers. The perimeter of $\\triangle ABC$ with a side of length $14$ and a side length of $8$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$26$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+8\\textgreater14$. Therefore, $P\\textgreater14+14$. The least integer value of $P$ is $29$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3065", "queId": "1ce6aa2cc04e4ae0a78ef22986778c89", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$2018$ is an interesting number. This is because when we add the first digit and the last digit, we will get the reverse of the middle two digits. Which of the options below is also an interesting number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3014$$ "}], [{"aoVal": "B", "content": "$$3129$$ "}], [{"aoVal": "C", "content": "$$4319$$ "}], [{"aoVal": "D", "content": "$$2017$$ "}], [{"aoVal": "E", "content": "$$4913$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3073", "queId": "187d23b145854fc3af538ceafbb56d10", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Given: $a-b\\textgreater a$ and $a+b\\textless b$. Which of the following must be true?~\\uline{~~~~~~~~~~}~ $I$. $a b$ is negative $II$. $a+b$ is negative $III$. $a-b$ is negative ", "answer_option_list": [[{"aoVal": "A", "content": "$I$ only "}], [{"aoVal": "B", "content": "$I$ and $III$ only "}], [{"aoVal": "C", "content": "$II$ only "}], [{"aoVal": "D", "content": "$I$, $II$, $III$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["$a-b\\textgreater a$ then $b\\textless0$ $a+b\\textless b$ then $a\\textless0$. So both $a$ and $b$ are negative. $I$ is false, since the product will be positive. $II$ is true since the sum of two negative numbers is negative. $III$ is false because if $a=-1$ and $b=-2$ then $a-b$ is positive. Only $II$ is true. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3082", "queId": "0c99a520a2684252805a3492987c0a25", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "What is the remainder when $2^{2023}+2023$ is divided by $2^{20}+1$? (Adapted From 2020 AMC 10B Problems, Question \\#22) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2015$$ "}], [{"aoVal": "B", "content": "$$2^{5}$$ "}], [{"aoVal": "C", "content": "$$2023$$ "}], [{"aoVal": "D", "content": "$$2048$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Let $x=2^{20}$. We are now looking for the remainder of $\\frac{8x^{101}+2023}{x+1}$. By Polynomial Remainder Theorem, the remainder is $8\\times (-1)^{101} + 2023 = 2015$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3084", "queId": "7dc26cf49b234cd4995ea03f3dcb57c7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The last four digits in Andy\\textquotesingle s ID card are $2025$. What is the the difference between the largest and the smallest digit in $2025$?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$7$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"], "answer_analysis": ["The largest digit is $5$, and the smallest digit is $0$. $5-0=5$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3085", "queId": "1cfbee250a164e71b742fb4b4f7dd1d0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Let $a$ and $b$ be relatively prime positive integers with $a\\textgreater b\\textgreater0$ and $\\frac{a^{3}-b^{3}}{(a-b)^{3}}=\\frac{73}{3}$. What is $a-b$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["Slightly expanding, we have that $\\frac{(a-b)\\left(a^{2}+a b+b^{2}\\right)}{(a-b)(a-b)(a-b)}=\\frac{73}{3}$. Canceling the $(a-b)$, cross multiplying, and simplifying, we obtain that $0=70 a^{2}-149 a b+70 b^{2}$. Dividing everything by $b^{2}$, we get that $$ 0=70\\left(\\frac{a}{b}\\right)^{2}-149\\left(\\frac{a}{b}\\right)+70 \\text {. } $$ Applying the quadratic formula and following the restriction that $a\\textgreater b\\textgreater0$ $$ \\frac{a}{b}=\\frac{10}{7} \\text {. } $$ Hence, $7 a=10 b$. Since they are relatively prime, $a=10, b=7$. $$ 10-7= 3 \\text {. } $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3086", "queId": "0ca2c393bd9448e08058dc264eb35c99", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which number has to be subtracted from $17$ in order to obtain $-33$? (Adapted from 2017 Math Kangaroo Problem, Level 7-8, Question \\#3) ", "answer_option_list": [[{"aoVal": "A", "content": "$$-50$$ "}], [{"aoVal": "B", "content": "$$-16$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$40$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$17-50=-33$, so the answer is $E$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3090", "queId": "462dbfeddd304192b5a0729c40eec657", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Fill in the blank:~\\uline{~~~~~~~~~~}~is $$3$$ tens $$7$$ ones less than $$4$$ tens $$6$$ ones. ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$19$$ "}], [{"aoVal": "C", "content": "$$73$$ "}], [{"aoVal": "D", "content": "$$83$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$3$$ tens $$7$$ ones: $$37$$ $$4$$ tens $$6$$ ones: $$46$$ less than: $$46-37=9$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3093", "queId": "3cf571d3965345a4bc833ed99c9cec48", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There were $$16$$ monkeys in total in the animal school. After the whistle, they arranged themselves into $$8$$ rows. How many monkeys were there in each row after the whistle? (Adapted from 2005 Math Kangaroo Problem, Level 3-4, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["There were $$16 \\div 8 = 2$$ monkeys in each row. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3097", "queId": "462ffa8d8796404ab3306171f72c5899", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Find all values of $x$ such that $\\textbar3 x+12\\textbar\\textless9$ and $\\textbar x+2\\textbar\\textless\\textbar-3 x-6\\textbar$.~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$x\\textless-2$ "}], [{"aoVal": "B", "content": "$-7\\textless x\\textless-1$ "}], [{"aoVal": "C", "content": "$-7\\textless x\\textless-2$ "}], [{"aoVal": "D", "content": "$-7\\textless x\\textless-1 ; x \\neq-2$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["Based on the first inequality, we know that $-9\\textless3 x+12\\textless9$ because $3 x+2$ must be less than 9 units away from zero. We can subtract 12 from all three parts of the inequality to arrive at $-21\\textless3 x\\textless-3 \\rightarrow-7\\textless x\\textless-1$. From the second inequality we can rewrite $\\textbar-3 x-6\\textbar$ as $\\textbar3 x+6\\textbar=3\\textbar x+2\\textbar$ because they must be equal. The second inequality must be true for all numbers except for when $\\textbar x+2\\textbar=0$, or when $x=-2$. Thus the answer includes all numbers from $-7$ to $-1$ with the exception of $-2$. The answer is $\\mathbf{D}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3099", "queId": "104cb24c29ac4e95a5906515857ad9c5", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all its side lengths are integers. The perimeter of $\\triangle ABC$ with a side of length $3$ and a side length of $4$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+3\\textgreater4$. Therefore, $P\\textgreater4+4$. The least integer value of $P$ is $9$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3101", "queId": "1050c8cd59ef4048b090596ce767379b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Suppose that $x$ and $y$ are nonzero real numbers such that $\\frac{3 x+y}{x-3 y}=-2$. What is the value of $\\frac{x+3 y}{3 x-y}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$-3$$ "}], [{"aoVal": "B", "content": "$$-1$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Proportional Equations"], "answer_analysis": ["Rearranging, we find $3 x+y=-2 x+6 y$, or $5 x=5 y \\Longrightarrow x=y$. Substituting, we can convert the second equation into $\\frac{x+3 x}{3 x-x}=\\frac{4 x}{2 x}= 2$ More step-by-step explanation: $$ \\begin{aligned} \\&\\frac{3 x+y}{x-3 y}=-2 \\textbackslash\\textbackslash{} \\&3 x+y=-2(x-3 y) \\textbackslash\\textbackslash{} \\&3 x+y=-2 x+6 y \\textbackslash\\textbackslash{} \\&5 x=5 y \\textbackslash\\textbackslash{} \\&x=y \\textbackslash\\textbackslash{} \\&\\frac{x+3 y}{3 x-y}=\\frac{1+3(1)}{3(1)-1}=\\frac{4}{2}=2 \\end{aligned} $$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3105", "queId": "0cd694cef6ec494b8071562f50e7d515", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Compare these fractions. $$\\frac{8}{31}$$~\\uline{~~~~~~~~~~}~$$\\frac{4}{15}$$, ~$$\\frac{9}{61}$$~\\uline{~~~~~~~~~~}~$$\\frac{3}{22}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\textgreater$$, $$\\textgreater$$ "}], [{"aoVal": "B", "content": "$$\\textgreater$$, $$\\textless$$ "}], [{"aoVal": "C", "content": "$$\\textless$$, $$\\textgreater$$ "}], [{"aoVal": "D", "content": "$$\\textless$$, $$\\textless$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["$$\\frac{8}{31}\\textless\\frac{8}{30}$$;~$$\\frac{9}{61}\\textgreater\\frac{9}{66}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3109", "queId": "2a9f364dcd2c4697a2002751ad9c9a06", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Compare these fractions. $$\\frac{3}{7}$$~\\uline{~~~~~~~~~~}~$$\\frac{5}{9}$$, $$\\frac{5}{8}$$~\\uline{~~~~~~~~~~}~$$\\frac{7}{11}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\textgreater$$, $$\\textgreater$$ "}], [{"aoVal": "B", "content": "$$\\textgreater$$, $$\\textless$$ "}], [{"aoVal": "C", "content": "$$\\textless$$, $$\\textgreater$$ "}], [{"aoVal": "D", "content": "$$\\textless$$, $$\\textless$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["$$\\frac{27}{63}\\textless\\frac{35}{63}$$;~$$\\frac{55}{88}\\textless\\frac{56}{88}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3120", "queId": "2aa671beb13e4c0e987bf38779f6f986", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $ a◆b$ means $(a\\times b)+b$ , then $（2◆3）◆4$ has the value． ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["If $a◆b$~ represents $(a\\times b)+b$ , $2◆3=(2\\times3)+3=9,9◆4=(9\\times4)+4=40$ . "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3125", "queId": "2aa8627cef2b444dbb189c1d669cf4dd", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "(2) Eddie had 120 dollars as his pocket money, and spent $$ \\frac{3}{4} $$of it. How much money is left? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["left！！！not spent! So you need to calculate the fraction of left money. Then use T*F=C "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3129", "queId": "107bd421b05c488a8b8c4edbe9555001", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Divide $$2$$、$$3$$、$$24$$、$$33$$、$$55$$ and $$60$$ into two groups with 3 numbers in each group to make the product of numbers in each group the same, so the product is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$3630$$ "}], [{"aoVal": "B", "content": "$$1584$$ "}], [{"aoVal": "C", "content": "$$3960$$ "}], [{"aoVal": "D", "content": "$$2880$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Power of Products"], "answer_analysis": ["$$2=2$$， $$3=3$$， $$24=2\\times 2\\times 2\\times 3$$， $$33=11\\times 3$$， $$55=11\\times 5$$， $$60=2\\times 2\\times 3\\times 5$$， $$2\\times 60\\times 33=24\\times 55\\times 3$$， $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde2\\times 60\\times 33$$ $$=(2\\times 33)\\times 60$$ $$=66\\times 60$$ $$=3960$$． $$\\text{C}$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3130", "queId": "2aaab2c7197449e39c7d48d630f9ad82", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following integers cannot be written as the sum of four consecutive odd integers? (2015 AMC 8 Problems, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$100$$ "}], [{"aoVal": "E", "content": "$$200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables"], "answer_analysis": ["Let our $4$ numbers be $n, n+2, n+4, n+6$, where $n$ is odd. Then our sum is $4 n+12$. The only answer choice that cannot be written as $4 n+12$, where $n$ is odd, is (D) 100 . "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3133", "queId": "4f79338751d14373824ad19253db5cda", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$100-99+98-97+96-95+\\cdots +4-3+2-1$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$80$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$\\begin{eqnarray}\\&\\&\\left( 100-99 \\right)+\\left( 98-97 \\right)\\cdots +\\left( 4-3 \\right)+\\left( 2-1 \\right)\\textbackslash\\textbackslash{} \\&=\\&50\\times 1\\textbackslash\\textbackslash{} \\&=\\&50．\\end{eqnarray}$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3135", "queId": "2f45ea48881c49ce935b004458a4e070", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Of the following, which has a value different from the others? ", "answer_option_list": [[{"aoVal": "A", "content": "$$40\\times 50$$ "}], [{"aoVal": "B", "content": "$$4\\times 5000$$ "}], [{"aoVal": "C", "content": "$$50\\times 400$$ "}], [{"aoVal": "D", "content": "$$40\\times 500$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["To see which value is different, count the total number of $$0$$\\textquotesingle s in each product. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3148", "queId": "18d151cf57304f1faabe74ceb029b2d3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$12 \\times \\left( \\frac{1}{2} \\times \\frac{1}{3} \\times \\frac{1}{4}\\right)=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$72$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$\\frac{4}{3}$$ "}], [{"aoVal": "D", "content": "$$\\frac{1}{2}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["$$12 \\times \\left( \\frac{1}{2} \\times \\frac{1}{3} \\times \\frac{1}{4}\\right)$$ $$=\\left(12 \\times \\frac{1}{2}\\right) \\times \\frac{1}{3} \\times \\frac{1}{4}$$ $$=6 \\times \\frac{1}{3} \\times \\frac{1}{4}$$ $$=2 \\times \\frac{1}{4}$$ $$= \\frac{2}{4}$$ $$=\\frac{1}{2}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3157", "queId": "149f548c79214e2e96d267efa3cd3e51", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all its side lengths are integers. The primeter of $\\triangle ABC$ with a side of length $3$ and a side length of $4$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+3\\textgreater4$. Therefore, $P\\textgreater4+4$. The least integer value of $P$ is $9$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3158", "queId": "1d3939fc360b4acf9bb5f701720ee8d3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$(60 \\div 5)\\times4 =$$.　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$96$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$(60\\div5)\\times4 = 12 \\times4 =48$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3170", "queId": "10bab04c693d45a682c2dd25c9be35be", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The fraction $$\\dfrac{214}{263}$$ keeps the same value when both its numerator and denominator are~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "multiplied by $$2~ $$ "}], [{"aoVal": "B", "content": "increased by $$2$$ "}], [{"aoVal": "C", "content": "decreased by $$2$$ "}], [{"aoVal": "D", "content": "$$ $$squared$$ $$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions"], "answer_analysis": ["The problem is about the basic property of fractions, namely, multiplying or dividing the numerator and denominator by the same number (except $$0$$), the value of the fraction is unchanged. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3174", "queId": "871a91f435174c6d874964fe2a512898", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all its side lengths are integer. The primeter of $\\triangle ABC$ with a side of length $12$ and a side length of $7$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "$$28$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+7\\textgreater12$. $P=s+7+12\\textgreater12+12$. Therefore, $P\\textgreater24+1=25$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3176", "queId": "10c410e94f714a968414b9fe9b49ddfd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$10\\times20\\times30\\times40=24\\times$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$10^{3}$$ "}], [{"aoVal": "B", "content": "$$10^{4}$$ "}], [{"aoVal": "C", "content": "$$10^{5}$$ "}], [{"aoVal": "D", "content": "$$10^{6}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$10\\times20\\times30\\times40=(1\\times2\\times3\\times4)\\times10^{4}=24\\times10^{4}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3178", "queId": "14b9a6231ea34a369555235854cd782b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the correct ordering of the three answers from $\\frac5{19}\\div \\frac{25}{38}$, $1\\frac12 \\div \\frac{15}8$, and $\\frac74 \\div \\frac{35}{12}$, in increasing order? (adapted from 2012 AMC 8 Problems, Question \\#20) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac5{19}\\div \\frac{25}{38}$ \\textless~$1\\frac12 \\div \\frac{15}8$ \\textless{} $\\frac74 \\div \\frac{35}{12}$ "}], [{"aoVal": "B", "content": "$\\frac74 \\div \\frac{35}{12}$ \\textless~$1\\frac12 \\div \\frac{15}8$ \\textless~$\\frac5{19}\\div \\frac{25}{38}$ "}], [{"aoVal": "C", "content": "$1\\frac12 \\div \\frac{15}8$ \\textless{} $\\frac74 \\div \\frac{35}{12}$ \\textless~$\\frac5{19}\\div \\frac{25}{38}$ "}], [{"aoVal": "D", "content": "$\\frac5{19}\\div \\frac{25}{38}$ \\textless{} $\\frac74 \\div \\frac{35}{12}$ \\textless~$1\\frac12 \\div \\frac{15}8$ "}], [{"aoVal": "E", "content": "$\\frac74 \\div \\frac{35}{12}$ \\textless~$\\frac5{19}\\div \\frac{25}{38}$ \\textless~$1\\frac12 \\div \\frac{15}8$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions->Division of Fractions"], "answer_analysis": ["$\\frac5{19}\\div \\frac{25}{38}=\\frac25$ ~ $\\frac74 \\div \\frac{35}{12}=\\frac35$ $1\\frac12 \\div \\frac{15}8=\\frac45$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3184", "queId": "0d8645b641864aaf89ccbabd1766f528", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Choose the answer in the simplest form. $$\\frac{9}{4}\\times \\frac{8}{27}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{72}{108}$$ "}], [{"aoVal": "B", "content": "$$\\frac{18}{27}$$ "}], [{"aoVal": "C", "content": "$$\\frac{8}{12}$$ "}], [{"aoVal": "D", "content": "$$\\frac{2}{3}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$\\frac{9}{4}\\times \\frac{8}{27}=\\frac{2}{3}$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3188", "queId": "8adb1db084c44752a477a8050b885e20", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the arithmetic sequence $3$, $7$, $11$, $15$, $\\cdots$ , the $26$\\textsuperscript{th} number is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$103$$ "}], [{"aoVal": "B", "content": "$$107$$ "}], [{"aoVal": "C", "content": "$$111$$ "}], [{"aoVal": "D", "content": "$$115$$ "}], [{"aoVal": "E", "content": "$$119$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$3+4\\times(26-1)=103$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3190", "queId": "e7a739171d584f8286b66dae9c61810d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If a whole number is multiplied by itself, the ones\\textquotesingle{} digit of the product \\emph{cannot} be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"], "answer_analysis": ["If a whole number is multiplied by itself, the ones\\textquotesingle{} digit of the product could be $$1 (1\\times1)$$ or $$5 (5\\times5)$$ or $$9 (3\\times3)$$, but not $$7$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3207", "queId": "1910c45a41094f67a6aefa7c4f2d8ab9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Bob: \" Hi, Stanley. What is the coefficient of the variable in this algebraic expression $3x^{2}-4$?\" Stanley:\" I can give you a hint. The value of the coefficient is $7$ more than the constant.\" Stanley\\textquotesingle s hint is~\\uline{~~~~~~~~~~}~and the coefficient of the variable is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "correct, $3$ "}], [{"aoVal": "B", "content": "correct, $-4$ "}], [{"aoVal": "C", "content": "incorrect, $3$ "}], [{"aoVal": "D", "content": "incorrect, $4$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["Constant: $-4$ Coefficient of the variable: $3$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3208", "queId": "3892760088974be3809057c4a34f9ea5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Gilda has a bag of marbles. She gives $20 \\textbackslash\\%$ of them to her friend Pedro. Then Gilda gives $25 \\textbackslash\\%$ of what is left to another friend, Ebony. Finally, Gilda gives $5 \\textbackslash\\%$ of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself? (adapted 2019 AMC 8, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$95\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$33\\textbackslash\\%$ "}], [{"aoVal": "C", "content": "$$45\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$57\\textbackslash\\%$$ "}], [{"aoVal": "E", "content": "$$63\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["After Gilda gives $20 \\textbackslash\\%$ of the marbles to Pedro, she has $80 \\textbackslash\\%$ of the marbles left. If she then gives $25 \\textbackslash\\%$ of what\\textquotesingle s left to Ebony, she has $(0.75 * 0.8)=60 \\textbackslash\\%$ of what she had at the beginning. Finally, she gives $5 \\textbackslash\\%$ of what\\textquotesingle s left to her brother, so she has $(0.6 * 0.95)$ (D) $57\\textbackslash\\%$~ of what she had in the beginning left. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3210", "queId": "10fd6979282b4979b9957a12921a5454", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that $$x\\otimes y=6\\times x-5\\times y$$, find $$7\\otimes 6$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$42$$ "}], [{"aoVal": "D", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["$$7\\otimes 6=6\\times 7-5\\times 6=12$$, so $$\\text{A}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3212", "queId": "389341fb19f24bb9854c00120b1497dd", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all its side lengths are integer. The primeter of $\\triangle ABC$ with a side of length $12$ and a side length of $7$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$27$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+7\\textgreater12$. $P=s+7+12\\textgreater12+12$. Therefore, $P\\textgreater24+1=25$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3213", "queId": "1913a1ef9a3f4a85b785d99103fe3aec", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A slug called Glug eats $$2$$ tomatoes for every $$3$$ strawberries. Yesterday it had eaten $$35$$ tomatoes and strawberries altogether. How many tomatoes did it eat? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$$35\\times \\frac {2} {2+3} = 14$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3223", "queId": "2661bd89429e4781b774bf3f04b5ee94", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "How many perfect cubes lie between $2^{2}+1$ and $2^{8}+1$, inclusive? (Adapted from 2018 AMC 8 Problem, Question \\#25) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers"], "answer_analysis": ["$2^{2}+1=5$, $2^{8}+1=257$. $2^{3}=8$, $3^{3}=27$, $4^{3}=64$, $5^{3}=125$, $6^{3}=216$. Thus, the answer is $5$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3228", "queId": "1922af64ee39418faf2982a09de961a8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Steven subtracts the units digit from the tens digit for each two-digit number. He then finds the sum of all his answers. What is the value of Steven\\textquotesingle s sum? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$45$$ "}], [{"aoVal": "C", "content": "$$55$$ "}], [{"aoVal": "D", "content": "$$90$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["The sum of all the tens digits is $$\\left(1+2+3+4+5 +6 +7+8+9\\right)\\times10$$. The sum of all the units digits is $$\\left(0 + 1+2+3 +4+5 +6 +7+8+9\\right)\\times9$$. Therefore Steven\\textquotesingle s sum is $$\\left(1+2+3 +4+5+6+7+8+9\\right)\\times1=45$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3229", "queId": "a6bbd2266dd14466b6278a5aa480f07a", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "The product of two different nonzero integers cannot be． ", "answer_option_list": [[{"aoVal": "A", "content": "prime　 "}], [{"aoVal": "B", "content": "zero　 "}], [{"aoVal": "C", "content": "even　 "}], [{"aoVal": "D", "content": "composite　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["The product of two different nonzero integers can never be $$0$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3237", "queId": "112339a3eed14f7a92441f199fdbd2ba", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Bob bought three kinds of meat: pork, beef and chicken with the total cost of $152. The ratio of the weight of pork, beef and chicken is~$2:4:3$. The ratio of the price per pound of pork, beef and chicken is~$6:5:2$. What is the sum of the last digits of the cost of each kind in dollars? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["Let~$x,\\textbackslash{} y\\textbackslash{} and\\textbackslash{} z$~be the weight of pork, beef and chicken, respectively. ~$\\textbackslash{} x:y:z=2:4:3$~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ (1) The ratio of the price will be~$\\left( 6x\\right):\\left( 5y\\right):\\left( 2z\\right).$ The costs of pork, beef and chicken are~$A,B\\textbackslash{} and\\textbackslash{} C,$~respectively. ~$A=\\dfrac{6x}{6x+5y+2z}\\times152$~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~(2) From (1), we get: ~$y=2x,\\textbackslash{} and\\textbackslash{} z=\\dfrac{3}{2}x$~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~(3) (2) becomes:~$A=\\dfrac{6x}{6x+5\\left( 2x\\right)+2\\times\\dfrac{3}{2}x}\\times152=\\dfrac{6x}{19x}\\times152=48$ Similarly,~$B=\\dfrac{5y}{6x+5y+2z}\\times152=\\dfrac{5y}{19x}\\times152=\\dfrac{10x}{19x}\\times152=80.$ And~$C=\\dfrac{2z}{6x+5y+2z}\\times152=\\dfrac{2z}{19x}\\times152=\\dfrac{3x}{19x}\\times152=24.$ Pork costs $48 per pound, beef costs $80, and chicken costs $24. The sum of the last digits of the costs is 8+0+4=12. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3239", "queId": "8ae1f9550be84771a09fb8060f539cde", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "$$1000\\text{m}$$ per second $$=$$$$\\text{km}$$ per hour. ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$360$$ "}], [{"aoVal": "C", "content": "$$3600$$ "}], [{"aoVal": "D", "content": "$$6000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Compound Units"], "answer_analysis": ["$$1000\\text{m/s}=1\\text{km/s}=3600\\text{km/hr}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3241", "queId": "266d6bbe3d344f59ba5f1e69b7aa9406", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Solve the equation: $$16\\times 25-13\\left( 3x+2 \\right)=179$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$39x=400-26-179$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde x=5$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3252", "queId": "15123010499b4516bea8a0dda21162d9", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Find the missing term in the following sequence: $$1, 2, 4, 7,~\\uline{~~~~~~~~~~}~, 16$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["The number sequence are in the pattern of $$+1, +2, +3, +4, +5, \\cdots $$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3254", "queId": "1d8b25027f93406ab007abfe91add3c8", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "On Kangaroo planet each kangyear has 20 kangmonths and each kangmonth has 6 kangweeks, How many kangweeks are there in one quarter of a kangyear? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$90$$ "}], [{"aoVal": "E", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$\\dfrac{1}{4}$kangyear x~$\\dfrac{20\\textbackslash{} kangmonths}{1\\textbackslash{} kangyear}$~x~$\\dfrac{6\\textbackslash{} kangweeks}{1\\textbackslash{} kangmonth}$~= 30 kangweeks. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3256", "queId": "2f8118d645384ada90ffe775e12e9d20", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A vase was being sold at the price of $250$ dollars. The store decides to sell it with a $40\\textbackslash\\%$ discount. If you buy the vase now, how much will you save? ", "answer_option_list": [[{"aoVal": "A", "content": "$$150$$ "}], [{"aoVal": "B", "content": "$$100$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["$250\\times 40\\textbackslash\\%$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3262", "queId": "58d3c74b24664a3cb0fc82356cb97f24", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$2.7\\times0.2\\div3=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$0.16$ "}], [{"aoVal": "B", "content": "$1.6$ "}], [{"aoVal": "C", "content": "$0.18$ "}], [{"aoVal": "D", "content": "$1.8$ "}], [{"aoVal": "E", "content": "$0.14$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals"], "answer_analysis": ["$$2.7\\times0.2\\div3$$ $$=0.54\\div3$$ $$=0.18$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3264", "queId": "21fded3a3d774d508f7ba65bcfc03795", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Mary wanted to buy $12$ lemons. The lemons were sold either for $90$ cents each or at $3$ dollars for a bag of $4$ lemons. How much money would Mary save if she buys three bags of lemons instead of buying $12$ lemons separately? ", "answer_option_list": [[{"aoVal": "A", "content": "$1.2$ dollars "}], [{"aoVal": "B", "content": "$1.5$ dollars "}], [{"aoVal": "C", "content": "$1.6$ dollars "}], [{"aoVal": "D", "content": "$1.8$ dollars "}], [{"aoVal": "E", "content": "$2.1$ dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$0.9 \\times 12 - 3 \\times 3 = 1.8$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3269", "queId": "4b057a81ece5453cbc863a9390e2a87d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The following are the weights (in pounds) of ten people: $100,115, 135, 140, 180, 197, 203, 230, x, y$ (not necessarily in increasing order). It is also given that the average weight of these ten people is $157$ pounds, and there is a unique mode of $135$. Find the $56$-th percentile. ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$115$$ "}], [{"aoVal": "C", "content": "$$125$$ "}], [{"aoVal": "D", "content": "$$135$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["First of all, we find the values of $x$ and $y$. Since the average is $157$, we have $(100+115+135+140+ 180+197+203+230+x+y = 157 \\times 10 = 1570$ $1300+x+y =1570$ $x+y = 270$. There is a unique mode, $135$, then $135$ must appear at least twice. Therefore, one of $x, y$ is $135$. It is easy to deduce that both $x$ and $y$ are $135$. List the weights in increasing order: $100,115, 135, 135, 135, 140, 180, 197, 203, 230$. $np=10(0.56)=5.6 \\uparrow 6$. The $56$-th percentile is $140$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3270", "queId": "19497aea1f704de08090350deae1c33b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following equations are NOT equivalent to $x+5=13$? ", "answer_option_list": [[{"aoVal": "A", "content": "$x+5-5=13-5$ "}], [{"aoVal": "B", "content": "$2(x+5)=26$ "}], [{"aoVal": "C", "content": "$x+5-13=0$ "}], [{"aoVal": "D", "content": "$x+5+13=0$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["Equations are equivalent when you can obtain one by subtracting, adding, dividing, or multiplying the same number on the other. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3274", "queId": "341a7691f2514dbc8fc63d2f3460b378", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\frac{1}{9}+ \\frac{3}{9}+ \\frac{5}{9}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$\\frac{10}{9}$$ "}], [{"aoVal": "D", "content": "$$\\frac{5}{243}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["$$\\frac{1}{9}+ \\frac{3}{9}+ \\frac{5}{9}= \\frac{9}{9}=1$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3277", "queId": "194ee6d931274284a25e5690ee08b9ce", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "What is $$9762 + 7 \\times 8 \\times 9 \\times 4 \\times 99 \\times 0$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$9762$$ "}], [{"aoVal": "B", "content": "$$9818$$ "}], [{"aoVal": "C", "content": "$$9889$$ "}], [{"aoVal": "D", "content": "$$209346$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Anything times $$0$$ equal $$0$$. $$9762 + 0 = 9762$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3278", "queId": "38ae263839cd4d3eba1db18b241ce7c9", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is $15$. What is the greatest possible perimeter of the triangle? （2006 AMC10B, Question 10) ", "answer_option_list": [[{"aoVal": "A", "content": "$$43$$ "}], [{"aoVal": "B", "content": "$$44$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$46$$ "}], [{"aoVal": "E", "content": "$$47$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["Let $x$ be the length of the first side. The lengths of the sides are: $x, 3 x$, and 15 . By the Triangle Inequality, $$ \\begin{aligned} \\&3 x\\textless x+15 \\textbackslash\\textbackslash{} \\&2 x\\textless15 \\textbackslash\\textbackslash{} \\&x\\textless\\frac{15}{2} \\end{aligned} $$ The greatest integer satisfying this inequality is 7 . So the greatest possible perimeter is $7+3 \\cdot 7+15=$ (A) 43 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3281", "queId": "794303f54c514be1ada033886d8e62ee", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$1 + 10 + 100 + 1000 =$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$1111$$ "}], [{"aoVal": "C", "content": "$$1234$$ "}], [{"aoVal": "D", "content": "$$4000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$1 + 10 + 100 + 1000 =11+11$$ hundred $$=1111$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3282", "queId": "98d26ede6f794ef48df034f32c552962", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $$2022$$th digit to the right of the decimal point in the decimal representation of $$\\frac 1{54}$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Sequence Operations"], "answer_analysis": ["The decimal is $$0.0185185\\cdots $$. An \"$$8$$\" appears in the $$3$$rd, $$6$$th, $$9$$th, $$\\cdots $$, $$2022$$th decimal place. So a \"$$8$$\" is in the $$2022$$th place. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3283", "queId": "41dda41f37a54ceeade78881ad9a241f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "According to the regulation of the pyramid series, the formula $$1+2+3+4+5+6+5+4+3+2+1=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$6\\times6$$ "}], [{"aoVal": "B", "content": "$$6\\times7$$ "}], [{"aoVal": "C", "content": "$$6\\times5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables"], "answer_analysis": ["``Pyramid series''$$1+2+3+4+\\cdots +\\left( n-1 \\right)+n+\\left( n-1 \\right)+\\cdots +3+2+1$$ $$={{n}^{2}}$$． So the answer is $$\\text{A}$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3286", "queId": "268bea9cb73a4149a8d99051ca743043", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following has a result of $183$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$103+86$$ "}], [{"aoVal": "B", "content": "$$117+76$$ "}], [{"aoVal": "C", "content": "$$90+83$$ "}], [{"aoVal": "D", "content": "$$82+101$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$103+86=189$$ $$117+76=193$$ $$90+83=173$$ $$82+101=183$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3287", "queId": "268cdc9de32f4468b6c377df36dc9679", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$\\frac{1}{4}\\times \\frac{5}{6}+\\frac{3}{7}\\times \\frac{7}{8}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{5}{12}$$ "}], [{"aoVal": "B", "content": "$$\\frac{5}{16}$$ "}], [{"aoVal": "C", "content": "$$\\frac{5}{17}$$ "}], [{"aoVal": "D", "content": "$$\\frac{7}{12}$$ "}], [{"aoVal": "E", "content": "$$\\frac{11}{12}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["$$\\frac{1}{4}\\times \\frac{5}{6}+\\frac{3}{7}\\times \\frac{7}{8}$$=$$\\frac{5}{24}+\\frac{3}{8}$$=$$\\frac{5}{24}+\\frac{9}{24}$$=$$\\frac{14}{24}$$=$$\\frac{7}{12}$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3294", "queId": "1184c85e9c074d8d964671f585e4cc72", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Simplify the following expression: $$a^{2}\\times a+b^{2}\\times b^{3}$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$a^{3}+b^{5}$$ "}], [{"aoVal": "B", "content": "$$a^{3}b^{5}$$ "}], [{"aoVal": "C", "content": "$$a^{2}+b^{5}$$ "}], [{"aoVal": "D", "content": "$$a^{2}+b^{6}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"], "answer_analysis": ["$$a^{2}\\times a+b^{2}\\times b^{3}=$$$$a^{3}+b^{5}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3297", "queId": "2b0d61123980438fa2a96e1bcae6c2af", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the next number in this sequence? $$1$$, $$2$$, $$3$$, $$6$$, $$11$$, $$20$$, $$37$$,~\\uline{~~~~~~~~~~}~? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$47$$ "}], [{"aoVal": "B", "content": "$$54$$ "}], [{"aoVal": "C", "content": "$$57$$ "}], [{"aoVal": "D", "content": "$$68$$ "}], [{"aoVal": "E", "content": "$$74$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["After the first three numbers, each number is the sum of the previous three numbers. So the next number is $$11 + 20 + 37 = 68$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3302", "queId": "1db905558a66450a8a1e6b387136a2f6", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distribution of Sean's weekly income is approximately normal with mean $\\textbackslash$225$ and standard deviation $\\textbackslash$25$. The distribution of Evan's weekly income is approximately normal with mean $\\textbackslash$240$ and standard deviation $15. Assuming their weekly incomes are independent of each other, which of the following is closest to the probability that Sean will have a greater income than Evan in a randomly selected week?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{0.067} "}], [{"aoVal": "B", "content": "\\textbf{0.159} "}], [{"aoVal": "C", "content": "\\textbf{0.227} "}], [{"aoVal": "D", "content": "\\textbf{0.303} "}], [{"aoVal": "E", "content": "\\textbf{0.354} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{Sean \\textasciitilde{} N(225, 25)} \\textbf{Evan \\textasciitilde{} N(240, 15)} \\textbf{→} \\textbf{Sean - Evan \\textasciitilde{} N(-15, 29.155)} \\textbf{P(Sean-Evan \\textgreater{} 0) = 1-P(X\\textless0) = 0.303} "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3304", "queId": "221fbe122a08482c918036dd259c03af", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "An amusement park has a collection of scale models, with ratio $1: 40$, of buildings and other sights from around the country. The height of empire state building is 1250 feet. What is the height in feet of its replica to the nearest whole number? (adapted from 2018 AMC 8, Question 1) ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$33$$ "}], [{"aoVal": "E", "content": "$$34$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["You can see that since the ratio of real building\\textquotesingle s heights to the model building\\textquotesingle s height is $1: 40$. We also know that the Empire State Building is 1250 feet, so to find the height of the model, we divide by 40 . That gives us $31.25$ which rounds to 31 . Therefore, to the nearest whole number, the duplicate is (B) 31 feet. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3308", "queId": "cbdfd117a28345e39ef4c31a6f120e4c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A basketball is on sale with 35\\% off, the discounted price is $$52$$ dollars, the original price of the basketball wasdollars． ", "answer_option_list": [[{"aoVal": "A", "content": "$$18.2$$ "}], [{"aoVal": "B", "content": "$$33.8$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$148$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$x \\times 65\\textbackslash\\% = 52$$ $$x = 80$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3312", "queId": "544b34950e3f413d94bfff58e2a2d61c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of these is equal to $$(0.3+0.4 + 0.5 -0.9)\\div0.6$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.02 $$ "}], [{"aoVal": "B", "content": "$$0.05 $$ "}], [{"aoVal": "C", "content": "$$0.2 $$ "}], [{"aoVal": "D", "content": "$$0.5$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Four Operations of Decimals"], "answer_analysis": ["Note that $$(0.3+0.4+0.5 -0.9)\\div0.6 =(1.2 -0.9)\\div0.6 =0.3\\div0.6 = 3\\div6$$ $$=0.5$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3318", "queId": "38c53be9572f4affbdbb72551ff8c50b", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "The ratio of $w$ to $x$ is $4: 3$, the ratio of $y$ to $z$ is $3: 2$, and the ratio of $z$ to $x$ is $1: 6$. What is the ratio of $w$ to $y$? (2020 AMC 10B Problems, Question \\#3) ", "answer_option_list": [[{"aoVal": "A", "content": "$4: 3$ "}], [{"aoVal": "B", "content": "$3: 2$ "}], [{"aoVal": "C", "content": "$8: 3$ "}], [{"aoVal": "D", "content": "$4: 1$ "}], [{"aoVal": "E", "content": "$16: 3$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["We need to somehow link all three of the ratios together. We can start by connecting the last two ratios together by multiplying the last ratio by two. $z: x=1: 6=2: 12$, and since $y: z=3: 2$, we can link them together to get $y: z: x=3: 2: 12$. Finally, since $x: w=3: 4=12: 16$, we can link this again to get: $y: z: x: w=3: 2: 12: 16$, so $w: y=(\\mathbf{E}) 16: 3$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3323", "queId": "11bf02814ab34c17909f045cd43a5820", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "The digit $9$ in what number represents a value of $0.09$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9.012$$ "}], [{"aoVal": "B", "content": "$$0.469$$ "}], [{"aoVal": "C", "content": "$$51.9$$ "}], [{"aoVal": "D", "content": "$$26.49$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["If the digit $$9$$ represents a value of $$0.09$$, it means the digit $$9$$ is located on the hundredth place on that number, which is the second digit after the decimal point. Check Lesson 4 Concept 1 on textbook "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3334", "queId": "8f9727d2e34943bbb7756e11519a210b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the smallest whole number larger than the perimeter of any triangle with a side of length $9$ and a side of length $1$? (adapted from 2015 AMC8, Question 8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$19$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s\\textless9+1=10$. Adding $9+1$ to both sides of the inequality, we get $s+9+1\\textless20$, and because $s+9+1$ is the perimeter of our triangle, (C) 20 is our answer. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3340", "queId": "4fb752545a624cc9b34f7ad4d607355c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of three numbers is $20$. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$28$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$40$$ "}], [{"aoVal": "E", "content": "$$294$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3345", "queId": "11daa872b99c46b4831afd0b857a18ec", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$4\\times4\\times20\\times20=80\\times$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$80$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$(4\\times20)\\times (4\\times20)=80\\times80$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3349", "queId": "19a2c6e824074bf4a232d87d48cff7ef", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The number $-11+(-7)$ is equal to: ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$-3$$ "}], [{"aoVal": "C", "content": "$$-25$$ "}], [{"aoVal": "D", "content": "$$25$$ "}], [{"aoVal": "E", "content": "$$-18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$-11+(-7)=-18$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3360", "queId": "94426feb080e432c82996da41b2b1b95", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$2x-3=y+5$$ and $$3y-1=5$$, then $$x=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["From $$3y -1=5$$, then we can get $$y=2$$. Therefore from $$2x-3=2+5$$, we obtain $$x=5$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3363", "queId": "224d543d02ad48dfa35f1086aaa2c7ea", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Write each of the numbers 0,1,2,3,4,5,6 in the sqaures to make the addition correct. What digit will be in the grey square? pic ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns->Encryption and Decryption"], "answer_analysis": ["work backwards "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3370", "queId": "344e2d2e73d348daaee93e69c4cce343", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the product of $125$ and $6$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$420$$ "}], [{"aoVal": "B", "content": "$$1230$$ "}], [{"aoVal": "C", "content": "$$750$$ "}], [{"aoVal": "D", "content": "$$720$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3372", "queId": "12030463e2a04760912a8fbfc9d07f67", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If 5 plates weigh as much as 9 mugs, then 99 mugs weigh as much as~\\uline{~~~~~~~~~~}~plates. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$55$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3391", "queId": "6b74c4d6297543859672b09a9aea3b98", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "On the first day of a $7-$day holiday, Judy reads $9$ pages of a book. On the second day, she reads $12$. Then each day later, she reads $3$ pages more than the day before. On the last day of the holiday, she reads the corresponding number of pages and exactly finishes reading the book. How many pages does the book have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$27$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$120$$ "}], [{"aoVal": "D", "content": "$$126$$ "}], [{"aoVal": "E", "content": "$$128$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["Use the formula of arithmetic sequence to solve this problem. On the last day, she reads $9+6\\times3=27$ pages. The book has $(9+27)\\times7 \\div2=126$ pages. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3393", "queId": "6b764442083a424f901b4e879b668396", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Linda, Alice, Joe, Lily, and Rachel lost their balloons. The numbers on their balloons were all smaller than $8$. The difference between the largest number and the smallest number was $5$. What are their balloon\\textquotesingle s numbers? (adapted from $$2021$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$8$$） ", "answer_option_list": [[{"aoVal": "A", "content": "$7, 5, 4, 3,2$ "}], [{"aoVal": "B", "content": "$4, 1, 7,9,6$ "}], [{"aoVal": "C", "content": "$6,4,2,5,3$ "}], [{"aoVal": "D", "content": "$0,7,4,9,5$ "}], [{"aoVal": "E", "content": "$1,8,5,4,6$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Subtraction of Whole Numbers->Subtraction in Horizontal Form"], "answer_analysis": ["In~ B, D, and E, the largest number more than $8$. In the C, the difference between the largest number and the smallest number is $4$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3394", "queId": "cbe7c5cf77d045cc877c080e41decd05", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$8+9+12+17+23+31=$$？． ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$70$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers"], "answer_analysis": ["$$=8+12+9+31+23+17$$ $$=20+40+40$$ $$=100$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3402", "queId": "4b33a4397d3e419db68d0ae52b802da2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$$$Calculate$$$$ $$\\left (403 \\frac{3}{5}+183 \\frac{5}{11}+155 \\frac{3}{13}+118 \\frac{12}{17}\\right ) \\div$$$$ \\left~~( \\frac{1009}{15}+ \\frac{1009}{33}+ \\frac{1009}{39}+ \\frac{1009}{51}\\right )$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$5.5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$6.5$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Fast Calculation in Fractions"], "answer_analysis": ["$$\\left (403 \\frac{3}{5}+183 \\frac{5}{11}+155 \\frac{3}{13}+118 \\frac{12}{17}\\right ) \\div$$$$ \\left ( \\frac{1009}{15}+ \\frac{1009}{33}+ \\frac{10009}{39}+ \\frac{1009}{51}\\right )$$ $$=2018\\left ( \\frac{1}{5}+ \\frac{1}{11}+ \\frac{1}{13}+ \\frac{1}{17}\\right ) \\div \\frac{1000}{3}\\left ( \\frac{1}{5}+ \\frac{1}{11}+ \\frac{1}{13}+ \\frac{1}{17}\\right )$$ $=6$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3405", "queId": "3d76d99232d14dd2aee1be5b933e1c4b", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "What is the next number in the sequence below? $$47, 44, 38, 29, 17, \\cdots $$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["The pattern is: $$-3, -6, -9, -12, -15, \\cdots $$ Thus, $$17-15=2$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3413", "queId": "19ddc6e443b74cf08a1a69d4cbd68974", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$10000$ years ago, Owen the fisher traded $3$ fishes for $1$ rabbit from Oscar the hunter. Then, Oscar traded $2$ rabbits for $3$ packs of wheat from Dennis the farmer. How many fishes should Owen give Dennis for a pack of wheat? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions->Simplifying Continued Ratios"], "answer_analysis": ["fish:rabbit$=3:1$ wheat:rabbit$=3:2$ fish: wheat$=2:1$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3416", "queId": "1e1825c7a3b146368f107f216fb7bc8a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Harry and Terry are each told to calculate $8-(2+5)$.~Harry gets the correct answer. Terry ignores the parentheses and calculates $8-2+5$.~If Harry\\textquotesingle s answer is $H$~and Terry\\textquotesingle s answer is $T$, what is $H-T$? (2014 AMC $8$ Problem, Question \\#1) ", "answer_option_list": [[{"aoVal": "A", "content": "$$-10$$ "}], [{"aoVal": "B", "content": "$$-6$$ "}], [{"aoVal": "C", "content": "$$0$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["We have $H=8-7=1$ and $T=8-2+5=11$. Clearly $1-11=-10$, so our answer is $A$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3418", "queId": "58fcf59618bf4aa8ac9626033ac19e96", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two non-zero real numbers, $x$ and $y$, satisfy $(x+y)^{2}=3xy$. Which of the following is a possible value of $$\\frac{x+y}{y}-\\frac{x-y}{x}$$? (Adapted From 2000 AMC 12 Problems, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$-1$ "}], [{"aoVal": "B", "content": "$-\\frac{1}{2}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{2}$ "}], [{"aoVal": "D", "content": "$1$ "}], [{"aoVal": "E", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Note that $(x+y)^{2} = x^{2}+y^{2}+2xy = 3xy \\Rightarrow x^{2}+y^{2} = xy$. Then, $$\\frac{x+y}{y}-\\frac{x-y}{x}=\\frac{x(x+y)-y(x-y)}{xy}=\\frac{{{x}^{2}}+xy-xy+{{y}^{2}}}{xy}=\\frac{{{x}^{2}}+{{y}^{2}}}{xy} = 1$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3419", "queId": "123e1c6a9ce048e682373cdfdf18e259", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Eddie has a card. The number on the card is a neighbouring number of 8, but is not a neighbouring number of 6. What is the number on Eddie\\textquotesingle s card?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$Omitted.$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3420", "queId": "b4b7aa1d17ed41b78291b053e664475b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What percent of $$20$$ is $$50$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$140$$ "}], [{"aoVal": "C", "content": "$$200$$ "}], [{"aoVal": "D", "content": "$$250$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions"], "answer_analysis": ["$$\\frac{50}{20}=2.5=2.5\\times100\\textbackslash\\%=250\\textbackslash\\%$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3423", "queId": "46a1f7bb3e2d4fa0a5b14a723092a395", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $A:B=3:5$, $B:C=3:2$, find $A:B:C$. ", "answer_option_list": [[{"aoVal": "A", "content": "$3:5:4$ "}], [{"aoVal": "B", "content": "$9:15:10$ "}], [{"aoVal": "C", "content": "$9:3:10$ "}], [{"aoVal": "D", "content": "$8:15:10$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$A:B=3:5$ $B:C=3:2$ $A:B:C=9:15:10$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3441", "queId": "1e31fddae4604de7993ca6651aaf83a6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $A:B=3:5$, $B:C=3:2$, find $A:B:C$=~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$3:5:4$ "}], [{"aoVal": "B", "content": "$9:15:10$ "}], [{"aoVal": "C", "content": "$9:3:10$ "}], [{"aoVal": "D", "content": "$8:15:10$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$A:B=3:5$ $B:C=3:2$ $A:B:C=9:15:10$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3445", "queId": "2b6382d9d4a4469e9ed9f8b673329bda", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$0.1\\times 0.2\\times 0.3=$$．($1979-1980$ Math League.com contest problem, $7$\\textsuperscript{th~}Grade, Question \\#$12$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.0006$$ "}], [{"aoVal": "B", "content": "$$0.006$$ "}], [{"aoVal": "C", "content": "$$0.06$$ "}], [{"aoVal": "D", "content": "$$0.6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals"], "answer_analysis": ["$$0.1\\times 0.2\\times 0.3=(0.1\\times 0.2)\\times 0.3=0.02\\times 0.3=0.006$$. Therefore, the answer is $$\\rm B$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3446", "queId": "624635a251b54314a8925a0ba454fb8b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$5$$ plates weigh as much as $$9$$ mugs, then $$45$$ mugs weigh as much as~\\uline{~~~~~~~~~~}~plates. ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$81$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["Since $$9$$ mugs $$=5$$ plates $$45\\div9=5$$ times of the above equation. $$45$$ mugs $$=25$$ plates "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3454", "queId": "1e3c3accf2c04b6598fb9a14a393487b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the missing number: $$512\\times2 = 32\\times $$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$512\\times2=1024=32\\times32$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3459", "queId": "127cb31e10214df495a74adbe7416b58", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$\\left( \\frac{5}{8}+\\frac{1}{17} \\right)\\times 8+\\frac{9}{17}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$\\left( \\frac{5}{8}+\\frac{1}{17} \\right)\\times 8+\\frac{9}{17}$$ $$=\\frac{5}{8}\\times 8+\\frac{1}{17}\\times 8+\\frac{9}{17}$$ $$=5+\\frac{8}{17}+\\frac{9}{17}$$ $$=5+1$$ $$=6$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3460", "queId": "1e3f0fa891f045519e1133da38909027", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A container had $27$ ℓ of longan drink. The drink is made up of three $2$-ℓ\\textbf{~}bottles of longan syrup and some water. What is the volume of water used to make the drink? ", "answer_option_list": [[{"aoVal": "A", "content": "6ℓ "}], [{"aoVal": "B", "content": "18ℓ "}], [{"aoVal": "C", "content": "21ℓ "}], [{"aoVal": "D", "content": "27ℓ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Volume and Capacity"], "answer_analysis": ["$$2 \\times 3 = 6$$ $$27 - 6 = 21$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3463", "queId": "7026cf6b608a4f818f5ff7ac650a5eb1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Express $108:9$ in the simplest form:． ", "answer_option_list": [[{"aoVal": "A", "content": "$12:1$ "}], [{"aoVal": "B", "content": "$24:6$ "}], [{"aoVal": "C", "content": "$16:4$ "}], [{"aoVal": "D", "content": "$4:1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["$(108\\div9):(9\\div9)=12:1$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3465", "queId": "1e454f8eab3f444aa67bf46e71ab21fb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$5 + 50 + 500 = 5 \\times$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$100$$ "}], [{"aoVal": "C", "content": "$$111$$ "}], [{"aoVal": "D", "content": "$$550$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$5 + 50 + 500 =555= 5 \\times111$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3466", "queId": "128812c80a2c488e974b72d57cf184fe", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$x+2 = y$$ and $$y+4x = 12$$, then $$x=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$x+2=y$$, then $$x=y-2$$. We can get $$y+4(y-2)=12$$, $$y=4$$, $$x=y-2=2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3470", "queId": "5da8438ecb1d4cbab0f3b729ef6d0c0c", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In the following Figures $\\left (a\\right )$ and $\\left (b\\right )$, each number inside a small triangle is the sum of the numbers inside in the neighbouring small circles. The number inside each circle is either $1$, $2$, $3$, $4$, $5$, $6$, $7$ or $8$. The sum of whole numbers inside the circles in Figure $\\left (a\\right )$ is $1+8+8+2+3+5=27$. What is the largest possible sum of whole numbers inside the circles in Figure $\\left (b\\right )$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$48$$ "}], [{"aoVal": "B", "content": "$$52$$ "}], [{"aoVal": "C", "content": "$$56$$ "}], [{"aoVal": "D", "content": "$$64$$ "}], [{"aoVal": "E", "content": "$$72$$ "}], [{"aoVal": "F", "content": "$$74$$ "}], [{"aoVal": "G", "content": "$$80$$ "}], [{"aoVal": "H", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3472", "queId": "874b263665b34a9da8ad6b6c590d4f59", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "Known $$A=\\frac{{{3}^{2019}}+1}{{{3}^{2020}}+1}$$，$$B=\\frac{{{3}^{2020}}+1}{{{3}^{2021}}+1}$$, compare between $$A$$ and $$B$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$A=B$ "}], [{"aoVal": "B", "content": "$A\\textgreater B$ "}], [{"aoVal": "C", "content": "$A\\textless B$ "}], [{"aoVal": "D", "content": "All of the above "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$${{3}^{2019}}=a$$，$$A=\\frac{a+1}{3a+1}$$，$$B=\\frac{3a+1}{9a+1}$$， $$\\frac{1}{A}=\\frac{3a+1}{a+1}=\\frac{3(a+1)-2}{a+1}=3-\\frac{2}{a+1}$$， $$\\frac{1}{B}=\\frac{9a+1}{3a+1}=\\frac{3(3a+1)-2}{3a+1}=3-\\frac{2}{3a+1}$$， ∴$$\\frac{1}{A} ~\\textless{} ~\\frac{1}{B}$$， ∴$$A\\textgreater B$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3474", "queId": "98edf6e63399407aa73543c2149a6bf1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The fraction $$\\frac23$$ keeps the same value when both its numerator and denominator are． ", "answer_option_list": [[{"aoVal": "A", "content": "multiplied by $$2~ $$ "}], [{"aoVal": "B", "content": "increased by $$2$$ "}], [{"aoVal": "C", "content": "decreased by $$2$$ "}], [{"aoVal": "D", "content": "$$ $$squared$$ $$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions"], "answer_analysis": ["The problem is about the basic property of fractions, namely, multiplying or dividing the numerator and denominator by the same number (except $$0$$), the value of the fraction is unchanged. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3476", "queId": "1a1cc88de0e64f09812019e4b1172b02", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The original price of a product was $$80$$ dollars, and it\\textquotesingle s on sale for 30\\% off, this product isdollars cheaper than before． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$56$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["the new price is $$70\\textbackslash\\%$$ of the original price，$$so$$ the new price is $$80\\times 70\\textbackslash\\%=56$$； $$80-56=24$$． so choose $$\\text{B}$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3479", "queId": "ab80fe0a39244700a0e526d7f0f2d8af", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the product of five fractions, whose denominators are $5-1$ in descending order, and the numerators are $1-5$ in ascending order？ ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac1{25}$ "}], [{"aoVal": "B", "content": "$\\frac1{2}$ "}], [{"aoVal": "C", "content": "$\\frac1{5}$ "}], [{"aoVal": "D", "content": "$$0$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$\\frac{1\\times2\\times3\\times4\\times5}{5\\times4\\times3\\times2\\times1}=1$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3480", "queId": "3d92e164087d42fa931c54b418b1e175", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Tony and Mary are waiting in line to go shopping. Tony is fifth in line, while Mary is 365th. How many people are standing between Tony and Mary in the line? ", "answer_option_list": [[{"aoVal": "A", "content": "$$359$$ "}], [{"aoVal": "B", "content": "$$360$$ "}], [{"aoVal": "C", "content": "$$361$$ "}], [{"aoVal": "D", "content": "$$315$$ "}], [{"aoVal": "E", "content": "$$314$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["The question is asking for the number of people between Tony and Mary, which is $$365-5-1=359$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3483", "queId": "46b440005be84fd18e846d3efe10b2bd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Evaluate $$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "B", "content": "$\\dfrac{2}{5}$ "}], [{"aoVal": "C", "content": "$\\dfrac{2}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{5}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions"], "answer_analysis": ["$$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}=\\frac{1}{2+ \\dfrac{1}{ \\dfrac{5}{2}}}= \\frac{1}{2+ \\dfrac{2}{5}}= \\frac{1}{ \\dfrac{12}{5}}= \\frac{5}{12}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3486", "queId": "22a0b3a190324c37ab626509b1732d76", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the value of $$ 6\\times \\frac{5}{3}$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$5$ "}], [{"aoVal": "B", "content": "$\\frac{33}{3}$ "}], [{"aoVal": "C", "content": "$10$ "}], [{"aoVal": "D", "content": "$6\\frac{12}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3490", "queId": "be08771eef3c49ddb9ba3db7db86ac3b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $$40^{}\\text{th}$$ number in the sequence $$2$$, $$6$$, $$10$$, $$14$$, $$\\cdots \\cdots $$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$171$$ "}], [{"aoVal": "B", "content": "$$158$$ "}], [{"aoVal": "C", "content": "$$164$$ "}], [{"aoVal": "D", "content": "$$160$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["4$\\times$40-2=158 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3506", "queId": "3003b148278e495c8e5fe00eb84c1489", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Teacher Nicole bought some sweets and divided it equally among $9$ children. If everyone got $6$ sweets, there would still be some sweets remaining. What is the most number of sweets Teacher Nicole could have bought? What is the least number of sweets Teacher Nicole could have bought? ", "answer_option_list": [[{"aoVal": "A", "content": "$$63$$，$$54$$ "}], [{"aoVal": "B", "content": "$$63$$，$$55$$ "}], [{"aoVal": "C", "content": "$$62$$，$$54$$ "}], [{"aoVal": "D", "content": "$$62$$，$$55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["~\\uline{~~~~~~~~~~}~$\\div 9=6$ $\\text{R}$~\\uline{~~~~~~~~~~}~ Greatest possible remainder is $8$ while smallest possible remainder is $1$. Greatest possible number of sweets is $$9\\times 6+8=62$$, while the least possible number of sweets is $$9\\times 6+1=55$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3513", "queId": "46c0be14bee14856837f2bb3bbba9e91", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the correct ordering of the three numbers $$\\dfrac{5}{19}$$, $$\\dfrac{7}{21}$$, and $$\\dfrac{9}{23}$$, in increasing order? ($$2012$$ AMC $$8$$ Problem, Question \\#$$4$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\dfrac{9}{23}\\textless{} \\dfrac{7}{21}\\textless\\dfrac{5}{19}$$ "}], [{"aoVal": "B", "content": "$$\\dfrac{5}{19}\\textless{} \\dfrac{7}{21}\\textless{} \\dfrac{9}{23}$$ "}], [{"aoVal": "C", "content": "$$\\dfrac{9}{23}\\textless{} \\dfrac{5}{19}\\textless{} \\dfrac{7}{21}$$ "}], [{"aoVal": "D", "content": "$$\\dfrac{5}{19}\\textless{} \\dfrac{9}{23}\\textless{} \\dfrac{7}{21}$$ "}], [{"aoVal": "E", "content": "$$\\dfrac{7}{21}\\textless{} \\dfrac{5}{19}\\textless{} \\dfrac{9}{23}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["Method $$1$$: The value of $$\\dfrac{7}{21}$$ is $$\\dfrac{1}{3}$$. Now we give all the fractions a common denominator. $$\\dfrac{5}{19} \\Rightarrow \\dfrac{345}{1311}$$, $$\\dfrac{1}{3} \\Rightarrow \\dfrac{437}{1311}$$, $$\\dfrac{9}{23} \\Rightarrow \\dfrac{513}{1311}$$. Ordering the fractions from least to greatest, we find that they are in the order listed. Therefore, $$\\frac{5}{19}\\textless{} \\frac{7}{21}\\textless{} \\frac{9}{23}$$. Method $$2$$: Instead of finding the LCD, we can subtract each fraction from $$1$$ to get a common numerator. Thus, $$1- \\dfrac{5}{19}= \\dfrac{14}{19}$$, $$1- \\dfrac{7}{21}= \\dfrac{14}{21}$$, $$1- \\dfrac{9}{23}= \\dfrac{14}{23}$$. All three fraction have the common numerator $$14$$. Now the order of the fractions is obvious. $$\\dfrac{14}{19}\\textgreater\\dfrac{14}{21}\\textgreater\\dfrac{14}{23}\\Rightarrow\\dfrac{5}{19}\\textless\\dfrac{7}{21}\\textless\\dfrac{9}{23}$$. Therefore, $$\\dfrac{5}{19}\\textless\\dfrac{7}{21}\\textless\\dfrac{9}{23}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3516", "queId": "74cc1b1392844f10a8296d9ca636f246", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is a linear equation written in function form? ", "answer_option_list": [[{"aoVal": "A", "content": "$x=15$ "}], [{"aoVal": "B", "content": "$y=5x+7b-120c$ "}], [{"aoVal": "C", "content": "$y^{2}=4$ "}], [{"aoVal": "D", "content": "$y=-3x^{2}-1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable"], "answer_analysis": ["An equation is in function form when it is solved for $y$. A linear equation is also an equation in which the highest power of the variable is always $1$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3524", "queId": "22c982cc58dd48bfa1c40c681be0cfe2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The school has $$11200$$ books. The school puts them into 70 equal piles. How many books are in each pile? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$160$$ "}], [{"aoVal": "C", "content": "$$1600$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division within the Multiplication Tables"], "answer_analysis": ["omitted "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3528", "queId": "1672bda384924e28854176bf2fb85dfd", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{The height and age of each child in a random sample of children was recorded. The value of the correlation coefficient between height and age for the children in the sample was 0.8. Based on the least-squares regression line created from the data to predict the height of a child based on age, which of the following is a correct statement?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{~On average, the height of a child is 80\\% of the age of the child.} "}], [{"aoVal": "B", "content": "\\textbf{The least-squares regression line of height versus age will have a slope of 0.8.} "}], [{"aoVal": "C", "content": "\\textbf{The proportion of the variation in height that is explained by a regression on age is 0.64.~} "}], [{"aoVal": "D", "content": "\\textbf{The least-squares regression line will correctly predict height based on age 80\\% of the time.} "}], [{"aoVal": "E", "content": "\\textbf{The least-squares regression line will correctly predict height based on age 64\\% of the time.} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$R^{2} = r^{2} = 0.8^{2} = 0.64$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3530", "queId": "3dabab5b96624787a245fc062dcceaac", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Karen works part-time at a local convenience store and earns 10 dollars per hour. She wants to spend next Saturday afternoon attending a music concert. The full price of a concert ticket is 75 dollars, but Karen was able to get a discounted price of 50 dollars from a friend who purchased the ticket but has become unable to attend. If Karen took 4 hours off from her job to attend the concert, what was her opportunity cost of attending the concert? ", "answer_option_list": [[{"aoVal": "A", "content": "$40 "}], [{"aoVal": "B", "content": "$50 "}], [{"aoVal": "C", "content": "$75 "}], [{"aoVal": "D", "content": "$90 "}], [{"aoVal": "E", "content": "$115 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Economic costs are the sum of explicit and implicit costs. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3548", "queId": "22e045f94d734c70ae620acf85abf427", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The measures of angles $A, B$ and $C$ are $32^{\\circ}, 68^{\\circ},90^{\\circ}$. The triangle formed by the three angles will be~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "right triangle "}], [{"aoVal": "B", "content": "acute triangle "}], [{"aoVal": "C", "content": "obtuse triangle "}], [{"aoVal": "D", "content": "no triangle "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns of Number Tables->Triangle Number Table"], "answer_analysis": ["$32^{\\circ} + 68^{\\circ} + 90^{\\circ}=190^{\\circ}$ The sum of a triangle\\textquotesingle s interior angles is $180^{\\circ}$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3550", "queId": "3931982941c345f0a8d76daf21fc40c2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Evaluate $$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "B", "content": "$\\dfrac{2}{5}$ "}], [{"aoVal": "C", "content": "$\\dfrac{2}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{5}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions"], "answer_analysis": ["$$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}=\\frac{1}{2+ \\dfrac{1}{ \\dfrac{5}{2}}}= \\frac{1}{2+ \\dfrac{2}{5}}= \\frac{1}{ \\dfrac{12}{5}}= \\frac{5}{12}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3551", "queId": "a6e5ead356d54fac99546aabe7f17d76", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "The zeroes of the function $f(x)=x^{2}-a x+a$ are integers. What is the sum of the possible values of $a$? (Adapted From 2015 AMC 10A Problems, Question \\#23) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["By Vieta\\textquotesingle s Formula, $a$ is the sum of the integral zeros of the function, and so $a$ is integral. Because the zeros are integral, the discriminant of the function, $a^{2}-4a$, is a perfect square, say $k^{2}$. Then adding $4$ to both sides and completing the square yields $$ (a-2)^{2}=k^{2}+4$$. Therefore, $(a-2)^{2}-k^{2}=4$ and $$((a-2)-k)((a-2)+k)=4$$. Let $(a-2)-k=u$ and $(a-2)+k=v$; then, $a-2=\\frac{u+v}{2}$ and so $a=\\frac{u+v}{2}+2$. Listing all possible $(u, v)$ pairs such that $a$ is integral: $(2,2), (-2,-2)$ (not counting transpositions because this does not affect $u+v$). Then, $a=4,0$. These $a$ sum to $4$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3559", "queId": "2bb183f57c874e5a9ccdb202e9c715a0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Consider these two operations: $a ~♦ ~b = a^{2}~−~b^{2}$ $a✭b = (a~−~b)^{2}$ What is the value of $(5♦3)✭6$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$-20$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$100$$ "}], [{"aoVal": "E", "content": "$$220$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3560", "queId": "66fee83f732e43809b1ace2cd72208e3", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the least possible value of $(x y-1)^{2}+(x+y)^{2}$ for real numbers $x$ and $y$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$\\frac{1}{4}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{2}$ "}], [{"aoVal": "D", "content": "$$1$$ "}], [{"aoVal": "E", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Indefinite Equations"], "answer_analysis": ["We expand the original expression, then factor the result by grouping: $$ \\begin{aligned} (x y-1)^{2}+(x+y)^{2} \\&=\\left(x^{2} y^{2}-2 x y+1\\right)+\\left(x^{2}+2 x y+y^{2}\\right) \\textbackslash\\textbackslash{} \\&=x^{2} y^{2}+x^{2}+y^{2}+1 \\textbackslash\\textbackslash{} \\&=x^{2}\\left(y^{2}+1\\right)+\\left(y^{2}+1\\right) \\textbackslash\\textbackslash{} \\&=\\left(x^{2}+1\\right)\\left(y^{2}+1\\right) . \\end{aligned} $$ Clearly, both factors are positive. By the Trivial Inequality, we have $$ \\left(x^{2}+1\\right)\\left(y^{2}+1\\right) \\geq(0+1)(0+1)= 1 . $$ Note that the least possible value of $(x y-1)^{2}+(x+y)^{2}$ occurs at $x=y=0$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3565", "queId": "66ff863edd3e4713acb053b95ba5a6bf", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many even numbers are there? 1, 3, 4, 6, 7, 9, 5, 8. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$Omitted.$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3568", "queId": "c756417bfada4d5aadd889f639895861", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the value of $$26+(12-9\\div3)\\times4-2$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$28$$ "}], [{"aoVal": "B", "content": "$$54$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$138$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$$26+(12-9\\div3)\\times4-2$$ $$=26+9\\times4-2$$ $$=26+36-2$$ $$=62-2$$ $$=60$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3573", "queId": "500024a621c14e5cbf54686eaa478cfa", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Avril has a card. The number on the card is a neighbouring number of 10, but is not a neighbouring number of 12. What is the number on Avril\\textquotesingle s card?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$Omitted.$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3580", "queId": "3dbed9270c2c4257a6404f9aa19147e9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$☆-10=△-5$$, then $$☆$$~\\uline{~~~~~~~~~~}~$$△$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\textgreater$$ "}], [{"aoVal": "B", "content": "$$\\textless$$ "}], [{"aoVal": "C", "content": "$$=$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["If $$☆=10$$, then $$△=5$$，$$☆\\textgreater△$$． So, the answer is $$\\text{A}$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3584", "queId": "7e1e900890fc425881271983d9edc4cf", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{In a population of university students, 20\\% of the students have experienced feelings of math anxiety. If we select 8 students, what is the probability that exactly three have experienced math anxiety?} ", "answer_option_list": [[{"aoVal": "A", "content": "$${8 \\choose 3} (0.20)^{3} (0.80)^{8}$$ "}], [{"aoVal": "B", "content": "$${8 \\choose 3} (0.20)^{3} (0.80)^{5}$$ "}], [{"aoVal": "C", "content": "$${5 \\choose 3} (0.20)^{3} (0.80)^{5}$$ "}], [{"aoVal": "D", "content": "$$(0.20)^{3} (0.80)^{5}$$ "}], [{"aoVal": "E", "content": "$$(0.20)^{5} (0.80)^{3}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{Binomial distribution with parameters n = 8 and p = 0.20.} \\textbf{$$P(X = 3) ={8 \\choose 3}(0.20)^{3}(0.80)^{5}$$} "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3593", "queId": "592e9f729f374ddeaea3da4042ae046a", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Points $A$ and $B$ are 10 units apart. Points $B$ and $C$ are 4 units apart. Points $C$ and $D$ are 3 units apart. If $A$ and $D$ are as close as possible, then the number of units between them is ．(1996 AJHSME, Question 8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$17$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["If $A B=10$ and $B C=4$, then $(10-4) \\leq A C \\leq(10+4)$ by the triangle inequality. In the triangle inequality, the equality is only reached when the \"triangle\" $A B C$ is really a degenerate triangle, and $A B C$ are collinear. Simplifying, this means the smallest value $A C$ can be is 6 . Applying the triangle inequality on $A C D$ with $A C=6$ and $C D=3$, we know that $6-3 \\leq A D \\leq 6+3$ when $A C$ is minimized. If $A C$ were larger, then $A D$ could be larger, but we want the smallest $A D$ possible, and not the largest. Thus, $A D$ must be at least 3 , but cannot be smaller than 3 . Therefore, $B$ is the answer. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3606", "queId": "70472ba92bb8462fbf1483f09bfeb716", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "There are $20$ balls of the same size in a box. Lucas says: \"Half of them are red.\" Peter says: \"The number of red balls is $5$ times that of green balls.\" Claire says: \"There are three colors of balls in the box: red, light blue, and green.\" How many dark blue balls are there in the box? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["There is no dark blue ball in the box. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3607", "queId": "3dc9f5b6faef4b578bfe9618979f1c5d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$9.25\\times 0.8+9\\frac{1}{4}\\times 0.2=$$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$9.25$$ "}], [{"aoVal": "B", "content": "$$92.5$$ "}], [{"aoVal": "C", "content": "$$925$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$9.25\\times 0.8+9\\frac{1}{4}\\times 0.2$$ $$=9.25\\times 0.8+9.25\\times 0.2$$ $$=9.25\\times (0.8+0.2)$$ $$=9.25\\times 1$$ $$=9.25$$ So, $$\\text{A}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3609", "queId": "7047692906134bddacffba16390027ae", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Suppose that $x$ and $y$ are nonzero real numbers such that $\\frac{x+y}{x}=2$, what is the value of $\\frac{x}{y}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "B", "content": "$$-1$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Rearranging, we find $x+y=2x, x=y, \\frac xy = 1$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3610", "queId": "1ecadfb2e16b439a87c6394a9e8deb72", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Cathy wants to cut a wooden stick. In how many places does she need to break a wooden stick in order to get $7$ pieces? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$7 - 1 = 6$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3611", "queId": "46e4a87e1ac24d54b0fd3d02a48231fc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $a◆b=a\\times 2+b$, then $2◆3=$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["$2◆3=2\\times2+3=7$ So the answer is $\\rm A$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3625", "queId": "b02d4ef1fe1543afb5f20cb92c75f843", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Starting with some gold coins and some empty treasure chests, I tried to put $9$ gold coins in each treasure chest, but that left $2$ treasure chests empty. So instead I put 6 gold coins in each treasure chest, but then I had $3$ gold coins left over. How many gold coins did I have? ( 2017 AMC8, Questions \\#17) ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$27$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$63$$ "}], [{"aoVal": "E", "content": "$$81$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables"], "answer_analysis": ["We can represent the amount of gold with $g$ and the amount of chests with $c$. We can use the problem to make the following equations: $$ \\begin{gathered} 9 c-18=g \\textbackslash\\textbackslash{} 6 c+3=g \\end{gathered} $$ We do this because for $9$ chests there are $2$ empty and if $9$ were in each $9$ multiplied by $2$ is $18$ left. Therefore, $6 c+3=9 c-18$. This implies that $c=7$. We therefore have $g=45$. So, our answer is (C) 45 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3626", "queId": "b96f1d1fa1b84755ae4eb58c3a5d8c40", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{A stationery store owner calculated the mean and median price of all types of pen: 5 and 3, respectively. He plans to have a 20\\% off sale. What are the new mean and median of pens in that store?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{mean: 4; median: 2.4} "}], [{"aoVal": "B", "content": "\\textbf{mean: 5; median: 2.4} "}], [{"aoVal": "C", "content": "\\textbf{~mean: 4; median: 3} "}], [{"aoVal": "D", "content": "\\textbf{~mean: 5; median: 3} "}], [{"aoVal": "E", "content": "\\textbf{mean: 2.4; median: 4} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{If you times some number to the data set,~ the mean or median needs to be times with the same number. So for here, everything times with 0.8.} "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3630", "queId": "1ede330fdd6049e8918a4285c09e4e07", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is the same as~$44\\times25$? (~\\uline{~~~~~~~~~~}~) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4\\times 25+4\\times 25$$ "}], [{"aoVal": "B", "content": "$$44\\times 2+44\\times 5$$ "}], [{"aoVal": "C", "content": "$$4\\times 2+4\\times 5$$ "}], [{"aoVal": "D", "content": "$$40\\times 25+4\\times 25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Distributive Law of Whole Numbers"], "answer_analysis": ["$44\\times25=\\left( 40+4\\right)\\times25=40\\times25+4\\times25$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3631", "queId": "ec6eed200b684d00bab77b36dd2527ad", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$50\\textbackslash\\%$$ of $$30\\textbackslash\\%=15\\textbackslash\\%$$of ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$10\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$25\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$100\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$150\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["$$50\\textbackslash\\%\\times 30\\textbackslash\\%=$$ half of $$30\\textbackslash\\%=15\\textbackslash\\%=15\\textbackslash\\%$$ of $$100\\textbackslash\\%$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3634", "queId": "6276aba0474f460c92cb2640a2ad7487", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$2001 + (2000 - 1999 + 1998 - 1997 + 1996 - \\cdots + 2 - 1) =$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2001$$ "}], [{"aoVal": "B", "content": "$$3001$$ "}], [{"aoVal": "C", "content": "$$4001$$ "}], [{"aoVal": "D", "content": "$$4002$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$2001+(2000-1999)+(1998-1997)+\\cdots +(2-1)=2001+(1000$$ones$$)$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3647", "queId": "1ad556b4e9064276bfd8751dfa17f620", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many polynomials are there in the following expressions: $$-4{{x}^{2}}+2$$，$$-\\frac{1}{3}mn$$，$$ \\pi $$，$$\\frac{{{(2x-y)}^{2}}}{3}$$，$$32\\frac{1}{4}$$~ ~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$-4{{x}^{2}}+2$$，$$\\frac{{{(2x-y)}^{2}}}{3}$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3655", "queId": "b4d4e937f058442fad371a5f852a74af", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "What value does the $4$ represent in the number $55.431$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$0.4$$ "}], [{"aoVal": "C", "content": "$$0.04$$ "}], [{"aoVal": "D", "content": "$$0.004$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["The number $$4$$ is located on the tenth place, thus representing $$0.04$$. Check Lesson 4 Concept 1 on textbook "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3659", "queId": "1715d2fdc80f4e09a84ab204d79438ca", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Assuming $a \\neq 3, b \\neq 4$, and $c \\neq 5$, what is the value in simplest form of the following expression? (Adapted From 2020 AMC 10A Problems, Question \\#3) $$ \\frac{2a-6}{5-c} \\cdot \\frac{b-4}{3-a} \\cdot \\frac{2c-10}{4-b} $$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$-4$$ "}], [{"aoVal": "C", "content": "$\\frac{a b c}{15}$ "}], [{"aoVal": "D", "content": "$\\frac{4}{a b c}-\\frac{1}{15}$ "}], [{"aoVal": "E", "content": "$\\frac{1}{15}-\\frac{1}{a b c}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["If $x \\neq y$, then $\\frac{x-y}{y-x}=-1$. We use this fact to simplify the original expression: $$ \\frac{2a-6}{5-c} \\cdot \\frac{b-4}{3-a} \\cdot \\frac{2c-10}{4-b} = -2\\times 2= 4$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3670", "queId": "54b649894b934e0cba3206221b716f49", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "The zeroes of the function $f(x)=x^{2}-a x+2 a$ are integers. What is the sum of the possible values of $a$? (2015 AMC 10A Problems, Question \\#23) ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["By Vieta\\textquotesingle s Formula, $a$ is the sum of the integral zeros of the function, and so $a$ is integral. Because the zeros are integral, the discriminant of the function, $a^{2}-8 a$, is a perfect square, say $k^{2}$. Then adding $16$ to both sides and completing the square yields $$ (a-4)^{2}=k^{2}+16 $$. Therefore, $(a-4)^{2}-k^{2}=16$ and $$((a-4)-k)((a-4)+k)=16$$. Let $(a-4)-k=u$ and $(a-4)+k=v$; then, $a-4=\\frac{u+v}{2}$ and so $a=\\frac{u+v}{2}+4$. Listing all possible $(u, v)$ pairs such that $a$ is integral: $(2,8),(4,4),(-2,-8),(-4,-4)$ (not counting transpositions because this does not affect $u+v$). Then, $a=9,8,-1,0$. These $a$ sum to $16$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3672", "queId": "6bb72cbcde7d487a91260b749950d349", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Alice, Tom, Chloe and Susan ate chicken nuggets together. Everyone ate at least 2 pieces. The person who ate the least ate 4 pieces less than the person who ate the most. How many pieces of chicken nuggets did they each eat? (adapted from $$2021$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$8$$） ", "answer_option_list": [[{"aoVal": "A", "content": "$8, 2, 4, 3$ "}], [{"aoVal": "B", "content": "$4, 1, 5,9$ "}], [{"aoVal": "C", "content": "$6,5,0,10$ "}], [{"aoVal": "D", "content": "$2,7,4,1$ "}], [{"aoVal": "E", "content": "$2,6,4,8$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Subtraction of Whole Numbers->Subtraction in Horizontal Form"], "answer_analysis": ["In B, C, D, the smallest number less than $2$. In the E, the difference between the largest number and the smallest number is $6$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3674", "queId": "a2555ac4be44460ba407c88b485ea2f7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following quotients is $$1$$ more than $$162\\div18$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$128\\div 16$$ "}], [{"aoVal": "B", "content": "$$120\\div 15$$ "}], [{"aoVal": "C", "content": "$$132\\div 12$$ "}], [{"aoVal": "D", "content": "$$110\\div 11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["Since $$162 \\div18 =9$$, we want a quotient of $$10$$. That\\textquotesingle s $$\\text{D}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3675", "queId": "a255be4b4c0f4b48ac0525419e8e37ec", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A box contains five cards, numbered $1,2,3,4$, and $5$. Three cards are selected randomly without replacement from the box. What is the probability that $4$ is the largest value selected? (2017 AMC 8 Problems, Question \\#10) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{10}$ "}], [{"aoVal": "B", "content": "$\\frac{1}{5}$ "}], [{"aoVal": "C", "content": "$\\frac{3}{10}$ "}], [{"aoVal": "D", "content": "$\\frac{2}{5}$ "}], [{"aoVal": "E", "content": "$\\frac{1}{2}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["There are $\\_5C\\_3 = 10$ possible groups of cards that can be selected. If $4$ is the largest card selected, then the other two cards must be either $1$,$2$, or $3$, for a total $\\_3C\\_2 = 3$ groups of cards. Then, the probability is just $(\\text{C}) \\frac{3}{10}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3680", "queId": "279dc43f53c444dfa63bc701e36fbba4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The distance between A and B is $$350$$ $\\text{km}$. Kin and Mary drive away from A and B respectively at $8$ a.m. and go towards each other at same time. Kin drives $$40$$ $\\text{km/h}$, and Mary drives $$50$$ $\\text{km/h}$. Mary rested for $$2$$ hours on her way and then continues driving. They will meet at~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ a.m. "}], [{"aoVal": "B", "content": "$$11$$ a.m. "}], [{"aoVal": "C", "content": "$$12$$ p.m. "}], [{"aoVal": "D", "content": "$$1$$ p.m. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$(350-80)$$$\\div$$$(40+50)=3$$hr $$8+2+3=13$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3688", "queId": "a6f758ab251c4224b7ee884e09e3eaa8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Bob sees that the license plate number of the car consists of $5$ digits: $1$, $2$, $6$, $7$, $9$. If these $5$ digits are filled in the square~$$\\huge\\square+\\square =\\square +\\square $$, which number is not used?~(adapted from $$2017$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$8$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"], "answer_analysis": ["$1+7=2+6$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3691", "queId": "705d7653e5f647f5bfa886bc80e7d4e1", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Tiantian drank $$6\\frac{3}{8}$$ litres of water. Matthew drank $$4\\frac{5}{6}$$ litres of water. How many litres of water did the both of them drink altogether? Give your answer as a mixed number in the simplest form. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10\\frac{4}{7}\\ell$$ "}], [{"aoVal": "B", "content": "$$10\\frac{5}{8}\\ell$$ "}], [{"aoVal": "C", "content": "$$10\\frac{15}{24}\\ell$$ "}], [{"aoVal": "D", "content": "$$11\\frac{5}{24}\\ell$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["$$6\\frac{3}{8}+4\\frac{5}{6}=6\\frac{9}{24}+4\\frac{20}{24}=11\\frac{5}{24}\\ell$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3696", "queId": "235f41c1516f4254a787441b51f58255", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "$$3\\times2016 + 0\\times2016 + 3\\times2016=$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2016$$ "}], [{"aoVal": "C", "content": "$$6048$$ "}], [{"aoVal": "D", "content": "$$12096$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$(3+0+3)\\times2016=6\\times2016=12096$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3697", "queId": "1b23ae71e3c64ad78ea448d4579e6f20", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In the diagram below, a circle centered at $O$ has radius $4 \\text{cm}$. It is divided into $4$ regions by two chords that are perpendicular to each other at point $N$. It is known that $OM=1 \\text{cm}$, $MN=2\\text{cm}$. Find the value of: Area of $(I + III) -$ Area of $(II+IV)$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Area"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3699", "queId": "4288c25670dd4ab69ce3b78675fb4028", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump $5$ pads to the right or $3$ pads to the left. What is the fewest number of jumps Greta must make to reach the lily pad located $2023$ pads to the right of her starting position? ", "answer_option_list": [[{"aoVal": "A", "content": "$$405$$ "}], [{"aoVal": "B", "content": "$$407$$ "}], [{"aoVal": "C", "content": "$$409$$ "}], [{"aoVal": "D", "content": "$$411$$ "}], [{"aoVal": "E", "content": "$$413$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["D "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3703", "queId": "5def908615b74af682ba4d7aa495b56b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$3^{336}\\times 9^{336}\\times 27^{336}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$3^{1008}$$ "}], [{"aoVal": "B", "content": "$$3^{1344}$$ "}], [{"aoVal": "C", "content": "$$3^{1680}$$ "}], [{"aoVal": "D", "content": "$$3^{2016}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"], "answer_analysis": ["$$3^{336}\\times 9^{336}\\times 27^{336}=3^{336}\\times 3^{672}\\times 3^{1008}=3^{336+672+1008}=3^{2016}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3704", "queId": "5defb5e9e14240dda7a12fa7ca76c198", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "What is the value of $$1+3+5+\\cdots +2017+2019-2-4-6-\\cdots -2016-2018$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1010$$ "}], [{"aoVal": "B", "content": "$$1009$$ "}], [{"aoVal": "C", "content": "$$1008$$ "}], [{"aoVal": "D", "content": "$$-1009$$ "}], [{"aoVal": "E", "content": "$$-1010$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Grouping in Fast Addition and Subtraction of Whole Numbers"], "answer_analysis": ["Solution 1 Rearranging the terms, we get $$(1-2)+(3-4)+(5-6)+\\cdots (2017-2018)+2019$$, and our answer is $$-1009+2019=1010$$. Solution 2 We can rewrite the given expression as $$1+(3-2)+(5-4)+\\cdots +(2017-2016)+(2019-2018)=1+1+1+\\cdots +1$$. The number of $$1$$s is the same as the number of terms in $$1$$, $$3$$, $$5$$, $$7\\cdots $$, $$2017$$, $$2019$$. Thus the answer is $$1010$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3710", "queId": "1b2cd5850dee4ee8b3d7a37ad88c73e5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$2\\times \\left( 3+1 \\right)\\times \\left( {{3}^{2}}+1 \\right)\\times \\left( {{3}^{4}}+1 \\right)\\times \\left( {{3}^{8}}+1 \\right)\\times \\left( {{3}^{16}}+1 \\right)\\times \\left( {{3}^{32}}+1 \\right)=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$${{3}^{64}}+1$$． "}], [{"aoVal": "B", "content": "$${{3}^{128}}-1$$． "}], [{"aoVal": "C", "content": "$${{3}^{32}}-1$$． "}], [{"aoVal": "D", "content": "$${{3}^{64}}-1$$． "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas-> Difference of Two Squares Formula"], "answer_analysis": ["$$=\\left( 3-1 \\right)\\times \\left( 3+1 \\right)\\times \\left( {{3}^{2}}+1 \\right)\\times \\left( {{3}^{4}}+1 \\right)\\times \\left( {{3}^{8}}+1 \\right)\\times \\left( {{3}^{16}}+1 \\right)\\times \\left( {{3}^{32}}+1 \\right)$$ $$=\\left( {{3}^{2}}-1 \\right)\\times \\left( {{3}^{2}}+1 \\right)\\times \\left( {{3}^{4}}+1 \\right)\\times \\left( {{3}^{8}}+1 \\right)\\times \\left( {{3}^{16}}+1 \\right)\\times \\left( {{3}^{32}}+1 \\right)$$ $$=\\left( {{3}^{4}}-1 \\right)\\times \\left( {{3}^{4}}+1 \\right)\\times \\left( {{3}^{8}}+1 \\right)\\times \\left( {{3}^{16}}+1 \\right)\\times \\left( {{3}^{32}}+1 \\right)$$ $$=\\cdots $$ $$=\\left( {{3}^{32}}-1 \\right)\\times \\left( {{3}^{32}}+1 \\right)$$ $$={{3}^{64}}-1$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3720", "queId": "2c1b705ff8804097b2500148e418d4f5", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 5 cups. What percent of the total capacity of the pitcher did each cup receive?~ (2020 AMC 8, Question \\#5) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["The pitcher is $\\frac{3}{4}$ full, i.e. $75 \\textbackslash\\%$ full. Therefore each cup receives $\\frac{75}{5}=(\\mathbf{C}) 15$ percent of the total capacity. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3724", "queId": "1f435fb31dc24633add9a3cee6e3c71d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The solution to the rational equation $$\\frac{16}{4-{{x}^{2}}}+\\frac{x-2}{x+2}=\\frac{x+2}{x-2}$$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$x=2$$ "}], [{"aoVal": "B", "content": "no solution "}], [{"aoVal": "C", "content": "$$x=2$$ or $$x=3$$ "}], [{"aoVal": "D", "content": "$$x=3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$\\begin{eqnarray}\\frac{16}{4-{{x}^{2}}}+\\frac{x-2}{x+2}\\&=\\&\\frac{x+2}{x-2}\\textbackslash\\textbackslash{} -16+{{(x-2)}^{2}}\\&=\\&{{(x+2)}^{2}}\\textbackslash\\textbackslash{} x\\&=\\&-2\\end{eqnarray}$$ After verification, $$x=-2$$ is not a solution. There is no solution. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3727", "queId": "7065c569679d41bc99f202a7fecccd64", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "The sum of $$5$$ consecutive numbers is $$500$$. Among all five numbers, what is the smallest value? ", "answer_option_list": [[{"aoVal": "A", "content": "$$95$$ "}], [{"aoVal": "B", "content": "$$96$$ "}], [{"aoVal": "C", "content": "$$97$$ "}], [{"aoVal": "D", "content": "$$98$$ "}], [{"aoVal": "E", "content": "$$99$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$$500\\div5=100$$(middle number is $$100$$) $$98, 99, 100, 101. 102$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3747", "queId": "5960412e9af14db390229664072b88fb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the product of $63$ and $4$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$242$$ "}], [{"aoVal": "B", "content": "$$252$$ "}], [{"aoVal": "C", "content": "$$262$$ "}], [{"aoVal": "D", "content": "$$272$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["omitted "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3749", "queId": "351782cab5df433daa5997cd2a28ed7a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the last number in Row $12$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$121$$ "}], [{"aoVal": "B", "content": "$$144$$ "}], [{"aoVal": "C", "content": "$$169$$ "}], [{"aoVal": "D", "content": "$$196$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns of Number Tables->Triangle Number Table"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3757", "queId": "aba9ad9073b54015953fc5b9ed974c18", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In multiplying a number by $\\dfrac{1}{100}$, the result may be obtained by moving the decimal point of that number． ", "answer_option_list": [[{"aoVal": "A", "content": "two places to the left "}], [{"aoVal": "B", "content": "one place to the left "}], [{"aoVal": "C", "content": "two places to the right "}], [{"aoVal": "D", "content": "one place to the right "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["Multiplying a number by $\\dfrac{1}{100}$, is the same as dividing by $100$. When dividing by $100$, move the decimal point $2$ places left. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3760", "queId": "8785f07bb64f4d199fce316435209f46", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$3$$ apples weigh as much as $$4$$ pears, and $$2$$ pears weigh as much as $$5$$ plums, then $$9$$ apples weigh as much as~ \\uline{?~} plums. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$19$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["If $$9$$ apples weigh as much as $$12$$ pears, and $$12$$ pears weigh as much as $$30$$ plums, then $$9$$ apples weigh as much as $$30$$ plums. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3765", "queId": "23a03c2f1a3644c98e89d5dc863788f1", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Let $P(x)$ be a polynomial such that when $P(x)$ is divided by $x-19$, the remainder is 99 , and when $P(x)$ is divided by $x-99$, the remainder is 19. What is the remainder when $P(x)$ is divided by $(x-19)(x-99)$? (1999 AHSME Problems, Question \\#17) ", "answer_option_list": [[{"aoVal": "A", "content": "$-x+80$ "}], [{"aoVal": "B", "content": "$x+80$ "}], [{"aoVal": "C", "content": "$-x+118$ "}], [{"aoVal": "D", "content": "$x+118$ "}], [{"aoVal": "E", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Since the divisor $(x-19)(x-99)$ is a quadratic, the degree of the remainder is at most linear. We can write $P(x)$ in the form $$ P(x)=Q(x)(x-19)(x-99)+c x+d $$ where $c x+d$ is the remainder. By the Remainder Theorem, plugging in 19 and 99 gives us a system of equations: $$ \\begin{aligned} \\& 99 c+d=19 \\textbackslash\\textbackslash{} \\& 19 c+d=99\\end{aligned} $$ Solving gives us $c=-1$ and $d=118$, thus, our answer is $(\\text{C})-x+118$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3766", "queId": "472a5c4cdb29469796258393af1a531d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$1-2-3+4+5-6-7+8-9=$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$-6$$ "}], [{"aoVal": "B", "content": "$$-7$$ "}], [{"aoVal": "C", "content": "$$-8$$ "}], [{"aoVal": "D", "content": "$$-9$$ "}], [{"aoVal": "E", "content": "$$-10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$(1-2-3+4)+(5-6-7+8)-9=-9$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3768", "queId": "1f7714f9e97147aa9e001efc8baf6915", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Given that $$a\\Delta b=a+b-4$$, for example, $$3\\Delta 2 = 3 +2-4$$, what is $$3\\Delta4$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition"], "answer_analysis": ["Nil "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3771", "queId": "504b32b250fb49a9bbc10bee97fee12e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Which of the following is/are categorical variable(s)?} \\textbf{I. The mean of Grade 1 boys' heights} \\textbf{II. The colors of jackets in the class} \\textbf{III. The types of pens in a stationary store} ", "answer_option_list": [[{"aoVal": "A", "content": "I "}], [{"aoVal": "B", "content": "II "}], [{"aoVal": "C", "content": "III "}], [{"aoVal": "D", "content": "I, II "}], [{"aoVal": "E", "content": "II, III "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{A categorical variable is defined by the set of groups or categories (qualitative values) that individuals are placed into; it is not a numerical value. The mean of~ Grade 1 boys' heights is a number. The colors of jackets in the class and the types of pens in a stationary store cannot be described by numbers.~} "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3772", "queId": "1f7eb4fb982d4bf5982c64129f97004a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A movie ticket costs $17$ dollars and the tax is $a$ dollars. George purchases a movie ticket and writes on his ledgar : \" the ticket cost $17+a$ dollars\". Is this description accurate? ", "answer_option_list": [[{"aoVal": "A", "content": "yes "}], [{"aoVal": "B", "content": "no "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["When writing an algebraic expression with units, we need to write it in parentheses. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3778", "queId": "4731d852550249d9b9a7309f4966d347", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\frac{5}{12}\\div \\frac{25}{24}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{2}{5}$$ "}], [{"aoVal": "B", "content": "$$\\frac{5}{2}$$ "}], [{"aoVal": "C", "content": "$$\\frac{35}{24}$$ "}], [{"aoVal": "D", "content": "$$\\frac{5}{12}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["omitted "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3787", "queId": "948bded92bbd4133890ba60f6f56897c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $${{2}^{2}}\\div {{2}^{3}}\\times {{2}^{4}}\\div {{2}^{5}}\\times {{2}^{6}}\\div \\cdots \\div {{2}^{99}}\\times {{2}^{100}}=$$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$${{2}^{48}}$$ "}], [{"aoVal": "B", "content": "$${{2}^{49}}$$ "}], [{"aoVal": "C", "content": "$${{2}^{50}}$$ "}], [{"aoVal": "D", "content": "$${{2}^{51}}$$ "}], [{"aoVal": "E", "content": "$${{2}^{1}}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers"], "answer_analysis": ["$$({{2}^{100}}\\div {{2}^{99}})\\times ({{2}^{98}}\\div {{2}^{97}})\\times \\cdot \\cdot \\cdot \\times ({{2}^{6}}\\div {{2}^{5}})\\times ({{2}^{4}}\\div {{2}^{3}})\\times {{2}^{2}}={{2}^{51}}$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3790", "queId": "1b9ac48c167d41bab1b4c01a21ed3f16", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "The next number in the sequence $$1, 3, 7, 13, 21, \\cdots$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$37$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$31$$ "}], [{"aoVal": "E", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["Difference between the numbers is $$2$$, $$4$$, $$6$$, $$8$$. Next one is $$21+10$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3796", "queId": "597787bbc80f439298db867b86cc5a09", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Given that the points $A(-2, y\\_1)$, $B(0, y\\_2)$ and $C(3, y\\_3)$ are all on the graph of $f(x)=-2x^{2}+4x+m$, then the relationship among $y\\_1$, $y\\_2$ and $y\\_3$ is: ", "answer_option_list": [[{"aoVal": "A", "content": "$y\\_2 \\textgreater{} y\\_3\\textgreater y\\_1$ "}], [{"aoVal": "B", "content": "$y\\_1~\\textgreater{} y\\_3\\textgreater y\\_2$ "}], [{"aoVal": "C", "content": "$y\\_2 \\textgreater{} y\\_1\\textgreater y\\_3$ "}], [{"aoVal": "D", "content": "$y\\_3~\\textgreater{} y\\_2\\textgreater y\\_1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The parabola opens down with axis of symmetry $x=1$. Therefore, point $B$ is closer the axis of symmetry than point $C$, and point $C$ is closer the axis of symmetry than point $A$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3812", "queId": "b98b1cb0032b4092b2dd0921cab69e1a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following fraction is smaller than $$\\frac{1}{9}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{6}$$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{7}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{8}$$ "}], [{"aoVal": "D", "content": "$$\\frac{1}{10}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["With same numerator, the one we split into more portion is smaller "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3813", "queId": "c773de52af524fe88c804f2ec4603b7b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{A statistical test involves the following null and alternative hypotheses.~} \\textbf{H0: $\\mu$ = 64} \\textbf{Ha: $\\mu$ \\textgreater{} 64} \\textbf{Which of the following describes a Type II error?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{Failing to reject the null hypothesis when the population mean is 64} "}], [{"aoVal": "B", "content": "\\textbf{Failing to reject the null hypothesis when the population mean is greater than 64} "}], [{"aoVal": "C", "content": "\\textbf{Rejecting the null hypothesis when the population mean is 64} "}], [{"aoVal": "D", "content": "\\textbf{Rejecting the null hypothesis when the population mean is greater than 64} "}], [{"aoVal": "E", "content": "\\textbf{Failing to reject the null hypothesis when the p-value is less than the significance level} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{Type II error ($\\beta$): the error of failing to reject the null hypothesis when it is false.~} "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3815", "queId": "54ee05569ec14bff8a720b098a19699b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the recurring decimals $$0.\\overline {62}$$ and $$0.\\overline {16}$$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.\\overline{78}$$ "}], [{"aoVal": "B", "content": "$$78\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$\\frac {78}{100}$$ "}], [{"aoVal": "D", "content": "$$0.788$$ "}], [{"aoVal": "E", "content": "$0.\\overline{46}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["$0.\\overline{62}+0.\\overline{16}=0.\\overline{78}$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3820", "queId": "30cf4704ddfc457da143a5ef52f6feb8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Three members of the Euclid Middle School girls\\textquotesingle~softball team had the following conversation. Ashley: I just realized that our uniform numbers are all $$2-$$digit primes. Bethany: And the sum of your two uniform numbers is the day of my birthday earlier this month. Caitlin: That\\textquotesingle s funny. The sum of your two uniform numbers is the day of my birthday later this month. Ashley: And the sum of your two uniform numbers is today\\textquotesingle s date. What number does Caitlin wear? ($$2014$$ AMC $$8$$ Problem, Question \\#$$23$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$19$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["The maximum amount of days any given month can have is $$31$$, and the smallest, two-digit primes are $$11$$, $$13$$, and $$17$$. There are a few different sums that can be deduced from the following numbers, which are $$24, 30$$, and $$28$$, all of which represent the three days. Therefore, since Brittany says that the other two people\\textquotesingle s uniform numbers add up to her birthday eadier in the month, that means Caitlin and Ashley\\textquotesingle s numbers must add up to $$24$$. Similarly, Caitlin says that the other two people\\textquotesingle s uniform numbers add up to her birhday later in the month, so the sum must add up to $$30$$. This leaves $$28$$ as today\\textquotesingle s date. From this, Caitlin was referring to the uniform numbers $$13$$ and $$17$$ telling us that her number is $$11$$, giving our solution as $$(\\text{A})=11$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3821", "queId": "b04cecab072c4865b55344aeec46b9d2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Given that $$23+25+27 +\\ldots+(2k-1)=m^{2}$$, where $$k$$ and $$m$$ are whole numbers, $$k\\textgreater30$$, find the value of $$m$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$41$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3823", "queId": "4bd0a22a8ad94e79ac55754732d4fee7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Evaluate $$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "B", "content": "$\\dfrac{2}{5}$ "}], [{"aoVal": "C", "content": "$\\dfrac{2}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{5}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions"], "answer_analysis": ["$$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}=\\frac{1}{2+ \\dfrac{1}{ \\dfrac{5}{2}}}= \\frac{1}{2+ \\dfrac{2}{5}}= \\frac{1}{ \\dfrac{12}{5}}= \\frac{5}{12}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3838", "queId": "39c9189f56a94f608b795b4483116ad7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is not equal to $$10$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$100\\div 10$$ "}], [{"aoVal": "B", "content": "$$10 \\div1$$ "}], [{"aoVal": "C", "content": "$$10\\times1$$ "}], [{"aoVal": "D", "content": "$$100\\times 10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["Since $$100 \\times 10 = 1000$$, choice $$\\text{D}$$ is not equal to $$10$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3839", "queId": "b05030fbabff417ca02c25cde2103cbf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the remainder when $$16+16+16 +16$$ is divided by $$4$$?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["Since $$16\\div4$$ has remainder $$0$$, the remainder is $$0 + 0+0+0 = 0$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3846", "queId": "42ccfae50dbc4187ba6af0433ee5c4be", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "An amusement park has a collection of scale models, with ratio $1: 45$, of buildings and other sights from around the country. If the height of the One World Trade Center is $1770$ feet. What is the height in feet of its replica to the nearest whole number? (adapted from 2018 AMC 8, Question 1) ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$37$$ "}], [{"aoVal": "C", "content": "$$38$$ "}], [{"aoVal": "D", "content": "$$39$$ "}], [{"aoVal": "E", "content": "$$41$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["You can see that since the ratio of real building\\textquotesingle s heights to the model building\\textquotesingle s height is $1: 45$. If the height of the center is $1770$ feet, to find the height of the model, we divide by $45$ . That gives us $39.3$ which rounds to $39$ . Therefore, to the nearest whole number, the duplicate is (D) $39$ feet. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3853", "queId": "1fd00e7f29c7486198a68ed3e6f15128", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which choice is correct: $$3.5:2.55=$$~\\uline{~~~~~~~~~~}~．$$4.6:1.15=$$~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$70:51$$，$$5:2$$ "}], [{"aoVal": "B", "content": "$$7:5$$，$$4:1$$ "}], [{"aoVal": "C", "content": "$$16:11$$，$$4:1$$ "}], [{"aoVal": "D", "content": "$$70:51$$，$$4:1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$$70:51$$，$$4:1$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3858", "queId": "2c867a7f68914e3cafd1dbf9b5f78978", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$24\\times 26\\times 28\\times 30\\times 32=48\\times 52\\times 56\\times 60\\times $$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$64$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$24\\times 26\\times 28\\times 30\\times 32=\\left(24\\times 26\\times 28\\times 30\\right)\\times \\left(2\\times 2\\times 2\\times 2\\right)\\times \\underline{2}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3859", "queId": "8b530aa0896648939109881f8cf2d117", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many positive integers can fill the blank in the sentence below? ``One positive integer is~\\uline{~~~~~~~~~~}~more than twice another, and the sum of the two numbers is $28$.'' ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3867", "queId": "b4f4df45f5ea410f9e2d89520ccb9904", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the value of $$5^{4}+5^{4}+5^{4}+5^{4}+5^{4}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5^{4}$$ "}], [{"aoVal": "B", "content": "$$5^{5}$$ "}], [{"aoVal": "C", "content": "$$5^{6}$$ "}], [{"aoVal": "D", "content": "$$5^{10}$$ "}], [{"aoVal": "E", "content": "$$5^{20}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"], "answer_analysis": ["$$5^{1}\\cdot5^{4}=5^{1+4}=5^{5}$$, \\uline{Teacher should introduce the formula of $$a^{m}a^{n}=a^{m+n}$$}. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3881", "queId": "fa75fd0dfe124ac7873a1559941601c8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A soccer player computes his win ratio by dividing the number of matches he has won by the total number of matches he has played. At the start of a weekend, his win ratio is exactly~$0.5$. During the weekend, he plays five games, winning three and losing two. At the end of the weekend, his win ratio is greater than~$0.505$. What\\textquotesingle s the largest number of matches he could\\textquotesingle ve won before the weekend began? ", "answer_option_list": [[{"aoVal": "A", "content": "$$46$$ "}], [{"aoVal": "B", "content": "$$47$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$92$$ "}], [{"aoVal": "E", "content": "$$96$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Assume she won~$x$~games before the weekend, we obtain the inequality~$\\frac{x+3}{2x+5}\\gt0.505$~. Solve the inequality, we get~$x\\lt47.5$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3884", "queId": "59929c594f1a463fb610507dad2eb6a3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Three positive integers are equally spaced on a number line. The middle number is $15$, and the largest number is $4$ times the smallest number. What is the smallest of these three numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3890", "queId": "1ff4ecabfcef440cb4eaa0bddd64eddc", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Eddie has a card. The number on the card is a neighbouring number of 10, but is not a neighbouring number of 12. What is the number on Eddie\\textquotesingle s card?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$Omitted.$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3899", "queId": "507b57bec3784290a4eab6f868a40544", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$20\\times 30$$ is divided by $$40$$, the remainder is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$(20\\times 30)\\div 40=600\\div 40=15$$; remainder $$=0$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3901", "queId": "709513e96abd4ded852505b21b2787a8", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following numbers\\textquotesingle{} value does not change after removing all ``$$0$$''s ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$90.221$$ "}], [{"aoVal": "B", "content": "$$4.106$$ "}], [{"aoVal": "C", "content": "$$22.990$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["Only $$22.990$$\\textquotesingle s $$\"0\"$$ can be removed without causing other digits to change their places from the original number. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3909", "queId": "7e6813975d7945cd8406d39daaca3a63", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Mary cooked $9$ cakes. She cut two of them into $3$ pieces. How many cakes does she have now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$9 - 2 + 2 \\times 3 = 13$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3916", "queId": "20107026968540f2b243a533c84d1cb2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Camila writes down five positive integers. The unique mode of these integers is 2 greater than their median, and the median is 2 greater than their arithmetic mean. What is the least possible value for the mode? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["1，$$3$$，$$9$$，$$11$$，11 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3917", "queId": "476c3cb23fbc4074b1cda64d7e13446b", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "If $$a$$@$$b=\\frac {a\\times b}{a+b}$$ for positive integers $$a$$ and $$b$$ , what is $$5$$@$$10$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac 3{10}$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$\\frac {10}3$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly->Ordinary Type"], "answer_analysis": ["Substitute $$a=5$$ and $$b=10$$ into the expression for $$a$$@$$b$$ to get: $$5$$@$$10=\\frac {5\\times 10}{5+10}=\\frac {50}{15}=\\frac {10}3$$. Thus, the answer choice $$\\frac {10}3$$ is correct. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3921", "queId": "a27f5d3e5c0249bca175128c973b0b88", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Is it true that If an odd function has zero in its domain, then it must pass through the origin. (Hint: $0$ is in the domain, we can apply $f(-x) = -f(x)$ at $x=0$) ", "answer_option_list": [[{"aoVal": "A", "content": "True "}], [{"aoVal": "B", "content": "False "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["By definition of an odd function, $f(-x) = -f(x)$ for all $x$ in the domain. Since $x = 0$ is in the domain, we have $f(-0) = -f(0)$, which means $f(0) = -f(0)$, or $2f(0) = 0$, and thus $f(0) = 0$ (this represents the origin). "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3923", "queId": "8b613d7ee3634ec9aae24ecdf9b9768d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Dividing a certain two-digit number by $$10$$ leaves a remainder of $$9$$, and dividing it by $$9$$ leaves a remainder of $$8$$. The sum of the number\\textquotesingle s two digits is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$17$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["Dividing a certain two-digit number by $$10$$ leaves a remainder of $$9$$, so it is $$19$$, $$29$$, $$39$$, $$49$$, $$59$$, $$69$$, $$79$$, $$89$$, or $$99$$. The only number listed with remainder $$8$$ when divided by $$9$$ is $$89$$, so the number is $$89$$ and $$8+9=17$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3925", "queId": "676861b4efa541bc97ff5cff6d7ec6e6", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Lucy writes numbers from $1$ to $200$ on the blackboard. Then, she plays a game with her friend Mike. Each time they take turn to delete the first two numbers in the sequence and write their sum by the end of the sequence. For example, Lucy deletes $1$ and $2$, then writes $3$ behind $200$ for the first time. They play this game until there is only one number on the blackboard. What is the number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$399$$ "}], [{"aoVal": "B", "content": "$$402$$ "}], [{"aoVal": "C", "content": "$$5050$$ "}], [{"aoVal": "D", "content": "$$20100$$ "}], [{"aoVal": "E", "content": "$$25050$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["The result is equal to the sum of all numbers from $1$ to $200$, which is $(1+200)\\times200\\div2=20100$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3927", "queId": "87a9d3ca6edc44bea6fe4797cabc2060", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$1+2+3+4+5+6+7+8+9+10+9+8+7+6+5+4=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$98$$ "}], [{"aoVal": "C", "content": "$$96$$ "}], [{"aoVal": "D", "content": "$$94$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences->Pyramid Sequences"], "answer_analysis": ["$$1+2+3+4+5+6+7+8+9+10+9+8+7+6+5+4$$ $$=1+2+3+4+5+6+7+8+9+10+9+8+7+6+5+4+3+2+1-3-2-1$$ $$=10\\times 10-6$$ $$=100-6$$ $$=94$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3930", "queId": "2437a4b060a84172b2fe9fb27984d73e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many types of vitamins are there in the fruits below? There are~\\uline{~~~~~~~~~~}~types ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3931", "queId": "39ff5c51e25d4cbeade789c9d38755ff", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following expression is a perfect square? ", "answer_option_list": [[{"aoVal": "A", "content": "$98! \\cdot 99!$ "}], [{"aoVal": "B", "content": "$98! \\cdot 100!$ "}], [{"aoVal": "C", "content": "$99! \\cdot 100!$ "}], [{"aoVal": "D", "content": "$99! \\cdot 101!$ "}], [{"aoVal": "E", "content": "$100! \\cdot 101!$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3941", "queId": "3a04d797f0274e548ca8e46d04952dcf", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Lee has $1$ red cube, $1$ yellow cube, $2$ blue cubes and $3$ green cubes. How many ways are there for Lee to arrange his cubes in a row if cubes of the same color is indistinguishable? ", "answer_option_list": [[{"aoVal": "A", "content": "$$210$$ "}], [{"aoVal": "B", "content": "$$420$$ "}], [{"aoVal": "C", "content": "$$630$$ "}], [{"aoVal": "D", "content": "$$840$$ "}], [{"aoVal": "E", "content": "$$1050$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3952", "queId": "ec8e77943f864dcb9dadbef22463b2ba", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "How many minutes are there in $$2$$ weeks? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2\\times7\\times24$$ "}], [{"aoVal": "B", "content": "$$(7+7)\\times24\\times60$$ "}], [{"aoVal": "C", "content": "$$2\\times7\\times12\\times60$$ "}], [{"aoVal": "D", "content": "$$2\\times24\\times60$$ "}], [{"aoVal": "E", "content": "$$(7+7)\\times12\\times60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["One week has $$7$$ days. Two weeks has $$7+7$$ One day has $$24$$ hours. One hour has $$60$$ minutes. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3954", "queId": "cc255503aac542338f7a98c10b33fbc0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "One ticket to a mini concert costs $\\textbackslash$20$ at full price. Nicole buys $4$ tickets using a coupon that gives her a $25\\textbackslash\\%$ discount. Bel buys $5$ tickets using a coupon that gives her a $30\\textbackslash\\%$ discount. How many more dollars does Nicole pay than Bel? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3958", "queId": "cc25ddea3f6b4f8b9b43acc601f82331", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The students in a class sit in rows. There is the same number of students in each row. There are $2$ rows of students in front of Robert and $1$ row of students behind him. In his row, there are $3$ students on his left and $5$ students on his right. How many students are there in this class? (2022 Math Kangaroo Problem, Level 3-4, Question \\#15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$17$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["There are $3+5+1=9$ students in each row, and there are $2+1+1=4$ rows. Thus, there are $9\\times4=36$ students in this class. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3964", "queId": "3e8115e45d1240ecbd968ad09c0d7025", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Avril has a card. The number on the card is a neighbouring number of 10, but is not a neighbouring number of 12. What is the number on Eddie\\textquotesingle s card?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$Omitted.$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3966", "queId": "2043d1fd0bd642a6a8f2120ac2557b06", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Find the sum of $$\\frac{1}{5}$$ and $$\\frac{7}{10}$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{8}{10}$$ "}], [{"aoVal": "B", "content": "$$\\frac{9}{10}$$ "}], [{"aoVal": "C", "content": "$$\\frac{8}{15}$$ "}], [{"aoVal": "D", "content": "$$\\frac{9}{20}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3981", "queId": "59b86de6beaa412181583fc6fc112974", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$10000\\div 200\\times$$$$=10000$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$200$$ "}], [{"aoVal": "C", "content": "$$1000$$ "}], [{"aoVal": "D", "content": "$$2000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$10000\\div 200=50$$; $$50\\times \\underline{200}=10000$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3982", "queId": "552f89d415084bb4b79126d266537f33", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a competitive market, a producer is able to sell their good for $\\textbackslash$ 10$ per unit, while the cost of producing each unit is $\\textbackslash$ 8$. What is the producer surplus in this scenario? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\textbackslash$ 2$ "}], [{"aoVal": "B", "content": "$\\textbackslash$ 8$ "}], [{"aoVal": "C", "content": "$\\textbackslash$ 10$ "}], [{"aoVal": "D", "content": "$\\textbackslash$ 12$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$\\textbackslash$2$, as the producer surplus is calculated as the difference between the price the good is sold for and the cost of production, which is $\\textbackslash$10$ - $\\textbackslash$8$ = $\\textbackslash$2$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3983", "queId": "246ab47567fb468b8e944a35c214079d", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The real numbers $c, b, a$ form an arithmetic sequence with $a \\geq b \\geq c \\geq 0$. The quadratic $a x^{2}+b x+c$ has exactly one root. What is this root? ", "answer_option_list": [[{"aoVal": "A", "content": "$-7-4 \\sqrt{3}$ "}], [{"aoVal": "B", "content": "$-2-\\sqrt{3}$ "}], [{"aoVal": "C", "content": "$$-1$$ "}], [{"aoVal": "D", "content": "$-2+\\sqrt{3}$ "}], [{"aoVal": "E", "content": "$-7+4 \\sqrt{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Unary Quadratic Equations"], "answer_analysis": ["It is given that $a x^{2}+b x+c=0$ has 1 real root, so the discriminant is zero, or $b^{2}=4 a c$. Because $a, b, c$ are in arithmetic progression, $b-a=c-b$, or $b=\\frac{a+c}{2}$. We need to find the unique root, or $-\\frac{b}{2 a}$ (discriminant is 0 ). From $b^{2}=4 a c$, we can get $-\\frac{b}{2 a}=-\\frac{2 c}{b}$ Ignoring the negatives(for now), we have $\\frac{2 c}{b}=\\frac{2 c}{\\frac{a+c}{2}}=\\frac{4 c}{a+c}=\\frac{1}{\\frac{1}{\\frac{4 c}{a+c}}}=\\frac{1}{\\frac{a+c}{4 c}}=\\frac{1}{\\frac{a}{4 c}+\\frac{1}{4}}$. Fortunately, finding $\\frac{a}{c}$ is not very hard. Plug in $b=\\frac{a+c}{2}$ to $b^{2}=4 a c$, we have $a^{2}+2 a c+c^{2}=16 a c$, or $a^{2}-14 a c+c^{2}=0$, and dividing by $c^{2}$ gives $\\left(\\frac{a}{c}\\right)^{2}-14\\left(\\frac{a}{c}\\right)+1=0$, so $\\frac{a}{c}=\\frac{14 \\pm \\sqrt{192}}{2}=7 \\pm 4 \\sqrt{3}$. But $7-4 \\sqrt{3}\\textless1$, violating the assumption that $a \\geq c$. Therefore, $\\frac{a}{c}=7+4 \\sqrt{3}$. Plugging this in, we have $\\frac{1}{\\frac{a}{4 c}+\\frac{1}{4}}=\\frac{1}{2+\\sqrt{3}}=2-\\sqrt{3}$. But we need the negative of this, so the answer is (D). "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3988", "queId": "28a63e79fa3c40fb8a4fa9d4d2514f45", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the $$100\\rm th$$ number in the arithmetic sequence $$1$$, $$5$$, $$9$$, $$13$$, $$17$$, $$21$$, $$25$$, $$\\cdots$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$397$$ "}], [{"aoVal": "B", "content": "$$399$$ "}], [{"aoVal": "C", "content": "$$401$$ "}], [{"aoVal": "D", "content": "$$403$$ "}], [{"aoVal": "E", "content": "$$405$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$$1+(5-1)\\times 99=397$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "3990", "queId": "35b1f47c760b40a8b17336ee55cde728", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of five consecutive natural numbers is equal to $$2005$$. The greatest of these numbers is:~\\uline{~~~~~~~~~~}~. (2005 Math Kangaroo Problem, Level 5-6, Question \\#17) ", "answer_option_list": [[{"aoVal": "A", "content": "$$401$$ "}], [{"aoVal": "B", "content": "$$403$$ "}], [{"aoVal": "C", "content": "$$404$$ "}], [{"aoVal": "D", "content": "$$405$$ "}], [{"aoVal": "E", "content": "$$2001$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["Based on the middle term rule, we can find the middle number is $$401$$, and the greatest number is $$401+1+1=403$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4007", "queId": "431e43054bcd4deea4fd9f971be29652", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$10^{5}+10^{6}=10^{5}\\times $$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$10^{2}$$ "}], [{"aoVal": "D", "content": "$$10^{6}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"], "answer_analysis": ["$$10^{5}+10^{6}=1100000=11\\times 10^{5}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4017", "queId": "28ba8b05d6e548349ef79dae279ab37b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In December, Tom-the-cat slept for exactly 3 weeks. Which calculations should we do in order to find how many minutes he stayed awake during this month? ", "answer_option_list": [[{"aoVal": "A", "content": "(31 - 7) x 3 x 24 x 60 "}], [{"aoVal": "B", "content": "(31 - 7) x 24 x 60 "}], [{"aoVal": "C", "content": "(31 -7 x 3) x 24 x 60 "}], [{"aoVal": "D", "content": "(31 -7 x 3) x 24 x 60 x 60 "}], [{"aoVal": "E", "content": "(30 -7 x 3) x 24 x 60 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion"], "answer_analysis": ["The cat slept for exactly 3 weeks for 7 x 3 days. The cat was awake for 31 - 7 x 3 days. A day has 24 hours, and an hour has 60 minutes. Therefore, the cat was awake in (31- 7 x 3) x 24 x 60 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4019", "queId": "e7f1da8e219c46fd9068d96e959931e3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$894-89-111-95-105-94=$$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$300$$ "}], [{"aoVal": "B", "content": "$$400$$ "}], [{"aoVal": "C", "content": "$$500$$ "}], [{"aoVal": "D", "content": "$$600$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Operation Strategy in Addition and Subtraction of Rounding Whole Numbers"], "answer_analysis": ["$$(894-94)-(89+111)-(95+105)$$ $$=800-200-200$$ $$=400$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4037", "queId": "b50f8840986243b7b8046b75c3ac737f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$2$$ dogs weigh as much as $$3$$ cats, and $$2$$ cats weigh as much as $$15$$ mice, how many dogs weigh as much as $$45$$ mice? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["In weight, $$45$$ mice $$=3\\times (15$$ mice$$)=3\\times (2$$ cats$$)= 2\\times (3$$ cats$$)=2\\times (2$$ dogs$$)= 4$$ dogs. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4038", "queId": "7e8a34121bea461584cad98d63ab5880", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the simplest form of $$2$$ yards $$:30$$ feet? (Note that $1$ yard is equal to $3$ feet)． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2:30$$ "}], [{"aoVal": "B", "content": "$$1:5$$ "}], [{"aoVal": "C", "content": "$$5:1$$ "}], [{"aoVal": "D", "content": "$$30:2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["We need to make the units same first. $$2$$ yards equal to $$6$$ feet. Now we could remove the same unit, feet. We get $$6:30$$ and simplify it to $$1:5$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4039", "queId": "50b7401c6019486a9f3ce4d5e041fcee", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the first $$100$$ positive even whole numbers is $$10100$$. What is the sum of the first $$101$$ positive even whole numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10302$$ "}], [{"aoVal": "B", "content": "$$10202$$ "}], [{"aoVal": "C", "content": "$$10201$$ "}], [{"aoVal": "D", "content": "$$10102$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["The $$100$$ even numbers that add up to $$10100$$ are $$2$$, $$4$$, $$\\cdots $$, $$200$$. The sum we want is $$2+4+ \\cdots + 200 + 202 = 10 100 + 202$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4042", "queId": "35cfd668d94b415f941315db546a7024", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The ones digit of $$106\\times107\\times108\\times109\\times110$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["The ones digit is the same as the ones digit of $$6 \\times7\\times8\\times9 \\times0$$. ` "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4047", "queId": "7552bf91e41b4afbade74987efe94035", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$2009\\times 2009-2008\\times 2008=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4017$$ "}], [{"aoVal": "B", "content": "$$4007$$ "}], [{"aoVal": "C", "content": "$$4027$$ "}], [{"aoVal": "D", "content": "$$3017$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas-> Difference of Two Squares Formula"], "answer_analysis": ["$$=(2008+1)\\times 2009-2008\\times 2008$$ $$=2008\\times 2009+2009-2008\\times 2008$$ $$=2008\\times (2009-2008)+2009$$ $$=2008+2009$$ $$=4017$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4057", "queId": "31727bbcf8684fd6acd490bc8c4dcdd0", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the tens digit of $7^{2011}$? (2011 AMC 8 Problems, Question \\#22) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Since we want the tens digit, we can find the last two digits of $7^{2011}$. We can do this by using modular arithmetic. $$ \\begin{aligned} 7 \\equiv 07 \\&(\\bmod 100) \\textbackslash\\textbackslash{} 7^{2} \\equiv 49 \\&(\\bmod 100) \\textbackslash\\textbackslash{} 7^{3} \\equiv 43 \\&(\\bmod 100) \\textbackslash\\textbackslash{} 7^{4} \\equiv 01 \\&(\\bmod 100) \\end{aligned} $$ We can write $7^{2011}$ as $\\left(7^{4}\\right)^{502} \\times 7^{3}$. Using this, we can say: $$ 7^{2011} \\equiv\\left(7^{4}\\right)^{502} \\times 7^{3} \\equiv 7^{3} \\equiv 343 \\equiv 43 \\quad(\\bmod 100) . $$ From the above, we can conclude that the last two digits of $7^{2011}$ are $43$. Since they have asked us to find the tens digit, our answer is (D) $4$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4063", "queId": "a738dd9924ec481c8af376d9020814ae", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A palindrome is a number that can be read the same forward and backward. For example, the numbers 99, 252 and 4884 are palindromes. How many 3. digit palindrome numbers are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$81$$ "}], [{"aoVal": "B", "content": "$$900$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables"], "answer_analysis": ["From 100-199: 101, 111, 121, 131, 141, 151, 161, 171, 181, 191 (10 numbers) From 200 - 299: 202, 212, 222, 232, 242, 252, 262, 272, 282, 292 (10 numbers) From 300 to 399: 10 numbers From 400 to 499: 10 numbers $$\\cdots $$ From 900 to 999: 10 numbers. Hence, there are 10 x 9 = 90 three-digit palindromes. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4071", "queId": "b9b11cdc16554f4db9b7fa7ee094ac30", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Given the equation $3x+4y=5$, find the slope and $y$-intercept. ", "answer_option_list": [[{"aoVal": "A", "content": "$m=-3, b=4$ "}], [{"aoVal": "B", "content": "$m=-3, b=5$ "}], [{"aoVal": "C", "content": "$m=\\frac{3}{4}, b=\\frac{5}{4}$ "}], [{"aoVal": "D", "content": "$m=-\\frac{3}{4}, b=\\frac{5}{4}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable"], "answer_analysis": ["$3x+4y=5$, $y=-\\frac{3}{4}x+\\frac{5}{4}$, Its slope is $-\\frac{3}{4}$ and intercept is $\\frac{5}{4}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4073", "queId": "35e7cff799f94c5aa6cb49307332ff9a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Store $A$ is selling watermelon at the price of $32$ dollars per pound. Store $B$ is selling the same watermelon at the price of $30$ dollars per $16$ ounces. Which store has a better buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$A$ "}], [{"aoVal": "B", "content": "$B$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion"], "answer_analysis": ["$16$ ounce equals $1$ pound "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4075", "queId": "28ef3fec2b3643f5a078682ef438d259", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The number of hours in $$10$$ days $$=$$ the number of minutes inhours. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Time"], "answer_analysis": ["The number of hours in $$10$$ days is $$240$$; $$240$$ minutes is $$240\\div60 =4$$ hours. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4076", "queId": "24c877b7ed664369982bb3832a01cd66", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$4:14=14:$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$49$$ "}], [{"aoVal": "D", "content": "$$114$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["Divide through by $$2$$ then multiply by $$7$$ to get $$4:14=2:7=14:49$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4082", "queId": "3186ca47f1d94c019dd0061c23e8de21", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the product of $763$ and $5$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3505$$ "}], [{"aoVal": "B", "content": "$$3815$$ "}], [{"aoVal": "C", "content": "$$3515$$ "}], [{"aoVal": "D", "content": "$$3805$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["omitted "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4085", "queId": "28f860080f2441eca11ae212a7aa7bfe", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $ a◆b$ means$(a\\times b)+b$ , then $2◆3$ has the value． ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["If $a◆b$~ represents$(a\\times b)+b$ , $2◆3=(2\\times3)+3=9$ . So the answer is $\\rm B$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4088", "queId": "a73dcad431b84e00bd0155f06b89edf9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$30$$ students in a classroom. They sit at desks in pairs in such a way that every boy sits with girl, and only half of girls sit with a boy. How many boys are in the classroom? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["NA "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4090", "queId": "2901366568904907914539f8bea9e255", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate：$$\\frac{1}{2}\\times \\frac{22}{7}\\div \\frac{11}{5}$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{5}{7}$$ "}], [{"aoVal": "B", "content": "$$\\frac{4}{7}$$ "}], [{"aoVal": "C", "content": "$$\\frac{6}{7}$$ "}], [{"aoVal": "D", "content": "$$\\frac{3}{7}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["$$\\frac{1}{2}\\times \\frac{22}{7}\\div \\frac{11}{5}=\\frac{1}{2}\\times \\frac{22}{7}\\times \\frac{5}{11}=\\frac{5}{7}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4091", "queId": "24dc02791c254e9f8dd4c0e8e8b776cf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The product of any whole number and $$2$$ is always． ", "answer_option_list": [[{"aoVal": "A", "content": "　prime "}], [{"aoVal": "B", "content": "　composite "}], [{"aoVal": "C", "content": "　odd "}], [{"aoVal": "D", "content": "　even "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["The product of a whole number and an even number must be even. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4098", "queId": "3ed25936d04e44a189d46729365702fa", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The arrows on the two spinners shown below are spun. Let the number $N$ equal $10$ times the number on Spinner $A$, added to the number on Spinner $B$. What is the probability that $N$ is a perfect square number? (2022 AMC 8 Problems, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{16}$ "}], [{"aoVal": "B", "content": "$\\frac{1}{8}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{4}$ "}], [{"aoVal": "D", "content": "$\\frac{3}{8}$ "}], [{"aoVal": "E", "content": "$\\frac{1}{2}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["First, we calculate that there are a total of $4 \\cdot 4=16$ possibilities. Now, we list all of two-digit perfect squares. $64$ and $81$ are the only ones that can be made using the spinner. Consequently, there is a $\\frac{2}{16}=$ (B) $\\frac{1}{8}$ probability that the number formed by the two spinners is a perfect square. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4099", "queId": "24e66e0d65ef478889a55b45364de069", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $16^{-2}=\\left(\\frac{1}{4}\\right)^{}x$, what is the value of $x$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Convert both sides into powers with the same bases: $4^{-4}=4^{-x}$ $x=4$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4103", "queId": "3ed6cf1361e84715870ff65d89e70b0e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The 2000 Census identified the ethnic breakdown of the state of California to be approximately as follows: White:46％, Latino:32\\%, Asian:11\\%, Blcak:7\\%,and Other:4\\%.~Assuming that these are mutually exclusive categories (this is not a realistic assumption), what is the probability that a randomly selected person from the state of California is of Asian or Latino descent? ", "answer_option_list": [[{"aoVal": "A", "content": "46\\% "}], [{"aoVal": "B", "content": "32\\% "}], [{"aoVal": "C", "content": "11\\% "}], [{"aoVal": "D", "content": "43\\% "}], [{"aoVal": "E", "content": "3.5\\% "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables"], "answer_analysis": ["The correct answer is(d). Because ethnic group categories are assumed to be mutually exclusive, P(Asian or Latino)=P(Asian)+P(Latino)=32\\%+11\\%=43\\% "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4105", "queId": "996298c1d825496d83ec68b412068a58", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Kitty writes down a sequence of five integers. The rule she uses is, \"after the first two terms, each term is the sum of the two previous terms.\" She sequence is ---, ---, ---, ~$$18$$, $$29$$. What is her first term? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0 $$ "}], [{"aoVal": "B", "content": "$$ 3 $$ "}], [{"aoVal": "C", "content": "$$ 4 $$ "}], [{"aoVal": "D", "content": "$$ 5 $$ "}], [{"aoVal": "E", "content": "$$ 7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["Let the first six terms of Kitty\\textquotesingle s sequence be $$a$$, $$b$$, $$c$$, $$18$$ and $$29$$ respectively. Then $$c+ 18= 29$$, so $$c= 11$$. Hence $$b+11= 18$$, so $$b=7$$. Therefore, $$a+7=11$$, so $$a=4$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4107", "queId": "cc3ad94f90544382b94fd921441f7495", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many multiples of $$7$$ are between $$20$$ and $$100$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$3\\times7=21$$, start from the $$3^{}\\rm{rd}$$ $$14\\times7=98$$, end at the $$14^{}\\rm{th}$$ Thus, the number of term remain: $$14-2=12$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4108", "queId": "47cd6284525d494a8b461325dd2b5015", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Half of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 4 cups. What percent of the total capacity of the pitcher did each cup receive?~ (adapted from 2020 AMC 8, Question \\#5) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12.5$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["The pitcher is half full, i.e. $50 \\textbackslash\\%$ full. Therefore each cup receives $\\frac{50}{4}=(\\mathbf{C}) 12.5$ percent of the total capacity. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4112", "queId": "6315694b973a497b9b51a3b6afaf714e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{The distribution of the number of hours worked by volunteers last year at a large hospital is approximately normal with mean 80 and standard deviation 7. Volunteers in the top 20 percent of hours worked will receive a certificate of merit. If a volunteer from last year is selected at random, which of the following is closest to the probability that the volunteer selected will receive a certificate of merit given that the number of hours the volunteer worked is less than 90?} ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.077$$ "}], [{"aoVal": "B", "content": "$$0.123$$ "}], [{"aoVal": "C", "content": "$$0.134$$ "}], [{"aoVal": "D", "content": "$$0.618$$ "}], [{"aoVal": "E", "content": "$$0.923$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{A: receive a merit B: hour \\textless{} 90} \\textbf{P(B) = P(hour \\textless{} 90) = P(Z\\textless(90-80)/7) = 0.9236} \\textbf{P(A) = 0.2} \\textbf{P(hour \\textgreater{} x) = 0.2} \\textbf{P(hour ≤ x) = 0.8} \\textbf{P(Z ≤ (x-80)/7) =0.8} \\textbf{P(A∩B) = P(x\\textless hour\\textless90) = P($$\\frac{x-80}{7} \\textless{} Z \\textless{} \\frac{90-80}{7}$$) = P($$Z \\textless{} \\frac{90-80}{7}$$) - P($$Z \\textless{} \\frac{x-80}{7}$$) = 0.9236-0.8 = 0.1236} \\textbf{P(A\\textbar B) = $$\\frac{P(A∩B)}{P(B)}$$ = $$\\frac{0.1236}{0.9236}$$=0.134} "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4128", "queId": "70ddc279ae8c4551a5ecc727bf7c72a1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$x=?$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["A "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4137", "queId": "436a1f3cac7e43c59257a831e1237d5f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a fruit market, $$1\\textasciitilde\\text{kg}$$ of apples is priced at $$\\textbackslash$a$$. $$1\\textasciitilde\\text{kg}$$ of strawberries costs $$\\textbackslash$b$$ more than $$2$$ times $$a$$. How much will $$3\\textasciitilde\\text{kg}$$ of strawberries cost? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3a+6b$$ "}], [{"aoVal": "B", "content": "$$2a+b$$ "}], [{"aoVal": "C", "content": "$$6a+3b$$ "}], [{"aoVal": "D", "content": "$$6a+b$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$1\\textasciitilde\\text{kg}$$ of strawberries costs $$2a+b$$, so $$3\\textasciitilde\\text{kg}$$ of strawberries costs $$3\\times (2a+b)=6a+3b$$. So, the answer is C. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4138", "queId": "7570ac19996e47fcbfc50ec18a6c3325", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the median of the following list of $4042$ number? $1$, $2$, $3$, $\\cdots $, $2021$, $1^{2}$, $2^{2}$, $3^{2}$, $\\cdots $, $2021^{2}$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$1974.5$$ "}], [{"aoVal": "B", "content": "$$1975.5$$ "}], [{"aoVal": "C", "content": "$$1976.5$$ "}], [{"aoVal": "D", "content": "$$1977.5$$ "}], [{"aoVal": "E", "content": "$$1978.5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables"], "answer_analysis": ["We want to know the $2021^{th}$ term and the $2022^{th}$ term to get the median. We know that $44^{2}=1936\\textless2021$, and $45^{2}=2025\\textgreater2021$. So, the number $1^{2}$, $2^{2}$, $3^{2}$, $\\cdots $, $44^{2}$ are between $1$ to $1936$. $1936+44=1980$, which mean that $1936$ is the $1980^{th}$ number. Thus, the $2021^{th}$ term will be $1936+41=1977$, and similarly the $2021^{th}$ term will be $1978$. So, the answer is $1977.5$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4139", "queId": "3eee61c7a9574de7a8f1fb0b32b0599c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If the degree measures of the angles of a triangle are in the ratio $3: 3: 4$, what is the degree measure of the largest angle of the triangle? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$72$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["The sum of the ratios is 10 . Since the sum of the angles of a triangle is $180^{\\circ}$, the ratio can be scaled up to $54: 54: 72(3 \\cdot 18: 3 \\cdot 18: 4 \\cdot 18)$. The numbers in the ratio $54: 54: 72$ represent the angles of the triangle. The question asks for the largest, so the answer is "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4148", "queId": "90363cb6a9994f468648b99e12fb0fa3", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The GPAs (grade point averages) of students who take the AP Statistics exam are approximately normally distributed with a mean of 3.4 and a standard deviation of 0.3. What is the probability that a student selected at random from this group has a GPA lower than 3.0? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.0918$$ "}], [{"aoVal": "B", "content": "$$0.4082$$ "}], [{"aoVal": "C", "content": "$$0.9082$$ "}], [{"aoVal": "D", "content": "$$-0.0918$$ "}], [{"aoVal": "E", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["P(X\\textless3.0) = $P(z\\textless\\frac{3-3.4}{0.3}=-1.33)$ = 0.0918 or normalcdf(-100, 3, 3.4, 0.3) = 0.0912 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4151", "queId": "d0defb50be7c4e989b5c1e8c66b7c18c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Let $a$ and $b$ be two consecutive odd integers. If $a$ is three times $b$, what is their sum $a+b$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$16$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["A "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4163", "queId": "4c75d18d44d140449b5812242eaedef9", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Which is the smallest fraction in $$\\frac{2020}{2021}$$, $$\\frac{2021}{2022}$$, $$\\frac{2022}{2023}$$ and $$\\frac{2023}{2024}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{2020}{2021}$$ "}], [{"aoVal": "B", "content": "$$\\frac{2021}{2022}$$ "}], [{"aoVal": "C", "content": "$$\\frac{2022}{2023}$$ "}], [{"aoVal": "D", "content": "$$\\frac{2023}{2024}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating"], "answer_analysis": ["Sugar water theory. 1 gram of sugar added each time, and the sugar water gets sweeter. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4164", "queId": "2d87cc7832134c72aa1b1e8513c9373d", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the smallest whole number larger than the perimeter of any triangle with a side of length $12$ and a side of length $13$? (adapted from 2015 AMC8, Question 8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$51$$ "}], [{"aoVal": "D", "content": "$$49$$ "}], [{"aoVal": "E", "content": "$$33$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s\\textless12+13$. Adding $12+13$ to both sides of the inequality, we get $s+12+13\\textless50$, and because $s+12+13$ is the perimeter of our triangle, (B) 50 is our answer. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4169", "queId": "55818f91eb674db29fd07110fbf7f6b6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following groups has equivalent ratios? ", "answer_option_list": [[{"aoVal": "A", "content": "$1$ to $5$, $\\frac{0.5}{1}$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{5}$$, $1:5$ "}], [{"aoVal": "C", "content": "$\\frac{1}{5}$, $5$ to $10$ "}], [{"aoVal": "D", "content": "$1:5$, $\\frac{5}{10}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas"], "answer_analysis": ["$$A$$, $1$ to $5$ $$=\\frac{1}{5}$$, $$\\frac{0.5}{1}=\\frac{5}{10}=\\frac{1}{2}$$, so wrong. $$B$$, $$\\frac{1}{5}=1:5$$, so true. $$C$$, $5$ to $10$ $$=\\frac{5}{10}=\\frac{1}{2}$$, so wrong. $$D$$, $$1:5=\\frac{1}{5}$$, $$\\frac{5}{10}=\\frac{1}{2}$$, so wrong. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4172", "queId": "eca82cbd8cfc4f16b5ed9cc8c6929b65", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$10000\\div 200\\times$$$$=10000$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$200$$ "}], [{"aoVal": "C", "content": "$$1000$$ "}], [{"aoVal": "D", "content": "$$2000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$10000\\div 200=50$$; $$50\\times \\underline{200}=10000$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4175", "queId": "2954468cf0c043beb5b488587ec46b2a", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following numbers\\textquotesingle{} value does not change after removing all \"$$0$$\" s ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$120.221$$ "}], [{"aoVal": "B", "content": "$$4.401$$ "}], [{"aoVal": "C", "content": "$$2424.390$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["$$2424.390=2424.39$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4187", "queId": "558a06db22c644d7841c7e0f16ddb041", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Match the linear equation, $6x-3y=2$, with its corresponding $y$-intercept. ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{2}{3}$ "}], [{"aoVal": "B", "content": "$-\\frac{2}{3}$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable"], "answer_analysis": ["$6x-3y=2$, $y=2x-\\frac{2}{3}$, Its $y$-intercept is $-\\frac{2}{3}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4188", "queId": "94dec780f5ec44c0a6b2a64fba1c3ef4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Given that $$a\\Psi b=a\\times b+2$$, for example, $$3\\Psi 1 = 3\\times1 +2$$, what is $$3\\Psi4$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition"], "answer_analysis": ["Nil "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4199", "queId": "2da6fce5fa734ab6af98c452ce6df9db", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Real numbers $x$ and $y$ satisfy $x+y=4$ and $x \\cdot y=-2$. What is the value of $$ x+\\frac{x^{3}}{y^{2}}+\\frac{y^{3}}{x^{2}}+y? $$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$360$$ "}], [{"aoVal": "B", "content": "$$400$$ "}], [{"aoVal": "C", "content": "$$420$$ "}], [{"aoVal": "D", "content": "$$440$$ "}], [{"aoVal": "E", "content": "$$480$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Proportional Equations"], "answer_analysis": ["$$ x+\\frac{x^{3}}{y^{2}}+\\frac{y^{3}}{x^{2}}+y=x+\\frac{x^{3}}{y^{2}}+y+\\frac{y^{3}}{x^{2}}=\\frac{x^{3}}{x^{2}}+\\frac{y^{3}}{x^{2}}+\\frac{y^{3}}{y^{2}}+\\frac{x^{3}}{y^{2}} $$ Continuing to combine $$ \\frac{x^{3}+y^{3}}{x^{2}}+\\frac{x^{3}+y^{3}}{y^{2}}=\\frac{\\left(x^{2}+y^{2}\\right)\\left(x^{3}+y^{3}\\right)}{x^{2} y^{2}}=\\frac{\\left(x^{2}+y^{2}\\right)(x+y)\\left(x^{2}-x y+y^{2}\\right)}{x^{2} y^{2}} $$ From the givens, it can be concluded that $x^{2} y^{2}=4$. Also, $$ (x+y)^{2}=x^{2}+2 x y+y^{2}=16 $$ This means that $x^{2}+y^{2}=20$. Substituting this information into $\\frac{\\left(x^{2}+y^{2}\\right)(x+y)\\left(x^{2}-x y+y^{2}\\right)}{x^{2} y^{2}}$, we have $\\frac{(20)(4)(22)}{4}=20 \\cdot 22=$ 440. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4204", "queId": "5ea9a8c625554e989dc00438418b68d7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The ratio of $A$ to $B$ is $3:4$. If we multiply $A$ by $3$, $B$ should~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "multiply by $4$ "}], [{"aoVal": "B", "content": "divide by $3$ "}], [{"aoVal": "C", "content": "add by $8$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$\\frac{3}{4}=\\frac{9}{12}$ $12-4=8$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4209", "queId": "a2b8a5f882574953b29e2d21423e15c0", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Fill in the blanks with ``$$+$$'' or ``$$-$$'' to make the equation true． $$6$$~~~~ $$6$$~~~~ $$6$$~~~~ $$6$$~~~~ $$6=6$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$+++-$$ "}], [{"aoVal": "B", "content": "$$++++$$ "}], [{"aoVal": "C", "content": "$$++-\\/-$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["$$6+6+6-6-6=6$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4212", "queId": "c30dfc2f509345d580095210c2f2d11f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "One apple, one banana, and two peaches together weigh $12$ lbs. One apple and one peach together weigh $5$ lbs. One banana and $2$ peaches together weigh $5$ lbs more than one apple and one peach weigh together. Each peach weighs the same. How many pounds does one banana weigh? ", "answer_option_list": [[{"aoVal": "A", "content": "$3$ lbs "}], [{"aoVal": "B", "content": "$4$ lbs "}], [{"aoVal": "C", "content": "$5$ lbs "}], [{"aoVal": "D", "content": "$6$ lbs "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution"], "answer_analysis": ["We can write their relationships as the equations below: $A+B+P+P=12$ $A+P=5$ $B+P+P=A+P+5$ So, $B+P+P=5+5=10$, $A=12-10=2$, $P=5-2=3$, $B=12-2-3-3=4$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4213", "queId": "297cc6aaf10b4c518bbc31b28ea8af49", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$\\sqrt{\\frac12 }+\\sqrt{12.5}-\\frac12\\sqrt{200}+\\sqrt{60\\frac12}$$=． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2\\sqrt{2}$$ "}], [{"aoVal": "B", "content": "$$\\frac{5}{2} \\sqrt{2}$$ "}], [{"aoVal": "C", "content": "$$3\\sqrt{2}$$ "}], [{"aoVal": "D", "content": "$$\\frac{7}{2} \\sqrt{2}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"], "answer_analysis": ["n/a. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4222", "queId": "31fb1f35be3b4b97a7caad4c53ac28f6", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "Let $a, b$, and $c$ be positive integers with $a \\geq b \\geq c$ such that $a^{2}-b^{2}-c^{2}+a b=2011$ and $a^{2}+3 b^{2}+3 c^{2}-3 a b-2 a c-2 b c=-1997$. What is $a$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$249$$ "}], [{"aoVal": "B", "content": "$$250$$ "}], [{"aoVal": "C", "content": "$$251$$ "}], [{"aoVal": "D", "content": "$$252$$ "}], [{"aoVal": "E", "content": "$$253$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Addition and Subtraction of Equations"], "answer_analysis": ["Add the two equations. $$ 2 a^{2}+2 b^{2}+2 c^{2}-2 a b-2 a c-2 b c=14 . $$ Now, this can be rearranged and factored. $$ \\begin{aligned} \\&\\left(a^{2}-2 a b+b^{2}\\right)+\\left(a^{2}-2 a c+c^{2}\\right)+\\left(b^{2}-2 b c+c^{2}\\right)=14 \\textbackslash\\textbackslash{} \\&(a-b)^{2}+(a-c)^{2}+(b-c)^{2}=14 \\end{aligned} $$. $a, b$, and $c$ are all integers, so the three terms on the left side of the equation must all be perfect squares. We see that the only is possibility is $14=9+4+1$ $(a-c)^{2}=9 \\Rightarrow a-c=3$, since $a-c$ is the biggest difference. It is impossible to determine by inspection whether $a-b=1$ or 2 , or whether $b-c=1$ or 2 . We want to solve for $a$, so take the two cases and solve them each for an expression in terms of $a$. Our two cases are $(a, b, c)=(a, a-1, a-3)$ or $(a, a-2, a-3)$. Plug these values into one of the original equations to see if we can get an integer for $a$. $a^{2}-(a-1)^{2}-(a-3)^{2}+a(a-1)=2011$, after some algebra, simplifies to $7 a=2021$. 2021 is not divisible by 7 , so $a$ is not an integer. The other case gives $a^{2}-(a-2)^{2}-(a-3)^{2}+a(a-2)=2011$, which simplifies to $8 a=2024$. Thus, $a=253$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4226", "queId": "3f255340210c44d0a3397ee2be988c35", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are four soccer teams that are competing in a round-robin format. In the event of a draw, $$1$$ point would be awarded to both teams. $$3$$ points would be given to the team that wins and $$0$$ points would be given to the team that loses. The scores of Team $$A$$, $$B$$, $$C$$ and $$D$$ are $$7$$, $$4$$, $$4$$ and $$1$$ point respectively. How many matches ended in a draw? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns"], "answer_analysis": ["We can first assume that all games ended in a $win-lose$ scenario. Number of games played $=3+2+1=6$ Maximum total score $=6\\times3=18$ Everytime a $win-lose$ scenario changes to a $draw-draw$ scenario, the total score decreases by $3-2=1$ Difference in score $=18-16=2$ Number of matches that ended in a draw $=2\\div1=2$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4235", "queId": "94e99e694b3442318ed50091af2f248d", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "The sum of the first $m$ positive odd integers is $212$ more than the sum of the first $n$ positive even integers. What is the sum of all possible values of $n$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$255$$ "}], [{"aoVal": "B", "content": "$$256$$ "}], [{"aoVal": "C", "content": "$$257$$ "}], [{"aoVal": "D", "content": "$$258$$ "}], [{"aoVal": "E", "content": "$$259$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Unary Quadratic Equations"], "answer_analysis": ["The sum of the first $m$ odd integers is given by $m^{2}$. The sum of the first $n$ even integers is given by $n(n+1)$. Thus, $m^{2}=n^{2}+n+212$. Since we want to solve for $n$, rearrange as a quadratic equation: $n^{2}+n+\\left(212-m^{2}\\right)=0$. Use the quadratic formula: $n=\\frac{-1+\\sqrt{1-4\\left(212-m^{2}\\right)}}{2}$. Since $n$ is clearly an integer, $1-4\\left(212-m^{2}\\right)=4 m^{2}-847$ must be not only a perfect square, but also an odd perfect square for $n$ to be an integer. Let $x=\\sqrt{4 m^{2}-847}$; note that this means $n=\\frac{-1+x}{2}$. It can be rewritten as $x^{2}=4 m^{2}-847$, so $4 m^{2}-x^{2}=847$. Factoring the left side by using the difference of squares, we get $(2 m+x)(2 m-x)=847=7 \\cdot 11^{2}$. Our goal is to find possible values for $x$, then use the equation above to find $n$. The difference between the factors is $(2 m+x)-(2 m-x)=2 m+x-2 m+x=2 x$. We have three pairs of factors, $847 \\cdot 1,121 \\cdot 7$, and $77 \\cdot 11$. The differences between these factors are 846,114 , and 66 - those are all possible values for $2 x$. Thus the possibilities for $x$ are $423$, $57$, and $33$. Now plug in these values into the equation $n=\\frac{-1+x}{2}$, so $n$ can equal $211$, $28$, or $16$, hence the answer is $255$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4242", "queId": "36627a0dfce24554becfef40db54ce0e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Adding five of the six fractions $$\\frac{1}{2}$$, $$\\frac{2}{3}$$, $$\\frac{1}{4}$$, $$\\frac{1}{6}$$, $$\\frac{1}{9}$$ and $$\\frac{1}{18}$$ gives a total of $$1.5$$. Which of the fractions is not used? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{4}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{6}$$ "}], [{"aoVal": "D", "content": "$$\\frac{1}{9}$$ "}], [{"aoVal": "E", "content": "$$\\frac{1}{18}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["The sum of the five given fractions is $$\\frac{1}{2}+\\frac{2}{3}+\\frac{1}{4}+\\frac{1}{6}+\\frac{1}{9}+\\frac{1}{18}=\\frac{18+24+9+6+4+2}{36}$$. $$\\frac{63}{36}= \\frac{7}{4}=1 \\frac{3}{4}$$. So the fraction which is not used is $$1 \\frac{3}{4}-1 \\frac{1}{2}=\\frac{1}{4}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4243", "queId": "da2aecb93fa7479ab98a57303b70fede", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "One tour minibus can seat no more than $$8$$ people. What is the smallest number of minibuses needed to take $$75$$ people? (Adapted from 2000 Math Kangaroo Problem, Level 3-4, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders"], "answer_analysis": ["$75\\div8=9R3$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4249", "queId": "9e2394f3a2554c81bd354f678fe93026", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Let $A$ and $B$ be positive whole numbers. $A$ is a $2$-digit number and $B$ is a $4$-digit number. If $A+B$ and $A^{2}+B^{2}$ are both multiples of $7$, find the largest possible value of $B-A$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$9968$$ "}], [{"aoVal": "B", "content": "$$9982$$ "}], [{"aoVal": "C", "content": "$$9989$$ "}], [{"aoVal": "D", "content": "$$9996$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4253", "queId": "2dd4d9389779499f95303c64aa1c6b21", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many millimetres are there in $$0.08$$ kilometres? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\rm 80 mm$$ "}], [{"aoVal": "B", "content": "$$\\rm 800 mm$$ "}], [{"aoVal": "C", "content": "$$\\rm 8000 mm$$ "}], [{"aoVal": "D", "content": "$$\\rm 80000 mm$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Length"], "answer_analysis": ["0.08km=80m；80m=80000mm "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4254", "queId": "634e34cc8b2948089ca5b408b7f7a6fb", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Two integers are inserted into the list $3,3,8,11,28$ to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$56$$ "}], [{"aoVal": "B", "content": "$$57$$ "}], [{"aoVal": "C", "content": "$$58$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$61$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["D "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4264", "queId": "ac020a86d49e4a84835acddb79d59cd2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The hundreds digit of the product $$2014\\times400$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$2014\\times400 = 805600$$; the hundreds digit is $$6$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4265", "queId": "3f3dad47c0074f1a8468009bb695cb63", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Function $f$ is defined for the set of all natural number as follows: $$f(x)=\\begin{cases}\\dfrac{x}{2},(\\text{when }x\\text{ is even}) \\textbackslash\\textbackslash{} x+1,(\\text{when }x\\text{ is odd}) \\textbackslash\\textbackslash{} \\end{cases}$$. For example: $$f(3)=3+1=4$$, $$f(2)=2\\div 2=1$$. What is the value of $$f(f(f(f(f(17)))))$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Number Machine"], "answer_analysis": ["$$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde f\\left( f\\left( f\\left( f\\left( f\\left( 17 \\right) \\right) \\right) \\right) \\right)$$ $$=f\\left( f\\left( f\\left( f\\left( 18 \\right) \\right) \\right) \\right)$$ $$=f\\left( f\\left( f\\left( 9 \\right) \\right) \\right)$$ $$=f\\left( f\\left( 10 \\right) \\right)$$ $$=f\\left( 5 \\right)$$ $$=6$$． "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4266", "queId": "3add7063f4d144da95a9303ff6cdd48b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$0.1\\times 0.2\\times 0.3=$$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.0006$$ "}], [{"aoVal": "B", "content": "$$0.006$$ "}], [{"aoVal": "C", "content": "$$0.06$$ "}], [{"aoVal": "D", "content": "$$0.6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals"], "answer_analysis": ["$$0.1\\times 0.2\\times 0.3=(0.1\\times 0.2)\\times 0.3=0.02\\times 0.3=0.006$$. Therefore, the answer is $$\\rm B$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4282", "queId": "ff405ab438154f37aa7e2e5dbfef1cb4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Preview Question: Which of the following is not an expression? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$a$$ "}], [{"aoVal": "C", "content": "$$a+b=a+b$$ "}], [{"aoVal": "D", "content": "$$b-3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["Equations are not expressions. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4284", "queId": "5ec826dc5b67446eb90a0a8b845fd829", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which one of the following fractions is larger than $\\dfrac{1}{4}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{5}$$ "}], [{"aoVal": "B", "content": "$$\\frac{5}{8}$$ "}], [{"aoVal": "C", "content": "$$\\frac{2}{9}$$ "}], [{"aoVal": "D", "content": "$$\\frac{4}{17}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["$$Omitted.$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4285", "queId": "67e73635611a475fbd31be647c6a0113", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Evaluate $$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "B", "content": "$\\dfrac{2}{5}$ "}], [{"aoVal": "C", "content": "$\\dfrac{2}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{5}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions"], "answer_analysis": ["$$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}=\\frac{1}{2+ \\dfrac{1}{ \\dfrac{5}{2}}}= \\frac{1}{2+ \\dfrac{2}{5}}= \\frac{1}{ \\dfrac{12}{5}}= \\frac{5}{12}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4290", "queId": "2df647b510fb4253ac3c875b38cd3fcc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the area of the triangle formed by the lines $y=5$, $y=1+x$, and $y=1-x$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4291", "queId": "55b893d7d43b449f935c6115f8c7dcd3", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Ten percent of all trucks undergoing a certain inspection will fail the inspection. Assume that trucks are independently undergoing this inspection one at a time. The expected number of trucks inspected before a truck fails inspection is} ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{This follows a geometric distribution.} $$\\mu = \\frac{1}{p} = \\frac{1}{0.10} = 10$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4304", "queId": "7116fd94910d4c719e4e3383fb50afff", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the product of $409$ and $6$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2454$$ "}], [{"aoVal": "B", "content": "$$2404$$ "}], [{"aoVal": "C", "content": "$$2444$$ "}], [{"aoVal": "D", "content": "$$2464$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["omitted "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4306", "queId": "6c7eee2980ca4a219c80e0d8902135e6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$3+6+9+\\cdots +66+69+72=$$~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$600$$ "}], [{"aoVal": "B", "content": "$$900$$ "}], [{"aoVal": "C", "content": "$$1200$$ "}], [{"aoVal": "D", "content": "$$1800$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences->Sum of Terms in Arithmetic Sequences"], "answer_analysis": ["$3\\times（1+24）\\times24\\div 2=3\\times300=900$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4307", "queId": "75a769565ff640f98353b425e9fa410e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "3, 6, , 12, 15.~~Which number should be filled in the bracket? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$$6+3=9$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4314", "queId": "faa32003e38e4ee1b9df163a957d6e6a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Which of the following events are independent?} \\textbf{P(A) = 0.7, P(B) = 0.2, P(C) = 0.1, P(B\\textbar A) = 0.5, P(B\\textbar C) = 0.2, P(A∩C) = 0.0} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{A and B only} "}], [{"aoVal": "B", "content": "\\textbf{A and C only} "}], [{"aoVal": "C", "content": "\\textbf{A, B, and C} "}], [{"aoVal": "D", "content": "\\textbf{B and C only} "}], [{"aoVal": "E", "content": "\\textbf{None are independent} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{P(B\\textbar A)\\ne P(B) → A and B not independent} \\textbf{P(B\\textbar C) =P(B) → B and C independent} \\textbf{P(A\\textbar C)=P(A∩B)/P(C)=0.05/0.1=0.5\\ne P(A)→ A and C not independent} "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4316", "queId": "4cbe802b673343af9f377b6881cb850d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Peter bought three apples of $5$ dollars, and $4$ bananas of $4$ dollars. How much did he spend in total?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$7$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ dollars "}], [{"aoVal": "B", "content": "$$7$$ dollars "}], [{"aoVal": "C", "content": "$$8$$ dollars "}], [{"aoVal": "D", "content": "$$9$$ dollars "}], [{"aoVal": "E", "content": "$$10$$ dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"], "answer_analysis": ["$5+4=9$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4318", "queId": "4cbebda9c1534e80a776e220606c4b9d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A class had more boys than girls. After winter transfer, $3$ boys and $3$ girls joined the class. What is the relationship between boys and girls in the class now? ", "answer_option_list": [[{"aoVal": "A", "content": "boys $\\textgreater$ girls "}], [{"aoVal": "B", "content": "boys $=$ girls "}], [{"aoVal": "C", "content": "boys $\\textless$ girls "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["When add the same number to both sides of the inequality, the equation is still true "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4323", "queId": "636581c45dc742599cbb321849f7fc91", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$6$$ hoots $$=3$$ hollers, then $$10$$ hollers $$=$$~\\uline{~~~~~~~~~~}~hoots. ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["If $$2$$ hoots $$=1$$ holler, then $$(10\\times 1)$$ hollers $$=(10\\times 2)$$ hoots. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4324", "queId": "a76dbbb044374e2bb3ccc4e3f0810e8a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which three numbers can be put in the blanks to make the statement correct? $6 \\times$~\\uline{~~~~~~~~~~}~$-$~\\uline{~~~~~~~~~~}~$=$ $21 +$~\\uline{~~~~~~~~~~}~$\\times 2$ ", "answer_option_list": [[{"aoVal": "A", "content": "$5$, $4$ and $2$ "}], [{"aoVal": "B", "content": "$6$, $2$ and $7$ "}], [{"aoVal": "C", "content": "$7$, $5$ and $8$ "}], [{"aoVal": "D", "content": "$8$, $7$ and $11$ "}], [{"aoVal": "E", "content": "$9$, $7$ and $12$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$6 \\times 7 - 5 = 21 + 8 \\times 2$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4326", "queId": "3aff955032044e8c9d171b900c107955", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The original price of a product was $$80$$ dollars, and it\\textquotesingle s on sale for 30\\% off, this product isdollars cheaper than before． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$56$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["the new price is $$70\\textbackslash\\%$$ of the original price, so the new price is $$80\\times 70\\textbackslash\\%=56$$； $$80-56=24$$． so choose $$\\text{B}$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4329", "queId": "3f5fd426fd0445f493899ff6fc83f9b2", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A recipe that makes~$5$~servings of hot chocolate requires~$2$~squares of chocolate,~$\\dfrac{1}{4}$~cup sugar,~$1$~cup water and~$4$~cups milk. Jordan has~$5$~squares of chocolate,~$2$~cups of sugar, lots of water, and~$7$~cups of milk. If he maintains the same ratio of ingredients, what is the greatest number of servings of hot chocolate he can make? ", "answer_option_list": [[{"aoVal": "A", "content": "$5\\dfrac{1}{8}$ "}], [{"aoVal": "B", "content": "$6\\dfrac{1}{4}$ "}], [{"aoVal": "C", "content": "$7\\dfrac{1}{2}$ "}], [{"aoVal": "D", "content": "$8\\dfrac{3}{4}$ "}], [{"aoVal": "E", "content": "$9\\dfrac{7}{8}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["Assuming excesses of the other ingredients, the chocolate can make~$\\dfrac{5}{2}\\cdot5=12.5$~servings, the sugar can make~$\\dfrac{2}{1/4}\\cdot5=40$~servings, the water can make unlimited servings, and the milk can make~$\\dfrac{7}{4}\\cdot5=8.75$~servings. Limited by the amount of milk, Jordan can make at most~$\\boxed{\\left( D\\right)\\textbackslash{} 8\\dfrac{3}{4}}$~servings. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4332", "queId": "48440ca34401476bbc385d8b053fd698", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Bob is standing in the sixth place from the front to the back. The teacher distributes the apples from front to back according to the pattern as $1$, $3$, $5$ and so on, which means the first student has $1$ apple, and the second student has $3$ apples\\ldots How many apples can Linda get if Linda is standing behind to Bob?~(adapted from $$2006$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$1$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["$1,3,5,7,9,11$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4334", "queId": "a2d028b64a9a47d7968c3a9a61b0f244", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term in the sequence is $4000$. What is the first term? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4336", "queId": "a770397843074d6fb4159a1587de699f", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Compare the following pair of fractions using an inequality sign. $$A=\\frac{773}{778}$$, $$B=\\frac{884}{889}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{773}{778}\\textgreater\\frac{884}{889}$$ "}], [{"aoVal": "B", "content": "$$\\frac{773}{778}\\textless{}\\frac{884}{889}$$ "}], [{"aoVal": "C", "content": "$$\\frac{773}{778}=\\frac{884}{889}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$\\frac{773}{778}\\textless{}\\frac{(773+111)}{(778+111)}=\\frac{884}{889}$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4340", "queId": "636b3136285549c5b1cd2456e1956291", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$9 + 99 + 99 + 101 + 101 + 101 =$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$200$$ "}], [{"aoVal": "B", "content": "$$300$$ "}], [{"aoVal": "C", "content": "$$600$$ "}], [{"aoVal": "D", "content": "$$919$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$99+101 + 99+101 + 99+101 = 200 + 200 + 200 = 600$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4341", "queId": "5a4cc5a023684b7fa4805f385b3f02ac", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alysha and Julia have some biscuits. Altogether they have $28$ biscuits. Alysha has $4$ more biscuits than Julia. How many biscuits does Alysha have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$(28 + 4) \\div 2 = 16$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4342", "queId": "6c8956ef7ddc42868d0ffd2049c5dd40", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Supposed that $x$ and $y$ are nonzero real numbers such that $\\frac{3 x+y}{x-3 y}=-2$. What is the value of $\\frac{x+3 y}{3 x-y}$? (2017 AMC 10B Problems, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$-3$$ "}], [{"aoVal": "B", "content": "$$-1$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Rearranging, we find $3 x+y=-2 x+6 y$, or $5 x=5 y \\Longrightarrow x=y$. Substituting, we can convert the second equation into $$\\frac{x+3 x}{3 x-x}=\\frac{4 x}{2 x}=\\text { (D) } 2$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4360", "queId": "a2d78d925d4d41fa82714b0ac146183a", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which set of numbers go into the missing blanks respectively to make the equation true? $7=14$ $\\div$~\\uline{~~~~~~~~~~}~$=\\frac{14}{\\square}=\\frac{14}{1}\\times\\frac{1}{\\square}$ ", "answer_option_list": [[{"aoVal": "A", "content": "$2, 1, 2$ "}], [{"aoVal": "B", "content": "$1, 2, 2$ "}], [{"aoVal": "C", "content": "$2, 2, 1$ "}], [{"aoVal": "D", "content": "$2, 2, 2$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Dividing a term by $2$ is the same as multiplying it by half ($\\frac{1}{2}$)! "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4368", "queId": "3f7c94cd4bbb4c64b7e6c9a6f4ad61c9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The sixteenth term of an arithmetic progression is 40. The fifty-fifth term of this arithmetic progression is 157. Find the eighty-first term of this arithmetic progression. ", "answer_option_list": [[{"aoVal": "A", "content": "$$235$$ "}], [{"aoVal": "B", "content": "$$241$$ "}], [{"aoVal": "C", "content": "$$299$$ "}], [{"aoVal": "D", "content": "$$274$$ "}], [{"aoVal": "E", "content": "$$171$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["By the formula~$d=\\dfrac{a\\_{m}-a\\_{n}}{m-n}\\textbackslash{} \\Rightarrow\\textbackslash{} d=\\dfrac{a\\_{55}-a\\_{16}}{55-16}=\\dfrac{157-40}{39}=3.$ By the formula~$a\\_{n}=a\\_{m}+\\left( n-m\\right)d\\textbackslash{} \\textbackslash{} \\textbackslash{} \\Rightarrow\\textbackslash{} \\textbackslash{} a\\_{81}=a\\_{55}+\\left( 81-55\\right)\\times3=235.$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4370", "queId": "906c83e5f4c44655846a55ea89a0e8dc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Fido the Dog, Philemon the Cat and $4$ monkeys together weigh $24$ lbs. Fido and one monkey together weigh $11$ lbs. Philemon and $2$ monkeys together weigh $1$ lb less than Fido and one monkey weigh together. Each monkey weighs the same. How much does Philemon weigh? (2011 Math Kangaroo Problem, Level 1-2, Question \\#21) ", "answer_option_list": [[{"aoVal": "A", "content": "$3$ lbs "}], [{"aoVal": "B", "content": "$4$ lbs "}], [{"aoVal": "C", "content": "$5$ lbs "}], [{"aoVal": "D", "content": "$6$ lbs "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution"], "answer_analysis": ["We can write their relationships as the equations below: $$F+P+M+M+M+M=24$$ $$F+M=11$$ $$P+M+M=F+M-1$$ $ $ $$P+M+M=F+M-1$$, so $P+M+M=10$ $$F+P+M+M+M+M=24$$, so $11+10+M=24$, $M=3$, $P=4$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4372", "queId": "55dc2945bd5547c394c6202eac9bfda8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$9.25\\times 0.8+9\\frac{1}{4}\\times 0.2=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$9.25$$ "}], [{"aoVal": "B", "content": "$$92.5$$ "}], [{"aoVal": "C", "content": "$$925$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$9.25\\times 0.8+9\\frac{1}{4}\\times 0.2$$ $$=9.25\\times 0.8+9.25\\times 0.2$$ $$=9.25\\times (0.8+0.2)$$ $$=9.25\\times 1$$ $$=9.25$$ So, $$\\text{A}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4377", "queId": "b9e47ff904584b2d9f958a45205060d5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is not an expression? ", "answer_option_list": [[{"aoVal": "A", "content": "$$a-b=2c$$ "}], [{"aoVal": "B", "content": "$$z$$ "}], [{"aoVal": "C", "content": "$$a+b-5$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["Equations are not expressions. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4380", "queId": "4cdff406715349abae4f179578c2d72c", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "David drives from his home to the airport to catch a flight. He drives $35$ miles in the first hour, but realizes that he will be $1$ hour late if he continues at this speed. He increases his speed by $15$ miles per hour for the rest of the way to the airport and arrives $30$ minutes early. How many miles is the airport from his home? (2014 AMC 10A Problems, Question \\#15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$140$$ "}], [{"aoVal": "B", "content": "$$175$$ "}], [{"aoVal": "C", "content": "$$210$$ "}], [{"aoVal": "D", "content": "$$245$$ "}], [{"aoVal": "E", "content": "$$280$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Note that he drives at $50$ miles per hour after the first hour and continues doing so until he arrives. Let $d$ be the distance still needed to travel after $1$ hour. We have that $\\frac{d}{50}+1.5=\\frac{d}{35}$, where the $1.5$ comes from $1$ hour late decreased to $0.5$ hours early. Simplifying gives $7 d+525=10 d$, or $d=175$. Now, we must add an extra $35$ miles traveled in the first hour, giving a total of (C) $210$ miles. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4385", "queId": "75c01e2665d54c01b87b6b9b7af5a1c6", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{A grocer would like to determine the proportion of milk cartons that have expired within 0.05 of the true proportion with a 95 percent confidence interval. What is the minimum required sample size?} ", "answer_option_list": [[{"aoVal": "A", "content": "$$300$$ "}], [{"aoVal": "B", "content": "$$383$$ "}], [{"aoVal": "C", "content": "$$384$$ "}], [{"aoVal": "D", "content": "$$385$$ "}], [{"aoVal": "E", "content": "$$400$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{$n \\geq (\\frac{Z\\_{\\alpha/2}}{ME})^{2} {p(1-p)}$} \\textbf{Since p is unknown, then use p = ½. $n \\geq (\\frac{Z\\_{\\alpha/2}}{2ME})^{2}$} \\textbf{$Z\\_{\\alpha/2}=1.96$ The ME is how far off from the true proportion you are willing to be, in this case, 0.05} \\textbf{$n \\geq (\\frac{1.96}{2*0.05})^{2} = 384.16$ round up} "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4393", "queId": "8bd4b33493fd4ca0a87af2cd06ac4e86", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$(101+100+\\cdots +3+2)-(100+99+\\cdots +2+1)=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$99$$ "}], [{"aoVal": "B", "content": "$$100$$ "}], [{"aoVal": "C", "content": "$$101$$ "}], [{"aoVal": "D", "content": "$$102$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$(101+100+\\cdots +3+2)-(100+99+\\cdots +2+1)=(101-1)=100$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4395", "queId": "36d64ea4b3954bc7862bed3f65aa9ab5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\sqrt{9+16+144}=\\sqrt{9}+\\sqrt{16}+$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\sqrt{36}$$ "}], [{"aoVal": "B", "content": "$$\\sqrt{100}$$ "}], [{"aoVal": "C", "content": "$$\\sqrt{144}$$ "}], [{"aoVal": "D", "content": "$$\\sqrt{169}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"], "answer_analysis": ["$$\\sqrt{9+16+144}=\\sqrt{169}=13=3+4+6=\\sqrt{9}+\\sqrt{16}+\\sqrt{36}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4396", "queId": "75c3eca0b3774a19a728b90d045439b5", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Convert the decimal $$0.65$$ to a fraction in its simplest form. ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{13}{20}$ "}], [{"aoVal": "B", "content": "$\\dfrac{3}{4}$ "}], [{"aoVal": "C", "content": "$$\\dfrac{17}{20}$$ "}], [{"aoVal": "D", "content": "$$\\dfrac{6}{5}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals->Converting Decimals into Fractions"], "answer_analysis": ["First, write down the decimal \"over\" the number 1 :~$0.65=\\dfrac{0.65}{1}$ Then multiply top and bottom by 100 since there are two numbers after the decimal point :~$\\dfrac{0.65}{1}=\\dfrac{0.65\\times100}{1\\times100}=\\dfrac{65}{100}$ This makes it a correctly formed fraction. Then simplify the fraction (in this case by dividing top and bottom by 5) :~$\\dfrac{65}{100}=\\dfrac{13}{20}$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4398", "queId": "b54fbe04bf2a4fccb62c6dce0ca434e0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Choose the correct number to make the number statement true. $$17-9+$$$$\\textgreater15+3-8$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$15+3-8=10$$，$$17-9=8$$，$$8+\\left( 2 \\right)=10$$，$$number$$ has to be bigger than $$2$$ so $$5$$ fits the requirement. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4399", "queId": "90741e7ee5ce4cf997dd192b4100723a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A consumer is willing to pay $\\textbackslash$ 12$ for a good, but is able to purchase it for $\\textbackslash$ 10$. What is the consumer surplus in this scenario? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\textbackslash$ 2$ "}], [{"aoVal": "B", "content": "$\\textbackslash$ 10$ "}], [{"aoVal": "C", "content": "$\\textbackslash$ 12$ "}], [{"aoVal": "D", "content": "$\\textbackslash$ 22$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Consumer surplus is calculated as the difference between the maximum price a consumer is willing to pay for a good and the actual price they pay, which is $\\textbackslash$ 12$- $\\textbackslash$10$ = $\\textbackslash$ 2$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4408", "queId": "487120e5292a4b9bb6ea0591012ec7af", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $1^{2}+2^{2}+3^{2}+\\cdots +10^{2}$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$55$$ "}], [{"aoVal": "B", "content": "$$385$$ "}], [{"aoVal": "C", "content": "$$1155$$ "}], [{"aoVal": "D", "content": "$$2310$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences->Sum of Terms in Arithmetic Sequences"], "answer_analysis": ["Answer is $385$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4414", "queId": "b5543fdc62014636abf6b4f63bce7d1d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$\\frac{1}{2}\\times \\frac{5}{3}+\\frac{11}{5}\\times \\frac{7}{6}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{77}{30}$$ "}], [{"aoVal": "B", "content": "$$\\frac{5}{6}$$ "}], [{"aoVal": "C", "content": "$$\\frac{17}{5}$$ "}], [{"aoVal": "D", "content": "$$\\frac{41}{18}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["$\\frac{5}{6}+\\frac{77}{30}=\\frac{25}{30}+\\frac{77}{30}=\\frac{102}{30}=\\frac{17}{5}$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4418", "queId": "2e6fe1645ce54206aa148437394eed9e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the next number in the sequence below? $$3, 5, 8, 13, 21, $$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$27$$ "}], [{"aoVal": "B", "content": "$$29$$ "}], [{"aoVal": "C", "content": "$$31$$ "}], [{"aoVal": "D", "content": "$$34$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["Sum of the previous two number. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4423", "queId": "4cfda29458b5435b839c9c39170f1967", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which calculation has a result of an odd number． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2\\times \\left( 0+2+2 \\right)\\times 2021$$ "}], [{"aoVal": "B", "content": "$$2\\times 2021-0-2-2$$ "}], [{"aoVal": "C", "content": "$$2021-2\\times 0\\times 2\\times 2$$ "}], [{"aoVal": "D", "content": "$$2+\\left( 0\\times 2\\times 2 \\right)\\times 2021$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4425", "queId": "639643d08cae4ec9b0fe9579a42210d4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $2021^{st}$ digit at the right of the decimal point in the decimal expression of $\\dfrac{2}{7}$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["$$\\frac{2}{7}=0.\\overline{285714}$$, it is a decimal which repeats in cycles of $6$ digits. Every $6$$^{th}$ digit is $4$. The $2022$$$^{nd}$$ digit is $4$, so the $2021$$^{st}$ digit is $1$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4426", "queId": "2e7c7c7acdbf482d9d0d8dcd470d6b22", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Betty has more than $90$ toys. All her toys can be divided evenly between $2$, $3$, or $4$ children. However, they cannot be divided evenly between $9$ children because $3$ more toys would be needed. How many toys does she have at least? ", "answer_option_list": [[{"aoVal": "A", "content": "$$87$$ "}], [{"aoVal": "B", "content": "$$96$$ "}], [{"aoVal": "C", "content": "$$132$$ "}], [{"aoVal": "D", "content": "$$135$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["After adding $3$ toys, the number of toys should be divisible by $9$, and it also should be divisible by $2, 3, $ and $4$. Thus, the answer is $B$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4438", "queId": "5f09d0e5ac69401b9e1e2fbf59eee2a8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$49\\div0.035=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1.4$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$140$$ "}], [{"aoVal": "D", "content": "$$1400$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals"], "answer_analysis": ["$$49\\div0.035=49000\\div35=1400$$, so the answer is $$\\rm{D}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4439", "queId": "5a8048732c0e488785d2256c6ad74875", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Four fair six-sided dice are rolled. What is the probability that at least three of the four dice show the same value? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{36}$ "}], [{"aoVal": "B", "content": "$\\frac{7}{72}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{9}$ "}], [{"aoVal": "D", "content": "$\\frac{5}{36}$ "}], [{"aoVal": "E", "content": "$\\frac{1}{6}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4451", "queId": "4428a23d72e7449e9d921856694ec446", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$$$Calculate$$$$ $$\\left (403 \\frac{3}{5}+183 \\frac{5}{11}+155 \\frac{3}{13}+118 \\frac{12}{17}\\right ) \\div$$$$ \\left~~( \\frac{1009}{15}+ \\frac{1009}{33}+ \\frac{1009}{39}+ \\frac{1009}{51}\\right )$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$5.5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$6.5$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Fast Calculation in Fractions"], "answer_analysis": ["$$\\left (403 \\frac{3}{5}+183 \\frac{5}{11}+155 \\frac{3}{13}+118 \\frac{12}{17}\\right ) \\div$$$$ \\left ( \\frac{1009}{15}+ \\frac{1009}{33}+ \\frac{10009}{39}+ \\frac{1009}{51}\\right )$$ $$=2018\\left ( \\frac{1}{5}+ \\frac{1}{11}+ \\frac{1}{13}+ \\frac{1}{17}\\right ) \\div \\frac{1000}{3}\\left ( \\frac{1}{5}+ \\frac{1}{11}+ \\frac{1}{13}+ \\frac{1}{17}\\right )$$ $=6$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4455", "queId": "c7d4af8983a5408b9fc3449ed35a571f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Express the recurring decimal~$0.2\\dot{5}$~as a fraction. ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{23}{99}$$ "}], [{"aoVal": "B", "content": "$$\\frac{23}{90}$$ "}], [{"aoVal": "C", "content": "$$\\frac{25}{99}$$ "}], [{"aoVal": "D", "content": "$$\\frac{25}{90}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals"], "answer_analysis": ["$$x=0.2\\dot{5}$$, $$100x=25. \\dot{5}$$, $$10x=2. \\dot{5}$$, $$90x=23$$, $$x= \\frac{23}{90}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4458", "queId": "3b622adc1af64957bf01c6be0ed76e9d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Ethan is shopping for an Eiffel Tower model online. The description says the scale of the model is $1:1000$. The height of the Eiffel Tower is $1083$ feet, so the model should be~\\uline{~~~~~~~~~~}~inches tall (round to the nearest integer, $12$ inches $=1$ foot ). ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$1083\\div 1000\\times 12=12.996$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4460", "queId": "8837a9e624044812be649db154512a96", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all of its side lengths are integers. The perimeter of $\\triangle ABC$ with a side of length $12$ and a side length of $7$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "$$28$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+7\\textgreater12$. $P=s+7+12\\textgreater12+12$. Therefore, $P\\textgreater24+1=25$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4462", "queId": "f613bb06d944420ca2adb00eaf652152", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are seven people in a bus. Four passengers get on and $6$ passengers get off at the first station. Then seven passengers get on and three get off at the second station. How many passengers are there on the bus at this time? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition and Subtraction of Whole Numbers"], "answer_analysis": ["$7+4-6+7-3=9$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4463", "queId": "6cb746166a334073ade8457665ba5c5f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum: $$3+7+2+8+1=?$$ (2007 Math Kangaroo Problem, Level 1-2, Question \\#17) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$27$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$3+7+2+8+1$ $=(3+7)+(2+8)+1$ $=10+10+1$ $=21$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4471", "queId": "8bea2ad164524a36ada6d681d55253b0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following statements is true? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4+7=3$$ "}], [{"aoVal": "B", "content": "$$3=4-7$$ "}], [{"aoVal": "C", "content": "$$3+4=7$$ "}], [{"aoVal": "D", "content": "$$4=7+3$$ "}], [{"aoVal": "E", "content": "$$3-7=4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$3+4=7$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4474", "queId": "3fc3ae5caa7445b1923fbe729430f3d8", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "What is the product of $$ \\frac { 3 } { 2 } \\times \\frac { 4 } { 3 } \\times \\frac { 5 } { 4 } \\times \\cdots \\times \\frac { 2 0 0 6 } { 2 0 0 5 }$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$1002$$ "}], [{"aoVal": "C", "content": "$$1003$$ "}], [{"aoVal": "D", "content": "$$2005$$ "}], [{"aoVal": "E", "content": "$$2006$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Fast Calculation in Fractions->Reducing Fractions by cancelling out successively"], "answer_analysis": ["By telescoping, it\\textquotesingle s easy to see the sum becomes $$\\frac {2006}2=1003$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4476", "queId": "a2f22d492715449683e72b319de3d639", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a dining room, there are $$15$$ chairs, $$5$$ tables, and $$20$$ cups. What is the ratio of chairs to cups? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1:4$$ "}], [{"aoVal": "B", "content": "$$15:20$$ "}], [{"aoVal": "C", "content": "$$4:3$$ "}], [{"aoVal": "D", "content": "$$3:4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["There are $$15$$ chairs and $$20$$ cups. So the ratio of chairs to cups is $$15:20$$. The simplest form is $$3:4$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4478", "queId": "3b71a04e128445878de3c20a31b5a64b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following expression has the maximum value? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3.2\\times0.16$$ "}], [{"aoVal": "B", "content": "$$0.32\\times0.16$$ "}], [{"aoVal": "C", "content": "$$32\\times0.016$$ "}], [{"aoVal": "D", "content": "$$0.032\\times160$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals"], "answer_analysis": ["$$3.2\\times0.16=0.512$$, $$0.32\\times0.16=0.0512$$, $$32\\times0.016=0.512$$, $$0.032\\times160=5.12$$. Therefore, expression $$\\rm D$$ has the maximum value. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4481", "queId": "83a162bcd50f4c1981727d65a22d271d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Teacher Judy has $71$ stickers in total, and she gives all the stickers to her students Martin and David. Martin gets $7$ more than David. How many stickers does David get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$29$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$35$$ "}], [{"aoVal": "E", "content": "$$39$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$(71-7) \\div 2 = 32$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4482", "queId": "b0c56d81153144a096612bf03766622b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the last number on the $20^{th}$ row? ", "answer_option_list": [[{"aoVal": "A", "content": "$$190$$ "}], [{"aoVal": "B", "content": "$$200$$ "}], [{"aoVal": "C", "content": "$$210$$ "}], [{"aoVal": "D", "content": "$$220$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns of Number Tables->Triangle Number Table"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4487", "queId": "83a2c4b92d38491683b7cdc0ccf21030", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Pinocchio has a magic nose, which will stretch out $5$ cm if he tells a lie and will shorten itself $1$ cm if he tells a truth. At the beginning his nose was $11$ cm long. The length of his nose changed into $13$ cm after he had said $10$ sentences. If these sentences were not true, they were definitely false. Thus, there were~\\uline{~~~~~~~~~~}~truths among these $10$ sentences. ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["If these $10$ sentences are true, the nose will shorten $10$ cm. There are $(13-11+10)\\div(5+1)=2$ sentences which are false. Thus, $10-2=8$ sentences are true. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4488", "queId": "be9d100871124f29b42b87c2c698b62d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "B", "content": "$\\dfrac{2}{5}$ "}], [{"aoVal": "C", "content": "$\\dfrac{3}{8}$ "}], [{"aoVal": "D", "content": "$\\dfrac{2}{9}$ "}], [{"aoVal": "E", "content": "$\\dfrac{5}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions"], "answer_analysis": ["$$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}=\\frac{1}{2+ \\dfrac{1}{ \\dfrac{5}{2}}}= \\frac{1}{2+ \\dfrac{2}{5}}= \\frac{1}{ \\dfrac{12}{5}}= \\frac{5}{12}$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4490", "queId": "443e47590fb54e3ab200e39dd8b823d8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which numbers should be filled in the parentheses to make the equation correct? $\\frac14=\\frac{(\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde)}{16}=\\frac8{(\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde)}$ ", "answer_option_list": [[{"aoVal": "A", "content": "$4; 20$ "}], [{"aoVal": "B", "content": "$16; 32$ "}], [{"aoVal": "C", "content": "$4; 32$ "}], [{"aoVal": "D", "content": "$4; 40$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["When the denominator and numerator are multiplied by the same number, the value of the fraction remains equal. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4493", "queId": "519cccc986bd49979a4af2ad60a5eab0", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $8^{\\text {th }}$-graders to $6^{\\text {th }}$-graders is $5: 3$, and the the ratio of $8^{\\text {th }}$-graders to $7^{\\text {th }}$ graders is $8: 5$. What is the smallest number of students that could be participating in the project? (2013 AMC 8, Question 16) ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$55$$ "}], [{"aoVal": "D", "content": "$$79$$ "}], [{"aoVal": "E", "content": "$$89$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["We multiply the first ratio by 8 on both sides, and the second ratio by 5 to get the same number for 8 th graders, in order that we can put the two ratios together: $$ \\begin{aligned} \\&5: 3=5(8): 3(8)=40: 24 \\textbackslash\\textbackslash{} \\&8: 5=8(5): 5(5)=40: 25 \\end{aligned} $$ Therefore, the ratio of 8th graders to 7th graders to 6th graders is $40: 25: 24$. Since the ratio is in lowest terms, the smallest number of students participating in the project is $$ 40+25+24=\\text { (E) } 89 $$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4496", "queId": "a7934222722e4fd6968beb974171e5e5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the largest number which is both less than $$2\\times3\\times5\\times7$$ and also a divisor of $$2 \\times 3 \\times 5\\times 7$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$357$$ "}], [{"aoVal": "B", "content": "$$2357$$ "}], [{"aoVal": "C", "content": "$$2 \\times5 \\times7$$ "}], [{"aoVal": "D", "content": "$$3 \\times5 \\times7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["The largest divisor of $$2\\times3\\times5\\times7$$ that is less than~ is $$3\\times5\\times7$$, which we get by dropping the smallest factor. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4499", "queId": "3b80a9c53f704c99a844edb86b5a8007", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Which of the following is not an algebraic expression? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$\\frac{1}{h}$ "}], [{"aoVal": "C", "content": "$3x=5y$ "}], [{"aoVal": "D", "content": "$xyzabc$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["equation is not algebraic expression "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4507", "queId": "715f5f88a1d44f43b61cc7074e35638b", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "$$2^{5}$$ means $$2$$ multipled by itself $$5$$ times, i.e. $$2^{5}=2\\times2\\times2\\times2\\times2=32$$. What is $$3^{4}$$ equal to? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$81$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$3\\times3\\times3\\times3=81$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4511", "queId": "5f287b4c4fb54522906d34896995d843", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "Given that $$\\left[ x+0.19 \\right]+\\left[ x+0.20 \\right]+\\left[ x+0.21 \\right]+\\cdots \\cdots +\\left[ x+0.91 \\right]=546$$. Find $$\\left[ 100x \\right]$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$793$$ "}], [{"aoVal": "B", "content": "$$737$$ "}], [{"aoVal": "C", "content": "$$757$$ "}], [{"aoVal": "D", "content": "$$743$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4515", "queId": "75ef7859374943fbba756d1b3eb3805b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is $132$. (2016 AMC 8 Problems, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["We can write the two digit number in the form of $10 a+b$; reverse of $10 a+b$ is $10 b+a$. The sum of those numbers is: $$ \\begin{gathered} (10 a+b)+(10 b+a)=132 \\textbackslash\\textbackslash{} 11 a+11 b=132 \\textbackslash\\textbackslash{} a+b=12 \\end{gathered} $$ We can use brute force to find order pairs $(a, b)$ such that $a+b=12$. Since $a$ and $b$ are both digits, both $a$ and $b$ have to be integers less than $10$. Thus our ordered pairs are $(3,9) ;(4,8) ;(5,7) ;(6,6) ;(7,5) ;(8,4) ;(9,3)$ or $(\\mathbf{B}) 7$ ordered pairs. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4517", "queId": "83ac9437e3f8433c8b6c9048b028d332", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There is an equal number of motorcycles and cars in the parking lot. They have $$48$$ wheels in total. How many cars are there in the parking lot? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable"], "answer_analysis": ["Let $$x$$ be the number of cars. $$2x+4x=48$$ $$6x=48$$ $$x=8$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4523", "queId": "f61c2a15272a4e89ba467e4b1aabee45", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Judy~ is waiting in a line to buy some toys. There are $7$ people in front of her, and $3$ people behind her. In total, how many people are there in the line? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$3 + 7 + 1 = 11$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4525", "queId": "884d6003604d428baa0cfb7262f2c219", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the value of $1+3+5+\\ldots+2017+2019-2 -4-6-\\ldots-2016-2018$? (Adapted from $2018$ AMC 8 Problem, Question \\#5) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1007$$ "}], [{"aoVal": "B", "content": "$$1008$$ "}], [{"aoVal": "C", "content": "$$1009$$ "}], [{"aoVal": "D", "content": "$$1010$$ "}], [{"aoVal": "E", "content": "$$1011$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Grouping in Fast Addition and Subtraction of Whole Numbers"], "answer_analysis": ["$1+3+5+\\ldots+2017+2019-2 -4-6-\\ldots-2016-2018$ $=1+(3-2)+(5-4)+\\cdots +(2017-2016)+(2019-2018)$ $=1+1+1+\\cdots +1+1$ $=1010$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4526", "queId": "a2feef63bb0f4272b119b11dfdd3e797", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "At an ice cream shop, a sundae is made by selecting two flavors of ice cream and topping them with fudge, whipped cream, nuts, and a cherry. The available flavors of ice cream are chocolate, vanilla, strawberry, rocky road, chocolate chip cookie dough, and mint chip. How many difference sundae combinations are possible? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$120$$ "}], [{"aoVal": "E", "content": "$$720$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["${6\\choose 2} = \\frac{6!}{2!(6-2)!} =15$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4530", "queId": "f1779088b5f44c11ae704a531e12f108", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Six pencils and two erasers cost $$3.20$$ dollars. One pencil costs $$40$$ cents. How much does one eraser cost? (Adapted from 2000 Math Kangaroo Problem, Level 3-4, Question \\#5) ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ cents "}], [{"aoVal": "B", "content": "$$30$$ cents "}], [{"aoVal": "C", "content": "$$40$$ cents "}], [{"aoVal": "D", "content": "$$50$$ cents "}], [{"aoVal": "E", "content": "$$60$$ cents "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division out of the Multiplication Table"], "answer_analysis": ["$3.20$ dollars = $320$ cents $(320-40\\times6)\\div2=40$ cents "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4534", "queId": "48c26d0423244621a0ba6059fab605ea", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Kitty writes down a sequence of five integers. The rule she uses is, \"after the first two terms, each term is the sum of the two previous terms.\" She sequence is~\\uline{~~~~~~~~~~}~,~\\uline{~~~~~~~~~~}~,~\\uline{~~~~~~~~~~}~, $$18$$, $$29$$. What is her first term? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0 $$ "}], [{"aoVal": "B", "content": "$$ 3 $$ "}], [{"aoVal": "C", "content": "$$ 4 $$ "}], [{"aoVal": "D", "content": "$$ 5 $$ "}], [{"aoVal": "E", "content": "$$ 7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["Let the first six terms of Kitty\\textquotesingle s sequence be $$a$$, $$b$$, $$c$$, $$18$$ and $$29$$ respectively. Then $$c+ 18= 29$$, so $$c= 11$$. Hence $$b+11= 18$$, so $$b=7$$. Therefore, $$a+7=11$$, so $$a=4$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4536", "queId": "4462c535de3346d5b57f1d6de65bc7af", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{A set of 5,000 scores on a college readiness exam are known to be approximately normally distributed with a mean of 72 and a standard deviation of 6. To the nearest integer value, approximately how many scores are between 63 and 75.} ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.6247$$ "}], [{"aoVal": "B", "content": "$$4115$$ "}], [{"aoVal": "C", "content": "$$3650$$ "}], [{"aoVal": "D", "content": "$$3123$$ "}], [{"aoVal": "E", "content": "$$3227$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{P(63 \\textless{} X \\textless{} 75) calculator: normalcdf(63, 75, 72, 6) = 0.6247~} \\textbf{0.6247*5000 = 3123.3} "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4538", "queId": "330c86df182d4ff4a0defb919d51109e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $$\\frac{2\\textbar x-2\\textbar+1}{3}\\textless{}1$$, the range of $x$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$-3\\textless x\\textless-1$$ "}], [{"aoVal": "B", "content": "$$x\\textgreater-1$$ or $$x\\textless-3$$ "}], [{"aoVal": "C", "content": "$$1\\textless x\\textless3$$ "}], [{"aoVal": "D", "content": "$$x\\textgreater3$$ or $$x\\textless1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["$$\\frac{2\\textbar x-2\\textbar+1}{3}\\textless{}1$$ $$2\\left\\textbar x-2\\right\\textbar+1\\textless3$$ $$2\\left\\textbar x-2\\right\\textbar\\textless2$$ $$1\\left\\textbar x-2\\right\\textbar\\textless1$$ $$-1\\textless x-2\\textless1$$ $$1\\textless x\\textless3$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4543", "queId": "5f3d37e34308441eb8800e29a684b5e3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$900+90+9+1=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$991$$ "}], [{"aoVal": "C", "content": "$$1000$$ "}], [{"aoVal": "D", "content": "$$9000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$900+90+9+1=999+1=1000$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4545", "queId": "9539ab90a77842b39231b803fabd1626", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alicia and Emily agreed to meet at the cinema at 3.55pm. Emily left her house at 1.47pm but arrived at the cinema 17 minutes late. How long was Emily\\textquotesingle s journey from her house to the cinema? ", "answer_option_list": [[{"aoVal": "A", "content": "$$189$$ minutes "}], [{"aoVal": "B", "content": "$$172$$ minutes "}], [{"aoVal": "C", "content": "$$216$$ minutes "}], [{"aoVal": "D", "content": "$$206$$ minutes "}], [{"aoVal": "E", "content": "None of the above. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion"], "answer_analysis": ["3: 55pm - 1: 47om + 15 minutes = 145 minutes. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4551", "queId": "33176ce5f75e40458b37085ef10e7683", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$55 + 55 + 55 = 44 + 44 +$$ . ", "answer_option_list": [[{"aoVal": "A", "content": "$$33$$ "}], [{"aoVal": "B", "content": "$$44$$ "}], [{"aoVal": "C", "content": "$$66$$ "}], [{"aoVal": "D", "content": "$$77$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$55+55+55 = 44+11+44+11+55 = 44+44+(11+11+55)= 44+44+77$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4564", "queId": "99d20ca34d664ba78ddfeede648639ec", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The average weight of dogs that come to a certain vet\\textquotesingle s office is 55.6 lbs, with a standard deviation of 2.2 lbs. If the weights are normally distributed, what percent of dogs weight more than 60 lbs? ", "answer_option_list": [[{"aoVal": "A", "content": "66.8\\% "}], [{"aoVal": "B", "content": "47.2\\% "}], [{"aoVal": "C", "content": "33.4\\% "}], [{"aoVal": "D", "content": "15.9\\% "}], [{"aoVal": "E", "content": "2.28\\% "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$P(X\\textgreater60) = P(Z\\textgreater\\frac{60-55.6}{2.2}) = p(Z\\textgreater2) =1-0.9772 = 0.0228$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4569", "queId": "400cdf94cc7344e7bede6d524f7cc701", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are four more girls than boys in Ms. Raub\\textquotesingle s class of 28 students. What is the ratio of number of girls to the number of boys in her class? (2014 AMC 8, Question 7) ", "answer_option_list": [[{"aoVal": "A", "content": "$3:4$ "}], [{"aoVal": "B", "content": "$4:3$ "}], [{"aoVal": "C", "content": "$3:2$ "}], [{"aoVal": "D", "content": "$7:4$ "}], [{"aoVal": "E", "content": "$2:1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["We can set up an equation with $x$ being the number of girls in the class. The number of boys in the class is equal to $x-4$. Since the total number of students is equal to 28 , we get $x+x-4=28$. Solving this equation, we get $x=16$. There are $16-4=12$ boys in our class, and our answer is $16: 12=$ (B) $4: 3$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4572", "queId": "48d7e5c8fd6643be88357cdaa851c8d0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A rectangular water tank is filled to a depth of $$70$$cm. It contains $$1050$$ litres of water. Some water is taken out of the tank. The water level drops by $$25$$cm. How much water is left in the tank? ", "answer_option_list": [[{"aoVal": "A", "content": "$$625\\rm L$$ "}], [{"aoVal": "B", "content": "$$375\\rm L$$ "}], [{"aoVal": "C", "content": "$$525\\rm L$$ "}], [{"aoVal": "D", "content": "$$270\\rm L$$ "}], [{"aoVal": "E", "content": "$$675\\rm L$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$$1050\\times \\frac {70-25}{70} = 675$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4574", "queId": "99d3fbdbfd0c4284bb366b9f062b411c", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There is a sequence of squares of some natural numbers: $1$, $4$, $9$, $16$, $\\cdots$ One of the numbers in this sequence is $10^{8}$. What is the next number after $10^{8}$? ($2001$ Math Kangaroo Problem, Level $$11$$-$$12$$, Question \\#$14$) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\left (10^{4}+1\\right )^{2}$ "}], [{"aoVal": "B", "content": "$\\left (10^{8}+1\\right )^{2}$ "}], [{"aoVal": "C", "content": "$\\left (10^{5}\\right )^{2}$ "}], [{"aoVal": "D", "content": "$\\left (10^{8}\\right )^{2}$ "}], [{"aoVal": "E", "content": "$\\left (10^{4}\\right )^{2}+1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Application of Powers"], "answer_analysis": ["As we know, $1$, $4$, $9$, $16$ are square numbers. $10^{8}=\\left (10^{4}\\right )^{2}$, so, the next one is $\\left (10^{4}+1\\right )^{2}$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4577", "queId": "3bbcaf4295fd46ccad836ab4d0154afe", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which is the solution of the following inequality: $-11x-10\\geq30-x$. ", "answer_option_list": [[{"aoVal": "A", "content": "$x\\leq-4$ "}], [{"aoVal": "B", "content": "$x\\geq-4$ "}], [{"aoVal": "C", "content": "$x\\leq-2$ "}], [{"aoVal": "D", "content": "$x\\geq-2$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["$-10x\\leq40$ $x\\leq-4$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4581", "queId": "447de8e8a0f2446eaea5c8e5e13dbfbb", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Mary went to the stationery store and she bought three pencils, a notebook, and a stationery box. A pencil costs $1$ dollar, a notebook costs $2$ dollars, a pencil case costs $3$ dollars, and Mary has a $1$ dollar discount coupon. How much did Mary spend in the end?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition and Subtraction of Whole Numbers->Questions Involving Addition and Subtraction"], "answer_analysis": ["Three pencils are three dollars. Notebook is two dollars. A three dollar pencil case and a one dollar free at last. So the last answer is $3+2+3-1=7$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4588", "queId": "a30ec070be1247e2b457fb3a12c77a92", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mike has $7y+1$ cans of coke. He gives his friends $$x$$ cans of coke. And he takes one out. How many cans of coke does he have left? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7y + 1$$ "}], [{"aoVal": "B", "content": "$$7y + 1 -x$$ "}], [{"aoVal": "C", "content": "$$7y-x$$ "}], [{"aoVal": "D", "content": "$$7y$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$7y+1-x-1=7y-x$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4589", "queId": "4d5c18676c634e0194c2d8c9866a35e3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the whole numbers from $$1$$ through $$100$$ is $$5050$$. What is the sum of the whole numbers from $$1$$ through $$200$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5150$$ "}], [{"aoVal": "B", "content": "$$10100$$ "}], [{"aoVal": "C", "content": "$$11050$$ "}], [{"aoVal": "D", "content": "$$20100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["($$1$$ to $$200$$)$$=$$($$1$$ to $$100$$)$$+[(100+1)+(100+2)+\\cdots +(100+100)]=$$($$1$$ to $$100$$)$$+[(100\\times 100)+$$($$1$$ to $$100$$)$$]=5050+[10000+5050]=20100$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4597", "queId": "449028a690324014a4ba09adbad3cc80", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following is the same as 2018 cm? ", "answer_option_list": [[{"aoVal": "A", "content": "2 metres and 18 centimetres "}], [{"aoVal": "B", "content": "2 kilometres and 18 centimetres "}], [{"aoVal": "C", "content": "20 metres and 18 centimetres "}], [{"aoVal": "D", "content": "201 metres and 8 centimetres "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion"], "answer_analysis": ["1m = 100cm; 1km=1000m A. 200 cm + 18 cm = 218 cm B. 200 000cm + 18cm = 200 018cm \\textbf{C. 2000cm + 18cm = 2018 cm} D. 20100cm + 8cm = 20108cm. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4599", "queId": "4029ca965cf94091a39a0ea92ba27550", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What fraction of the integers from $$1$$ to $$1000$$ inclusive are cubes? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{50}$$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{100}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{200}$$ "}], [{"aoVal": "D", "content": "$$\\frac{1}{400}$$ "}], [{"aoVal": "E", "content": "$$\\frac{1}{800}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"], "answer_analysis": ["As $$1=1^{3}$$ and $$1000 = 10^{3}$$, there are $$10$$ cubes from $$1$$ to $$1000$$. So the fraction of the integers from $$1$$ to $$1000$$ inclusive which are cubes is $$\\frac{10}{1000}= \\frac{1}{100}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4601", "queId": "5f57f0e62f1b4c21ad422b63e02dd6e7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "After the final exam results came out, four students wanted to compare who had done best. Who had the best grades?~(adapted from $$2007$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$4$$) Alice：$12+8$ Bob：$7+9$ Alan：$14+5$~ Tom：$6+8$ Susan: $6+15$ ", "answer_option_list": [[{"aoVal": "A", "content": "Alice "}], [{"aoVal": "B", "content": "Bob "}], [{"aoVal": "C", "content": "Alan "}], [{"aoVal": "D", "content": "Tom "}], [{"aoVal": "E", "content": "Susan "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering->Comparing and Ordering the Value of Expressions"], "answer_analysis": ["Alice：$12+8=20$ Bob：$7+9=16$ Alan：$14+5=19$~ Tom：$6+8=14$ Susan: $6+15=21$ $21\\textgreater20\\textgreater19\\textgreater16\\textgreater14$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4607", "queId": "c3519d61e7ea44479dadbc655651d696", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$3-(-4)=$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$-7$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$-1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Negative Numbers->Operations on Negative numbers"], "answer_analysis": ["Subtract a negative number is the same as add a postive number with the same absolute value. $a-(-b)=a+b$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4612", "queId": "90b3ba599e284346aff75acbe7769e58", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Kit played computer games for $225$ minutes. When he stopped gaming and decided to head to sleep, he checked the time and noticed that it was $11.20\\text{p.m.}$ What time did he start playing computer games? ", "answer_option_list": [[{"aoVal": "A", "content": "$7.35\\text{p.m.}$ "}], [{"aoVal": "B", "content": "$8.35\\text{p.m.}$ "}], [{"aoVal": "C", "content": "$8.55\\text{p.m.}$ "}], [{"aoVal": "D", "content": "$9.45\\text{p.m.}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules", "Overseas In-curriculum->Knowledge Point->Measurement->Time->Time Calculation"], "answer_analysis": ["$225$ minutes $=3$ hours $45$ minutes. He started playing at $7.35\\text{p.m.}$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4614", "queId": "4d73fa6df8374adb9786ac5db42dad00", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Daniel had a package of $$36$$ pieces of candy. Without breaking any pieces of candy, he divided all the candy equally among his friends without remaining. Which of the following was definitely not the number of his friends? (2013 Math Kangaroo Problem, Level 3 - 4, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders"], "answer_analysis": ["$$36 \\div 5 = 7R1$$, so the answer is $$5$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4615", "queId": "5662c1a7719a4a768cf29135c87fb52d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "One tour bus can seat no more than $$50$$ people. What is the smallest number of buses needed to take $$160$$ people? (Adapted from 2000 Math Kangaroo Problem, Level 3-4, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders"], "answer_analysis": ["$160\\div50=3R10$, $3+1=4$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4628", "queId": "955312dd42a345e2abf051b554829a99", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If the degree measures of the angles of a convex quadrilateral are in the ratio~$3:4:5:6$, by how many degrees does the measure of the largest angle exceed the measure of the smallest angle? ", "answer_option_list": [[{"aoVal": "A", "content": "$30^{\\circ}$ "}], [{"aoVal": "B", "content": "$45^{\\circ}$ "}], [{"aoVal": "C", "content": "$60^{\\circ}$ "}], [{"aoVal": "D", "content": "$75^{\\circ}$ "}], [{"aoVal": "E", "content": "$90^{\\circ}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$\\dfrac{6}{3+4+5+6}\\times360^{\\circ}-\\dfrac{3}{3+4+5+6}\\times360^{\\circ}=\\dfrac{360}{18}\\left( 6-3\\right)=20\\times3=60^{\\circ}$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4640", "queId": "3c019c65d7dd427582d0cabb5d47f3cf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There were five books on the shelf. Later, Jack took away three, and Mike took back four. Jim also took back three. How many books were there on the shelf?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$5$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition and Subtraction of Whole Numbers->Questions Involving Addition and Subtraction"], "answer_analysis": ["$5-3+4+3=9$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4646", "queId": "99ecbab320434a9d887de747f2d49a9f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many different four-digit numbers can be formed by rearranging the four digits in $2004$?~(2004 AMC 8 Problem, Question \\#2) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$81$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$2 \\times \\_3P\\_1 \\times \\_2C\\_2=6$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4647", "queId": "a320dee04e1e4374a71d21a4cd8dee40", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The sum of the first $m$ positive odd integers is 212 more than the sum of the first $n$ positive even integers. What is the sum of all possible values of $n$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$255$$ "}], [{"aoVal": "B", "content": "$$256$$ "}], [{"aoVal": "C", "content": "$$257$$ "}], [{"aoVal": "D", "content": "$$258$$ "}], [{"aoVal": "E", "content": "$$259$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Unary Quadratic Equations"], "answer_analysis": ["The sum of the first $m$ odd integers is given by $m^{2}$. The sum of the first $n$ even integers is given by $n(n+1)$. Thus, $m^{2}=n^{2}+n+212$. Since we want to solve for $n$, rearrange as a quadratic equation: $n^{2}+n+\\left(212-m^{2}\\right)=0$. Use the quadratic formula: $n=\\frac{-1+\\sqrt{1-4\\left(212-m^{2}\\right)}}{2}$. Since $n$ is clearly an integer, $1-4\\left(212-m^{2}\\right)=4 m^{2}-847$ must be not only a perfect square, but also an odd perfect square for $n$ to be an integer. Let $x=\\sqrt{4 m^{2}-847}$; note that this means $n=\\frac{-1+x}{2}$. It can be rewritten as $x^{2}=4 m^{2}-847$, so $4 m^{2}-x^{2}=847$. Factoring the left side by using the difference of squares, we get $(2 m+x)(2 m-x)=847=7 \\cdot 11^{2}$. Our goal is to find possible values for $x$, then use the equation above to find $n$. The difference between the factors is $(2 m+x)-(2 m-x)=2 m+x-2 m+x=2 x$. We have three pairs of factors, $847 \\cdot 1,121 \\cdot 7$, and $77 \\cdot 11$. The differences between these factors are 846,114 , and 66 - those are all possible values for $2 x$. Thus the possibilities for $x$ are 423,57 , and 33 . Now plug in these values into the equation $n=\\frac{-1+x}{2}$, so $n$ can equal 211,28 , or 16 , hence the answer is 255 . "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4648", "queId": "7abb2815c6fe42399a526c0d2aae0dcf", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "1. In the number 98, the digit \"9\" is in the ones place.~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "Yes "}], [{"aoVal": "B", "content": "No "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4649", "queId": "4056b9fa70144c1ea92ce3465f1c3c9f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the area of the triangle formed by the lines $y=5, y=1+x$, and $y=1-x$? (2019 AMC 8 Problems, Question \\#21) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$y=x+1$ and $y=-x+1$ have $y$-intercepts at $(0,1)$ and slopes of 1 and $-1$, respectively. Since the product of these slopes is $-1$, the two lines are perpendicular. From $y=5$, we see that $(-4,5)$ and $(4,5)$ are the other two intersection points, and they are 8 units apart. By symmetry, this triangle is a $45-45-90$ triangle, so the legs are $4 \\sqrt{2}$ each and the area is $\\frac{(4 \\sqrt{2})^{2}}{2}=(\\mathbf{E}) 16$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4651", "queId": "688460c7d36d4e009e8b2d4381aad6ee", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "1. In the number 98, the digit \"9\" is in the ones place. ", "answer_option_list": [[{"aoVal": "A", "content": "Yes "}], [{"aoVal": "B", "content": "No "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4654", "queId": "37c7a0f31f224871894556c4e9727993", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Teacher Ying bought some sweets and divided them equally among $$9$$ children. If everyone got $$6$$ sweets, there would still be some sweets remaining. What is the most number of sweets Teacher Ying could have bought? What is the least amount of sweets Teacher Ying could have bought? ", "answer_option_list": [[{"aoVal": "A", "content": "$$63$$，$$54$$ "}], [{"aoVal": "B", "content": "$$63$$，$$55$$ "}], [{"aoVal": "C", "content": "$$62$$，$$54$$ "}], [{"aoVal": "D", "content": "$$62$$，$$55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders"], "answer_analysis": ["$$(\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} )\\div 9=6 R (\\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} )$$ Largest remainder: $$8$$, $$9\\times 6+8=62$$ Smallest remainder: $$1$$, $$9\\times 6+1=55$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4655", "queId": "68873a3ce8984297b2df9f72f72b797c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the class, the teacher gave $4$ numbers:$15, 27, 36, 8$. Billy added another number to make the sum result of these $5$ digits to $100$. Guess what\\textquotesingle s the number Billy added ? ( adapted from $$2009$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$5$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$16$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Subtraction of Whole Numbers->Subtraction in Horizontal Form"], "answer_analysis": ["$100-15-27-36-8=14$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4657", "queId": "6887d8dec21a4ad5bd6e416850c7f79c", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many of the following equations are written in function form? ($1$) $2x-y=3x+1$;~($2$) $2x=-5y+2$;~($3$) $y=7x+12$;~($4$) $y+6=12x-17$;~($5$) $y=x+z+ab$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables"], "answer_analysis": ["Function Form is written as: $y=$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4658", "queId": "bec2fb66fa1d4701ae5ce9b24fee4e7f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For how many values of $a$ is it true that the line $y=x+a^{2}-6$ passes through the vertex of the parabola $y=4x^{2}-8x+a^{2}$? (Adapted From 2005 AMC 12B Problem, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "infinitely many "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["We see that the vertex of the quadratic function $y=4x^{2}-8x+a^{2}$ is $\\left(1, a^{2}-4\\right)$. If $\\left(2, a^{2}-1\\right)$ will be on the line $y=x+a^{2}-6$, $a^{2} -4=1+a^{2}-6$. Solve for $a$, there is no solution. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4659", "queId": "a3245928eeae414b9e613f6355f06968", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Recently you learned that the probability of getting a critical hit on an attack in your favorite game is 15\\%. You've noticed that you do 20 attacks per fight. You're interested in figuring out how likely it is that you would get 5 critical hits during a fight. Which of the following distributions should you use to answer this question?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{A binomial distribution with p = 0.15 and n = 20} "}], [{"aoVal": "B", "content": "\\textbf{A binomial distribution with p = 0.2 and n = 15} "}], [{"aoVal": "C", "content": "\\textbf{A geometric distribution with p = 0.15} "}], [{"aoVal": "D", "content": "\\textbf{A geometric distribution with p = 0.2} "}], [{"aoVal": "E", "content": "\\textbf{A cumulative geometric distribution with p = 0.15} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{Binomial distribution: how likely it is to get x successes in n trials given that your probability of success is p} \\textbf{Geometric distribution: how likely is it that I'll have my first critical strike on the 5th attack} \\textbf{Cumulative geometric distribution: how likely is it that I'll have my first critical strike on or before the 5th attack.} "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4663", "queId": "567e9d4e140e4129b5bc193d39daba3e", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "True or False: It is impossible for the $25$-th percentile to be equal to the mean. ", "answer_option_list": [[{"aoVal": "A", "content": "True "}], [{"aoVal": "B", "content": "False "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["For example, consider a dataset with the following values: 0, 2, 2, 3, 3. The mean of this dataset is $2$, and the $25$-th percentile is also $2$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4674", "queId": "3c1d576dd8994676b6938ffbb7272699", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "One ticket to a mini concert costs $\\textbackslash$20$ at full price. Nicole buys $4$ tickets using a coupon that gives her a $25\\textbackslash\\%$ discount. Bel buys $5$ tickets using a coupon that gives her a $30\\textbackslash\\%$ discount. How many more dollars does Bel pay than Nicole? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4679", "queId": "44d017175ba042d3b7947dcc3e6257c5", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the smallest whole number larger than the perimeter of any triangle with a side of length $7$ and a side of length $15$? (2015 AMC8, Question 8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$29$$ "}], [{"aoVal": "C", "content": "$$43$$ "}], [{"aoVal": "D", "content": "$$44$$ "}], [{"aoVal": "E", "content": "$$57$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s\\textless7+15$. Adding $7+15$ to both sides of the inequality, we get $s+7+15\\textless44$, and because $s+7+15$ is the perimeter of our triangle, (D) 44 is our answer. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4681", "queId": "b58fb32a9073462ba726df29875af553", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the missing number: $$12345 + 123450 = 12345\\times $$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$$12345+123450=12345\\times1+12345\\times10=12345\\times11$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4691", "queId": "407406fddf864982834e72c75967cc8a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the result of $$1\\times12\\times23\\times34\\times45\\times \\cdots \\times78\\times89$$. What is the sum of its last $2$ digits? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["$$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde1\\times12\\times23\\times34\\times45\\times \\cdots \\times78\\times89$$ $$=1\\times6\\times23\\times34\\times9\\times \\cdots \\times78\\times89\\times2\\times5$$ $$1\\times6\\times3\\times4\\times9\\times6\\times7\\times8\\times9$$ has the last digit of $2$. The last two digits are $2$ and $0$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4696", "queId": "a7c58272d5bf4b0a927aad3f238a75ad", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$2^{2}\\times 2^{4} =$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2^{8}$$ "}], [{"aoVal": "B", "content": "$$2^{6}$$ "}], [{"aoVal": "C", "content": "$$4^{8}$$ "}], [{"aoVal": "D", "content": "$$4^{7}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"], "answer_analysis": ["omitted "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4698", "queId": "83eb29fd829e4addbe8c80be1cf49ca7", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $8^{\\text {th }}$-graders to $6^{\\text {th }}$-graders is $5: 3$, and the the ratio of $8^{\\text {th }}$-graders to $7^{\\text {th }}$ graders is $8: 5$. What is the smallest number of students that could be participating in the project? ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$55$$ "}], [{"aoVal": "C", "content": "$$79$$ "}], [{"aoVal": "D", "content": "$$89$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["We multiply the first ratio by 8 on both sides, and the second ratio by 5 to get the same number for 8 th graders, in order that we can put the two ratios together: $$ \\begin{aligned} \\&5: 3=5(8): 3(8)=40: 24 \\textbackslash\\textbackslash{} \\&8: 5=8(5): 5(5)=40: 25 \\end{aligned} $$ Therefore, the ratio of 8th graders to 7th graders to 6th graders is $40: 25: 24$. Since the ratio is in lowest terms, the smallest number of students participating in the project is $$ 40+25+24=\\text { (E) } 89 $$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4699", "queId": "9e91b6cbcf5c4ee0bf787d6f4e4c02e2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A box has fewer than $50$ cookies in it. The cookies can be divided evenly between $2, 3,$ or $4$ children. However, they cannot be divided evenly between $7$ children because $6$ more cookies would be needed. How many cookies are there in the box? (2021 Math Kangaroo Problem, Level 3-4, Question \\#21) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$36$$ "}], [{"aoVal": "E", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders"], "answer_analysis": ["~\\uline{~~~~~~~~~~}~$\\div$ $7=$~\\uline{~~~~~~~~~~}~$R1$ $36-1=35$, $35\\div7=5$, so the answer is $D$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4702", "queId": "8c31b0b51ca04d5e91e8f2b3e1c2886f", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following numbers\\textquotesingle{} value does not change after removing all ``$$0$$''s ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$30.41$$ "}], [{"aoVal": "B", "content": "$$3.5260$$ "}], [{"aoVal": "C", "content": "$$42.09$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["Only $$3.5260$$\\textquotesingle s $$\"0\"$$ can be removed without causing other digits to change their places from the original number. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4710", "queId": "956571458b464f7ba1feb9c18cdc1b77", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Gilda has a bag of marbles. She gives $20 \\textbackslash\\%$ of them to her friend Pedro. Then Gilda gives $10 \\textbackslash\\%$ of what is left to another friend, Ebony. Finally, Gilda gives $25 \\textbackslash\\%$ of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself? (2019 AMC 8, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$33 \\frac{1}{3}$ "}], [{"aoVal": "C", "content": "$$38$$ "}], [{"aoVal": "D", "content": "$$45$$ "}], [{"aoVal": "E", "content": "$$54$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["After Gilda gives $20 \\textbackslash\\%$ of the marbles to Pedro, she has $80 \\textbackslash\\%$ of the marbles left. If she then gives $10 \\textbackslash\\%$ of what\\textquotesingle s left to Ebony, she has $(0.8 * 0.9)=72 \\textbackslash\\%$ of what she had at the beginning. Finally, she gives $25 \\textbackslash\\%$ of what\\textquotesingle s left to her brother, so she has $(0.75 * 0.72)$ (E) 54 . of what she had in the beginning left. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4716", "queId": "83ef8809291145aba9d29487df91191a", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "$$25+35+45=60+$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$25+35+45=(25+35)+45=60+45$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4731", "queId": "c8067c8624d24750bf993b0ceafd1933", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "For what positive value of $k$ does the following system of equations have no solutions?~\\uline{~~~~~~~~~~}~ $$ \\begin{cases} 8 x+6 k y=17 \\textbackslash\\textbackslash{} k x+12 y=16 \\end{cases}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$\\frac{56}{15}$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["We want the lines to be parallel and not the same line in order to have 0 solutions. Parallel implies the slopes of the lines are equal, so we have $-\\frac{8}{6 k}=-\\frac{k}{12}$. Cross multiplying, we get $96=6 k^{2}$, so $k^{2}=$ 16 and our positive solution is then $k=4$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4733", "queId": "3c442d24ea2041e1b93aa474a139bfa7", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "A little rabbit wants to cross the river. He needs to lay ten stones on the river. At this time, there are five stones on the river. The rabbit moves three stones back for the first time and two stones back for the second time. But the river washes away one stone. How many stones the rabbit still need to move?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition and Subtraction of Whole Numbers->Questions Involving Addition and Subtraction"], "answer_analysis": ["$5+3+2-1=9$，$10-9=1$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4739", "queId": "40949daccb9847909e8600da635bbf57", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the $5^{}\\text{th}$ number in the $21^{}\\text{st}$ row? ", "answer_option_list": [[{"aoVal": "A", "content": "$$210$$ "}], [{"aoVal": "B", "content": "$$215$$ "}], [{"aoVal": "C", "content": "$$231$$ "}], [{"aoVal": "D", "content": "$$236$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns of Number Tables->Triangle Number Table"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4740", "queId": "3c4792c7cdc446b2be7bf0ce74bdcd3a", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Which of the numbers below is the greatest? ($2003$ Math Kangaroo Problem, Level $9-10$, Question \\#$11$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$22222$$ "}], [{"aoVal": "B", "content": "$2222^{2}$ "}], [{"aoVal": "C", "content": "$222^{22}$ "}], [{"aoVal": "D", "content": "$22^{222}$ "}], [{"aoVal": "E", "content": "$2^{2222}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Application of Powers"], "answer_analysis": ["$2^{2222}\\textgreater2^{2220}=\\left (2^{10}\\right )^{222}=1024^{222}\\textgreater22^{222}$. According to this rule, $\\text{E}\\textgreater\\text{D}\\textgreater\\text{C}\\textgreater\\text{B}\\textgreater\\text{A}$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4741", "queId": "764a090b383943ca84131268b214a872", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the ones digit of the result of $3$\\textsuperscript{50}? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers"], "answer_analysis": ["The ones digits of exponents based on $3$ follow the rule: $3, 9, 7, 1, 3, 9, 7, 1\\cdots $ $50\\div4=12R2$, which means the ones digit is $9$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4745", "queId": "5b1bc2de47a24151a0bdccbbe9537130", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Express $$0.\\dot{6}\\dot{3}$$ as a fraction. ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{7}{11}$ "}], [{"aoVal": "B", "content": "$\\dfrac{57}{90}$ "}], [{"aoVal": "C", "content": "$\\dfrac{636}{1000}$ "}], [{"aoVal": "D", "content": "$\\dfrac{63}{100}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals"], "answer_analysis": ["Let $$x = 0.636363\\cdots$$ Multiply by $$100$$, which means move the decimal point two places to the right: $$100x = 63.636363\\cdots$$ $$x$$ and $$100x$$ have exactly the same decimal part, so if we subtract, it will disappear: $$100x - x = 63.636363\\cdots - 0.636363\\cdots$$ Which is: $$99x = 63$$ ,$x=\\dfrac{63}{99}=\\dfrac{7}{11}$ So there is our answer： $$0.636363\\cdots=$$$\\dfrac{7}{11}$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4746", "queId": "d13cb4e0374d4ca7a0d57dcf7986a850", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The 2000 Census identified the ethnic breakdown of the state of California to be approximately as follows: White:46％, Latino:32\\%, Asian:11\\%, Blcak:7\\%,and Other:4\\%.~Assuming that these are mutually exclusive categories (this is not a realistic assumption), what is the probability that a randomly selected person from the state of California is of Asian or Latino descent? ", "answer_option_list": [[{"aoVal": "A", "content": "46\\% "}], [{"aoVal": "B", "content": "32\\% "}], [{"aoVal": "C", "content": "11\\% "}], [{"aoVal": "D", "content": "43\\% "}], [{"aoVal": "E", "content": "3.5\\% "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables"], "answer_analysis": ["The correct answer is (c).There are 12 values in the A and E cell out the total of 125. When we are given colwnn E, the total is 63. Of those,28 are C. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4755", "queId": "7f6f3d70c9a84d7f9cbf6a317fc00818", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Express $$0.\\dot{5}$$ as a fraction . ． ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{111}{200}$ "}], [{"aoVal": "B", "content": "$\\dfrac{11}{20}$ "}], [{"aoVal": "C", "content": "$\\dfrac{5}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{2}{3}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals"], "answer_analysis": ["Let $$x = 0.555\\cdots$$ Multiply by $$10$$ , which means move the decimal point one place to the right: $$10x = 5.555\\cdots$$. $$x$$ and $$10x$$ have exactly the same decimal part, so if we subtract, it will disappear: $$10x - x = 5.555\\cdots - 0.555\\cdots$$. Simplify:~ $$9x = 5$$，$x=\\dfrac{5}{9}$ So there\\textquotesingle s our answer : $$0.555\\cdots=$$$\\dfrac{5}{9}$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4762", "queId": "c36ede0918a64827ac2640e93833e55e", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Alina writes the numbers $1,2,\\cdots ,9$ on a separate cards, one number per card. She wishes to divide the cards into $3$ groups of $3$ cards so that the sum of the numbers in each group will be the same. In how many ways can this be done? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["C "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4763", "queId": "ba33eb6894a04cfa82164d749fc2461c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The ones digit of the fourth power of an integer cannot be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["The ones digit of a $$4\\text{th}$$ power canbe $$0$$, $$1$$, $$5$$, or $$6$$. It can never be $$3$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4764", "queId": "6d3c89438a6445fa857566b9b52c0383", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If a study has three factors, each with three levels, how many treatments are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$27$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The number of values you multiply together is equal to the number of factors in a study. There are three factors, so multiply \\_\\_x\\_\\_x\\_\\_. The values that go into each slot represent the number of levels for each factor. In this case, 3x3x3=27. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4771", "queId": "b106def33ef84529a4593e292c6e3d15", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "$5+19$ is the same as~\\uline{~~~~~~~~~~}~$+8$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["NA "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4777", "queId": "450e3838f2dc471fb0c1c7d4b53c27b1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$99\\times9=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$990-9$$ "}], [{"aoVal": "B", "content": "$$990-90$$ "}], [{"aoVal": "C", "content": "$$900-99$$ "}], [{"aoVal": "D", "content": "$$900-9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$99\\times9=(100-1)\\times9$$. This is slightly less than $$100\\times9$$, so it\\textquotesingle s $$\\text{D}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4783", "queId": "524d29467c1342369cf422cf7417137e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Ten balls numbered from $1$ to $10$ are put into a bag. $3$ balls are taken out and numbers on them are added up. The ball with number $5$ is included in the balls that are taken out, and the sum of numbers on the $3$ balls can be divisible by both $3$ and $4$. Which of the following balls is definitely not taken out? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The sum can be divisible by both $3$ and $4$, so the sum is the common multiple of $3$ and $4$. If the sum is $12$, $12-5=7$, so the sum of the other numbers should be $7$. The other two numbers can be $1$ and $6$ or $3$ and $4$. If the sum is $24$, $24-5=19$, the other two numbers can only be $10$ and $9$. If the sum is $36$, it is impossible, because $36-5=31$ and the largest sum of two numbers from $1$ to $10$ is $19$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4787", "queId": "b10a657237824e59a21b7a5bbc92542e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In which of the following expressions, the value of the constant is larger than the value of the coefficient of $x$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$33x-55$$ "}], [{"aoVal": "B", "content": "$$-25x-32$$ "}], [{"aoVal": "C", "content": "$-\\frac{x}{3}-\\frac{1}{4}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["the sign in front is also part of constant or coefficient "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4790", "queId": "ccab3ac252ef43e6b6b5c053d82ab5e7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There is a rule that the symbol \"\\#\" represents an operation of producing the smaller one of the two numbers (for example, $17$ \\# $8 = 8$). Calculate: ($6$ \\# $3$ ) $\\times$($10$ \\# $9$)=~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$27$$ "}], [{"aoVal": "C", "content": "$$54$$ "}], [{"aoVal": "D", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["$6$\\#$3=3$, $10$\\#$9=9$ $3 \\times 9=27$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4807", "queId": "b5a9a4d6a17d49eaa8b5ead7813eb999", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Let $ a◆b=a+(2\\times b)$, then $1◆(2◆3)$ =~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["$1◆(2◆3)=1◆[2+(2\\times3)]=1◆8=1+16=17$. So the answer is $\\rm C$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4808", "queId": "56cc40cfbb64439cb7d386fb385981b1", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Which is the smallest fraction in $$\\frac{2020}{2021}$$, $$\\frac{2021}{2022}$$, $$\\frac{2022}{2023}$$ and $$\\frac{2023}{2024}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{2020}{2021}$$ "}], [{"aoVal": "B", "content": "$$\\frac{2021}{2022}$$ "}], [{"aoVal": "C", "content": "$$\\frac{2022}{2023}$$ "}], [{"aoVal": "D", "content": "$$\\frac{2023}{2024}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating"], "answer_analysis": ["Sugar water theory. 1 gram of sugar added each time, and the sugar water gets sweeter. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4811", "queId": "40cd52b131c840e9b33ac6ff94c151f1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$111$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4815", "queId": "9eb142131543410085165d78e33061c7", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Which of the following data sets has the largest standard deviation?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{{100, 101, 102, 103, 104}} "}], [{"aoVal": "B", "content": "\\textbf{{1000.3, 999.56, 1000.49, 1000, 998.32}} "}], [{"aoVal": "C", "content": "\\textbf{{1, 1, 1, 1, 1}} "}], [{"aoVal": "D", "content": "\\textbf{{5, 10, 15, 20, 25}} "}], [{"aoVal": "E", "content": "\\textbf{{1, 2, 3, 4, 5}} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{variance is used to measure the spread of data. A, B, C, E are densely distributed.We can verify by calculating the variances out. (A) 2.5, (B) 0.598, (C) 0, (D) 50, (E) 2} "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4819", "queId": "71e2b392f8de437e88428b0cb43d3d8f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$$$Calculate$$$$ $$\\frac{1}{2}~ (2019 \\times 2018-2018 \\times 2017+2017 \\times 2016-2016 \\times 2015+\\cdots$$$$ +5\\times4-4\\times3 +3\\times2-2\\times1 )$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1007090$$ "}], [{"aoVal": "B", "content": "$$1019090$$ "}], [{"aoVal": "C", "content": "$$1028090$$ "}], [{"aoVal": "D", "content": "$$1037090$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$$\\dfrac{1}{2}(2019\\times2018-2018\\times2017+2017\\times2016-2016\\times2015+\\cdots$$$$+5\\times4-4\\times3+3\\times2-2\\times1)$$ $$= \\frac{1}{2}\\left (2 \\times 2018+2 \\times 2016+ \\cdots +2 \\times 4+2 \\times 2\\right )$$ $=\\left (2018+2016+\\cdots+4+2\\right )=1009\\times1010=1019090$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4821", "queId": "7f88a8336fea4cd5a09aa75fbf853acb", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Events D and E are independent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{P(E) = 0.12} "}], [{"aoVal": "B", "content": "\\textbf{P(E) = 0.4} "}], [{"aoVal": "C", "content": "\\textbf{P(D or E) = 0.28} "}], [{"aoVal": "D", "content": "\\textbf{P(D or E) = 0.72} "}], [{"aoVal": "E", "content": "\\textbf{P(D or E) = 0.9} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{Since D and E are independent, P(D ∩ E) = P(D)*P(E). So P(E) = 0.3.} \\textbf{P(D ∪ E) = P(D) + P(E) -- P(D ∩ E) = 0.6 +0.3 -0.18 = 0.72} "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4822", "queId": "766cd17eb08841dc8a80347960b06ab9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "13+4=, 87-17=． ", "answer_option_list": [[{"aoVal": "A", "content": "17, 80 "}], [{"aoVal": "B", "content": "18, 70 "}], [{"aoVal": "C", "content": "9,~~94 "}], [{"aoVal": "D", "content": "17, 70 "}], [{"aoVal": "E", "content": "20, 80 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["13+4=17 , 87-17=70 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4824", "queId": "7f8aca5b93b14c4c8a016282ff5eff43", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "If $2^{200}\\times4^{1000}\\times8^{40}=16^{}x$, then $x=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$295$$ "}], [{"aoVal": "B", "content": "$$520$$ "}], [{"aoVal": "C", "content": "$$570$$ "}], [{"aoVal": "D", "content": "$$580$$ "}], [{"aoVal": "E", "content": "$$620$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"], "answer_analysis": ["$2^{200} \\times 4^{1000} \\times 8^{40}=16^{200 \\div 4} \\times 16^{1000 \\div 2} \\times 2^{120}$$=16^{50} \\times 16^{500} \\times 16^{30}=16^{580}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4835", "queId": "ccb30a18efaa42e09662bcaae892da34", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the 100\\textsuperscript{th}~number in the arithmetic sequence $$1$$, $$5$$, $$9$$, $$13$$, $$17$$, $$21$$, $$25$$, $$\\cdots$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$397$$ "}], [{"aoVal": "B", "content": "$$399$$ "}], [{"aoVal": "C", "content": "$$401$$ "}], [{"aoVal": "D", "content": "$$403$$ "}], [{"aoVal": "E", "content": "$$405$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$$4$\\times$100-3=397$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4837", "queId": "453d105c08b94cd294dba4ba1eb7f238", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If $\\frac{1}{3}$ of all the ninth graders are paired with $\\frac{2}{5}$ of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy? (2015 AMC 8 Problems, Question \\#16) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{2}{15}$ "}], [{"aoVal": "B", "content": "$\\frac{4}{11}$ "}], [{"aoVal": "C", "content": "$\\frac{11}{30}$ "}], [{"aoVal": "D", "content": "$\\frac{3}{8}$ "}], [{"aoVal": "E", "content": "$\\frac{11}{15}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Let the number of sixth graders be $s$, and the number of ninth graders be $n$. Thus, $\\frac{n}{3}=\\frac{2 s}{5}$, which simplifies to $n=\\frac{6 s}{5}$. Since we are trying to find the value of $\\frac{\\frac{n}{3}+\\frac{2 s}{5}}{n+s}$, we can just substitute $\\frac{6 s}{5}$ for $n$ into the equation. We then get a value of $\\frac{\\frac{6 s}{5}\\cdot\\frac13+\\frac{2 s}{5}}{\\frac{6 s}{5}+s}=\\frac{\\frac{6 s+6 s}{15}}{\\frac{11 s}{5}}=\\frac{\\frac{4 s}{5}}{\\frac{11 s}{5}}=\\frac{4}{11}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4838", "queId": "40e4dd5fe8fe400eb9874907f5aa80a2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Line $l\\_1$ has equation $3 x-2 y=1$ and goes through $A=(-1,-2)$. Line $l\\_2$ has equation $y=1$ and meets line $l\\_1$ at point $B$. Line $l\\_3$ has positive slope, goes through point $A$, and meets $l\\_2$ at point $C$. The area of $\\triangle A B C$ is $3$ . What is the slope of $l\\_3$? (2013 AMC 12B Problems, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac23$$ "}], [{"aoVal": "B", "content": "$$\\frac34$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$\\frac43$$ "}], [{"aoVal": "E", "content": "$$\\frac32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Line $l\\_1$ has the equation $y=\\frac{3x}{2}-\\frac12$ when rearranged. Substituting $1$ for $y$, we find that line $l\\_2$ will meet this line at point $(1,1)$, which is point $B$. We call $\\overline{B C}$ the base and the altitude from $A$ to the line connecting $B$ and $C, y=1$, the height. The altitude has length $\\textbar-2-1\\textbar=3$, and the area of $\\triangle A B C=3$. Since $A=\\frac{bh}{2}, b=2$. Because $l\\_3$ has positive slope, it will meet $l\\_2$ to the right of $B$, and the point that is $2$ to the right of $B$ is $(3,1)$. $l\\_3$ passes through $(-1,-2)$ and $(3,1)$, and thus has slope $\\frac{\\textbar1-(-2)\\textbar}{\\textbar3-(-1)\\textbar}=(\\mathbf{B}) \\frac{3}{4}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4839", "queId": "7f9156aa16424adf8625d30d47ca0e17", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$1+2+3+4+996 +997+998 + 999 =$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$3998$$ "}], [{"aoVal": "B", "content": "$$3999$$ "}], [{"aoVal": "C", "content": "$$4000$$ "}], [{"aoVal": "D", "content": "$$4001$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["This is $$(1+999)+(2+998)+(3+997)+(4 +996) = 4000$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4842", "queId": "9a234b606b824d1aa4630a08e1ae0b02", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following equations are not equivalent to $x+3=11$ ", "answer_option_list": [[{"aoVal": "A", "content": "$x+3+5=11+5$ "}], [{"aoVal": "B", "content": "$2x=28$ "}], [{"aoVal": "C", "content": "$x+3-11=11-11$ "}], [{"aoVal": "D", "content": "$x+3-11=0$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["Equations are equivalent when you can obtain one by subtracting, adding, dividing, or multiplying the same number on the other. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4849", "queId": "faea232f4bf24bb2991d71452f794503", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $18$ bottles of water in each of $10$ boxes. Six customers want to buy some botlles of water. Four of them buy $30$ bottles of water, and two of them buy $20$ bottles of water. How many bottles of water are left in the boxes ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$35$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$18 \\times 10 - 30 \\times 4 - 20 \\times 2 = 20$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4858", "queId": "49a22cd4d9214ce8b69130a5543e22ed", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Erik and Ivy each writes down a fraction. They are surprised to find that the fractions they write are very similar: the denominator of each fraction is exactly the same as the other\\textquotesingle s numerator. What is the product of the two fractions? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$\\frac12$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "It cannot be determined. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["Their fractions are just reciprocal of the other one. Thus, the product of the two fractions should be $1.$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4862", "queId": "d5ee3673c5844873a43dc3b78718151c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$x+2 = y$$ and $$y+4x = 12$$, then $$x=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$x+2=y$$, then $$x=y-2$$. We can get $$y+4(y-2)=12$$, $$y=4$$, $$x=y-2=2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4864", "queId": "45534f4deba54ae588682a873febbdbe", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$100001^{2}$$ exceeds $$100000^{2}$$ by． ", "answer_option_list": [[{"aoVal": "A", "content": "$$200001$$ "}], [{"aoVal": "B", "content": "$$100001$$ "}], [{"aoVal": "C", "content": "$$200001\\times 10^{6}$$ "}], [{"aoVal": "D", "content": "$$100001\\times 10^{6}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas-> Difference of Two Squares Formula"], "answer_analysis": ["$$100001^{2}-100000^{2}=10000200001-10000000000=200001$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4872", "queId": "56f76ef1144d480a9ab1d7d2b1de38c5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that $$1^{2}+2^{2}+3^{2}+\\cdots +n^{2}=\\frac{n(n+1)(2n+1)}{6}$$, then $$1^{2}+2^{2}+3^{2}+\\cdots +18^{2}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2016$$ "}], [{"aoVal": "B", "content": "$$2107$$ "}], [{"aoVal": "C", "content": "$$2018$$ "}], [{"aoVal": "D", "content": "$$2109$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas->1²+2²+3²+......+n²=1/6n(n+1)(n+2)"], "answer_analysis": ["Directly substitute $$n$$ with $$18$$ into the formula to get $$1^{2}+2^{2}+3^{2}+\\cdots +18^{2}=\\frac{18\\times 19\\times 37}{6}=2109$$. So the answer is $$\\text{D}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4884", "queId": "4e2807601af34811ba56d7dc62239684", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For how many integers $x$ is the number $x^{4}-25 x^{2}+24$ negative? ( 2014 AMC 10B Problems, Question \\#20) ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["First, note that $24+1=25$, which motivates us to factor the polynomial as $\\left(x^{2}-24\\right)\\left(x^{2}-1\\right)$. Since this expression is negative, one term must be negative and the other positive. Also, the first term is obviously smaller than the second, so $x^{2}-24\\textless0\\textless x^{2}-1$. Solving this inequality, we find $1\\textless x^{2}\\textless24$. There are exactly $6$ integers $x$ that satisfy this inequality, $\\pm\\textbackslash{2,3,4\\textbackslash}$. Thus our answer is $(\\mathbf{B}) 6$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4887", "queId": "529666b70e2943428ffcacdb9b9a3873", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a class of $$40$$ pupils, there are $$10$$ more boys than girls. What is the ratio of the number of girls to the number of boys? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5:3$$ "}], [{"aoVal": "B", "content": "$$3:1$$ "}], [{"aoVal": "C", "content": "$$1:3$$ "}], [{"aoVal": "D", "content": "$$3:5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["Total people $=2u+10=40$ $2u=40-10=30$ Girls $=1u=30\\div2=15$ Boys $=1u+10=15+10=25$ Girls $:$ Boys $\\to$ $15:25$ $\\to$ $3:5$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4888", "queId": "5702f88291f54f14847696374af298f4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the largest factor of $$2^{2}\\times3^{3} \\times5^{5} \\times7^{7}\\times11^{11}$$ less than $$100$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$66$$ "}], [{"aoVal": "B", "content": "$$77$$ "}], [{"aoVal": "C", "content": "$$88$$ "}], [{"aoVal": "D", "content": "$$99$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["The largest two-digit factor is $$3^{2} \\times11 = 99$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4891", "queId": "768d589856c14993bcd137588c800c05", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The following are the weights (in pounds) of seven people: $100, 115, 135, 140, 180, 197, 230$. Find the $36$-th percentile. ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$115$$ "}], [{"aoVal": "C", "content": "$$125$$ "}], [{"aoVal": "D", "content": "$$135$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$np=7(0.36)=2.52 \\uparrow 3$. The $36$-th percentile is $135$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4892", "queId": "5706875e296f4de3b4dcfd5d3abe8d44", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Given that $\\frac{2}{5}(2x-3)+\\frac{4}{11}x-\\frac{6}{11}=0$. The solution is $x=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{2}$ "}], [{"aoVal": "B", "content": "$\\frac{3}{2}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{5}$ "}], [{"aoVal": "D", "content": "$\\frac{7}{55}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$\\frac{2}{5}(2x-3)+\\frac{4}{11}x-\\frac{6}{11}=0$ $\\frac{2}{5}(2x-3)+\\frac{2}{11}(2x-3)=0$ $(\\frac{2}{5}+\\frac{2}{11})(2x-3)=0$ $2x-3=0$ $x=\\frac{3}{2}$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4899", "queId": "7b19cb1b305641b08ce555bac432ab79", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following pairs is a solution of $$\\begin{cases}2x-4=0 \\textbackslash\\textbackslash{} 4x-y=7 \\end{cases}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "($x$,$y$)=($2$,$-1$) "}], [{"aoVal": "B", "content": "($x$,$y$)=($2$,$1$) "}], [{"aoVal": "C", "content": "($x$,$y$)=($-2$,$1$) "}], [{"aoVal": "D", "content": "($x$,$y$)=($-2$,$-1$) "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables"], "answer_analysis": ["$x=2$ $8-y=7$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4901", "queId": "5b7ae286f03040fca7389a8c4f851c19", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which one is an equivalent fraction of $$\\frac{16}{24}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{8}{16}$$ "}], [{"aoVal": "B", "content": "$$\\frac{2}{3}$$ "}], [{"aoVal": "C", "content": "$$\\frac{4}{20}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions->Properties of Fractions"], "answer_analysis": ["$$\\frac{16}{24}=\\frac{8\\times 2}{8\\times 3}=\\frac{2}{3}$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4903", "queId": "45779d2b9fbf46e3ae9126cdaf96ccfc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the product of $$272$$ and $$3$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$68$$ "}], [{"aoVal": "B", "content": "$$168$$ "}], [{"aoVal": "C", "content": "$$270$$ "}], [{"aoVal": "D", "content": "$$816$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division", "Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Multiplication of Whole Numbers->Multiplication of Multi-Digit Numbers and 1-Digit Numbers->Multiplication of 3-Digit and 1-Digit (with regrouping for more than once)"], "answer_analysis": ["Stack the two numbers as shown below ,~ lining up the unit digits Remember that the 7 in 272 stands for 7 tens(70) ,the first 2 in the 272 stands for 2 hundreds(200) First, multiply the ones~ $2\\times3=6$~, regroup the 0 tens to the tens column Write ~6 in the ones place. Then,~ Multiply and add the tens .~$3\\times7+0=21$ Write 1 in the tens place and regroup the 2 hundreds. Last, multiply and add the hundreds.~$3\\times2+2=8$ Write 8 in the hundreds place "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4905", "queId": "7fae642840794424bf6abcac2ad9e973", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\dfrac{5}{14}\\div \\dfrac{10}{21}=$$~\\uline{~~~~~~~~~~}~，$$\\dfrac{4}{15}\\div \\dfrac{28}{45}=$$~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\dfrac{3}{4}$$，$$\\dfrac{4}{7}$$． "}], [{"aoVal": "B", "content": "$$\\dfrac{3}{5}$$，$$\\dfrac{3}{7}$$． "}], [{"aoVal": "C", "content": "$$\\dfrac{3}{4}$$，$$\\dfrac{3}{7}$$． "}], [{"aoVal": "D", "content": "$$\\dfrac{3}{5}$$，$$\\dfrac{4}{7}$$． "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$\\dfrac{5}{14}\\div \\dfrac{10}{21}=\\dfrac{5}{7\\times 2}\\times \\dfrac{3\\times 7}{2\\times 5}=\\dfrac{3}{4}$$． $$\\dfrac{4}{15}\\div \\dfrac{28}{45}=\\dfrac{4}{15}\\times \\dfrac{3\\times 15}{7\\times 4}=\\dfrac{3}{7}$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4906", "queId": "769485d7ea4b445e906e623e0258367e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Teacher Jason leaves home every day at $8:00\\text{AM}$ to go to work. If he drives at an average speed of $40$ km/h, he will be late by $3$ minutes. If he drives at an average speed of $60$ km/h, he will be early by $3$ minutes. How many km/h does Teacher Jason need to drive to get to work exactly on time? ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$55$$ "}], [{"aoVal": "E", "content": "$$58$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4907", "queId": "457c01b5fded4462a3a939a6e81a80b8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of these numbers is largest? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1.1$$ "}], [{"aoVal": "B", "content": "$$0.98$$ "}], [{"aoVal": "C", "content": "$$0.9$$ "}], [{"aoVal": "D", "content": "$$1.09$$ "}], [{"aoVal": "E", "content": "$$1.9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals->Comparing Decimals"], "answer_analysis": ["Nil "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4922", "queId": "ac99566111054331ad8ef7a3a2102658", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Fill ``$$+$$'' or ``$$-$$'' between neighbouring numbers to make the number statement correct. $$5$$ 　$$5$$ 　$$5$$ 　$$5$$　$$5$$ 　$$5=0$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$+$$；$$-$$；$$+$$；$$-$$；$$+$$ "}], [{"aoVal": "B", "content": "$$-$$；$$+$$；$$-$$；$$+$$；$$-$$ "}], [{"aoVal": "C", "content": "$$+$$；$$+$$；$$+$$；$$-$$；$$-$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$5-5+5-5+5-5=0$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4924", "queId": "9a40729323fb45dc9f8a160a5fa661ed", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Find the value of the expression: $$3- \\frac{6}{1 \\times \\left (1+2\\right )}- \\frac{9}{\\left (1+2\\right ) \\times \\left (1+2+3\\right )}-\\frac{12}{\\left (1+2+3\\right ) \\times \\left (1+2+3+4\\right )}- \\cdots$$ $$- \\frac{60}{\\left (1+2+ \\cdots +19\\right ) \\times \\left (1+2+ \\cdots +20\\right )}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1}{60}$ "}], [{"aoVal": "B", "content": "$\\frac{1}{70}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{210}$ "}], [{"aoVal": "D", "content": "$\\frac{1}{380}$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4925", "queId": "648ab9b064284580944d7f73c95e3096", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the missing number: $$64 \\div 2 = 2 \\times $$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$64$$ "}], [{"aoVal": "D", "content": "$$128$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$64\\div2=32=2\\times16$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4928", "queId": "f6571e9692084416b68c5a4fa8b6a8d4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many real numbers $x$ satisfy the following equation: $$ (x^{2}+7)^{2} = 289$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4929", "queId": "8c841d72968743428d97068dd6f97cc1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Aline writes a correct calculation. Then she covers two digits which are the same with a sticker: [insert pic] What digit is under the stickers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns->Encryption and Decryption"], "answer_analysis": ["Two same digits that add up to \"4\" in the last digit, hence it must be either 2 or 7. If we try digit 2, 42+52=94, wrong. If we try digit 7, 27+57=104. correct. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4930", "queId": "6d91210f2b05414db5efe2cb8cf66354", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The number that is 8.9 larger than 1.2 is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7.7$$ "}], [{"aoVal": "B", "content": "$$9.1$$ "}], [{"aoVal": "C", "content": "$$9.7$$ "}], [{"aoVal": "D", "content": "$$10.1$$ "}], [{"aoVal": "E", "content": "$$9.9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Addition and Subtraction of Decimals"], "answer_analysis": ["$$1.2+8.9=10.1$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4936", "queId": "a37033a49e654e87b6dde5f32247e2a6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the value of $$\\left( 330+22 \\right)\\div 11$$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$23$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$34$$ "}], [{"aoVal": "D", "content": "$$52$$ "}], [{"aoVal": "E", "content": "$$54$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$$\\left( 330+22 \\right)\\div 11=352\\div 11=32$$. Alternatively, $$\\left(330 + 22 \\right)\\div 11 = 330 \\div 11 + 22 \\div 11= 30 + 2 = 32$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4940", "queId": "e3d4f71980834ae8bb5f25023a69417d", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Let $p, q$, and $r$ be the distinct roots of the polynomial $x^{3}-22 x^{2}+80 x-67$. It is given that there exist real numbers $A, B$, and $C$ such that $$ \\frac{1}{s^{3}-22 s^{2}+80 s-67}=\\frac{A}{s-p}+\\frac{B}{s-q}+\\frac{C}{s-r} $$ for all $s \\notin\\textbackslash{p, q, r\\textbackslash}$. What is $\\frac{1}{A}+\\frac{1}{B}+\\frac{1}{C}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$243$$ "}], [{"aoVal": "B", "content": "$$244$$ "}], [{"aoVal": "C", "content": "$$245$$ "}], [{"aoVal": "D", "content": "$$246$$ "}], [{"aoVal": "E", "content": "$$247$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Proportional Equations"], "answer_analysis": ["Multiplying both sides by $(s-p)(s-q)(s-r)$ yields $$ 1=A(s-q)(s-r)+B(s-p)(s-r)+C(s-p)(s-q) $$ As this is a polynomial identity, and it is true for infinitely many $s$, it must be true for all $s$ (since a polynomial with infinitely many roots must in fact be the constant polynomial 0$)$. This means we can plug in $s=p$ to find that $\\frac{1}{A}=(p-q)(p-r)$. Similarly, we can find $\\frac{1}{B}=(q-p)(q-r)$ and $\\frac{1}{C}=(r-p)(r-q)$. Summing them up, we get that $$ \\frac{1}{A}+\\frac{1}{B}+\\frac{1}{C}=p^{2}+q^{2}+r^{2}-p q-q r-p r $$ By Vieta\\textquotesingle s Formulas, we know that $p^{2}+q^{2}+r^{2}=(p+q+r)^{2}-2(p q+q r+p r)=324$ and $p q+q r+p r=80$. Thus the answer is $324-80=$ 244 . "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4945", "queId": "a37422fc401041cbbc54866c77ecfad8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There were four piles of strawberries and a rabbit wanted to eat some. Each pile had $24$ strawberries. The rabbit ate a few strawberries from the first pile and then ate as many strawberries from the third pile as were left in the first pile. After that the rabbit ate a few strawberries from the second pile and then ate as many strawberries from the fourth pile as were left in the second pile. How many strawberries in total did the rabbit eat? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$48$$ "}], [{"aoVal": "E", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$24 \\times 4 \\div 2 = 48$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4950", "queId": "5b9ee8e97a6d450e88e7b54d7476b750", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Consider the set of all fractions $\\frac{x}{y}$, where $x$ and $y$ are relatively prime positive integers. How many of these fractions have the property that if both numerator and denominator are increased by $1$, the value of the fraction is increased by $10 \\textbackslash\\%$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "infinitely many "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["You can create the equation $\\frac{x+1}{y+1}=\\frac{11 x}{10 y}$. Cross multiplying and combining like terms gives $x y+11 x-10 y=0$. This can be factored into $(x-10)(y+11)=-110$. $x$ and $y$ must be positive, so $x\\textgreater0$ and $y\\textgreater0$, so $x-10\\textgreater-10$ and $y+11\\textgreater11$. Using the factors of 110 , we can get the factor pairs: $(-1,110),(-2,55)$, and $(-5,22)$. But we can\\textquotesingle t stop here because $x$ and $y$ must be relatively prime. $(-1,110)$ gives $x=9$ and $y=99.9$ and 99 are not relatively prime, so this doesn\\textquotesingle t work. $(-2,55)$ gives $x=8$ and $y=44$. This doesn\\textquotesingle t work. $(-5,22)$ gives $x=5$ and $y=11$. This does work. We found one valid solution so the answer is (B)$1$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4952", "queId": "e3d72fb76dc944c5b6987f79b5d47fd7", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had sabing $20$ days? (2015 AMC 8 Problems, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$39$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$210$$ "}], [{"aoVal": "D", "content": "$$400$$ "}], [{"aoVal": "E", "content": "$$401$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables"], "answer_analysis": ["We can easily find out she makes $2 \\cdot 20-1=39$ widgets on Day $20$ . Then, we make the sum of $1,3,5, \\ldots \\ldots, 35,37,39$ by adding in this way: $(1+39)+(3+37)+(5+35)+\\ldots+(19+21)$, which include $10$ pairs of $40$ . So the sum of $1,3,5, \\ldots \\ldots \\ldots 39$ is $(40 \\cdot 10)=(\\text{D}) 400$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4953", "queId": "c39923283e9f46b888de543c0ae462db", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Three fifths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 6 cups. What percent of the total capacity of the pitcher did each cup receive?~ (adapted from 2020 AMC 8, Question \\#5) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["The pitcher is $\\frac{3}{5}$ full, i.e. $60 \\textbackslash\\%$ full. Therefore each cup receives $\\frac{60}{6}=(\\mathbf{C}) 10$ percent of the total capacity. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4955", "queId": "5ba38c5be8c24e249335a56e247ddbfc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Observe the characteristics of the numbers given and write the numbers underlined below.~(adapted from $$2006$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$8$$) $$3$$~ ~ $$4$$~ ~ $$7$$~ ~ $$11$$~ ~$18$~\\uline{~~~~~~~~~~}~$47$~ ~$76$~ ~$123$~ $$\\cdots$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences->Concepts of Arithmetic Sequences"], "answer_analysis": ["The sum of the first digit and the second digit is the third digit, and so on. The horizontal line is $11+18=29$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4956", "queId": "6da031e1bc3c430ea0e4e32d9a3ec48c", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $8^{\\text {th }}$-graders to $6^{\\text {th }}$-graders is $11: 6$, and the the ratio of $8^{\\text {th }}$-graders to $7^{\\text {th }}$ graders is $8: 13$. What is the smallest number of students that could be participating in the project? (2013 AMC 8, Question 16) ", "answer_option_list": [[{"aoVal": "A", "content": "$$44$$ "}], [{"aoVal": "B", "content": "$$84$$ "}], [{"aoVal": "C", "content": "$$107$$ "}], [{"aoVal": "D", "content": "$$150$$ "}], [{"aoVal": "E", "content": "$$214$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["We multiply the first ratio by 4 on both sides, and the second ratio by 3 to get the same number for 8 th graders, in order that we can put the two ratios together: $$ \\begin{aligned} \\&11: 6=11(4): 6(4)=44: 24 \\textbackslash\\textbackslash{} \\&8: 13=8(3): 13(3)=24: 39 \\end{aligned} $$ Therefore, the ratio of 8th graders to 7th graders to 6th graders is $44: 24: 39$. Since the ratio is in lowest terms, the smallest number of students participating in the project is $$ 44+24+39=\\text { (C) } 107 $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4961", "queId": "5ba80f8e390f4e3b873a50870206bd0f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Let $f$ be a linear function for which $f(5)-f(2)=10$. What is $f(8)-f(2)$? ( Adapted From 2003 AMC 12B Problems, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$22$$ "}], [{"aoVal": "E", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Let $f$ be a linear function with slope $m$. $$ \\begin{gathered} m=\\frac{f(5)-f(2)}{\\Delta x}=\\frac{10}{5-2}=\\frac{10}{3} \\textbackslash\\textbackslash{} f(8)-f(2)=m \\Delta x=\\frac{10}{3}(8-2)=20 \\Rightarrow(C) \\end{gathered}$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4962", "queId": "bf05a1b823984a0ea3ef68cc8c19a8f9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many odd numbers are there? 1, 3, 4, 6, 7, 9, 5, 8. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$Omitted.$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4965", "queId": "45b425e4519a4b3aa8e5e6a772ad6af6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "For how many integers $x$ is the number $x^{4}-51 x^{2}+50$ negative? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["First, note that $50+1=51$, which motivates us to factor the polynomial as $\\left(x^{2}-50\\right)\\left(x^{2}-1\\right)$. Since this expression is negative, one term must be negative and the other positive. Also, the first term is obviously smaller than the second, so $x^{2}-50\\textless0\\textless x^{2}-1$. Solving this inequality, we find $1\\textless x^{2}\\textless50$. There are exactly 12 integers $x$ that satisfy this inequality, $\\pm\\textbackslash{2,3,4,5,6,7\\textbackslash}$. Thus our answer is $(\\mathbf{C}) 12$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4966", "queId": "95b8fcd9efa34ec5971e7490e2b2738b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The following are the heights (in cm) of eight people: $157$, $175$, $165$, $184$, $180$, $197$, $160$, $177$. Find the $42$-th percentile. ", "answer_option_list": [[{"aoVal": "A", "content": "$$165$$ "}], [{"aoVal": "B", "content": "$$175$$ "}], [{"aoVal": "C", "content": "$$177$$ "}], [{"aoVal": "D", "content": "$$180$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Arrange the data from the least to the largest: $157$, $160$, $165$, $175$, $177$, $180$, $184$, $197$. $np=8(0.42)=3.36 \\uparrow 4$. The $42$-th percentile is $175$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4971", "queId": "df39c160999e4bb1a1b71d5a76445e77", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$x+2 = y$$ and $$y+4x = 12$$, then $$x=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables"], "answer_analysis": ["If $$x+2=y$$, then $$x=y-2$$. We can get $$y+4(y-2)=12$$ implying that $$y=4$$ and hence $$x=y-2=2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4973", "queId": "d16acd8cb3f648a2868694010d9a53f2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is approximately normal with mean 100 years and standard deviation 15 years. Based on the estimate, which of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the distribution?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{80 years} "}], [{"aoVal": "B", "content": "\\textbf{115 years} "}], [{"aoVal": "C", "content": "\\textbf{120 years} "}], [{"aoVal": "D", "content": "\\textbf{125 years} "}], [{"aoVal": "E", "content": "\\textbf{130 years} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{P(X\\textgreater x) = 0.9~} \\textbf{P(Z\\textgreater$$\\frac{x-100}{15}$$) = 0.9} \\textbf{$$\\frac{x-100}{15}$$ = 1.29} \\textbf{X = 119.35} "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4976", "queId": "aca6da0a75d34e0a91e1ebd56de813f9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of three numbers is $96$. The first number is $6$ times the third number, and the third number is $40$ less than the second number. What is the absolute value of the difference between the first and second numbers? (2022 AMC 10A Problems, Question \\#3) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Let $x$ be the third number. It follows that the first number is $6 x$, and the second number is $x+40$. We have $$ 6 x+(x+40)+x=8 x+40=96, $$ from which $x=7$. Therefore, the first number is $42$ , and the second number is $47$ . Their absolute value of the difference is $\\textbar42-47\\textbar=(\\mathbf{E}) 5$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4979", "queId": "5bafb288f42b4e21acfa112bd70d4993", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "$7$ less than $32$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$27$$ "}], [{"aoVal": "C", "content": "$$25$$ "}], [{"aoVal": "D", "content": "$$28$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$32-7=25$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4984", "queId": "7fd1b4e51adb4efca7564e586e6bdd7c", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following expression is written correctly? ", "answer_option_list": [[{"aoVal": "A", "content": "$3 \\times x+4$ "}], [{"aoVal": "B", "content": "$x \\times y+z$ "}], [{"aoVal": "C", "content": "$6a+b$ "}], [{"aoVal": "D", "content": "$3a+b \\times c$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["Only $ \\text C$ is in accordance with the rules of writing expression. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4991", "queId": "c3a071b6f2d44627bf065d4a39da086b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What should be the last number in the series be? $$1$$, $$2$$, $$5$$, $$10$$, $$17$$, $$26$$, ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$35$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$47$$ "}], [{"aoVal": "D", "content": "$$37$$ "}], [{"aoVal": "E", "content": "$$33$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["$$+1$$, $$+3$$, $$+5$$, $$+7$$, $$+9$$, $$+11$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "4997", "queId": "692f56a669d74e309f5b7dbddf797ca1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is the largest fraction? $$\\dfrac{2}{15}$$,$$\\dfrac{11}{15}$$,$$\\dfrac{7}{15}$$,$$\\dfrac{4}{15}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\dfrac{2}{15}$$ "}], [{"aoVal": "B", "content": "$$\\dfrac{11}{15}$$ "}], [{"aoVal": "C", "content": "$$\\dfrac{7}{15}$$ "}], [{"aoVal": "D", "content": "$$\\dfrac{4}{15}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["Same denominator, so larger numerator means larger fraction "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5000", "queId": "6930ccef953143588ad54f133ae192c3", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{One of the values in a normal distribution is 43, and its z-score is 1.65. If the mean of the distribution is 40, what is the standard deviation of the distribution?} ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$-1.82$$ "}], [{"aoVal": "C", "content": "$$0.55$$ "}], [{"aoVal": "D", "content": "$$1.82$$ "}], [{"aoVal": "E", "content": "$$-0.55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{Z = 1.65 = $\\frac{43-40}{\\sigma}$ → $\\sigma = \\frac{3}{1.65}=1.82$} "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5004", "queId": "5bbdcc0a47124ad5adcfb91f226c8e8a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the ones digit of $$2015^{2015}+2016^{2016}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["The ones digit of $$2015^{2015}+ 2016^{2016}$$ is the same as that of $$5+ 6$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5013", "queId": "6939fde064514002a7c868babd0c8e38", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Joe writes an expression $\\frac59\\times\\frac9{13}\\times\\frac{13}{17}\\cdots $ Following the pattern, he writes the expression with $\\frac{45}{49}$ as the multiplier in the middle. What is the result of the expression? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac5{49}$ "}], [{"aoVal": "B", "content": "$\\frac5{89}$ "}], [{"aoVal": "C", "content": "$\\frac5{17}$ "}], [{"aoVal": "D", "content": "$\\frac1{31}$ "}], [{"aoVal": "E", "content": "$\\frac5{81}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["The last fraction should be $\\frac{85}{89}$, so the answer is $\\frac5{89}.$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5024", "queId": "4a2d89130c8547f0b455a1b5bc08054c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $\\frac{2022+4567\\times 7890}{4568\\times 7890 - 5778}$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["A "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5038", "queId": "7fe5a895ef6a4a3785f0bc4240bb7002", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$1+3+5+7+9+ 11 + 13+ 15+17 +19=$~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$80$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$121$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$1+3+5+7+9+ 11 + 13+ 15+17 +19=10^{2}=100$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5039", "queId": "913cb9615d01470590dd1d19d3d8f9d7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The most likely height of a single-decker bus is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.25\\rm cm$$ "}], [{"aoVal": "B", "content": "$$2.5\\rm cm$$ "}], [{"aoVal": "C", "content": "$$25\\rm cm$$ "}], [{"aoVal": "D", "content": "$$250\\rm cm$$ "}], [{"aoVal": "E", "content": "$$2500\\rm cm$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Length"], "answer_analysis": ["omitted "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5044", "queId": "5bd1f63ea361415b85a466770b7ee6ee", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\frac{1}{2}~ (19 \\times 18-18 \\times 17+17 \\times 16-16 \\times 15+\\cdots$$$$ +5\\times4-4\\times3 +3\\times2-2\\times1 )$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$80$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$110$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$\\dfrac{1}{2}(19\\times18-18\\times17+17\\times16-16\\times15+\\cdots$$$$+5\\times4-4\\times3+3\\times2-2\\times1)$$ $$=\\dfrac{1}{2} (2(18) + 2(16) + \\cdots + 2(2))$$ $$= 18 + 16 + 14 +\\cdots + 2$$ $$= 2(1 + 2 + \\cdots + 9)$$ $$= 2(45)$$ $$= 90$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5049", "queId": "c8479c81707343a7b466c172f9653ca7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Round $$398^{}\\circ \\rm C$$ to the nearest $$10^{}\\circ $$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$380^{}\\circ \\rm C$$ "}], [{"aoVal": "B", "content": "$$390^{}\\circ \\rm C$$ "}], [{"aoVal": "C", "content": "$$399^{}\\circ \\rm C$$ "}], [{"aoVal": "D", "content": "$$400^{}\\circ \\rm C$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Estimating Large Numbers"], "answer_analysis": ["Rounding, $$398^{}\\circ \\rm C$$ is closer to $$400^{}\\circ \\rm C$$ than to $$390^{}\\circ \\rm C$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5053", "queId": "9a66f27c3add4ac4b4031be8aeefad84", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "What is the median of the following list of 4040 numbers: $$ 1,2,3, \\ldots, 2020,1^{2}, 2^{2}, 3^{2}, \\ldots, 2020^{2}$$? (2020 AMC 10A Problems, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1974.5$$ "}], [{"aoVal": "B", "content": "$$1975.5$$ "}], [{"aoVal": "C", "content": "$$1976.5$$ "}], [{"aoVal": "D", "content": "$$1977.5$$ "}], [{"aoVal": "E", "content": "$$1978.5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["We want to know the $2020$-th term and the $2021$-st term to get the median. We know that $44^{2}=1936$. So, numbers $1^{2}, 2^{2}, \\ldots, 44^{2}$ are in between $1$ and $1936$. So, the sum of $44$ and $1936$ will result in $1980$ , which means that $1936$ is the $1980$-th number. Also, notice that $45^{2}=2025$, which is larger than $2021$. Then the $2020$-th term will be $1936+40=1976$, and similarly the $2021$-th term will be $1977$. Solving for the median of the two numbers, we get (C) $1976.5$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5066", "queId": "5312fc2d748642afb9e6e82f5cc9abe0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Big Al, the ape, ate $100$ bananas from May $1$ through May $5$ . Each day he ate six more bananas than on the previous day. How many bananas did Big Al eat on May $5$ ? (2005 AMC 8 Problems, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$32$$ "}], [{"aoVal": "E", "content": "$$34$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating"], "answer_analysis": ["There are $5$ days from May $1$ to May $5$ . If we set the first day as $n$, the second day can be expressed as $n+6$, the third as $n+12$, and so on, for five days. The sum $n+(n+6)+(n+12)+(n+18)+(n+24)$ is equal to $100$ , as stated in the problem. We can write a very simple equation, that is: $5 n+60=100$. Now all we do is just solve. $5 n=40$, so Big Al eats 8 bananas on the first day. The fifth day, $n+24$, is then 32 , which is your answer. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5072", "queId": "4a529325047547f3aefec8516f7148cc", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all its side lengths are integer. The primeter of $\\triangle ABC$ with a side of length $2$ and a side length of $5$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+2\\textgreater5$. Therefore, $P\\textgreater5+5$. The least integer value of $P$ is $11$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5084", "queId": "72634a0b952e4932a54b593741df7673", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "One basket can contain no more than $5$ eggs. What is the smallest number of baskets needed to contain $37$ eggs? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$37\\div5=7R2$ $7+1=8$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5093", "queId": "8cbe51e59d244dcdaecd5f0e0be067e5", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Let $f(x)=a x^{2}+b x+c$, where $a, b$, and $c$ are integers. Suppose that $f(1)=0,50\\textless f(7)\\textless60,70\\textless f(8)\\textless80$, $5000 k\\textless f(100)\\textless5000(k+1)$ for some integer $k$. What is $k$? (2011 AMC 12A Problems, Question 20) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["From $f(1)=0$, we know that $a+b+c=0$. From the first inequality, we get $50\\textless49 a+7 b+c\\textless60$. Subtracting $a+b+c=0$ from this gives us $50\\textless48 a+6 b\\textless60$, and thus $\\frac{25}{3}\\textless8 a+b\\textless10$. Since $8 a+b$ must be an integer, it follows that $8 a+b=9$. Similarly, from the second inequality, we get $70\\textless64 a+8 b+c\\textless80$. Again subtracting $a+b+c=0$ from this gives us $70\\textless63 a+7 b\\textless80$, or $10\\textless9 a+b\\textless\\frac{80}{7}$. It follows from this that $9 a+b=11$. We now have a system of three equations: $a+b+c=0,8 a+b=9$, and $9 a+b=11$. Solving gives us $(a, b, c)=(2,-7,5)$ and from this we find that $f(100)=2(100)^{2}-7(100)+5=19305$. Since $15000\\textless19305\\textless20000 \\rightarrow 5000(3)\\textless19305\\textless5000(4)$, we find that $k=3 \\rightarrow(\\mathbf{C}) 3$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5099", "queId": "6de6b582d02044e2859e92d75e66ae08", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of the tenths and the hundredths digits in the num-ber $$12345.6789$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Addition and Subtraction of Decimals"], "answer_analysis": ["The tenths digit is $$6$$ and the hundredths digit is $$7$$. Their sum is $$13$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5106", "queId": "4ec9893f1ba7453a8307290c8a2fa9e7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$3.87+4.62+6.13+5.38=$$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$19$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$21$$ "}], [{"aoVal": "D", "content": "$$22$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals"], "answer_analysis": ["$$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde3.87+4.62+6.13+5.38$$ $$=(3.87+6.13)+(4.62+5.38)$$ $$=10+10$$ $$=20$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5107", "queId": "b5f4f203c3d34c8195b9ea0245a420ec", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Find the difference between $$\\frac{5}{9}$$ and $$\\frac{1}{3}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{4}{6}$$ "}], [{"aoVal": "B", "content": "$$\\frac{2}{9}$$ "}], [{"aoVal": "C", "content": "$$\\frac{4}{9}$$ "}], [{"aoVal": "D", "content": "$$\\frac{2}{3}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5109", "queId": "532fcf819ff84b9d9cf36c037cf31cf8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the arithmetic sequence $5$, $7$, $9$, $11$ $\\cdots$ , the $9$\\textsuperscript{th} term is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$19$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["Observe that each number is the sum of the number of previous term and the difference between adjacent numbers. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5110", "queId": "7b7ab626944c46d5a1bf3fe8d5f49f6d", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A 95\\% confidence interval for the difference between two population proportions is found to be (0.07, 0.19). Which of the following statement is (are) true? I. It is unlikely that the two populations have the same proportions. II. We are 95\\% confidence that the true difference between population proportions is between 0.07 and 0.19. III. The probability is 0.95 that the true difference between the population proportions is between 0.07 and 0.19. ", "answer_option_list": [[{"aoVal": "A", "content": "I "}], [{"aoVal": "B", "content": "II "}], [{"aoVal": "C", "content": "I, II "}], [{"aoVal": "D", "content": "I, III "}], [{"aoVal": "E", "content": "II, III "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Because 0 is not in the interval (0.07, 0.19). It is unlikely to be the true difference between the proportions. III is just plain wrong! We cannot make a probability statement about an interval we have already constructed. All we can say is that the process used to generate this interval has a 0.95 chance of producing an interval that does contain the true population proportion. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5121", "queId": "acce38f7db4a4a35afdca0e8d4f8ddaf", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The following are the weights (in pounds) of seven people: $100, 115, 135, 140, 180, 197, 230$. Find the $36$-th percentile. ", "answer_option_list": [[{"aoVal": "A", "content": "$$180$$ "}], [{"aoVal": "B", "content": "$$115$$ "}], [{"aoVal": "C", "content": "$$135$$ "}], [{"aoVal": "D", "content": "$$140$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$np=7(0.36)=2.52 \\uparrow 3$ The $36$-th percentile is $135$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5122", "queId": "57a24e161db644c2bb33599df908d2e3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\frac{4}{9}\\div \\frac{1}{4}=$$~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{9}$$ "}], [{"aoVal": "B", "content": "$$\\frac{16}{9}$$ "}], [{"aoVal": "C", "content": "$$\\frac{2}{9}$$ "}], [{"aoVal": "D", "content": "$$\\frac{8}{9}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$\\frac{4}{9}\\div \\frac{1}{4}=\\frac{4}{9}\\times \\frac{4}{1}=\\frac{16}{9}$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5123", "queId": "64fab7ee7e744c999025147cb5a862ce", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $x\\textgreater0$, which of the following is equivalent to $\\sqrt[3]{x^{4}}$ ? $ $ $I. x+x^{\\frac{1}{3}}$ $ $ $II. \\left(x^{\\frac{1}{3}}\\right)^{4}$ $ $ $III. x^{2}\\left(x^{-\\frac{2}{3}}\\right)$ ", "answer_option_list": [[{"aoVal": "A", "content": "None "}], [{"aoVal": "B", "content": "$I$ and $II$ only "}], [{"aoVal": "C", "content": "$II$ and $III$ only "}], [{"aoVal": "D", "content": "$I$, $II$, and $III$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$\\sqrt[3]{x^{4}}$ can be written as $x^{}\\frac{4}{3}$, which is equivalent to II and III. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5133", "queId": "608a48f1388a48889a38d941d0768a93", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "What is the $$30$$th term of the following arithmetic sequence $$1, 4, 7, 10, \\cdots$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$82$$ "}], [{"aoVal": "B", "content": "$$85$$ "}], [{"aoVal": "C", "content": "$$88$$ "}], [{"aoVal": "D", "content": "$$91$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$$1+(30-1)\\times 3=88$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5134", "queId": "4ee6e129a6e846e99a431d462f56ce87", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many digits are there in the correct answer to the calculation $$123123123123\\div 123$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["The correct answer to the calculation $$123123123123\\div123=1001001001$$. This has $$10$$ digits. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5141", "queId": "b169f16c08e94d48bf3abcdbb1f936b7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A computer makes $$4\\times {{10}^{9}}$$ operations per second. How many operations does it make in $$5\\times {{10}^{2}}$$ seconds? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4\\times {{10}^{11}}$$ "}], [{"aoVal": "B", "content": "$$2\\times {{10}^{11}}$$ "}], [{"aoVal": "C", "content": "$$2\\times {{10}^{12}}$$ "}], [{"aoVal": "D", "content": "$$20\\times {{10}^{18}}$$ "}], [{"aoVal": "E", "content": "$$2\\times {{10}^{19}}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas"], "answer_analysis": ["$$4\\times {{10}^{9}}\\times 5\\times {{10}^{2}}$$ $$=20\\times {{10}^{11}}$$ $$=2\\times {{10}^{12}}$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5145", "queId": "8cd965d078e14b50b8debdedfc2e437f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Kitty writes down a sequence of five integers. The rule she uses is, \"after the first two terms, each term is the sum of the two previous terms.\" Her sequence is ---, ---, ---, ~$$18$$, $$29$$. What is her first term? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0 $$ "}], [{"aoVal": "B", "content": "$$ 3 $$ "}], [{"aoVal": "C", "content": "$$ 4 $$ "}], [{"aoVal": "D", "content": "$$ 5 $$ "}], [{"aoVal": "E", "content": "$$ 7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["Let the first six terms of Kitty\\textquotesingle s sequence be $$a$$, $$b$$, $$c$$, $$18$$ and $$29$$ respectively. Then $$c+ 18= 29$$, so $$c= 11$$. Hence $$b+11= 18$$, so $$b=7$$. Therefore, $$a+7=11$$, so $$a=4$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5154", "queId": "dac45af48645433fbdd72290ac6e5444", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Chantal and Jean start hiking from a trailhead toward a fire tower. Jean is wearing a heavy backpack and walks slower. Chantal starts walking $4$ miles per hour. Halfway to the tower, the trail becomes really steep, and Chantal slows down to $2$ miles per hour. After reaching the tower, she immediately turns around and descends the steep part of the trail at $3$ miles per hour. She meets Jean at the halfway point. What was Jean\\textquotesingle s average speed, in miles per hour, until they meet? (2021 AMC 10A Problems, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{12}{13}$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$\\frac{13}{12}$ "}], [{"aoVal": "D", "content": "$\\frac{24}{13}$ "}], [{"aoVal": "E", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Let $2 d$ miles be the distance from the trailhead to the fire tower, where $d\\textgreater0$. When Chantal meets Jean, the two have traveled for $$ \\frac{d}{4}+\\frac{d}{2}+\\frac{d}{3}=d\\left(\\frac{1}{4}+\\frac{1}{2}+\\frac{1}{3}\\right)=d\\left(\\frac{3}{12}+\\frac{6}{12}+\\frac{4}{12}\\right)=\\frac{13}{12} d $$ hours. At that point, Jean has traveled for $d$ miles, so his average speed is $\\frac{d}{\\frac{13}{12} d}=(\\mathbf{A}) \\frac{12}{13}$ miles per hour. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5155", "queId": "84a58bb8665d440db6cdba816650920d", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "After simplying the following expressions, which one is different from others? ", "answer_option_list": [[{"aoVal": "A", "content": "$(x+y)-(x-y)$ "}], [{"aoVal": "B", "content": "$(2x+3y)+(-2x-y)$ "}], [{"aoVal": "C", "content": "$(3x-2y)+(-3x+4y)$ "}], [{"aoVal": "D", "content": "$(x-y)+(-x+y)$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$(x+y)-(x-y)=2y$ $(2x+3y)+(-2x-y)=2x+3y-2x-y=2y$ $(3x-2y)+(-3x+4y)=3x-2y-3x+4y=2y$ $(x-y)+(-x+y)=x-y-x+y=0$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5162", "queId": "b607d20be652447c8d3b482c037c4c8d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$ 0.33 =$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3}{10}$$ "}], [{"aoVal": "B", "content": "$$\\frac{33}{100}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "D", "content": "$$\\frac{3}{8}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["$0.33 = 33\\div100 = \\dfrac{33}{100}$, so choice $\\text{B}$ is correct. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5169", "queId": "fb1e86abffe64f3f9aaffa966605e4d5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$81+72+63+54=9\\times $$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$9\\times 9+9\\times 8+9\\times 7+9\\times 6=9\\times~ \\left( {9+8+7+6} \\right) $$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5174", "queId": "ace25077dfa241c5b78d5e466d484fcb", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{From a random sample of 1,005 adults in the United States, it was found that 32 percent own an e-reader. Which of the following is the appropriate 90 percent confidence interval to estimate the proportion of all adults in the United States who own an e-reader?~} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{$0.32 \\pm 1.960(\\frac{(0.32)(0.68)}{\\sqrt{1,005}})$} "}], [{"aoVal": "B", "content": "\\textbf{$0.32 \\pm 1.645(\\frac{(0.32)(0.68)}{\\sqrt{1,005}})$} "}], [{"aoVal": "C", "content": "\\textbf{$0.32 \\pm 2.575\\sqrt{(\\frac{(0.32)(0.68)}{1,005})}$} "}], [{"aoVal": "D", "content": "\\textbf{$0.32 \\pm 1.960\\sqrt{(\\frac{(0.32)(0.68)}{1,005})}$} "}], [{"aoVal": "E", "content": "\\textbf{$0.32 \\pm 1.645\\sqrt{(\\frac{(0.32)(0.68)}{1,005})}$} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{$\\hat{p} \\pm z^{*}\\sigma\\_{\\hat{p}}=\\hat{p} \\pm Z\\_{\\frac{\\alpha}{2}}\\sqrt{\\frac{\\hat{p}(1-\\hat{p})}{n}}= 0.32 \\pm Z\\_{0.05}\\sqrt{\\frac{(0.32)(0.68)}{1005}}$} "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5181", "queId": "771c583ab02541f0898cdcd82695f81b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "~$\\dfrac{2022}{2021-\\dfrac{2020}{2019-\\dfrac{2018}{5-\\dfrac{4}{3-\\dfrac{2}{1}}}}}$$=$． ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{2022}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{2021}$ "}], [{"aoVal": "C", "content": "$$2022$$ "}], [{"aoVal": "D", "content": "$$2021$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions"], "answer_analysis": ["$$3- \\frac{2}{1}=1$$ $$5- \\frac{4}{1}=1$$ $$\\cdots \\cdots$$ $$2022- \\frac{2021}{1}=1$$ $$\\frac{2022}{1}=2022$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5182", "queId": "6529fd99a2f343f9b7a34562bede3505", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "It is known that the number $2017$ is placed at $M^{\\text{th}}$ row, $N^{\\text{th}}$ entry. Find the value of $M+N$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$126$$ "}], [{"aoVal": "B", "content": "$$127$$ "}], [{"aoVal": "C", "content": "$$128$$ "}], [{"aoVal": "D", "content": "$$129$$ "}], [{"aoVal": "E", "content": "$$130$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns of Number Tables->Triangle Number Table"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5189", "queId": "df644f5d9e5c483aadea0538c7e5ce3e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Definite @ as the operation of choosing the larger number between two numbers. Definite \\&~as the operation of choosing the smaller number between two numbers. Find the result of $(37$\\&$23)\\times(25$@$45)\\div(23$@$15)$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$23$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$225$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition"], "answer_analysis": ["$23\\times45\\div23=45$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5193", "queId": "5381eb90ac134a59b57491f5bb9eccfc", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Fill \"$$+$$\" or~\"$$-$$\" in the blanks to make the equation true.~\\uline{~~~~~~~~~~}~ $$6$$~~~~ $$6$$~~~~ $$6$$~~~~ $$6$$~~~~ $$6=6$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$+++-$$ "}], [{"aoVal": "B", "content": "$$++++$$ "}], [{"aoVal": "C", "content": "$$++-\\/-$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["$$6+6+6-6-6=6$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5194", "queId": "69ac9e85713643adb9eef84d39898003", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$2$$ dogs weigh as much as $$3$$ cats, and $$2$$ cats weigh as much as $$15$$ mice, how many dogs weigh as much as $$45$$ mice? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"], "answer_analysis": ["In weight, $$45$$ mice $$=3\\times (15$$ mice$$)=3\\times (2$$ cats$$)= 2\\times (3$$ cats$$)=2\\times (2$$ dogs$$)= 4$$ dogs. On Planet Pythagoras, the people use a different money system to us. two pog is worth six pings. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5196", "queId": "a3c495f593614e4aad86f50512b1e379", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$99+99+99+99+99+99+99+99+99+99=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$10\\times 99$$ "}], [{"aoVal": "B", "content": "$$10\\div 99$$ "}], [{"aoVal": "C", "content": "$$9\\times 99$$ "}], [{"aoVal": "D", "content": "$$99\\times 99$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["The sum of ten $$99$$\\textquotesingle s is the same as $$10\\times 99$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5197", "queId": "96105dc7f32743c289ee33886c42b3f0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$100-98+96-94+92-90+\\ldots +8-6+4-2+0=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$26$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$52$$ "}], [{"aoVal": "D", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$\\left( 100-98 \\right)+\\left( 96-94 \\right)+\\ldots +\\left( 8-6 \\right)+\\left( 4-2 \\right)+0=2\\times 25+0=50$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5203", "queId": "60c4a412adff447cba608175d26cc2b2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is $$4\\frac{7}{20}$$ as a decimal? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4.035$$ "}], [{"aoVal": "B", "content": "$$4.14$$ "}], [{"aoVal": "C", "content": "$$4.35$$ "}], [{"aoVal": "D", "content": "$$4.7$$ "}], [{"aoVal": "E", "content": "$$4.72$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["$$4\\frac{7}{20}=4\\frac{35}{100}=4.35$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5205", "queId": "b1814d3dba8b474cb130b8af0cfcecc7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When three positive integers $a$, $b$, and $c$ are multiplied together, their product is 100. Suppose $a \\textless{} b \\textless{} c$. In how many ways can the numbers be chosen? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5208", "queId": "8cf77b5c33b247c3bcb10ebb5dab7427", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $*abcd*=a\\times d+b\\times c$ ,then $*2543*=$ ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$120$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["$*2543*=2\\times3+5\\times4=6+20=26$. So the answer is $\\rm C$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5217", "queId": "5399be54a515483eb2172788816f733f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{According to a report for veterinarians in the United States, 36.5 percent of households in the United States own dogs and 30.4 percent of households in the United States own cats. If one household in the United States is selected at random, what is the probability that the selected household will own a dog or a cat?} ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.111$$ "}], [{"aoVal": "B", "content": "$$0.331$$ "}], [{"aoVal": "C", "content": "$$0.558$$ "}], [{"aoVal": "D", "content": "$$0.669$$ "}], [{"aoVal": "E", "content": "\\textbf{Not enough information is given to determine the probability} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{The sample in the report is about veterinarians. The population cannot be a household in the United States.} "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5225", "queId": "84c8c426ec3e4f5d8e3615a9a5dbd679", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "An amusement park has a collection of scale models, with ratio $1: 35$, of buildings and other sights from around the country. If the height of a signal tower is $2250$ feet. What is the height in feet of its replica to the nearest whole number? (adapted from 2018 AMC 8, Question 1) ", "answer_option_list": [[{"aoVal": "A", "content": "$$62$$ "}], [{"aoVal": "B", "content": "$$63$$ "}], [{"aoVal": "C", "content": "$$64$$ "}], [{"aoVal": "D", "content": "$$65$$ "}], [{"aoVal": "E", "content": "$$66$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["You can see that since the ratio of real building\\textquotesingle s heights to the model building\\textquotesingle s height is $1: 35$. If the height of the tower is $2250$ feet, to find the height of the model, we divide by $35$ . That gives us $64.28$ which rounds to $64$ . Therefore, to the nearest whole number, the duplicate is (C) $64$ feet. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5227", "queId": "53a034bf12a64c0f941f5e5bc85d1109", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The total value of $$25$$ dimes is $$125$$ times to total value of． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ penny "}], [{"aoVal": "B", "content": "$$1$$ nickel "}], [{"aoVal": "C", "content": "$$2$$ pennies "}], [{"aoVal": "D", "content": "$$2$$ nickels "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$$25$$ dimes $$=250$$￠$$=125\\times 2$$￠$$=125\\times 2$$ pennies. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5230", "queId": "fb2b3029336e45ea8499abdeba6c1032", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If the 9-digit number $$2017122\\square2$$ can be divisible by $$4$$, then the number in $$\\square $$ can be ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["We check if it is divisible by $$4$$ by looking at the last two digits. $$72$$ is divisible by $$4$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5238", "queId": "ed4730a8d6064b96a2740892e7011641", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The last four digits of Linda\\textquotesingle s phone number are $2022$. If the numbers $2,0,2,2$ are summed, what is the final result?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$7$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2022$$ "}], [{"aoVal": "B", "content": "$$202$$ "}], [{"aoVal": "C", "content": "$$22$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$2026$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"], "answer_analysis": ["$2+0+2+2=6$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5239", "queId": "9ab02e5a5f0e46b3bfde97210a6343c9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\dfrac{8}{9}\\div \\dfrac{4}{7}\\div \\dfrac{1}{3}=$$~\\uline{~~~~~~~~~~}~，$$\\dfrac{7}{9}\\div \\dfrac{1}{3}\\div 1\\dfrac{5}{9}=$$~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\dfrac{13}{3}$$，$$2$$． "}], [{"aoVal": "B", "content": "$$\\dfrac{14}{3}$$，$$2$$． "}], [{"aoVal": "C", "content": "$$\\dfrac{14}{3}$$，$$\\dfrac{3}{2}$$． "}], [{"aoVal": "D", "content": "$$\\dfrac{13}{3}$$，$$\\dfrac{3}{2}$$． "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$\\dfrac{8}{9}\\div \\dfrac{4}{7}\\div \\dfrac{1}{3}=\\dfrac{4\\times 2}{3\\times 3}\\times \\dfrac{7}{4}\\times \\dfrac{3}{1}=\\dfrac{2\\times 7}{3}=\\dfrac{14}{3}$$． $$\\dfrac{7}{9}\\div \\dfrac{1}{3}\\div 1\\dfrac{5}{9}=\\dfrac{7}{9}\\times \\dfrac{3}{1}\\times \\dfrac{9}{14}==\\dfrac{7}{9}\\times \\dfrac{3}{1}\\times \\dfrac{9}{2\\times 7}=\\dfrac{3}{2}$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5244", "queId": "6555a02957f04b93bc7d0dc3ffafe36a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Amelia cuts a $75$ cm by $30$ cm rectangle into identical squares without any leftovers. If the length of the squares is a whole number of cm, what is the least number of squares can she get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$90$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Extracting Common Factors from Whole Numbers"], "answer_analysis": ["75 is divisible by 1, 3, 5,15, 25 and 75. 30 is divisible by 1, 2, 3, 5\\textsubscript{Z} 6,10,15 and 30. 15 is the highest common divisor for both 75 and 30. $\\textasciitilde$ To get the least number of squares, the length of the squares must be the largest possible. Hence the length must be 15 and there must be 5 x 2 = \\textbf{10} squares. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5249", "queId": "655893c3f57b401da0332cd0d020e27a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Seven numbers add up to $2022$ and one of the numbers is $522$. Replace $522$ with $321$. What is the new sum of the seven numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2223$$ "}], [{"aoVal": "B", "content": "$$2022$$ "}], [{"aoVal": "C", "content": "$$1921$$ "}], [{"aoVal": "D", "content": "$$1821$$ "}], [{"aoVal": "E", "content": "$$1793$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$522-321=201$, so the sum will decrease by $201$. $2022-201=1821$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5250", "queId": "60e49708b9e34ef3b53b8dd152acdb39", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There is a rule that the symbol \"\\&\" represents an operation of producing the larger one of the two numbers (for example, $7$ \\&~$15 = 15$). Calculate: ($13$ \\&~$22$ ) $\\times$ ($3$ \\&~$6$)=~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$39$$ "}], [{"aoVal": "B", "content": "$$66$$ "}], [{"aoVal": "C", "content": "$$78$$ "}], [{"aoVal": "D", "content": "$$132$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["($13$ \\&~$22$) $\\times$ ($3$ \\&~$6$) = $22\\times6=132$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5252", "queId": "acfce08f3ec94b3d963ca78669adbc3e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the $$100\\rm th$$ number in the arithmetic sequence $$1$$, $$5$$, $$9$$, $$13$$, $$17$$, $$21$$, $$25$$, $$\\cdots$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$397$$ "}], [{"aoVal": "B", "content": "$$399$$ "}], [{"aoVal": "C", "content": "$$401$$ "}], [{"aoVal": "D", "content": "$$403$$ "}], [{"aoVal": "E", "content": "$$405$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$$1+(5-1)\\times 99=397$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5254", "queId": "bf4ef0ec8bed4181a97c0bddaa12ce6e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "If $3^{}p+3^{4}=90$, and $2^{}r+44=76$, what is the product of $p$ and $r$? (Adapted from 2013 AMC 8 Problem, Question \\#15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers"], "answer_analysis": ["First, solve for $p$. Start with $3^{}p+3^{4}=90$. Then, change $3^{4}$ to $81$. Subtract $81$ from both sides to get $3^{}p=9$ and see that $p$ is $2$. Now, solve for $r$. Since $2^{}r+44=76$, $2^{}r$ must equal $32$, $r=5$. $pr$ equals $2\\times5$ which equals $10$. So, the answer is $10$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5259", "queId": "72c8ee34c3f447c99c167ecaf5504635", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the biggest digit in ones place? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5261", "queId": "ed4a8a8b019343b88b10091e96abad70", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the least possible value of $$ (x+1)(x+2)(x+3)(x+4)+2019 $$ where $x$ is a real number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2017$$ "}], [{"aoVal": "B", "content": "$$2018$$ "}], [{"aoVal": "C", "content": "$$2019$$ "}], [{"aoVal": "D", "content": "$$2020$$ "}], [{"aoVal": "E", "content": "$$2021$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["Grouping the first and last terms and two middle terms gives $\\left(x^{2}+5 x+4\\right)\\left(x^{2}+5 x+6\\right)+2019$, which can be simplified to $\\left(x^{2}+5 x+5\\right)^{2}-1+2019$. Noting that squares are nonnegative, and verifying that $x^{2}+5 x+5=0$ for some real $x$, the answer is 2018. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5267", "queId": "8056be5bdcf84c578d85e012b7c7c43f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Avril\\textquotesingle s father bought 14 books. Avril takes away 6 books. How many books does Avril\\textquotesingle s father have left? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$14-6=8$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5269", "queId": "89666c6efccb490ca46e5d865ba9d94d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Before I began snacking, there were $$60\\div 4+1\\times 3$$ gumballs here. If I ate all of them, how many gumballs did I eat? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["To evaluate $$60\\div 4+1\\times 3$$, we first do the $$\\times $$ and $$\\div $$ in the order in which they appear. Do the addition last. We get $$15+3=18$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5271", "queId": "774b46ee9b06415297c460a57a63d695", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$99\\times 99=$$$$-99$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$199\\times 99$$ "}], [{"aoVal": "B", "content": "$$198\\times 99$$ "}], [{"aoVal": "C", "content": "$$100\\times 100$$ "}], [{"aoVal": "D", "content": "$$100\\times 99$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Distributive Law of Whole Numbers"], "answer_analysis": ["$$(100-1)\\times 99=(100\\times 99)-(1\\times 99)$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5277", "queId": "962d195b84844ff483965cee0a11feae", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Calculate: $$1+2+3+\\ldots\\ldots+37+38+39+40+39+38+37+\\ldots\\ldots+13+12+11$$=~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$4000$$ "}], [{"aoVal": "B", "content": "$$1000$$ "}], [{"aoVal": "C", "content": "$$1545$$ "}], [{"aoVal": "D", "content": "$$4545$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$1+2+3+\\ldots\\ldots+37+38+39+40+39+38+37+\\ldots\\ldots+13+12+11$$ $$=（1+2+3+\\ldots\\ldots+37+38+39+40+39+38+37+\\ldots\\ldots+3+2+1）-（1+2+3+\\ldots\\ldots+8+9+10）$$ $$=40\\times40-55$$ $$=1545.$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5279", "queId": "d64742e113a14f17966e9090f4e759fe", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Gary sold $5$ times as many tickets as Louis.They sold a total of $54$ tickets. How many tickets did Louis sell? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$36$$ "}], [{"aoVal": "E", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$54 \\div (5 + 1) = 9$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5291", "queId": "96336d94488d401ca365ee4d1cab4d55", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the value of $\\dfrac{21w}{10}-w+1$ when $w=2$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1.2$$ "}], [{"aoVal": "B", "content": "$$3.1$$ "}], [{"aoVal": "C", "content": "$$3.2$$ "}], [{"aoVal": "D", "content": "$$5.2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["When $w= 2$, $$\\frac{21w}{10}-w+1= \\frac{21 \\times 2}{10}-2+1$$ $$= \\frac{42}{10}-2+1$$ $=4.2-2+1$ $= 2.2 + 1$ $= 3.2$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5292", "queId": "d1b188cd6ef3437d8b01776423a3fc10", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the correct ordering of the three numbers, $$10^{8}$$, $$5^{12}$$, and $$2^{24}$$? ($$2010$$ AMC $$8$$ Problem, Question \\#$$24$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2^{24}$$\\textless{} $$10^{8}$$\\textless$$5^{12}$$ "}], [{"aoVal": "B", "content": "$$2^{24}$$\\textless$$5^{12}$$\\textless$$10^{8}$$ "}], [{"aoVal": "C", "content": "$$5^{12}$$\\textless$$2^{24}$$\\textless$$10^{8}$$ "}], [{"aoVal": "D", "content": "$$10^{8}$$\\textless$$5^{12}$$\\textless$$2^{24}$$ "}], [{"aoVal": "E", "content": "$$10^{8}$$\\textless$$2^{24}$$\\textless$$5^{12}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["$$\\rm Method$$ $$1$$: Since all of the exponents are multiples of $4$, we can simplify the problem by taking the fourth root of each number. Evaluating we get $$10^{2}=100$$, $$5^{3}=125$$, and $$2^{6}=64$$. $$64\\textless100\\textless125$$. So, $$2^{24} \\textless$$ $$10^{8}$$ $$\\textless{} 5^{12}$$. $$\\rm Method$$ $$2$$: First, let us make all exponents equal to $$8$$. Then, it will be easy to order the numbers without doing any computations. $$10^{8}$$ is fine as it is. We can rewrite $$2^{24}$$ as $$(2^{3})^{8}=8^{8}$$. We can rewrite $$5^{12}$$ as $$\\left( 5^{\\frac{3}{2}}\\right)^{8}=\\left( \\sqrt{125}\\right)^{8}$$. We take the eighth root of all of these to get $$10$$, $$8$$,~$\\sqrt{125}$. Obviously, $$8\\textless10\\textless\\sqrt{ 125}$$, so $$2^{24}\\textless10^{8}\\textless5^{12}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5294", "queId": "775a99e07c484eefa676191e7e7873ed", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$3+\\dfrac{1}{1+\\dfrac{1}{5+\\dfrac{1}{16}}}=\\left( \\textbackslash{} \\textbackslash{} \\textbackslash{} \\textbackslash{} \\right).$ ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{307}{97}$ "}], [{"aoVal": "B", "content": "$\\dfrac{16}{97}$ "}], [{"aoVal": "C", "content": "$\\dfrac{145}{16}$ "}], [{"aoVal": "D", "content": "$\\dfrac{372}{97}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions"], "answer_analysis": ["$=3+\\dfrac{1}{1+\\dfrac{1}{\\dfrac{81}{16}}}$ $=3+\\dfrac{1}{1+\\dfrac{16}{81}}$ $=3+\\dfrac{1}{\\dfrac{97}{81}}$ $=3+\\dfrac{81}{97}$ $=\\dfrac{372}{97}$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5297", "queId": "7be1954193cc4f6b8afb4ebc38b0e506", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is an algebraic equation with variable(s)? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$xy+91$ "}], [{"aoVal": "B", "content": "$5=3$ "}], [{"aoVal": "C", "content": "$x+1=y+4$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["both sides are algebraic expressions. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5299", "queId": "f6963cc62fb44d0086389b13e87af261", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate:． $$\\frac{3}{4}+ \\frac{1}{4}\\times \\frac{2}{3}- \\frac{1}{3}=$$~\\uline{~~~~~~~~~~}~; $$\\frac{2}{47}\\times 15 \\times \\frac{47}{36}\\times \\frac{2}{15}\\div \\frac{1}{18}=$$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{7}{12};2$$ "}], [{"aoVal": "B", "content": "$$\\frac{2}{3}; \\frac{1}{2}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{12};2$$ "}], [{"aoVal": "D", "content": "$$\\frac{2}{3}; \\frac{1}{9}$$ "}], [{"aoVal": "E", "content": "$$\\frac{1}{12}; \\frac{1}{9}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["$$\\frac{3}{4}+ \\frac{1}{4}\\times \\frac{2}{3}- \\frac{1}{3}= \\frac{3}{4}+\\frac{1}{6}- \\frac{1}{3}=\\frac{9}{12}+\\frac{2}{12}-\\frac{4}{12}=\\frac{7}{12}$$; $$\\frac{2}{47}\\times 15 \\times \\frac{47}{36}\\times \\frac{2}{15}\\div \\frac{1}{18}= \\frac{4}{36}\\times 18=2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5301", "queId": "f696bf9a84eb4ddd9e033a0636b1f351", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $n$ is an even positive integer, the double factorial notation $n!!$ represents the product of all the even integers from $2$ to $n$. For example, $8!! = 2·4·6·8$. What is the units digit of the following sum? $2!! + 4!! + 6!! + · · · + 2018!! + 2020!! + 2022!!$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5302", "queId": "69ef835392fa4cadb00f2343073d7238", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Happy Hotel is offering $$40 \\textbackslash\\%$$ off discount for any bookings. David booked a room, the new price is $$80$$ dollars cheaper than the original price, the original price is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$180$$ "}], [{"aoVal": "B", "content": "$$200$$ "}], [{"aoVal": "C", "content": "$$300$$ "}], [{"aoVal": "D", "content": "$$480$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$80\\div40\\textbackslash\\%=200$$． so choose $$\\text{B}$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5303", "queId": "9aca1265bb354a6da4d9b69037cb6c2b", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Among all the whole numbers from $$1$$ to $$30$$, how many numbers are multiples of $$3$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$30\\div3=10$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5304", "queId": "e41c29d5b6924f4ea7d5210d475263aa", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$1423$$, $$1723$$, $$2123$$,~\\uline{~~~~~~~~~~}~, $$3223$$ Which one of the following is the missing number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2523$$ "}], [{"aoVal": "B", "content": "$$2623$$ "}], [{"aoVal": "C", "content": "$$2723$$ "}], [{"aoVal": "D", "content": "$$2823$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["The sequence increases in this order: $$300$$, $$400$$, $$500$$, $$600$$, $$\\dots$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5307", "queId": "583df7943ff14b1faaf89cc25e326fad", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Starting with some gold coins and some empty treasure chests, I tried to put $15$ gold coins in each treasure chest, but that left $$1$$ treasure chests empty. So instead I put $12$ gold coins in each treasure chest, but then I had $6$ gold coins left over. How many gold coins did I have? ( adapted from 2017 AMC8, Questions \\#17) ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$49$$ "}], [{"aoVal": "C", "content": "$$75$$ "}], [{"aoVal": "D", "content": "$$84$$ "}], [{"aoVal": "E", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables"], "answer_analysis": ["We can represent the amount of gold with $g$ and the amount of chests with $c$. We can use the problem to make the following equations: $$ \\begin{gathered} 15 c-15=g \\textbackslash\\textbackslash{} 12 c+6=g \\end{gathered} $$ Therefore, $15 c-15=12 c+6$. This implies that $c=7$. We therefore have $g=90$. So, our answer is (E) $90$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5329", "queId": "84fb59d8acaa4d5ba102f3bb74066076", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "$$6\\times \\dfrac{11}{12}=$$~\\uline{~~~~~~~~~~}~，$$\\dfrac{11}{24}\\times 16=$$~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5\\dfrac{1}{2}$$，$$7\\dfrac{1}{2}$$． "}], [{"aoVal": "B", "content": "$$5\\dfrac{1}{3}$$，$$7\\dfrac{1}{3}$$． "}], [{"aoVal": "C", "content": "$$5\\dfrac{1}{3}$$，$$7\\dfrac{1}{2}$$． "}], [{"aoVal": "D", "content": "$$5\\dfrac{1}{2}$$，$$7\\dfrac{1}{3}$$． "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$6\\times \\dfrac{11}{12}=\\dfrac{11}{2}=5\\dfrac{1}{2}$$． $$\\dfrac{11}{24}\\times 16=\\dfrac{22}{3}=7\\dfrac{1}{3}$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5333", "queId": "6123d831f144491eb4fa431a7f49f8a9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "From a regular octagon, a triangle is formed by connecting three randomly chosen vertices of the octagon. What is the probability that at least one of the sides of the triangle is also a side of the octagon? (2018 AMC 8 Problems, Question \\#23) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{2}{7}$ "}], [{"aoVal": "B", "content": "$\\frac{5}{42}$ "}], [{"aoVal": "C", "content": "$\\frac{11}{14}$ "}], [{"aoVal": "D", "content": "$\\frac{5}{7}$ "}], [{"aoVal": "E", "content": "$\\frac{6}{7}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["We will use constructive counting to solve this. There are $2$ cases: Either all $3$ points are adjacent, or exactly $2$ points are adjacent. If all $3$ points are adjacent, then we have $8$ choices. If we have exactly $2$ adjacent points, then we will have $8$ places to put the adjacent points and $4$ places to put the remaining point, so we have $8 \\cdot 4$ choices. The total amount of choices is $\\left(\\begin{array}{l}8 \\textbackslash\\textbackslash{} 3\\end{array}\\right)=8 \\cdot 7$. Thus, our answer is $\\frac{8+8 \\cdot 4}{8 \\cdot 7}=\\frac{1+4}{7}=$ (D) $\\frac{5}{7}$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5334", "queId": "ad195b7301644fa085acdbedcf511ad2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the result of $$1\\times12\\times23\\times34\\times45\\times \\cdots \\times78\\times89$$. What is the sum of its last $2$ digits? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["$$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde1\\times12\\times23\\times34\\times45\\times \\cdots \\times78\\times89$$ $$=1\\times6\\times23\\times34\\times9\\times \\cdots \\times78\\times89\\times2\\times5$$ ∴$$1\\times6\\times3\\times4\\times9\\times6\\times7\\times8\\times9$$ has the last digit of $2$ ∴ the last two digits are $20.$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5335", "queId": "898c0dda65b241879b663199c498b050", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$3.75\\times 20\\textbackslash\\%\\times \\frac{3}{23}-4\\times \\frac{7}{23}+\\frac{9}{23}\\times 3\\frac{1}{4}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{9}{23}$$ "}], [{"aoVal": "B", "content": "$$\\frac{7}{23}$$ "}], [{"aoVal": "C", "content": "$$\\frac{7}{46}$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$$3.75\\times 20\\textbackslash\\%\\times \\frac{3}{23}-4\\times \\frac{7}{23}+\\frac{9}{23}\\times 3\\frac{1}{4}$$ $$=\\frac{15}{4}\\times \\frac{1}{5}\\times \\frac{3}{23}-\\frac{4\\times 7}{23}+\\frac{9}{23}\\times \\frac{13}{4}$$ $$=\\frac{3}{4}\\times \\frac{3}{23}-\\frac{28}{23}+\\frac{9\\times 13}{4\\times 23}$$ $$=\\frac{9}{92}-\\frac{28\\times 4}{23\\times 4}+\\frac{117}{92}$$ $$=\\frac{9-112+117}{92}$$ $$=\\frac{14}{92}$$ $$=\\frac{7}{46}$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5337", "queId": "6e835e62a3f540c0888e3d9a4dcea866", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$5+10+15+20+25=\\left(1+2+3+4+5\\right)\\times$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Extracting Common Factors from Whole Numbers"], "answer_analysis": ["$$5+10+15+20+25=1\\times 5+2\\times 5+\\cdots+5\\times 5$$ $$=\\left(1+2+3+4+5\\right)\\times 5$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5340", "queId": "b63f5adaeaa1403fb242b506b7c5871f", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump $5$ pads to the right or $3$ pads to the left. What is the fewest number of jumps Greta must make to reach the lily pad located $2023$ pads to the right of her starting position? ", "answer_option_list": [[{"aoVal": "A", "content": "$$405$$ "}], [{"aoVal": "B", "content": "$$407$$ "}], [{"aoVal": "C", "content": "$$409$$ "}], [{"aoVal": "D", "content": "$$411$$ "}], [{"aoVal": "E", "content": "$$413$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5342", "queId": "5cbd32f4846341b88eef5039e1e1302e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{If P(A) = 0.34 and P(A or B) = 0.71, which of the following is false?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{P(B) = 0.37 , if A and B are mutually exclusive.} "}], [{"aoVal": "B", "content": "\\textbf{P(B) = 0.561, if A and B are independent.} "}], [{"aoVal": "C", "content": "\\textbf{P(B) cannot be determined if A and B are neither mutually exclusive nor independent.} "}], [{"aoVal": "D", "content": "\\textbf{P(A and B) = 0.191 , if A and B are independent.} "}], [{"aoVal": "E", "content": "\\textbf{P(A\\textbar B) = 0.34 , if A and B are mutually exclusive.} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{P(A) = 0.34, P(A ∪ B) = 0.71 =~ P(A) + P(B) -- P(A ∩ B)} \\textbf{(A) If A and B are mutually exclusive, P(A ∩ B) = 0. Then, P(A ∪ B) = P(A) + P(B) which is 0.71= 0.34+P(B). So P(B) = 0.37.} \\textbf{(B) If A and B is independent, P(A ∩ B) = P(A)*P(B). Then, P(A ∪ B) =~ P(A) + P(B) --~ P(A)*P(B) which 0.71 = 0.34 + P(B) - 0.34*P(B). So P(B) = 0.561} \\textbf{(C) P(A ∪ B) = P(A) + P(B) -- P(A ∩ B). We have to know it is mutually exclusive or independent in order to know P(A ∩ B).} \\textbf{(D) If A and B is independent, P(A ∩ B) = P(A)*P(B) =0.34*0.561=0.191} \\textbf{(E) P(A \\textbar{} B)=P(A∩B)P(B) = 0} "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5343", "queId": "a88def43967c414e8c8757077611c50d", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "$$a:b=5:6$$, $$b:c=8:3$$, $$a:c=$$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20:9$$ "}], [{"aoVal": "B", "content": "$$5:3$$ "}], [{"aoVal": "C", "content": "$$40:21$$ "}], [{"aoVal": "D", "content": "$$5:8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$$a:b=20:24$$, $$b:c=24:9$$, $$a:c=20:9$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5346", "queId": "91c2218d96484da3bfd4647140f5e32b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "After the trainer\\textquotesingle s first whistle, the monkeys at the circus formed $$4$$ rows. There were $$4$$ monkeys in each row. After the second whistle, they rearranged themselves into $$8$$ rows. How many monkeys were there in each row after the second whistle? (2005 Math Kangaroo Problem, Level 3-4, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["There were $$4 \\times 4 = 16$$ monkeys in total. After the second whistle, there were $$16 \\div 8 = 2$$ monkeys in each row. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5347", "queId": "d65aed0b78c544e7a461ffe41065b1f3", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Let $X$ be the smallest positive integer, consisting of only the digit $4$ and $9$ (at least one of each), that is divisible by both $4$ and $9$. What is the last four digits of $X$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4444$$ "}], [{"aoVal": "B", "content": "$$4494$$ "}], [{"aoVal": "C", "content": "$$4944$$ "}], [{"aoVal": "D", "content": "$$9444$$ "}], [{"aoVal": "E", "content": "$$9944$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5354", "queId": "850798e455f0460aad9551253c3fddf3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many of the following pairs of terms are like terms? ($1$) $2$ and $6$;~($2$) $-2a$ and $-2c$;~($3$) $78x$ and $-200x$;~($4$) $8$ and $y$;~($5$) $4ab$ and $4b$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["Like terms are terms that have the same variables. For each variable, the number of times it is multiplied by itself is also the same. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5358", "queId": "9f6f732b991f488ebd13bc5919441fda", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$\\frac{1}{3}\\times \\frac{3}{5}\\times \\frac{5}{7}\\times \\cdots \\times \\frac{2019}{2021}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{2021}$$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{2019}$$ "}], [{"aoVal": "C", "content": "$$\\frac{2019}{2021}$$ "}], [{"aoVal": "D", "content": "$$\\frac{2019}{3}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\frac{1}{3}\\times \\frac{3}{5}\\times \\frac{5}{7}\\times \\cdots \\cdots \\times \\frac{2019}{2021}$$ $$=\\frac{1}{2021}$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5359", "queId": "65abd05f70e747758af04ace8152db7f", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Erik and Ivy each writes down a fraction. They are surprised to find that the fractions they write are very similar: the denominator of each fraciton is exactly the same as the other\\textquotesingle s numerator. What is the product of the two fractions? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$\\frac12$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "It cannot be determined. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["Their fractions are just reciprocal of the other one. Thus, the product of the two fractions should be $1.$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5365", "queId": "91ca682bd7dd4638861a4603cfa5e882", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the area of the triangle formed by the lines $y=-2$, $y=3+x$, and $y=3-x$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$25$$ "}], [{"aoVal": "D", "content": "$$49$$ "}], [{"aoVal": "E", "content": "$$64$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5371", "queId": "899ec76cabe04020a8fc676b85aefee8", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{A basketball player makes 160 out of 200 free throws. We would estimate the probability that the player makes his next free throw to be heads the fourth time.} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{0.15} "}], [{"aoVal": "B", "content": "\\textbf{0.50; either he makes it or he doesn't} "}], [{"aoVal": "C", "content": "\\textbf{0.80} "}], [{"aoVal": "D", "content": "\\textbf{1.2} "}], [{"aoVal": "E", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{160/200=0.8} "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5372", "queId": "778fb09ad27b466cb118b698e55f8464", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of the following numbers? $$5+15+17+23+5+15+17+23+5+15+17+23=$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$140$$ "}], [{"aoVal": "B", "content": "$$160$$ "}], [{"aoVal": "C", "content": "$$180$$ "}], [{"aoVal": "D", "content": "$$240$$ "}], [{"aoVal": "E", "content": "None of the answer above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Grouping: $$5+15+17+23=60$$ $$60\\times3=180$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5380", "queId": "a89ca4eed3144b6690d52a071254d0bf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that $$1^{2}+2^{2}+3^{2}+\\cdots +n^{2}=\\frac{n(n+1)(2n+1)}{6}$$, then $$1^{2}+2^{2}+3^{2}+\\cdots +18^{2}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2016$$ "}], [{"aoVal": "B", "content": "$$2107$$ "}], [{"aoVal": "C", "content": "$$2018$$ "}], [{"aoVal": "D", "content": "$$2109$$ "}], [{"aoVal": "E", "content": "$$2020$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas->1²+2²+3²+......+n²=1/6n(n+1)(n+2)"], "answer_analysis": ["Directly substitute $$n$$ with $$18$$ into the formula to get $$1^{2}+2^{2}+3^{2}+\\cdots +18^{2}=\\frac{18\\times 19\\times 37}{6}=2109$$. So the answer is $$\\text{D}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5381", "queId": "a89cdca350394ff79a1046198c2ba298", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The pages of a book are numbered $1, 2, 3, 4, 5$, and so on. The digit $5$ appears exactly $16$ times. What is the maximum number of pages this book could have? (2019 Math Kangaroo Problem, Level 3-4, Question \\#19) ", "answer_option_list": [[{"aoVal": "A", "content": "$$49$$ "}], [{"aoVal": "B", "content": "$$64$$ "}], [{"aoVal": "C", "content": "$$66$$ "}], [{"aoVal": "D", "content": "$$74$$ "}], [{"aoVal": "E", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Before page $50$, the digit $5$ appears $5$ times. From page $50$ to $59$, the digit $5$ appears $11$ times. Then, the digit $5$ appears the $17$\\textsuperscript{th}~time in $65$. Thus, the maximum page number is $64$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5383", "queId": "badae00fc0ab49c587a61665cafaf091", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Refer to the previous problem. On the final exam Carla scored 98. What is the value of her residual?} ", "answer_option_list": [[{"aoVal": "A", "content": "$$98$$ "}], [{"aoVal": "B", "content": "$$2.5$$ "}], [{"aoVal": "C", "content": "$$-2.5$$ "}], [{"aoVal": "D", "content": "$$0$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{residual =$$\\hat{y}$$-y = 98-95.5 = 2.5} "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5387", "queId": "6a30a411e6f14c1a8900ff63e3cf9586", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The base of a triangle increases by $30\\textbackslash\\%$ and its height decreases $20\\textbackslash\\%$ at the same time. The area of the new triangle is~\\uline{~~~~~~~~~~}~$\\textbackslash\\%$ of the original triangle. ", "answer_option_list": [[{"aoVal": "A", "content": "$110$ "}], [{"aoVal": "B", "content": "$$104$$ "}], [{"aoVal": "C", "content": "$$84$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["$1.3\\times 0.8=1.04$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5395", "queId": "dafe1dceb8ba45919f471b1311ac500a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$(2+4+6 +8+10)-(1+3+5 +7+9)=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$(2-1)+(4 -3)+(6-5)+(8-7)+(10-9)=5$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5403", "queId": "bae1067ce7ed4f42b973ab8f5d6dada5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$401 + 402 + 403 + 404 + 405 = $$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$2010$$ "}], [{"aoVal": "B", "content": "$$2008$$ "}], [{"aoVal": "C", "content": "$$1610$$ "}], [{"aoVal": "D", "content": "$$2015$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$400 \\times 5 + 1+2+3+4+5 = 2000 + 15 = 2015$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5410", "queId": "966bd5b057244c5a9724c1c438d324d2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Among these numbers, $-4.3$, $$12\\%$$, $0$, $$\\frac{2}{5}$$, $-9.97$, $$-\\frac{20}{21}$$, how many numbers are negative? ", "answer_option_list": [[{"aoVal": "A", "content": "two "}], [{"aoVal": "B", "content": "three "}], [{"aoVal": "C", "content": "four "}], [{"aoVal": "D", "content": "five "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Negative Numbers"], "answer_analysis": ["$-4.3$, $-9.97$, and $$-\\frac{20}{21}$$ are negative numbers. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5414", "queId": "ed6c16e1435a4df4bbe26e61d49ef9e4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many different isosceles triangles have integer side lengths and perimeter $23$ ? (2005 AMC 8 Problem, Question \\#15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["let $a$ be legs, $b$ be the base. $a: 1,2,3,4,5,6,7,8,9,10,11$ $b:21,19,17,15,13,11,9,7,5,3,1$ Since $2a\\textgreater b$, $a\\textgreater5$, there are $6$ possible $a$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5417", "queId": "fb4fcad3915f4ae5b4c67f8e2fa22ede", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Robin had a great meal in a local Thai restaurant and he spent $34$ dollars on the dishes. The tax is $10\\textbackslash\\%$ of the dishes and Robin also needed to pay for the tip after paying the food and tax. Robin brought $60$ dollars with him and he\\textquotesingle s thinking about how many tips should he give. Which of the following is an inequality that represents the situation? ", "answer_option_list": [[{"aoVal": "A", "content": "$x=60-34\\times 10\\textbackslash\\%-34$, let $x$ be the amount of tips "}], [{"aoVal": "B", "content": "$x=60-34$, let $x$ be the amount of tips "}], [{"aoVal": "C", "content": "$x \\leq 60-34\\times 10\\textbackslash\\%-34$, let $x$ be the amount of tips "}], [{"aoVal": "D", "content": "$x\\leq 60-34$, let $x$ be the amount of tips "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["Robin needs to pay the food and taxes, the rest he can decide how much he wants to pay for tips. Therefore, the tip should be represented using inequality. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5424", "queId": "c8ab9543df40413dbeddae3c20a44994", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $2021^{}\\text{st}$ digit to the right of the decimal point in the decimal expansion of $\\dfrac{5}{37}$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["$$\\frac{5}{37}=0.\\overline{135}$$, it is a decimal which repeats in cycles of $3$ digits. $2021\\div 3=673$$R2$, so the $2021$$^{st}$ digit is $3$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5426", "queId": "fb5125650bf94271b6835f1be38f1b10", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Martin and Dai divide some sweets between them. There are $65$ sweets, and Martin takes $7$ more than Dai. How many does Martin take? ", "answer_option_list": [[{"aoVal": "A", "content": "$$29$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$35$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$(65 + 7) \\div 2 = 36$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5430", "queId": "8d5df7a02d8741f2976bb9e90e0f1b4e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the result of $$\\frac{{{2}^{2}}}{{{2}^{2}}-1}\\times \\frac{{{3}^{2}}}{{{3}^{2}}-1}\\times \\cdots \\times \\frac{{{99}^{2}}}{{{99}^{2}}-1}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{99}{50}$$ "}], [{"aoVal": "B", "content": "$$\\frac{99}{100}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{99}$$ "}], [{"aoVal": "D", "content": "$$\\frac{99}{200}$$ "}], [{"aoVal": "E", "content": "$$\\frac{50}{99}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas"], "answer_analysis": ["$${{a}\\_{n}}=\\frac{{{\\left( n+1 \\right)}^{2}}}{\\left( n+1+1 \\right)\\left( n+1-1 \\right)}=\\frac{{{\\left( n+1 \\right)}^{2}}}{n\\left( n+2 \\right)}$$. $$=\\frac{2\\times 2}{(2+1)\\times (2-1)}\\times \\frac{3\\times 3}{(3+1)\\times (3-1)}\\times \\frac{4\\times 4}{(4+1)\\times (4-1)}\\times \\cdots \\times \\frac{98\\times 98}{(98+1)\\times (98-1)}\\times \\frac{99\\times 99}{(99+1)\\times (99-1)}$$ $$=\\frac{2\\times 2}{3\\times 1}\\times \\frac{3\\times 3}{4\\times 2}\\times \\frac{4\\times 4}{5\\times 3}\\times \\frac{5\\times 5}{6\\times 4}\\times \\cdots \\times \\frac{98\\times 98}{99\\times 97}\\times \\frac{99\\times 99}{100\\times 98}$$ $$=\\frac{2}{1}\\times \\frac{2}{3}\\times \\frac{3}{2}\\times \\frac{3}{4}\\times \\frac{4}{3}\\times \\frac{4}{5}\\times \\cdots \\times \\frac{98}{97}\\times \\frac{98}{99}\\times \\frac{99}{98}\\times \\frac{99}{100}$$ $$=\\frac{2}{1}\\times \\frac{99}{100}$$ $$=\\frac{99}{50}$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5432", "queId": "89bc3dfc97ad484981f786f9aee18e62", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Three positive integers are equally spaced on a number line. The middle number is $15$, and the largest number is $4$ times the smallest number. What is the smallest of these three numbers? (2022 AMC 8 Problems, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Let the smallest number be $x$. It follows that the largest number is $4 x$. Since $x, 15$, and $4 x$ are equally spaced on a number line, we have $$ \\begin{aligned} 4 x-15 \\& =15-x \\textbackslash\\textbackslash{} 5 x \\& =30 \\textbackslash\\textbackslash{} x \\& =(C) 6. \\end{aligned} $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5435", "queId": "f6b17b38d72049d986168512f5dca5b8", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Calculate：$$100-99+98-97+96-95+\\cdots +4-3+2-1=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$45$$ "}], [{"aoVal": "C", "content": "$$49$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$=\\left( 100-99 \\right)+\\left( 98-97 \\right)+\\left( 96-95 \\right)+\\cdots +\\left( 4-3 \\right)+\\left( 2-1 \\right)$$ $$=1+1+1+\\cdots +1+1=50$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5439", "queId": "8d61886c226e49e487b2dc21271f59fe", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$12:3=20:$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions"], "answer_analysis": ["$$\\frac{12}{3}=\\frac{4}{1}=\\frac{20}{5}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5446", "queId": "b1d00e10d13d4b4299b55b8c5dfb3ec4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is $$40\\textbackslash\\%$$ of $$28.5$$ plus $$28.5\\textbackslash\\%$$ of $$60$$? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$14.25 $$ "}], [{"aoVal": "B", "content": "$$28.5 $$ "}], [{"aoVal": "C", "content": "$$42.75 $$ "}], [{"aoVal": "D", "content": "$$57 $$ "}], [{"aoVal": "E", "content": "$$71.25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Extracting Common Factors from Decimals"], "answer_analysis": ["It is a general rule that $$x\\textbackslash\\%$$ of $$y$$ equals $$y\\textbackslash\\%$$ of $$x$$. This is because $$x\\textbackslash\\%$$ of $$y= \\frac{x}{100} \\times y= \\frac{xy}{100}$$ and $$y \\textbackslash\\% $$ of $$x= \\frac{y}{100} \\times x= \\frac{yx}{100}$$. So $$40\\textbackslash\\%$$ of $$28.5$$ plus $$28.5\\textbackslash\\%$$ of $$60 = 40\\textbackslash\\%$$ of $$28.5$$ plus $$60\\textbackslash\\%$$ of $$28.5 = 100\\textbackslash\\%$$ of $$28.5 = 28.5$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5449", "queId": "e43d0730e9eb4299b936fb765073f58e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In an arithmetic sequence, the $1$\\textsuperscript{st} number is $5$, the $2$\\textsuperscript{nd} number is $8$, the $3$\\textsuperscript{rd} number is $11$, and so on. What is the $25$\\textsuperscript{th} term of this sequence? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$77$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["The $25$\\textsuperscript{th} number: $5+(25-1)\\times3=77$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5452", "queId": "967e6e1c6204495a890c12e36648d3bf", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In the arithmetic sequence: $77$, $86$, $95$, $104$, $\\cdots$, the $14$\\textsuperscript{th}~term is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$203$$ "}], [{"aoVal": "B", "content": "$$181$$ "}], [{"aoVal": "C", "content": "$$194$$ "}], [{"aoVal": "D", "content": "$$212$$ "}], [{"aoVal": "E", "content": "$$185$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$77+9\\times (14-1)=194$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5457", "queId": "8d6bbc95778f484c9ae5b898e39612c6", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "In a sequence of positive integers, each term after the second is the product of the previous two terms. The sixth term in the sequence is $4000$. What is the first term? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["D "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5458", "queId": "9b0be41bd69b402b95e346e9d98a8719", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "$$94$$ is $$49$$ more than． ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$54$$ "}], [{"aoVal": "D", "content": "$$55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$94 - 49 = 45$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5459", "queId": "a8ba72580d6c4f8695ecb21395b869d1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is $$0.9949$$ when rounded to the nearest hundredth? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.99$$ "}], [{"aoVal": "B", "content": "$$0.994$$ "}], [{"aoVal": "C", "content": "$$0.995$$ "}], [{"aoVal": "D", "content": "$$1.00$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["Since the thousandth\\textquotesingle s digit is $$4$$, round $$0.9949$$ down to $$0.99$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5462", "queId": "80c9569e594f49398d969b68095b1c43", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are four types of number machines: $$A$$, $$B$$, $$C$$, $$D$$. Device A: Add $$3$$ to the input number; Device B: Divide the input number by $$3$$; Device C: Subtract $$3$$ from the input; Device D: Multiply the input number by $$3$$. These devices can be connected. If the device $$A$$ is followed by the device $$B$$, it is written as $$A-B$$. For example, input $$6$$, $$6 + 3 = 9, 9 \\div3 = 3 $$. Thus the output would be $$3$$. If you input a number in the device $$B$$-$$A$$-$$D$$-$$C$$, and get $$60$$, the input number was ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$54$$ "}], [{"aoVal": "B", "content": "$$55$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition"], "answer_analysis": ["$$B$$-$$A$$-$$D$$-$$C$$ has the rule: divide the input number by $$3$$; add $$3$$ to the input number;~multiply the input number by $$3$$; subtract $$3$$ from the input. So the inverse operation gives $$((60+3)\\div3-3)\\times3=54$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5464", "queId": "b666c9a927af4f0f8e97be70514f2aca", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$1+3\\frac{1}{6}+5\\frac{1}{12}+7\\frac{1}{20}+9\\frac{1}{30}+11\\frac{1}{42}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$36\\frac{5}{14}$$ "}], [{"aoVal": "B", "content": "$$25\\frac{5}{14}$$ "}], [{"aoVal": "C", "content": "$$36\\frac{1}{3}$$ "}], [{"aoVal": "D", "content": "$$25\\frac{1}{3}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$\\begin{eqnarray}\\&\\&1+3\\frac{1}{6}+5\\frac{1}{12}+7\\frac{1}{20}+9\\frac{1}{30}+11\\frac{1}{42}\\textbackslash\\textbackslash{} \\&=\\&1+3+5+7+9+11+\\frac{1}{6}+\\frac{1}{12}+\\frac{1}{20}+\\frac{1}{30}+\\frac{1}{42}\\textbackslash\\textbackslash{} \\&=\\&\\left[ (1+9)+(3+7)+(5+11) \\right]+\\left( \\frac{1}{2}-\\frac{1}{3} \\right)+\\left( \\frac{1}{3}-\\frac{1}{4} \\right)+\\left( \\frac{1}{4}-\\frac{1}{5} \\right)+\\left( \\frac{1}{5}-\\frac{1}{6} \\right)+\\left( \\frac{1}{6}-\\frac{1}{7} \\right)\\textbackslash\\textbackslash{} \\&=\\&36+\\left( \\frac{1}{2}-\\frac{1}{7} \\right)\\textbackslash\\textbackslash{} \\&=\\&36\\frac{5}{14}\\end{eqnarray}$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5467", "queId": "6190cdb7a5054af3b3e38a528fe0e766", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are some identical candies on a electronic scale. The little bear wants to eat some of them. After eating $3$ candies, the scale shows $105$ grams. After eating a total of $5$ candies, the scale shows $75$ grams. How many candies are on the scale at first? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The quality of each candy: $(105 - 75) \\div 2 = 15$ g The amount of the apples at first: $75~ \\div 15 + 5 = 10$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5469", "queId": "735637bfde334e1e92b14e6b41e99314", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Nicolas is planning to send a package to his friend Anton, who is a stamp collector. To pay for the postage, Nicolas, would like to cover the package with a large number of stamps. Suppose he has a collection of $5$-cent, $10$-cent, and $25$-cent stamps, with exactly $20$ of each type. What is the greatest number of stamps Nicolas can use to make exactly $\\textbackslash$7.10$ in postage? ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$46$$ "}], [{"aoVal": "C", "content": "$$51$$ "}], [{"aoVal": "D", "content": "$$54$$ "}], [{"aoVal": "E", "content": "$$55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5474", "queId": "77d126ea162a4b9a96e61f2f9edc0acc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the second to last digit when $$5^{7}$$ is calculated? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"], "answer_analysis": ["The second to last digit is always $$2$$. For example $$5^{3}$$ is $$125$$. When multiplying this by $$5$$, we see that is it inevitable that the second to last digit remains $$2$$. Try repeated multiplication of $$5$$ on a calculator. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5483", "queId": "6eebbc621cd84659a4d09f7e92810e35", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$x=10$$, what is the value of $$(8x+2)^{2}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6724$$ "}], [{"aoVal": "B", "content": "$$6402$$ "}], [{"aoVal": "C", "content": "$$6416$$ "}], [{"aoVal": "D", "content": "$$6714$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas->Perfect Square Factorization"], "answer_analysis": ["$$(8x)^{2}+2\\cdot(8x)\\cdot2+2^{2}=8^{2}x^{2}+32x+4=8^{2}10^{2}+32\\times10+4=6724$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5485", "queId": "89dbaa4bd87f4cc69dc44940e2762df5", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the value of the letter $H$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns->Encryption and Decryption"], "answer_analysis": ["A "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5487", "queId": "c8c01e61915740f59478ebca9e943261", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The ones digit of $$106\\times107\\times108\\times109\\times110$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["The ones digit is the same as the ones digit of $$6 \\times7\\times8\\times9 \\times0$$. ` "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5492", "queId": "6a7f7c452c024feb9b11e91bcacd6fcf", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Starting with some gold coins and some empty treasure chests, I tried to put $8$ gold coins in each treasure chest, but that makes $1$ gold short to fill all the chests. So instead I put $6$ gold coins in each treasure chest, but then I had $15$ gold coins left over. How many gold coins did I have? ( adapted from 2017 AMC8, Questions \\#17) ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$49$$ "}], [{"aoVal": "D", "content": "$$63$$ "}], [{"aoVal": "E", "content": "$$81$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables"], "answer_analysis": ["We can represent the amount of gold with $g$ and the amount of chests with $c$. We can use the problem to make the following equations: $$ \\begin{gathered} 8 c-1=g \\textbackslash\\textbackslash{} 6 c+15=g \\end{gathered} $$ Therefore, $8 c-1=6 c+15$. This implies that $c=8$. We therefore have $g=63$. So, our answer is (D) $63$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5496", "queId": "736b99a88aee42f59ca7d0091b392993", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which does NOT have $-1$ as a solution?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$2 x-4\\textless-5$ "}], [{"aoVal": "B", "content": "$1-x \\geq 2$ "}], [{"aoVal": "C", "content": "$2+x=1$ "}], [{"aoVal": "D", "content": "$\\frac{2}{x}\\textgreater x$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["$A$ gives $-6\\textless-5$. True. $B$ gives $2 \\geq 2$. True. $C$ gives 1=1. True. $D$ gives $-2\\textgreater-1$. False. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5506", "queId": "77eb85ed5c9249f4b57b00955abe0c5e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a middle-school mentoring program, a number of the sixth graders are paired with a ninth-grade student as a buddy. No ninth grader is assigned more than one sixth-grade buddy. If $\\frac{1}{3}$ of all the ninth graders are paired with $\\frac{2}{5}$ of all the sixth graders, what fraction of the total number of sixth and ninth graders have a buddy? (2015 AMC 8 Problems, Question \\#16) ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{2}{15}$ "}], [{"aoVal": "B", "content": "$\\frac{4}{11}$ "}], [{"aoVal": "C", "content": "$\\frac{11}{30}$ "}], [{"aoVal": "D", "content": "$\\frac{3}{8}$ "}], [{"aoVal": "E", "content": "$\\frac{11}{15}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Let the number of sixth graders be $s$, and the number of ninth graders be $n$. Thus, $\\frac{n}{3}=\\frac{2 s}{5}$, which simplifies to $n=\\frac{6 s}{5}$. Since we are trying to find the value of $\\frac{\\frac{n}{3}+\\frac{2 s}{5}}{n+s}$, we can just substitute $\\frac{6 s}{5}$ for $n$ into the equation. We then get a value of $\\frac{\\frac{6 s}{5}+\\frac{2 s}{5}}{\\frac{6 s}{5}+s}=\\frac{\\frac{6 s+6 s}{15}}{\\frac{11 s}{5}}=\\frac{\\frac{4 s}{5}}{\\frac{11 s}{5}}=\\left(\\right.$ B) $\\frac{4}{11}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5509", "queId": "a441e112b9d144c78b113da409f50742", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$10-9+8-7+6-5+ 4-3+2-1=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$10-9+8-7+6-5+4-3+2-1=1+1+1+1+1=5$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5510", "queId": "ed8365e107d84156b05627fee3caa3d4", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Twelve friends met for dinner at Oscar\\textquotesingle s Overstuffed Oyster House, and each ordered one meal. The portions were so large, there was enough food for $18$ people. If they shared, how many meals should they have ordered to have just enough food for the $12$ of them? (2004 AMC 8 Problems, Question \\#3) ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Set up the proportion $\\frac{12 \\text { meals }}{18 \\text { people }}=\\frac{x \\text { meals }}{12 \\text { people }}$. Solving for $x$ gives us $x=8$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5531", "queId": "a449faf5d3714467a767aac7a1be8bca", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is the largest fraction? $$\\dfrac{2}{6}$$,$$\\dfrac{2}{7}$$,$$\\dfrac{2}{8}$$,$$\\dfrac{2}{9}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\dfrac{2}{5}$$ "}], [{"aoVal": "B", "content": "$$\\dfrac{2}{7}$$ "}], [{"aoVal": "C", "content": "$$\\dfrac{2}{11}$$ "}], [{"aoVal": "D", "content": "$$\\dfrac{2}{9}$$ "}], [{"aoVal": "E", "content": "$$\\dfrac{2}{10}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating"], "answer_analysis": ["Same numerator, so smaller denominator means larger fraction. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5538", "queId": "a44c74c13cf643399c10f12f49f88dcd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "David measured the length of his garden. It was $$15$$ metres to the nearest tenth of a metre. Between what limits was the actual length? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14.995\\leqslant $$ the actual length $$\\leqslant 15.005$$ "}], [{"aoVal": "B", "content": "$$14.9\\leqslant $$ the actual length $$\\textless~15.1$$ "}], [{"aoVal": "C", "content": "$$14.95\\leqslant $$ the actual length $$\\textless{} 15.05$$ "}], [{"aoVal": "D", "content": "$$14.99\\leqslant $$ the actual length $$\\textless15.01$$ "}], [{"aoVal": "E", "content": "$$14.5\\textless$$ the actual length $$\\textless15.5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals->Finding Approximate Values"], "answer_analysis": ["14.9500000\\ldots{} 15.0499999\\ldots{} "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5541", "queId": "6aa7032ffd844d459251045c94d4f72e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There were three piles of plums and a camel wanted to eat some. Each pile had $30$ plums. The camel ate a few plums from the first pile and then ate as many strawberries from the third pile as were left in the first pile. Then it ate some plums in the second plie, and finally there were $5$ plums left in the second pile. How many plums in total did the camel eat? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$45$$ "}], [{"aoVal": "C", "content": "$$55$$ "}], [{"aoVal": "D", "content": "$$65$$ "}], [{"aoVal": "E", "content": "$$70$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$30 + (30 - 5) = 55$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5558", "queId": "9fca6658a81f47d9b2940016ed463f82", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In a group of $40$ students, $40\\textbackslash\\%$ of them can swim. In this group of students, how many of them can swim? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["$40\\times40\\textbackslash\\%=16$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5560", "queId": "9b40e546cffd45f2b2737307a9e07977", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$33$$ hours and $$36$$ minutes $$=$$ minutes. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1996$$ "}], [{"aoVal": "B", "content": "$$2006$$ "}], [{"aoVal": "C", "content": "$$2016$$ "}], [{"aoVal": "D", "content": "$$2026$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Time"], "answer_analysis": ["$$33$$ hours and $$36$$ minutes $$=33\\times60+36$$ minutes $$=2016$$ minutes. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5567", "queId": "fb7017c6aa3d446e821c68ec14580c02", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Polly has more than $90$ candies. The candies cabe divided evenly between $2$, $3$ or $4$, children. However, they cannot be divided evenly between $9$ children because $3$ more candies would be needed. How many candies does she have at least? ", "answer_option_list": [[{"aoVal": "A", "content": "$$96$$ "}], [{"aoVal": "B", "content": "$$132$$ "}], [{"aoVal": "C", "content": "$$135$$ "}], [{"aoVal": "D", "content": "$$168$$ "}], [{"aoVal": "E", "content": "$$171$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$9 \\times 11 - 3 = 96$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5571", "queId": "858a7e41f20743e3952286b3fafe5fe0", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Avril\\textquotesingle s father bought 15 books. Avril takes away 8 books. How many books does Avril\\textquotesingle s father have left? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$15-8=7$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5578", "queId": "858fbc6dbf68417eae10dcd39b5c2f6d", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "$$8002-2008=$$$$-2009$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$9003$$ "}], [{"aoVal": "B", "content": "$$9002$$ "}], [{"aoVal": "C", "content": "$$8003$$ "}], [{"aoVal": "D", "content": "$$8002$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$8002-2008=(8002+1)-(2008+1)=8003-2009$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5587", "queId": "a464f679c8ea408b9e2958ea0332be76", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the value of $$\\left\\textbar{} -19 \\right\\textbar$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$19$$ "}], [{"aoVal": "B", "content": "$$-19$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["By the definition, we can remove the mimus sign before $$-19$$. We get $$19$$ and choose $$\\text{A}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5589", "queId": "f6d5fe6c451647a0a6126d6c4356db15", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The ones digit of $$1!\\times2!\\times3!\\times ···\\times50!$$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas"], "answer_analysis": ["As long as we can find the factor $2$ and $5$, the ones digit is $0$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5593", "queId": "ad82ea3b3b8b4f28a632579a3a22358a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Evaluate the following expression: $$2^{7}+2^{8}+\\cdots +2^{19}+2^{20}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$2^{20}-2^{6}$$ "}], [{"aoVal": "B", "content": "$$2^{20}-2^{7}$$ "}], [{"aoVal": "C", "content": "$$2^{21}-2^{6}$$ "}], [{"aoVal": "D", "content": "$$2^{21}-2^{7}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$1+2+\\cdots +2^{20}=2^{21}-1$$ $$1+2+\\cdots +2^{6} = 2^{7}-1$$ Subtracting the two equations we have: $$2^{7}+2^{8}+\\cdots +2^{20} = 2^{21}-2^{7}$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5598", "queId": "812c0f0ddd4b48dab5c34c6d01dfbc04", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Fill iin the missing number. $$-7\\textless{}11+9$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["NA "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5602", "queId": "8dc8ceda938c477096e35ef52e4ddba2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Some numbers add up to $4077$ and one of the number is $93$. Double this number. What is the new sum of the these numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4077$$ "}], [{"aoVal": "B", "content": "$$4160$$ "}], [{"aoVal": "C", "content": "$$4167$$ "}], [{"aoVal": "D", "content": "$$4170$$ "}], [{"aoVal": "E", "content": "$$4177$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$4077 + 93 = 4170$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5607", "queId": "783e1414237d4d5cb45b95de1cc8056f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "If the repeating decimal $2.0232323\\cdots $ can be written as $\\frac{m}{n}$, where the fraction is in its simplest form. Find $m+n$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$2122$$ "}], [{"aoVal": "B", "content": "$$2993$$ "}], [{"aoVal": "C", "content": "$$3013$$ "}], [{"aoVal": "D", "content": "$$3293$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5608", "queId": "c4531a0a2d0a427eb1bb8ed02892687f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Think Academy will hold a concert. The stage and seats have been set up. There are $$40$$ benches that can only seat one people each, and there are $$7$$ benches that can seat three people each ,How many people can all the chairs and benches hold? ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$54$$ "}], [{"aoVal": "C", "content": "$$61$$ "}], [{"aoVal": "D", "content": "$$70$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$7\\times3=21$$~ $21+40=61$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5612", "queId": "bfca38e53d8241809aaa37e34c9ff960", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "There are $20$ balls of the same size in a box. Lucas says: \"$\\frac12$ of them are red.\" Peter says: \"The probability of drawing a green ball without observing them is $\\frac15$.\" Claire says: \"There are three colors of balls in the box: red, light blue, and green.\" How many dark blue balls are there in the box? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["There is no dark blue ball in the box. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5613", "queId": "cd7a892cef7f495da909ebbb12080335", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In order to estimate the value of $x-y$ where $x$ and $y$ are real numbers with $x\\textgreater y\\textgreater0$, Xiaoli rounded $x$ up by a small amount, rounded $y$ down by the same amount, and then subtracted her rounded values. Which of the following statements is necessarily correct? (2012 AMC 10B Problem, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "Her estimate is larger than $x-y$ "}], [{"aoVal": "B", "content": "Her estimate is smaller than $x-y$ "}], [{"aoVal": "C", "content": "Her estimate equals $x-y$ "}], [{"aoVal": "D", "content": "Her estimate equals $y-x$ "}], [{"aoVal": "E", "content": "Her estimate is $0$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Let\\textquotesingle s define $z$ as the amount rounded up by and down by. The problem statement tells us that Xiaoli performed the following computation: $(x+z)-(y-z)=x+z-y+z=x-y+2 z$ We can see that $x-y+2 z$ is greater than $x-y$, and so the answer is $A$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5614", "queId": "d213662951114dfb89287714eeaedde7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the correct ordering of the three numbers $$\\dfrac{5}{6}$$, $$\\dfrac{7}{8}$$, and $$\\dfrac{9}{10}$$, in increasing order? (Adapted from$$2012$$ AMC $$8$$ Problem, Question \\#$$4$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\dfrac{9}{10}\\textless{} \\dfrac{7}{8}\\textless\\dfrac{5}{6}$$ "}], [{"aoVal": "B", "content": "$$\\dfrac{5}{6}\\textless{} \\dfrac{7}{8}\\textless{} \\dfrac{9}{10}$$ "}], [{"aoVal": "C", "content": "$$\\dfrac{9}{10}\\textless{} \\dfrac{5}{6}\\textless{} \\dfrac{7}{8}$$ "}], [{"aoVal": "D", "content": "$$\\dfrac{5}{6}\\textless{} \\dfrac{9}{10}\\textless{} \\dfrac{7}{8}$$ "}], [{"aoVal": "E", "content": "$$\\dfrac{7}{8}\\textless{} \\dfrac{5}{6}\\textless{} \\dfrac{9}{10}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["Instead of finding the LCD, we can subtract each fraction from $$1$$ to get a common numerator. Thus, $$1- \\dfrac{5}{6}= \\dfrac{1}{6}$$, $$1- \\dfrac{7}{8}= \\dfrac{1}{8}$$, $$1- \\dfrac{9}{10}= \\dfrac{1}{10}$$. All three fractions have the common numerator $$1$$. Now the order of the fractions is obvious. $$\\dfrac{1}{6}\\textgreater\\dfrac{1}{8}\\textgreater\\dfrac{1}{10}\\Rightarrow\\dfrac{5}{6}\\textless\\dfrac{7}{8}\\textless\\dfrac{9}{10}$$. Therefore, $$\\dfrac{5}{6}\\textless\\dfrac{7}{8}\\textless\\dfrac{9}{10}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5620", "queId": "b21ccd4761b14a31a7a487e6dd7bff20", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Supposed that $x$ and $y$ are nonzero real numbers such that $\\frac{3 x+y}{x-3 y}=-2$. What is the value of $\\frac{x+3 y}{3 x-y}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$-3$$ "}], [{"aoVal": "B", "content": "$$-1$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Proportional Equations"], "answer_analysis": ["Rearranging, we find $3 x+y=-2 x+6 y$, or $5 x=5 y \\Longrightarrow x=y$. Substituting, we can convert the second equation into $\\frac{x+3 x}{3 x-x}=\\frac{4 x}{2 x}= 2$ More step-by-step explanation: $$ \\begin{aligned} \\&\\frac{3 x+y}{x-3 y}=-2 \\textbackslash\\textbackslash{} \\&3 x+y=-2(x-3 y) \\textbackslash\\textbackslash{} \\&3 x+y=-2 x+6 y \\textbackslash\\textbackslash{} \\&5 x=5 y \\textbackslash\\textbackslash{} \\&x=y \\textbackslash\\textbackslash{} \\&\\frac{x+3 y}{3 x-y}=\\frac{1+3(1)}{3(1)-1}=\\frac{4}{2}=2 \\end{aligned} $$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5625", "queId": "925e0f061eb34d93b6bb105558d9d5b1", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A binomial event has n = 60 trials. The probability of success on each trial is 0.4. Let X be the count of successes of the vent during the 60 trials. Whart are the $$\\mu\\_x$$ and $$\\sigma\\_x$$? ", "answer_option_list": [[{"aoVal": "A", "content": "24, 3.49 "}], [{"aoVal": "B", "content": "24, 14.4 "}], [{"aoVal": "C", "content": "4.90, 3.79 "}], [{"aoVal": "D", "content": "4.90, 14.4 "}], [{"aoVal": "E", "content": "2.4, 3.79 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$\\mu\\_X = 60 * 0.4 = 24$$ $$\\sigma\\_X = \\sqrt{60*0.4*0.6} = 3.79$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5630", "queId": "925ede0227ce486fb22b3e0f6e0645c8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Observe the sequence below and fill in the blank. $$2, 1, 3, 4, 7, $$~\\uline{~~~~~~~~~~}~$$,18, 29, 47$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["The sum of the previous two number. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5631", "queId": "fb80c080fb5c40ac96b1dfb08edc1842", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Which of the following is not an algebraic expression? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$x=y$ "}], [{"aoVal": "C", "content": "$\\frac{1}{h}$ "}], [{"aoVal": "D", "content": "$123xyzabc$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["equation is not algebraic expression "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5633", "queId": "bb387e7b9abc442b84bbeeff657505d1", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts $210$ equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts $42$ steps of the same size from the front of the ship to the back. In terms of Emily\\textquotesingle s equal steps, what is the length of the ship? (2021 Fall AMC 10A Problems, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$$70$$ "}], [{"aoVal": "B", "content": "$$84$$ "}], [{"aoVal": "C", "content": "$$98$$ "}], [{"aoVal": "D", "content": "$$105$$ "}], [{"aoVal": "E", "content": "$$126$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Let $x$ be the length of the ship. Then, in the time that Emily walks $210$ steps, the ship moves $210-x$ steps. Also, in the time that Emily walks $42$ steps, the ship moves $x-42$ steps. Since the ship and Emily both travel at some constant rate, $\\frac{210}{210-x}=\\frac{42}{x-42}$. Dividing both sides by $42$ and cross multiplying, we get $5(x-42)=210-x$, so $6 x=420$, and $x=70$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5635", "queId": "f6e3dca22b7b490288089b0b22f7b28f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Fill in the operation sign \"$$+$$\" or~\"$$-$$\" in the circles below to make the number statement true. $$5$$ 　$$5$$ 　$$5$$ 　$$5$$　$$5$$ 　$$5=0$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$+$$；$$-$$；$$+$$；$$-$$；$$+$$ "}], [{"aoVal": "B", "content": "$$-$$；$$+$$；$$-$$；$$+$$；$$-$$ "}], [{"aoVal": "C", "content": "$$+$$；$$+$$；$$+$$；$$-$$；$$-$$ "}], [{"aoVal": "D", "content": "I don\\textquotesingle t know o(╥﹏╥)o "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas"], "answer_analysis": ["$$5-5+5-5+5-5=0$$． Option$$\\text{B}$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5636", "queId": "6f726e8669e044a2beaee7d8c59c40b7", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{At a certain restaurant, the distribution of wait times between ordering a meal and receiving the meal has mean 11.4 minutes and standard deviation 2.6 minutes. The restaurant manager wants to find the probability that the mean wait time will be greater than 12.0 minutes for a random sample of 84 customers. Assuming the wait times among customers are independent, which of the following describes the sampling distribution of the sample mean wait time for random samples of size 84 ?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{~Approximately normal with mean 11.4 minutes and standard deviation 2.6 minutes} "}], [{"aoVal": "B", "content": "\\textbf{~Approximately normal with mean 11.4 minutes and standard deviation $\\frac{2.6}{\\sqrt{84}}$ minute~} "}], [{"aoVal": "C", "content": "\\textbf{Approximately normal with mean 12.0 minutes and standard deviation 2.6 minutes} "}], [{"aoVal": "D", "content": "\\textbf{Binomial with mean 84(0.41) minutes and standard deviation 84(0.41)(0.59) minutes~} "}], [{"aoVal": "E", "content": "\\textbf{Binomial with mean 84(0.5) minutes and standard deviation 84(0.5)(0.5) minutes} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{For a sufficiently large n, the sampling distribution of $$\\bar\\_{X}$$ is approximately normal, with mean $\\mu\\_{\\bar\\_{X}}=\\mu$ and standard deviation $\\sigma\\_\\bar\\_{X}=\\sqrt{\\frac{\\sigma}{\\sqrt{n}}}$} "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5642", "queId": "85bd9d2209aa4ff1b059fcb80043bf22", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned $6$ years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is $30$ years. How many years older than Bella is Anna? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\uline{NA} "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5643", "queId": "8a4265033eae4e5ebbdba0494514d27d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which calculation has the greatest value? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2\\times \\left( 0+2+2 \\right)$$ "}], [{"aoVal": "B", "content": "$$2-0-2-2$$ "}], [{"aoVal": "C", "content": "$$2\\times 0\\times 2\\times 2$$ "}], [{"aoVal": "D", "content": "$$2+0+2+2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["A "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5645", "queId": "cd8569bc70c949bfb090f167f6866023", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The result of $\\frac12\\times \\frac23\\times \\frac34$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac 1{3}$$ "}], [{"aoVal": "B", "content": "$$\\frac 14$$ "}], [{"aoVal": "C", "content": "$$\\frac 12$$ "}], [{"aoVal": "D", "content": "$$\\frac {3}{4}$$ "}], [{"aoVal": "E", "content": "$$\\frac {1}{8}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions->Multiplication of Fractions"], "answer_analysis": ["We notice that a lot of terms can be canceled. In fact, every term in the numerator except for the $$1$$ and every term in the denominator except for the $$4$$ will be canceled out, so the answer is $$\\frac 1{4}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5651", "queId": "7cd542c9cbf64637992b2651e62f160c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Dave bought $3$ packets of chips at $2.40$ dollars each and $3$ cans of soft drink at $70$ cents each. How much did he spend altogether? ", "answer_option_list": [[{"aoVal": "A", "content": "$3.10$ dollars "}], [{"aoVal": "B", "content": "$10.70$ dollars "}], [{"aoVal": "C", "content": "$9.30$ dollars "}], [{"aoVal": "D", "content": "$8.70$ dollars "}], [{"aoVal": "E", "content": "$10.50$ dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$2.40$ dollars=$240$ cents $240\\times 3+3\\times70=930$ cents=$9.30$ dollars. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5655", "queId": "d2210875c56642be92f91353ce96c8f5", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "$${{100}^{2}}-{{99}^{2}}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$100$$ "}], [{"aoVal": "C", "content": "$$199$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas-> Difference of Two Squares Formula"], "answer_analysis": ["$${{100}^{2}}-{{99}^{2}}=(100+99)\\times (100-99)=199$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5656", "queId": "815392475fa94046b102fbc1d869c4ed", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The bookstore has the \"Exchanging Sales\". One school bag exchanges 3 books, 2 books exchange 6 pens, and 3 pens exchange 6 erasers. One school bag exchangeserasers． ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5659", "queId": "a48cb9e695ce4433a7d565fbead933af", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For how many integers $x$ is the number $x^{4}-51 x^{2}+50$ negative? (2014 AMC 10B Problems, Question \\#20) ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["First, note that $50+1=51$, which motivates us to factor the polynomial as $\\left(x^{2}-50\\right)\\left(x^{2}-1\\right)$. Since this expression is negative, one term must be negative and the other positive. Also, the first term is obviously smaller than the second, so $x^{2}-50\\textless0\\textless x^{2}-1$. Solving this inequality, we find $1\\textless x^{2}\\textless50$. There are exactly $12$ integers $x$ that satisfy this inequality, $\\pm\\textbackslash{2,3,4,5,6,7\\textbackslash}$. Thus our answer is $(\\mathbf{C}) 12$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5660", "queId": "e476430d44274efa86feeccefc2acc40", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$2015$$ Rosyth School, First Continual Assessment, Primary $$5$$, Question \\#$$11$$ What is the value of $$\\left( 84\\div 7 \\right)+7\\times 6-3$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$33$$ "}], [{"aoVal": "B", "content": "$$51$$ "}], [{"aoVal": "C", "content": "$$57$$ "}], [{"aoVal": "D", "content": "$$111$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$84\\div7=12$ $7\\times6=42$ $$12+42-3=51$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5664", "queId": "bfdc46f4cdde4a8b9418162ba90debef", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following fractions is equivalent to $$0.3\\dot{8}$$？ ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{7}{18}$$ "}], [{"aoVal": "B", "content": "$$\\frac{38}{990}$$ "}], [{"aoVal": "C", "content": "$$\\frac{35}{99}$$ "}], [{"aoVal": "D", "content": "$$\\frac{19}{45}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals"], "answer_analysis": ["$$0.3\\dot{8}=\\frac{38-3}{90}$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde=\\frac{35}{90}$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde=\\frac{7}{18}$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5667", "queId": "9b7d54f832ab44cbb4ce5c82f1e6c550", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$100\\div \\dfrac{2}{3}=$$~\\uline{~~~~~~~~~~}~，$$\\dfrac{15}{16}\\div 5=$$~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\dfrac{200}{3}$$，$$\\dfrac{75}{16}$$． "}], [{"aoVal": "B", "content": "$$150$$，$$\\dfrac{75}{16}$$． "}], [{"aoVal": "C", "content": "$$\\dfrac{200}{3}$$，$$\\dfrac{3}{16}$$． "}], [{"aoVal": "D", "content": "$$150$$，$$\\dfrac{3}{16}$$． "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$100\\div \\dfrac{2}{3}=\\dfrac{50\\times 2}{1}\\times \\dfrac{3}{2}=150$$． $$\\dfrac{15}{16}\\div 5=\\dfrac{3\\times 5}{16}\\times \\dfrac{1}{5}=\\dfrac{3}{16}$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5669", "queId": "815c6566fc81438cbf1242bbd47632a0", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Bruce is a talented writer and graphic artist who enjoys both types of work equally. Instead of earning 45,000 dollars as a writer, Bruce now earns 25,000 dollars in accounting profits as a graphic artist using the same computer equipment he would have used as a writer. What is Bruce\\textquotesingle s economic profit from choosing to work as a graphic artist? ", "answer_option_list": [[{"aoVal": "A", "content": "-45,000 dollars "}], [{"aoVal": "B", "content": "-20,000 dollars "}], [{"aoVal": "C", "content": "20,000 dollars "}], [{"aoVal": "D", "content": "45,000 dollars "}], [{"aoVal": "E", "content": "70,000 dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Economic profit = total revenue - economic costs = total revenue - (explicit costs + implicit costs) "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5682", "queId": "b6bd8e2984064826a58775982ac176e8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If~$\\dfrac{3}{5}=\\dfrac{M}{45}=\\dfrac{60}{N}$ , what is $M+N$? （2008 AMC 8,7） ", "answer_option_list": [[{"aoVal": "A", "content": "$$27$$ "}], [{"aoVal": "B", "content": "$$29$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$105$$ "}], [{"aoVal": "E", "content": "$$127$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions->Simplifying Continued Ratios"], "answer_analysis": ["Separate into two equations~$\\dfrac{3}{5}=\\dfrac{M}{45}$~and~$\\dfrac{3}{5}=\\dfrac{60}{N}$~and solve for the unknowns.~$M=27$~and $N=100$, therefore $M+N=\\boxed{\\left( E\\right)127}.$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5693", "queId": "f25021cd25824f77809d10f215d48068", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many digits are there in the correct answer to the calculation $$1234123412340\\div 1234$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["The correct answer to the calculation $$1234123412340\\div1234=1000100010$$. This has $$10$$ digits. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5696", "queId": "b6c4ebdbfd6345e687805c5627b28131", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Four numbers are written in a row. The average of the first two is $21$, the average of the middle two is $26$, and the average of the last two is $30$. What is the average of the first and last of the numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "$$28$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5697", "queId": "8e03114b986b4f988a8e063f2e29f6a8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Compare these fractions. $$\\frac{3}{8}$$~\\uline{~~~~~~~~~~}~$$\\frac{1}{2}$$, $$\\frac{5}{18}$$~\\uline{~~~~~~~~~~}~$$\\frac{1}{3}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\textgreater$$, $$\\textgreater$$ "}], [{"aoVal": "B", "content": "$$\\textgreater$$, $$\\textless$$ "}], [{"aoVal": "C", "content": "$$\\textless$$, $$\\textgreater$$ "}], [{"aoVal": "D", "content": "$$\\textless$$, $$\\textless$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["$$\\frac{3}{8}\\textless\\frac{4}{8}$$;~$$\\frac{5}{18}\\textless\\frac{6}{18}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5703", "queId": "8e05a065704149cfadeb4aad0eda272a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Solve the equation: $30-9x=28-5x$. ", "answer_option_list": [[{"aoVal": "A", "content": "$x=1$ "}], [{"aoVal": "B", "content": "$x=0.5$ "}], [{"aoVal": "C", "content": "$x=2$ "}], [{"aoVal": "D", "content": "$x=1.5$ "}], [{"aoVal": "E", "content": "$x=1.6$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["$30-28=9x-5x$ $2=4x$ $x=0.5$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5707", "queId": "a01c42b5cb1a4882b086db898edcc585", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Find the next number in the following sequence $$21, 24, 19, 26, 17, \\cdots $$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$19$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["$$21, 19, 17, \\cdots $$ (pattern of $$-2$$) $$24, 26, ?, \\cdots $$ (pattern of $$+2$$) Thus, the \"?\" is equal to $$26+2=28$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5708", "queId": "a931ad6215944ebaa73de9f4e285bad1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The ones digit of $$1!+2!+3!+···+100!$$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas"], "answer_analysis": ["$$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde1+1\\times 2+1\\times 2\\times 3+1\\times 2\\times 3\\times 4$$ $$=1+2+6+24$$ $$=33$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5711", "queId": "85ee6f4a15d44c0ea64d66607d6c2bbb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are two girls and two cats in the room. How many legs are there in this room? (Adapted from 2011 Math Kangaroo Problem, Level 1-2, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$2+2+4+4=12$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5713", "queId": "971071f93e9947c18f78e491eb8fb3ed", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Peter Rabbit eats cabbages and carrots. Each day he eats either $$10$$ carrots or $$2$$ cabbages. Last week Peter ate $$6$$ cabbages. How many carrots did he eat last week? (2014 Math Kangaroo Problem, Level 1-2, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$34$$ "}], [{"aoVal": "D", "content": "$$40$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["Peter ate $6$ cabbages in $6\\div2=3$ days. In $7-3=4$ days, Peter ate $4\\times10=10+10+10+10=40$ carrots. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5715", "queId": "74221ffccc5d44688752cadb12382f47", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "An amusement park has a collection of scale models, with ratio $1: 20$, of buildings and other sights from around the country. The height of the United States Capitol is 289 feet. What is the height in feet of its replica to the nearest whole number? (2018 AMC 8, Question 1) ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["You can see that since the ratio of real building\\textquotesingle s heights to the model building\\textquotesingle s height is $1: 20$. We also know that the U.S Capitol is 289 feet in real life, so to find the height of the model, we divide by 20 . That gives us $14.45$ which rounds to 14 . Therefore, to the nearest whole number, the duplicate is (A) 14 feet. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5716", "queId": "c479a4443c134efa9478531cd1a98edd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Seventy $$-$$ seven hundred is equal to． ", "answer_option_list": [[{"aoVal": "A", "content": "$$70\\times 70$$ "}], [{"aoVal": "B", "content": "$$7\\times 7000$$ "}], [{"aoVal": "C", "content": "$$7\\times 10$$ "}], [{"aoVal": "D", "content": "$$11 \\times 700$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["Seventy $$-$$ seven hundred $$= 7700 = 11\\times700$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5726", "queId": "b2495473faed44c194cfb4bc28a8b727", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$180\\div 6=6\\times $$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$180$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$180\\div 6=30=6\\times 5$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5736", "queId": "860264f32c03437680a1edbb0cd8053d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alen and Austin share $60$ apples between them. Alen has twice as much as Austin. How many apples does Alen have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$45$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$60 \\div (2 + 1) \\times 2 = 40$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5738", "queId": "860465da932d483b9fd8d9c651ca2c12", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "Fifteen integers $a\\_1, a\\_2, a\\_3, \\cdots , a\\_{15}$ are arranged in order on a number line. The integers are equally spaced and have the property that $$ 1 \\leq a\\_1 \\leq 10$$,~~$$13 \\leq a\\_2 \\leq 20$$, and $$241 \\leq a\\_{15} \\leq 250$$. What is the sum of the digits of $a\\_{14}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["A "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5741", "queId": "a02f33af2807415586c2899695763e08", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Given a twelve-digit number $$370592318436$$. Brandon wants to delete $4$ odd digits from the number to create an eight-digit number. What is the smallest eight-digit number that Brandon can form? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30214836$$ "}], [{"aoVal": "B", "content": "$$30128436$$ "}], [{"aoVal": "C", "content": "$$30231436$$ "}], [{"aoVal": "D", "content": "$$30523136$$ "}], [{"aoVal": "E", "content": "$$30218436$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5743", "queId": "c4846080de1e4721a24aed4e18b7ec27", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many inequalities are there in the following options? 1. $x = 1$ 2. $y \\textless{} 2$ 3. $1 + a \\geq g + p$ 4. $1 \\textgreater{} 2$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["$23$ and $4$ are inequalities. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5750", "queId": "819d016f869d4fa88daf92bab3ae7ece", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Express $108:9$ in simplest form:． ", "answer_option_list": [[{"aoVal": "A", "content": "$12:1$ "}], [{"aoVal": "B", "content": "$24:6$ "}], [{"aoVal": "C", "content": "$16:4$ "}], [{"aoVal": "D", "content": "$4:1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["$(108\\div9):(9\\div9)=12:1$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5751", "queId": "b6dce72e23e5457d87358ee9cbc14037", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$5 -- 4 + 3 -- 2 + 1 =$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$= (5 -- 4) + (3 -- 2) + 1 = 1 + 1 + 1 = 3$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5755", "queId": "8a9551f7735340ec94587b30c49fcafb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Devi is $$9$$ years old and Valli is $$13$$ years old now. What is the ratio of Devi\\textquotesingle s age to Valli\\textquotesingle s age in $$5$$ years\\textquotesingle{} time? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3:7$$ "}], [{"aoVal": "B", "content": "$$7:9$$ "}], [{"aoVal": "C", "content": "$$13:14$$ "}], [{"aoVal": "D", "content": "$$9:18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["$5$ years later, Devi is $9+5=14$ years old and Valli is $13+5=18$ years old. $D:V$ $=$ $14:18$ $\\to$ $7:9$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5762", "queId": "7d3509ba702e41dea831472bbc90de6e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Four fifths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 10 cups. What percent of the total capacity of the pitcher did each cup receive?~ (adapted from 2020 AMC 8, Question \\#5) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["The pitcher is $\\frac{4}{5}$ full, i.e. $80 \\textbackslash\\%$ full. Therefore each cup receives $\\frac{80}{10}=(\\mathbf{C}) 8$ percent of the total capacity. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5765", "queId": "8e362b3f4149423194ff167e23aa68f3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If Anna takes one step forward, it means she walks $\"+1\"$ step; If Anna takes one step backward, it means she walks $\"-1\"$ step. Now, Anna walks $\"-5\"$ steps, then she walks $\"+4\"$ steps, then she walks another $\"-1\"$ step. Anna\\textquotesingle s position is from her original location. ", "answer_option_list": [[{"aoVal": "A", "content": "$1$ step forward "}], [{"aoVal": "B", "content": "$1$ step backward "}], [{"aoVal": "C", "content": "$2$ step forward "}], [{"aoVal": "D", "content": "$2$ step backward "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Negative Numbers"], "answer_analysis": ["Since walking one step forward and one step backward gets you back to your original location. Anna takes $4$ steps foward and $1+5=6$ steps backward. $6-4=2$(steps) Therefore, Anna is now $2$ steps backward from her original location. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5768", "queId": "8a9ce4c8d1e54ab284ca9b36e2df85a7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$(12 \\times7)-(12 + 12 + 12 + 12) =$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$108$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$$(12 \\times7)-(12 + 12 + 12 + 12) =83-48=36$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5770", "queId": "d6d9639a0a2c4f9d8c6c354865bf3df0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The last five digits of Zoe\\textquotesingle s phone number are $3,4,8,5,7.$ If these $5$ digits are filled in the square~$$\\huge\\square+\\square =\\square +\\square $$, which number is not used?~(adapted from $$2017$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$8$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"], "answer_analysis": ["$4+7=3+8$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5772", "queId": "81b2e0d7f53d4b478268194aadb42708", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When $$115$$ is divided by~ \\uline{?~} , the quotient is 4 and remainder is $$3$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$27$$ "}], [{"aoVal": "B", "content": "$$28$$ "}], [{"aoVal": "C", "content": "$$460$$ "}], [{"aoVal": "D", "content": "$$463$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$115 - 3 = 112$ $? \\times 4 = 112$ $? = 112 \\div ~4 = 28$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5776", "queId": "dffe7934778e4dceb3eca43c1122b699", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\left( {} \\right.$$The number of seconds in a week$$\\left. {} \\right)$$$$\\div$$$$\\left( {} \\right.$$the number of minutes in a week$$\\left. {} \\right)=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$420$$ "}], [{"aoVal": "C", "content": "$$3600$$ "}], [{"aoVal": "D", "content": "$$7200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["There are $$60$$ seconds in each minute, so the quotient of the two quantities is $$60$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5781", "queId": "974209e1ef2e40c1bf8d9710f1c7c064", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $12$ boys in the class. The ratio of boys to girls is $1:2$. How many students are there in the class? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$12-\\textgreater1$ $24-\\textgreater2$ $12+24=36$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5788", "queId": "81c6279f5a76407c96e2ccc91019da24", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{A news organization conducted a survey about preferred methods for obtaining the news. A random sample of 1,605 adults living in a certain state was selected, and 16.2 percent of the adults in the sample reported that television was their preferred method. Which of the following is an appropriate margin of error for a 90 percent confidence interval to estimate the population proportion of all adults living in the state who would report that television is their preferred method for obtaining the news?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{$1.645 \\sqrt{\\frac{(0.162)(1-0.162)}{1605}}$} "}], [{"aoVal": "B", "content": "\\textbf{$1.645 \\sqrt{\\frac{(0.5)(1-0.5)}{1605}}$} "}], [{"aoVal": "C", "content": "\\textbf{$1.96 \\sqrt{\\frac{(0.162)(1-0.162)}{1605}}$} "}], [{"aoVal": "D", "content": "\\textbf{$1.96 \\sqrt{\\frac{(0.5)(1-0.5)}{1605}}$} "}], [{"aoVal": "E", "content": "\\textbf{$1.83 \\sqrt{\\frac{(0.162)(1-0.162)}{1605}}$} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{$\\hat{p} = 0.162$} \\textbf{MOE = $Z\\_{0.05}\\sqrt{\\frac{0.162*(1-0.162)}{1605}}$ = 1.65*$\\sqrt{\\frac{0.162*(1-0.162)}{1605}}$} "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5789", "queId": "f70d9974f97a4cfcaecc4e3dcad37d3e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Cassandra sets her watch to the correct time at noon. At the actual time of $1: 00$ PM, she notices that her watch reads $12: 57$ and $36$ seconds. Assuming that her watch loses time at a constant rate, what will be the actual time when her watch first reads $$10:00$$ PM? (2003 AMC 12B Problems, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$10:22$ PM and $24$ seconds "}], [{"aoVal": "B", "content": "$10:24$ PM "}], [{"aoVal": "C", "content": "$10:25$ PM "}], [{"aoVal": "D", "content": "$10:27$ PM "}], [{"aoVal": "E", "content": "$10:30$ PM "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["For every $60$ minutes that pass by in actual time, $57+\\frac{36}{60}=57.6$ minutes pass by on Cassandra\\textquotesingle s watch. When her watch first reads, $10: 00$ PM, $10(60)=600$ minutes have passed by on her watch. Setting up a proportion, $$ \\frac{57.6}{60}=\\frac{600}{x} $$ where $x$ is the number of minutes that have passed by in actual time. Solve for $x$ to get $625$ minutes, or $10$ hours and $25$ minutes $$ \\Rightarrow \\text { (C) 10:25} $$ PM. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5794", "queId": "7d56933ba1534f95843e118e6ae3d3d4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Yesterday is Saturday, what day is the day after tomorrow? (Adapted from 2019 Math Kangaroo Problem, Level 3-4, Question \\#3) ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Wednesday "}], [{"aoVal": "D", "content": "Thursday "}], [{"aoVal": "E", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Yesterday: Saturday Today: Sunday Tomorrow: Monday The day after tomorrow: Tuesday "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5795", "queId": "ade9a46d154e4f8795be7786a405f366", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Free-response questions on the AP Statistics Exam are graded 4, 3, 2, 1, or~ 0. Question 2 on the exam was of moderate difficulty. The average score on question 2 was 2.05 with a standard deviation of 1. To the nearest tenth, what score was achieved by a student who was at the 90th percentile of all students on the test? You may assume that the scores on the question were approximately normally distributed.} ", "answer_option_list": [[{"aoVal": "A", "content": "$$3.5$$ "}], [{"aoVal": "B", "content": "$$3.3$$ "}], [{"aoVal": "C", "content": "$$2.9$$ "}], [{"aoVal": "D", "content": "$$3.7$$ "}], [{"aoVal": "E", "content": "$$3.1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["\\textbf{Z = 1.28} \\textbf{$$\\frac{x-2.05}{1}$$ = 1.28} \\textbf{x= 3.33} "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5801", "queId": "8e54d0f77a634a9d9c837cb96cf764da", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "What is the simplest form of $\\frac{15}{20}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{4}{5}$ "}], [{"aoVal": "B", "content": "$\\frac{3}{4}$ "}], [{"aoVal": "C", "content": "$\\frac{2}{3}$ "}], [{"aoVal": "D", "content": "$\\frac{15}{20}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions->Using Common Factors to Simplify Fractions"], "answer_analysis": ["Factors of numerator $15$ are $1, 3, 5, 15$ and factors of denominator $20$ are $1, 2, 4, 5, 10, 20$. The highest common factor(HCF) is $5$. Divide $15$ and $20$ by the HCF: $\\frac{15 \\div 5}{20 \\div 5}$=$\\frac{3}{4}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5805", "queId": "81d254e2509c48a0a681a9b5306604e7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following sequences is different from the rest? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$，$$1$$，$$2$$，$$3$$，$$5$$，$$8$$，$$13$$，$$\\cdots $$ "}], [{"aoVal": "B", "content": "$$0$$，$$2$$，$$2$$，$$4$$，$$6$$，$$10$$，$$16$$，$$\\cdots $$ "}], [{"aoVal": "C", "content": "$$1$$，$$3$$，$$4$$，$$7$$，$$11$$，$$18$$，$$29$$，$$\\cdots $$ "}], [{"aoVal": "D", "content": "$$1$$，$$2$$，$$3$$，$$6$$，$$11$$，$$20$$，$$37$$，$$\\cdots $$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["All sequences are Fibonacci numbers except for ($$\\text{D}$$). （Maths Olympiad 《Looking for a Pattern》 Pr$$3$$\\&$$4$$ Question \\#$$18$$） "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5814", "queId": "c4a6559641bc486eb2b85af6b89b6639", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the product of $286$ and $4$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1144$$ "}], [{"aoVal": "B", "content": "$$1124$$ "}], [{"aoVal": "C", "content": "$$844$$ "}], [{"aoVal": "D", "content": "$$824$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["omitted "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5815", "queId": "c01f83bac32c42bd9f899292ec53b461", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Let $ a◆b=a+(2\\times b)$, then $1◆(2◆3) =$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["$1◆(2◆3)=1◆[2+(2\\times3)]=1◆8=1+16=17$. So the answer is $\\rm C$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5832", "queId": "db8658d1e3274cf5bc56fe4081b0ddc0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There is a total of $3567$ dollars in Thompson\\textquotesingle s wallet. What is the sum of the digits of his money? (adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$7$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$356$$ "}], [{"aoVal": "B", "content": "$$57$$ "}], [{"aoVal": "C", "content": "$$22$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"], "answer_analysis": ["$3+5+6+7=21$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5833", "queId": "e94521167e2e443a9c0f2d95ea9b4542", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Sreshtha needs to estimate the quantity $\\frac{a}{b}-c$, where $a, b$, and $c$ are large positive integers. She rounds each of the integers so that the calculation will be easier to do mentally. In which of these situations will her answer necessarily be greater than the exact value of $\\frac{a}{b}-c ?$ ．(2015 AMC 12A Problem, Question \\#5) ", "answer_option_list": [[{"aoVal": "A", "content": "She rounds all three numbers up. "}], [{"aoVal": "B", "content": "She rounds $a$ and $b$ up, and she rounds $c$ down. "}], [{"aoVal": "C", "content": "She rounds $a$ and $c$ up, and she rounds $b$ down. "}], [{"aoVal": "D", "content": "She rounds $a$ up, and she rounds $b$ and $c$ down. "}], [{"aoVal": "E", "content": "She rounds $c$ up, and she rounds $a$ and $b$ down. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["To maximize our estimate, we want to maximize $\\frac{a}{b}$ and minimize $c$, because both terms are positive values. Therefore we round $c$ down. To maximize $\\frac{a}{b}$, round $a$ up and $b$ down. $\\Rightarrow(\\mathbf{D})$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5834", "queId": "bb9416c5d7984a8ea40c018554e3377c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Let $a, b$, and $c$ be three distinct one-digit numbers. What is the maximum value of the sum of the roots of the equation $(x-a)(x-b)+(x-b)(x-c)=0$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$15.5$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$16.5$$ "}], [{"aoVal": "E", "content": "$$17$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Unary Quadratic Equations"], "answer_analysis": ["Expanding the equation and combining like terms results in $2 x^{2}-(a+2 b+c) x+(a b+b c)=0$. By Vieta\\textquotesingle s formula the sum of the roots is $\\frac{-[-(a+2 b+c)]}{2}=\\frac{a+2 b+c}{2}$. To maximize this expression we want $b$ to be the largest, and from there we can assign the next highest values to $a$ and $c$. So let $b=9, a=8$, and $c=7$. Then the answer is $\\frac{8+18+7}{2}=16.5$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5835", "queId": "7d7c5fb8d3024bbcb8a66316217fdce1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$10+11+12+13+14=\\left(30+31+32+33+34\\right)-$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$3\\times 20$$ "}], [{"aoVal": "D", "content": "$$5\\times 20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["Add five $$20$$\\textquotesingle s to $$10+11+12+13+14$$ to get $$30+31+32+33+34$$. The answer is $$\\text{D}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5841", "queId": "eddcf3ede7774204823315506c7811c4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is the correct order of the fractions $$\\dfrac{15}{11}$$, $$\\dfrac{19}{15}$$ and $$\\dfrac{17}{13}$$, from least to greatest? ($$2019$$ AMC $$8$$ Problem, Question \\#$$3$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\dfrac{15}{11}\\textless{} \\dfrac{17}{13}\\textless{} \\dfrac{19}{15}$$ "}], [{"aoVal": "B", "content": "$$\\dfrac{15}{11}\\textless{} \\dfrac{19}{15}\\textless{} \\dfrac{17}{13}$$ "}], [{"aoVal": "C", "content": "$$\\dfrac{17}{13}\\textless{} \\dfrac{19}{15}\\textless{} \\dfrac{15}{11}$$ "}], [{"aoVal": "D", "content": "$$\\dfrac{19}{15}\\textless{} \\dfrac{15}{11}\\textless{} \\dfrac{17}{13}$$ "}], [{"aoVal": "E", "content": "$$\\dfrac{19}{15}\\textless{} \\dfrac{17}{13}\\textless{} \\dfrac{15}{11}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["Method $$1$$: Each one is $$x+\\dfrac{4}{x}$$ so we are really comparing $$\\dfrac{4}{11}$$, $$\\dfrac{4}{15}$$, and $$\\dfrac{4}{13}$$, where you can see $$\\dfrac{4}{11}$$ $$\\textgreater$$ $$\\dfrac{4}{13}$$ $$\\textgreater$$ $$\\dfrac{4}{15}$$. So, $$\\dfrac{19}{15}\\textless{} \\dfrac{17}{13}\\textless{} \\dfrac{15}{11}$$. Method $$2$$: We take a common denominator: $$\\dfrac{15}{11}, \\dfrac{19}{15}, \\dfrac{17}{13}= \\dfrac{15 \\cdot 15 \\cdot 13}{11 \\cdot 15 \\cdot 13}, \\dfrac{19 \\cdot 11 \\cdot 13}{15 \\cdot 11 \\cdot 13}, \\dfrac{17 \\cdot 11 \\cdot 15}{13 \\cdot 11 \\cdot 15}= \\dfrac{2925}{2145}, \\dfrac{2717}{2145}, \\dfrac{2805}{2145}$$. $$2717 \\textless{} 2805\\textless{} 2925$$. So, $$\\dfrac{19}{15}\\textless{} \\dfrac{17}{13}\\textless{} \\dfrac{15}{11}$$. Method $$3$$: When $$\\frac{x}{y}\\textgreater1$$, $$\\frac{x+z}{y+z}\\textless\\frac{x}{y}$$. Hence, $$\\dfrac{19}{15}\\textless{} \\dfrac{17}{13}\\textless{} \\dfrac{15}{11}$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5842", "queId": "976b3d1a1b144a04a900bb2230e6ae0a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$1+3\\frac{1}{6}+5\\frac{1}{12}+7\\frac{1}{20}+9\\frac{1}{30}+11\\frac{1}{42}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$36\\frac{5}{14}$$ "}], [{"aoVal": "B", "content": "$$25\\frac{5}{14}$$ "}], [{"aoVal": "C", "content": "$$36\\frac{1}{3}$$ "}], [{"aoVal": "D", "content": "$$25\\frac{1}{3}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$\\begin{eqnarray}\\&\\&1+3\\frac{1}{6}+5\\frac{1}{12}+7\\frac{1}{20}+9\\frac{1}{30}+11\\frac{1}{42}\\textbackslash\\textbackslash{} \\&=\\&1+3+5+7+9+11+\\frac{1}{6}+\\frac{1}{12}+\\frac{1}{20}+\\frac{1}{30}+\\frac{1}{42}\\textbackslash\\textbackslash{} \\&=\\&\\left[ (1+9)+(3+7)+(5+11) \\right]+\\left( \\frac{1}{2}-\\frac{1}{3} \\right)+\\left( \\frac{1}{3}-\\frac{1}{4} \\right)+\\left( \\frac{1}{4}-\\frac{1}{5} \\right)+\\left( \\frac{1}{5}-\\frac{1}{6} \\right)+\\left( \\frac{1}{6}-\\frac{1}{7} \\right)\\textbackslash\\textbackslash{} \\&=\\&36+\\left( \\frac{1}{2}-\\frac{1}{7} \\right)\\textbackslash\\textbackslash{} \\&=\\&36\\frac{5}{14}\\end{eqnarray}$$ $$\\text{A}$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5844", "queId": "9bee9ed41d56456e806f5b644156f880", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "For real numbers $w$ and $z$, $$ \\frac{\\frac{1}{w}+\\frac{1}{z}}{\\frac{1}{w}-\\frac{1}{z}}=2014 $$ What is $\\frac{w+z}{w-z} ?$ ", "answer_option_list": [[{"aoVal": "A", "content": "- 2014 "}], [{"aoVal": "B", "content": "$\\frac{-1}{2014}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{2014}$ "}], [{"aoVal": "D", "content": "$$1$$ "}], [{"aoVal": "E", "content": "$$2014$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Proportional Equations"], "answer_analysis": ["Muliply both sides by $\\left(\\frac{1}{w}-\\frac{1}{z}\\right)$ to get $\\frac{1}{w}+\\frac{1}{z}=2014\\left(\\frac{1}{w}-\\frac{1}{z}\\right)$. Then, add $2014 \\cdot \\frac{1}{z}$ to both sides and subtract $\\frac{1}{w}$ from both sides to get $2015 \\cdot \\frac{1}{z}=2013 \\cdot \\frac{1}{w}$. Then, we can plug in the most simple values for $z$ and $w(2015$ and 2013 , respectively), and find $\\frac{2013+2015}{2013-2015}=\\frac{2(2014)}{-2}=-2014$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5847", "queId": "c03024067ed4459fb0da177563799922", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a dining room, there are $$15$$ chairs, $$5$$ tables, and $$20$$ cups. What is the ratio of chairs to cups in the simplest form? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1:4$$ "}], [{"aoVal": "B", "content": "$$15:20$$ "}], [{"aoVal": "C", "content": "$$4:3$$ "}], [{"aoVal": "D", "content": "$$3:4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["There are $$15$$ chairs and $$20$$ cups. So the ratio of chairs to cups is $$15:20$$. The simplest form is $$3:4$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5848", "queId": "8669095855174076aa52cd6a6d6a6403", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $8^{\\text {th }}$-graders to $6^{\\text {th }}$-graders is $7: 6$, and the the ratio of $8^{\\text {th }}$-graders to $7^{\\text {th }}$ graders is $4: 7$. What is the smallest number of students that could be participating in the project? (2013 AMC 8, Question 16) ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$47$$ "}], [{"aoVal": "C", "content": "$$56$$ "}], [{"aoVal": "D", "content": "$$94$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["We multiply the first ratio by 2 on both sides, and the second ratio by 3 to get the same number for 8 th graders, in order that we can put the two ratios together: $$ \\begin{aligned} \\&7: 6=7(2): 6(2)=14: 12 \\textbackslash\\textbackslash{} \\&4: 7=4(3): 7(3)=12: 21\\end{aligned} $$ Therefore, the ratio of 8th graders to 7th graders to 6th graders is $14: 12: 21$. Since the ratio is in lowest terms, the smallest number of students participating in the project is $$ 14+12+21=\\text { (B) } 47 $$ Notice if you get $$28:24:42$$, you have to simplfy to $14: 12: 21$ for the smallest number of students. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5853", "queId": "a98c08c7398f41c58acf73281169a666", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There is a tournament at the pool. First, $$13$$ children signed up and then another $$19$$ children signed up. Six teams with an equal number of members each are needed for the tournament. At least how many more children need to sign up so that the six teams can be formed?~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders"], "answer_analysis": ["$$13 + 19 = 32$$; $$32 \\div 6 = 5R2$$. There are $$2$$ students left, which means that $$6 - 2 = 4$$ more students are needed to form $6$ teams. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5856", "queId": "820601bdad7a4229a6e69c7bbb945720", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A data set consists of $6$ (not distinct) positive integers: $1,7,5,2,5$, and $X$. The average (arithmetic mean) of the 6 numbers equals a value in the data set. What is the sum of all positive values of $X$? (2022 AMC 10A Problems, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$26$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$36$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["First, note that $1+7+5+2+5=20$. The mean cannot be $1$ or $2$. There are $3$ possible cases: Case 1: the mean is $5$ . $$ X=5 \\cdot 6-20=10 \\text {. } $$ Case 2: the mean is $7$. $$ X=7 \\cdot 6-20=22 \\text {. } $$ Case 3: the mean is $X$. $$ \\frac{20+X}{6}=X \\Rightarrow X=4 \\text {. } $$ Hence, the answer is $10+22+4=$ (D) $36$ . "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5859", "queId": "bba22136ee2e41d497870149fd53535d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The average value of ＄$$2$$, ＄$$4$$, ＄$$6$$, ＄$$8$$, and ＄$$10$$ is~\\uline{~~~~~~~~~~}~pennies. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3000$$ "}], [{"aoVal": "B", "content": "$$600$$ "}], [{"aoVal": "C", "content": "$$550$$ "}], [{"aoVal": "D", "content": "$$500$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"], "answer_analysis": ["Average $$=$$(＄$$2+$$＄$$4+$$＄$$6+$$＄$$8+$$＄$$10$$)$$\\div 5=$$＄$$6=600$$ pennies. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5863", "queId": "9305e091cd7a464797336270905727df", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following number is different from the others． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.08$$ "}], [{"aoVal": "B", "content": "$$8\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$\\frac{8}{10}$$ "}], [{"aoVal": "D", "content": "Eight percents "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions->Converting Between Fractions, Percentage and Decimals"], "answer_analysis": ["$$8\\textbackslash\\%=0.08$$， But $$\\frac{8}{10}=0.8$$． So, the answer is $$\\text{C}$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5866", "queId": "c4c0ccc675fa45f08fb4b1cb6eb30735", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "An operator $$\\star$$ acts on two numbers to give the following outcomes: $$3\\star2=51$$ $$5\\star3=82$$ $$6\\star1=75$$ $$9\\star4=135$$ What is $$7\\star5$$ equal to? ", "answer_option_list": [[{"aoVal": "A", "content": "$$112$$ "}], [{"aoVal": "B", "content": "$$121$$ "}], [{"aoVal": "C", "content": "$$122$$ "}], [{"aoVal": "D", "content": "$$212$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition"], "answer_analysis": ["$$a\\star b=\\underbrace{(a+b)}\\_{\\rm{tens}} \\underbrace{(a-b)}\\_{\\rm{ones}}$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5869", "queId": "c03d4f5effc148258bd033ce97615339", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "What value does the hundredth place represent in the number $12.345$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.005$$ "}], [{"aoVal": "B", "content": "$$0.04$$ "}], [{"aoVal": "C", "content": "$$0.3$$ "}], [{"aoVal": "D", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["The hundredth place of a number is the second digit after the decimal point, which is $$4$$. Since the number $$4$$ is on the hundredth place, it represents $$0.04$$. Check Lesson 4 Concept 1 on textbook "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5877", "queId": "c0438245cc614aa0b3a08a58ac9b2025", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{Suppose a certain scale is not calibrated correctly, and as a result, the mass of any object is displayed as 0.75 kilogram less than its actual mass. What is the correlation between the actual masses of a set of objects and the respective masses of the same set of objects displayed by the scale?} ", "answer_option_list": [[{"aoVal": "A", "content": "$$-1$$ "}], [{"aoVal": "B", "content": "$$-0.75$$ "}], [{"aoVal": "C", "content": "$$0$$ "}], [{"aoVal": "D", "content": "$$0.75$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{Since the actual mass is always 0.75kg more than the displayed mass, they are perfectly correlated.~} "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5879", "queId": "931614bbd6f647378d43fdd495c4e8dd", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{High school students from track teams in the state participated in a training program to improve running times. Before the training, the mean running time for the students to run a mile was 402 seconds with standard deviation 40 seconds. After completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds. Let X represent the running time of a randomly selected student before training, and let Y represent the running time of the same student after training. Which of the following is true about the distribution of X - Y ?} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{The variables X and Y are independent; therefore, the mean is 34 seconds and the standard deviation is 10 seconds.} "}], [{"aoVal": "B", "content": "\\textbf{~The variables X and Y are independent; therefore, the mean is 34 seconds and the standard deviation is 50 seconds.} "}], [{"aoVal": "C", "content": "\\textbf{The variables X and Y are not independent; therefore, the standard deviation is 50 seconds and the mean cannot be determined with the information given.} "}], [{"aoVal": "D", "content": "\\textbf{The variables X and Y are not independent; therefore, the mean is 34 seconds and the standard deviation cannot be determined with the information given.} "}], [{"aoVal": "E", "content": "\\textbf{The variables X and Y are not independent; therefore, neither the mean nor the standard deviation can be determined with the information given.} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{Mean: 402 - 368 = 34} \\textbf{SD: X and Y are not independent, correlation is unknown → SD unknown} "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5882", "queId": "b2a3c9afc7a3409ea6fdceeb0d342cc5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There is a number $X.$ Three times the sum of $4$ and number $X$ is $36$. What is the value of number $X$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["$3(4+x)=36, x=8$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5886", "queId": "97923c13be2345a7bc3a4a76bf73fc55", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "insert pic Which number is hidden behind the square? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns->Encryption and Decryption"], "answer_analysis": ["triangle: 7-4=3 square: 9-3=6 "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5891", "queId": "fbcb884a3c254dc1a780ac7ece18fea3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\left( {3+2+1} \\right)\\times 10=30+20+$$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$44$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Distributive Law of Whole Numbers"], "answer_analysis": ["$$\\left( {3+2+1} \\right)\\times 10=60=30+20+10$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5893", "queId": "a098d006651a45ff941c9cbd6f4663a2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Vivian creates a new operation: $m$@$n=m\\times m-n\\times n$. What is the value of $11$@$9$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$99$$ "}], [{"aoVal": "B", "content": "$$121$$ "}], [{"aoVal": "C", "content": "$$81$$ "}], [{"aoVal": "D", "content": "$$40$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition"], "answer_analysis": ["$11^{2}-9^{2}=40$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5894", "queId": "97967926c768457d8d2fda04f71b43aa", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many two-digits positive integers has at least one $8$ as its digit? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$19$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5897", "queId": "86983524dd3c40168f4432922b147c6c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When Koko and Koala does not sleep, he eats 50 grams of leaves per hour. Yesterday, he slept 20 hours. How many grams of leaves did he eat yesterday? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$200$$ "}], [{"aoVal": "E", "content": "$$400$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion"], "answer_analysis": ["(24 - 20) x 5 = 200. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5904", "queId": "a9ac7f3b0b0d4e3ab730b9d73120a87e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate：$$\\frac{1}{2}+\\frac{1}{6}+\\frac{1}{12}+\\frac{1}{20}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{4}{5}$$ "}], [{"aoVal": "B", "content": "$$\\frac{5}{6}$$ "}], [{"aoVal": "C", "content": "$$\\frac{11}{12}$$ "}], [{"aoVal": "D", "content": "$$\\frac{19}{20}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\frac{1}{2}+\\frac{1}{6}+\\frac{1}{12}+\\frac{1}{20}$$ $$=\\frac{30}{60}+\\frac{10}{60}+\\frac{5}{60}+\\frac{3}{60}$$ $$=\\frac{48}{60}$$ $$=\\frac{4}{5}$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5905", "queId": "f731a9e56db84d72b7d84506bd3d61fb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two non-zero real numbers, $a$ and $b$, satisfy $a b=a-b$. Which of the following is a possible value of $\\frac{a}{b}+\\frac{b}{a}-a b$? (2000 AMC 12 Problems, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$-2$ "}], [{"aoVal": "B", "content": "$\\frac{-1}{2}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{3}$ "}], [{"aoVal": "D", "content": "$\\frac{1}{2}$ "}], [{"aoVal": "E", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$\\frac{a}{b}+\\frac{b}{a}-a b=\\frac{a^{2}+b^{2}}{a b}-(a-b)=\\frac{a^{2}+b^{2}}{a-b}-\\frac{(a-b)^{2}}{(a-b)}=\\frac{2 a}{a-b}=\\frac{2(a-b)}{a-b}=2 \\Rightarrow \\text{E}.$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5923", "queId": "ffbda26415564c15978cf0e993f0c3c3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of these is closest to $$4$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4.07 $$ "}], [{"aoVal": "B", "content": "$$ 3.925 $$ "}], [{"aoVal": "C", "content": "$$3.979 $$ "}], [{"aoVal": "D", "content": "$$4.12 $$ "}], [{"aoVal": "E", "content": "$$4.024$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["Note that $$4.07-4 = 0.07$$; $$4-3.925 = 0.075$$; $$4-3.979 =0.021$$; $$4.12-4 = 0.12$$ and $$4.024-4 = 0.024$$. So, of the five options, $$3.979$$ is nearest to $$4$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5927", "queId": "fbd7a8f1a94d491aaead04db07f4c11c", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the unit digit of $23^{2023}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5928", "queId": "8ec0c46149f64ad69d70a63e9a712178", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Nancy bought 17 cones of ice-cream for her three children. Misha ate twice as many cones as Ana. Dan ate more ice-cream than Ana but less than Misha. How many cones of ice-cream did Dan eat? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities->Solving Inequalities"], "answer_analysis": ["Let x be the number of ice-cream cones that Ana ate. Then, 2x is the number of cones that Misha ate, and the number of cones that Dan ate is: 17 - x - 2x = 17 - 3x. It is given that Dan ate more than Misha but less than Ana; therefore, x \\textless{} 17 - 3x \\textless{} 2x 4x \\textless{} 17 \\textless{} 5x only x=4 satisfies this inequality. The number of cones that Dan ate is thus 17- 3 x 4 = 5. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5933", "queId": "933c936488a14a869d9d0df5c3cf1f62", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all its side lengths are integer. The primeter of $\\triangle ABC$ with a side of length $14$ and a side length of $8$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$26$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+8\\textgreater14$. Therefore, $P\\textgreater14+14$. The least integer value of $P$ is $29$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5938", "queId": "8ec66856efb5485296a8605b07abb64a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Gilda has a bag of marbles. She gives $30 \\textbackslash\\%$ of them to her friend Pedro. Then Gilda gives $25 \\textbackslash\\%$ of what is left to another friend, Ebony. Finally, Gilda gives $10 \\textbackslash\\%$ of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself? (adapted 2019 AMC 8, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$47.25\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$50.25\\textbackslash\\%$ "}], [{"aoVal": "C", "content": "$$65\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$70\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["After Gilda gives $30 \\textbackslash\\%$ of the marbles to Pedro, she has $70 \\textbackslash\\%$ of the marbles left. If she then gives $25 \\textbackslash\\%$ of what\\textquotesingle s left to Ebony, she has $(0.75 * 0.70)=52.5 \\textbackslash\\%$ of what she had at the beginning. Finally, she gives $10 \\textbackslash\\%$ of what\\textquotesingle s left to her brother, so she has $(0.9 * 0.525) =$ (A) $47.25\\textbackslash\\%$ of what she had in the beginning left. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5940", "queId": "cdfc906b992b4e32909143593c16003c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $$a=2$$, $$b=4$$, $${{a}^{2}}+3b=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$3^{2}+2\\times1.5=12$$． "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5950", "queId": "86c964220e704651a6a96c84896574e0", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "If $$\\left\\textbar{} 2x-5 \\right\\textbar=7$$, $x=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$-1$$ or $$6$$ "}], [{"aoVal": "C", "content": "$$1$$ or $$-6$$ "}], [{"aoVal": "D", "content": "$$1$$ or $$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities->Solving Inequalities"], "answer_analysis": ["$$2x-5=\\pm 7$$ $$x=6$$ or $$x=-1$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5951", "queId": "f2a03f7cfe02484b9790140f0ff89d06", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A circle is centered at $O$, $AB$ is a diameter and $C$ is a point on the circle with $\\angle COB=50^{\\circ}$. What is the degree measure of $\\angle CAB$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$50$$ "}], [{"aoVal": "E", "content": "$$65$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5954", "queId": "e040aefe934845ce8e79ec8dc8c79414", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For how many values of $a$ is it true that the line $y=x+a^{2}-6$ passes through the vertex of the parabola $y=4x^{2}-8x+a^{2}$? (Adapted From 2005 AMC 12B Problem, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "infinitely many "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["We see that the vertex of the quadratic function $y=4x^{2}-8x+a^{2}$ is $\\left(1, a^{2}-4\\right)$. If $\\left(1, a^{2}-4\\right)$ will be on the line $y=x+a^{2}-6$, $a^{2} -4=1+a^{2}-6$. Solve for $a$, there is no solution. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5961", "queId": "a9d2c15a7f7a4b8d8279195b6dd1492e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Tiara\\textquotesingle s toll pass account has a value of $$$24$$. Each time she uses the toll road, $$$1.4$$ is deducted from the account. When the value drops below $$$10$$, she must add value to the toll pass. Assume there are $$x$$ times Tiara can use the toll road without having to add value to the toll pass. Which inequality can represent the situation? ", "answer_option_list": [[{"aoVal": "A", "content": "$24-1.4x\\geq10$ "}], [{"aoVal": "B", "content": "$24-1.4x\\textgreater10$ "}], [{"aoVal": "C", "content": "$24+1.4x\\geq10$ "}], [{"aoVal": "D", "content": "$24-1.4x\\leq10$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["$24-1.4x\\geq10$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5965", "queId": "e0486418bf7d44f3b2e83a41aef2dbf2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many $0$s are there in the end of the result of the factorial of $25$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas->Factorization"], "answer_analysis": ["We can get $1+1+1+1+2=6$ factor $5$s from $5, 10, 15, 20, 25$ in total, which can make six $10$s after multiplying $2$. Six $10$s means that there should be $6$ $0$s in the end. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5966", "queId": "ae5616138e414d46ad65462e58a02b0d", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "From a starting number, Olivia was supposed to subtract $3$, and then divide by $9$, but instead, Olivia subtracted $9$, then divided by $3$, getting $43$. If the correct instructions were followed, what would the result be? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$34$$ "}], [{"aoVal": "C", "content": "$$43$$ "}], [{"aoVal": "D", "content": "$$51$$ "}], [{"aoVal": "E", "content": "$$138$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["A "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5977", "queId": "b7621c0ba71c42c3a75a5239a7c542c9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the product of $$5$$ and $$830$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$166$$ "}], [{"aoVal": "B", "content": "$$825$$ "}], [{"aoVal": "C", "content": "$$835$$ "}], [{"aoVal": "D", "content": "$$4150$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["omitted "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5979", "queId": "ae5f03bb32424af0a391e9574cd0d4e4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In how many ways can the letters in \\textbf{BEEKEEPER} be rearranged so that two or more \\textbf{E}s do not appear together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5983", "queId": "9c624e6926624477bfc6e5dbd9c275d1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There is some water in a bowl, which is on a electronic scales. Mike pours water into the bowl. After pouring $2$ glasses of water, the sacle shows $300$ grams. After pouring a total of $6$ glasses of water, the scale shows $700$ grams. What is the quality of the water at the start? ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ g "}], [{"aoVal": "B", "content": "$$150$$ g "}], [{"aoVal": "C", "content": "$$200$$ g "}], [{"aoVal": "D", "content": "$$250$$ g "}], [{"aoVal": "E", "content": "$$275$$ g "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The quality of each glass of water: $(700 - 300) \\div (6 - 2) = 100$ g At first: $300 - 100 \\times 2 = 100$ g "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5987", "queId": "9c64b65e33764d92b463680bc6f57fce", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$\\left (876\\times543\\right ) -\\left (543\\times876\\right )=$． ", "answer_option_list": [[{"aoVal": "A", "content": "$0$ "}], [{"aoVal": "B", "content": "$1$ "}], [{"aoVal": "C", "content": "$237834$ "}], [{"aoVal": "D", "content": "$475668$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$\\left (876\\times543\\right ) - \\left (543\\times876\\right ) = \\left (876\\times543\\right ) - (876\\times543) = 0$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5989", "queId": "f752a5714d1849c1aea67db0ee0736f6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$ 0.33 =$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3}{10}$$ "}], [{"aoVal": "B", "content": "$$\\frac{33}{100}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "D", "content": "$$\\frac{3}{8}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["$0.33 = 33\\div100 = \\dfrac{33}{100}$, so choice $\\text{B}$ is correct. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5990", "queId": "fbf096c3bbba4cf699e239e70ae477c0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$26+24-22+20-18+16-14+12-10+8-6+4-2=$$？． ", "answer_option_list": [[{"aoVal": "A", "content": "$$48$$ "}], [{"aoVal": "B", "content": "$$38$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers"], "answer_analysis": ["$$=26+(24-22)+(20-18)+(16-14)+(12-10)+(8-6)+(4-2)$$ $$=26+2+2+2+2+2+2$$ $$=38$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "5992", "queId": "dbcf0a189a0c4d04ad5e92bc7ff8610b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Ace and Sam were painting a house. Ace painted $$\\frac{3}{10}$$ of the house. Sam painted $$\\frac{2}{10}$$ more than Ace. What fraction of the house still needs to be painted? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{2}{10}$$ "}], [{"aoVal": "B", "content": "$$\\frac{3}{10}$$ "}], [{"aoVal": "C", "content": "$$\\frac{5}{10}$$ "}], [{"aoVal": "D", "content": "$$\\frac{8}{10}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["Sam: $$\\frac{2}{10}+\\frac{3}{10}=\\frac{5}{10}$$ Total: $$\\frac{5}{10}+\\frac{3}{10}=\\frac{8}{10}$$ Left: $$\\frac{10}{10}-\\frac{8}{10}=\\frac{2}{10}$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6005", "queId": "ffddeae52b284e15bab7cfc255bf60fd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is not an expression? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$a$$ "}], [{"aoVal": "C", "content": "$$a+b=a+b$$ "}], [{"aoVal": "D", "content": "$$b-3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["Equations are not expressions. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6007", "queId": "ce24b20353324308beb9c5816e64e785", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of these pairs of fractions are equivalent? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3\\frac{1}{2}$$ and $$2\\frac{1}{4}$$ "}], [{"aoVal": "B", "content": "$$1\\frac{1}{3}$$ and $$\\frac{8}{6}$$ "}], [{"aoVal": "C", "content": "$$1\\frac{1}{4}$$ and $$\\frac{3}{4}$$ "}], [{"aoVal": "D", "content": "$$3\\frac{3}{9}$$ and $$\\frac{9}{9}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"], "answer_analysis": ["$\\frac{8}{6}=\\frac{4}{3}=1\\frac{1}{3}$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6016", "queId": "a57ddb37d6ed43c5870c0eaf89f138b4", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Cassandra is helping her mother to pack $$75$$ cupcakes. The boxes that her mother prepare can only fit $$7$$ cupcakes. She must ensure the box is full before she can use the next box. How many boxes she can fill up? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$68$$ "}], [{"aoVal": "E", "content": "$$70$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers"], "answer_analysis": ["$$75\\div7=10R5$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6017", "queId": "a57df383beac40338b217b1165af8c31", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Judy has less than $40$ game coins. The game coins can be divided evenly between $3, 4$ or $6$ students. However, they cannot be divided evenly between $7$ students because $4$ more game coins would be needed. How many game coins does Judy have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The game coins can be divided evenly between $3, 4$ or $6$ students, which means the number of game coins should be divisible by $3, 4,$ or $6$, so we can eliminate the options $E$ . The game coins cannot be divided evenly between $7$ students because $4$ more game coins would be needed, so after the number of game coins plus $4$, the result can be divisible by $7$. Thus, the answer is $24$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6018", "queId": "93995029076142a185c7e58b04684ffb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate $$0.3\\dot{8}\\div 0.\\dot{5}1\\dot{8}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac12$$ "}], [{"aoVal": "B", "content": "$$\\frac23$$ "}], [{"aoVal": "C", "content": "$$\\frac34$$ "}], [{"aoVal": "D", "content": "$$\\frac45$$ "}], [{"aoVal": "E", "content": "$$\\frac56$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6030", "queId": "8f2f2fce4e684914b6babbb9c5fc8cb6", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many odd numbers are there? 5, 12, 3, 6, 7, 9, 10, 4 ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$Omitted.$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6031", "queId": "a58ad6ba591241df99dd6133a72663a2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the followings is not an algebraic expression? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$ax+32$$ "}], [{"aoVal": "C", "content": "$\\frac{2}{y}$+88 "}], [{"aoVal": "D", "content": "$$x=33y$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$D$ is an equation "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6032", "queId": "8f32dec7ba814dbe96c5aa84535509aa", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all its side lengths are integers. The perimeter of $\\triangle ABC$ with a side of length $25$ and a side length of $18$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$52$$ "}], [{"aoVal": "D", "content": "$$51$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+18\\textgreater25$. Therefore, $P\\textgreater25+25$. The least integer value of $P$ is $51$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6035", "queId": "a5906eaa101a4069a4b553bcdf768e6b", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Alina writes the numbers $1,2,\\cdots ,9$ on a separate cards, one number per card. She wishes to divide the cards into $3$ groups of $3$ cards so that the sum of the numbers in each group will be the same. In how many ways can this be done? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6037", "queId": "dbe86917a4d24e928d025f19e56f0202", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the least dividend and divisor in each division equation below. $\\textasciitilde$ ~\\uline{~~~~~~~~~~}~$$\\div$$5$$=4R4$$ $\\textasciitilde$ $$22\\div$$~\\uline{~~~~~~~~~~}~$$=7R1$$ ", "answer_option_list": [[{"aoVal": "A", "content": "24,3 "}], [{"aoVal": "B", "content": "23,3 "}], [{"aoVal": "C", "content": "24,4 "}], [{"aoVal": "D", "content": "23,5 "}], [{"aoVal": "E", "content": "$$23.4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders"], "answer_analysis": ["The remainder should be less than the divisor. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6040", "queId": "ae95adebc9624fe99f9304387342c0c6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "At equilibrium in the market of apartments, the consumer surplus is $\\textbackslash$ 120,000$ and the producer surplus is $\\textbackslash$ 180,000$. The government decide to set a price ceiling. As a result, the consumer surplus becomes $ \\textbackslash$ 140,000$ and the producer surplus becomes $\\textbackslash$ 140,000$. What is the deadweight loss from the price ceiling? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\textbackslash$140,000$ "}], [{"aoVal": "B", "content": "$\\textbackslash$60,000$ "}], [{"aoVal": "C", "content": "$\\textbackslash$40,000$ "}], [{"aoVal": "D", "content": "$\\textbackslash$20,000$ "}], [{"aoVal": "E", "content": "$\\textbackslash$0$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["At the equilibrium, the total surplus is the sum of consumer and producer surplus, which is $ \\textbackslash$120,000 + \\textbackslash$180,000 = \\textbackslash$300,000$. After the price ceiling is imposed, the consumer surplus increases to $\\textbackslash$140,000$, while the producer surplus decreases to $\\textbackslash$140,000$. The new total surplus is $ \\textbackslash$140,000 + \\textbackslash$140,000 = \\textbackslash$280,000$. Therefore, the deadweight loss is the difference between the total surplus before and after the price ceiling, which is $\\textbackslash$300,000 - \\textbackslash$280,000 = \\textbackslash$20,000$ . "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6043", "queId": "e074ac0e89a5481f8502879b30e3db43", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$ 0.33 =$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3}{10}$$ "}], [{"aoVal": "B", "content": "$$\\frac{33}{100}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "D", "content": "$$\\frac{3}{8}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["$0.33 = 33\\div100 = \\dfrac{33}{100}$, so choice $\\text{B}$ is correct. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6064", "queId": "d762e7cbc3404964bea5f74cd4c3c300", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Simplify: $$b\\left( a+1 \\right)-a\\left( b-1 \\right)$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$b+a$$ "}], [{"aoVal": "B", "content": "$$2ab+b-a$$ "}], [{"aoVal": "C", "content": "$$b-a$$ "}], [{"aoVal": "D", "content": "$$ab-1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$b\\left( a+1 \\right)-a\\left( b-1 \\right)=ab+b-ab+a=b+a$$, so the answer is$\\text{A}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6066", "queId": "983a7dbf7dc04c58ac9c2e7a2774641d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Stefani is ordering fertilizer for her garden. A local garden supply store sells fertilizer by the yard (that really means cubic yard, but that is what they call it).For every yard she orders there is a $\\textbackslash$$15charge and ,in addition ,there is a $\\textbackslash$$40 delivery charge. ( Total Cost =~$\\textbackslash$$15(yard)+~$\\textbackslash$$40.) $\\textasciitilde$ If the average order is 4.3 yards with standard deviation of 2.9 yards, what is the mean and standard deviation of the Total Cost of a typical order? ", "answer_option_list": [[{"aoVal": "A", "content": "mean = $\\textbackslash$$4.30; standard deviation =~$\\textbackslash$$2.90 "}], [{"aoVal": "B", "content": "mean = $\\textbackslash$$64.50; standard deviation = $\\textbackslash$$43.50 "}], [{"aoVal": "C", "content": "mean = $\\textbackslash$$105.50; standard deviation =~$\\textbackslash$$43.50 "}], [{"aoVal": "D", "content": "mean = $\\textbackslash$$105.50; standard deviation = $\\textbackslash$$83.50 "}], [{"aoVal": "E", "content": "Cannot be determined because each order may not be independent~ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The correct answer is (c). When using a linear transformation (Total cost 15 (yard)+40), the mean is changed by both the multiplication and addition. But the standard deviation is only changed by the multiplication. Mean = 15(4.3) +40=$\\textbackslash$$ 104.50; =15(2.9) =~$\\textbackslash$$43.50. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6067", "queId": "b7a593d9d8e64821a5647aded84bfe94", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$40 \\times 50 \\times 60 = 4 \\times 5\\times 6 \\times$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$100$$ "}], [{"aoVal": "C", "content": "$$456$$ "}], [{"aoVal": "D", "content": "$$1000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$4\\times10\\times5\\times10\\times6\\times10=4\\times5\\times6\\times10\\times10\\times10=4\\times5\\times6\\times1000$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6068", "queId": "aeab27cc64c148aabc871312158023fd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The average of $$4000$$ fours is four times the average of $$2000$$． ", "answer_option_list": [[{"aoVal": "A", "content": "ones　 "}], [{"aoVal": "B", "content": "twos　 "}], [{"aoVal": "C", "content": "fours　 "}], [{"aoVal": "D", "content": "eights　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["The average of $$4000$$ fours is $$4$$; this is $$4$$ times the average of $$2000$$ ones. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6078", "queId": "dbff2710027845f39384ecf984724aea", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Evaluate $$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "B", "content": "$\\dfrac{2}{5}$ "}], [{"aoVal": "C", "content": "$\\dfrac{2}{9}$ "}], [{"aoVal": "D", "content": "$\\dfrac{5}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions"], "answer_analysis": ["$$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}=\\frac{1}{2+ \\dfrac{1}{ \\dfrac{5}{2}}}= \\frac{1}{2+ \\dfrac{2}{5}}= \\frac{1}{ \\dfrac{12}{5}}= \\frac{5}{12}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6079", "queId": "b331700948ea4fa3be956f5f08549a1c", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The mean, median, and mode of the $7$ data values $60,100, x, 40,50,200,90$ are all equal to $x$. What is the value of $x$? (2016 AMC 10A Problems, Question \\#7) ", "answer_option_list": [[{"aoVal": "A", "content": "$$50$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$75$$ "}], [{"aoVal": "D", "content": "$$90$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Since $x$ is the mean, $$ \\begin{aligned} x \\& =\\frac{60+100+x+40+50+200+90}{7} \\textbackslash\\textbackslash{} \\& =\\frac{540+x}{7} . \\end{aligned} $$ Therefore, $7 x=540+x$, so $x=$ (D) $90$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6084", "queId": "c0c4bc0c0192486cb41fede6ae2bd026", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the simplest form of $5$ minutes $: 30$ seconds? ", "answer_option_list": [[{"aoVal": "A", "content": "$5:30$ "}], [{"aoVal": "B", "content": "$1:6$ "}], [{"aoVal": "C", "content": "$6:1$ "}], [{"aoVal": "D", "content": "$10:1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio"], "answer_analysis": ["We need to make units same first. $5$ minutes equal to $300$ seconds. Now we could remove the same unit, second. We get $300:30$ and simplify it to $10:1$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6088", "queId": "d2e6b1555ac049e9b7b256512c843841", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given the symbol $$\\otimes $$ defines a new operation and $$3\\otimes 3=3\\times 4\\times 5$$, $$7\\otimes 2=7\\times 8$$, and $$2\\otimes 4=2\\times 3\\times 4\\times 5$$, then $$5\\otimes 3=$$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$190$$ "}], [{"aoVal": "B", "content": "$$200$$ "}], [{"aoVal": "C", "content": "$$210$$ "}], [{"aoVal": "D", "content": "$$220$$ "}], [{"aoVal": "E", "content": "Non of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns"], "answer_analysis": ["$$5\\otimes 3=5\\times 6\\times 7=210$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6090", "queId": "aa40f8ab94bd4bc98bcad9cd6195027f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Observe the sequence $10$, $15$, $20$, $25$, $\\cdots$ , the $9$\\textsuperscript{th} term is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$45$ "}], [{"aoVal": "B", "content": "$50$ "}], [{"aoVal": "C", "content": "$55$ "}], [{"aoVal": "D", "content": "$60$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$10+5\\times(9-1)=50$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6093", "queId": "985760c1adde474888d94420d68cd65e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$(11+ 11 + 11 + 11 + 11 + 11)-(9 + 9 + 9 +9 +9 +9)=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$102$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["Rearranging: $$11-9 +\\cdots + 11-9 =2+\\cdots +2 =2\\times6 = 12$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6099", "queId": "e9ba7ce9fe9a40b1bb62c52a8c64d911", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the value of $1+3+5+\\ldots+2017+2019-2 -4-6-\\ldots-2016-2018$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$-1010$$ "}], [{"aoVal": "B", "content": "$$-1009$$ "}], [{"aoVal": "C", "content": "$$1008$$ "}], [{"aoVal": "D", "content": "$$1009$$ "}], [{"aoVal": "E", "content": "$$1010$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Grouping in Fast Addition and Subtraction of Whole Numbers"], "answer_analysis": ["$1+3+5+\\ldots+2017+2019-2 -4-6-\\ldots-2016-2018$ $=1+(3-2)+(5-4)+\\cdots +(2017-2016)+(2019-2018)$ $=1+1+1+\\cdots +1+1$ $=1010$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6106", "queId": "ce6045a0127e49cc8b17564c0aecffc6", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Calculate: $$1\\frac{1}{1024}+2\\frac{1}{512}+4\\frac{1}{256}+\\cdots 256\\frac{1}{4}+512\\frac{1}{2}=$$~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1023\\frac{1}{1024}$$ "}], [{"aoVal": "B", "content": "$$1023\\frac{1023}{1024}$$ "}], [{"aoVal": "C", "content": "$$1024$$ "}], [{"aoVal": "D", "content": "$$1024\\frac{1}{1024}$$ "}], [{"aoVal": "E", "content": "$$1024\\frac{1023}{1024}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions"], "answer_analysis": ["Nil "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6122", "queId": "e09c366dbc0e4ff0ae885f44e89aa44b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "1. In the number 98, the digit \"9\" is in the ones place.~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "Yes "}], [{"aoVal": "B", "content": "No "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6124", "queId": "aa60168711834a8dbbffa9b1c110b445", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Evaluate $$\\left(\\frac{2017}{2018}+\\frac{20172017}{20182018}\\right)\\div \\frac{201720172017}{201820182018}$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6126", "queId": "f792d06a3abb4f1e94632639fcd3fbd3", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which digit is smaller? ", "answer_option_list": [[{"aoVal": "A", "content": "tens "}], [{"aoVal": "B", "content": "ones "}], [{"aoVal": "C", "content": "we don\\textquotesingle t know "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6129", "queId": "a5e7dff3c3e84c67925d290ad95bb2e2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Evaluate the expression shown below: $$36 \\left( \\frac{1}{1\\times 6} + \\frac{1}{6\\times 11} +\\frac{1}{11\\times 16} + \\frac{1}{16\\times 21} + \\frac{1}{21\\times 26} + \\frac{1}{26\\times 31} + \\frac{1}{31\\times 36} \\right)$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6140", "queId": "b3653129b7bd492eb22db828c43cc136", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A container had $27$ ℓ of longan drink. The drink is made up of three $2$-ℓ\\textbf{~}bottles of longan syrup and some water. What was the volume of water used to make the drink? ", "answer_option_list": [[{"aoVal": "A", "content": "6ℓ "}], [{"aoVal": "B", "content": "18ℓ "}], [{"aoVal": "C", "content": "21ℓ "}], [{"aoVal": "D", "content": "27ℓ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Volume and Capacity"], "answer_analysis": ["$$2 \\times 3 = 6$$ $$27 - 6 = 21$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6142", "queId": "bc681758dfda44cfbf2b88ea2d96c112", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that $$a \\Omega b=a\\times b-3$$, find $$4\\Omega 5$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"], "answer_analysis": ["Nil "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6143", "queId": "fc3521d2ad9343c180d0a1b419c6111a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$2+4 +6 +8=1+3 +5 +7 +$$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$2+4 +6 +8=1+1+3+1+5+1+7+1=1+3 +5 +7 +4$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6157", "queId": "b7eb528ce60c46568f38d2c4f9e1031b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$4x-x-12=51$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$x=12.6$$ "}], [{"aoVal": "B", "content": "$$x=-12.6$$ "}], [{"aoVal": "C", "content": "$$x=21$$ "}], [{"aoVal": "D", "content": "$$x=-21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6167", "queId": "aefa285667ba4eb38abaa3c97fd7230d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$8\\times9\\times10\\times11=80\\times$$ . ", "answer_option_list": [[{"aoVal": "A", "content": "$$81$$ "}], [{"aoVal": "B", "content": "$$88$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$99$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$8\\times9\\times10\\times11=(8\\times10)\\times (9\\times11)=80\\times99$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6170", "queId": "b37de5822e144ae19f39497030bb8d81", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The following are the weights (in pounds) of ten people: $100, 115, 135, 140, 180, 197, 230, 250, 260, 270$. Find the $80$-th percentile. ", "answer_option_list": [[{"aoVal": "A", "content": "$$115$$ "}], [{"aoVal": "B", "content": "$$135$$ "}], [{"aoVal": "C", "content": "$$250$$ "}], [{"aoVal": "D", "content": "$$260$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$np=10(0.8)=8$ The $80$-th percentile is $\\frac{250+260}{2} = 255$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6172", "queId": "a19901b3895a4854ad4763a7f74897fa", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of all numbers x for which~$\\left\\textbar{} x^{2}-12x+34\\right\\textbar=2$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$4+6+8=18$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6176", "queId": "ca1012de68274b4daa8b80eb76a903c8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "13+4=, 57-17=． ", "answer_option_list": [[{"aoVal": "A", "content": "17, 85 "}], [{"aoVal": "B", "content": "18, 40 "}], [{"aoVal": "C", "content": "9,~ 64 "}], [{"aoVal": "D", "content": "17, 40 "}], [{"aoVal": "E", "content": "20, 50 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["13+4=17 , 57-17=40 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6192", "queId": "9d342fc550e04ccea5694184a9fcb714", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A consumer is willing to pay $\\textbackslash$12$ for a good, but is able to purchase it for $\\textbackslash$10$. What is the consumer surplus in this scenario? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\textbackslash$2$ "}], [{"aoVal": "B", "content": "$\\textbackslash$10$ "}], [{"aoVal": "C", "content": "$\\textbackslash$12$ "}], [{"aoVal": "D", "content": "$\\textbackslash$22$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The correct answer is A. $\\textbackslash$2$, as consumer surplus is calculated as the difference between the maximum price a consumer is willing to pay for a good and the actual price they pay, which is $\\textbackslash$12 - \\textbackslash$10 = \\textbackslash$2$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6196", "queId": "c115ae8f2a90446ab1e60077a492a98c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$x+2 = y$$ and $$y+4x = 12$$, then $$x=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables"], "answer_analysis": ["$$x+2=y$$, then $$x=y-2$$. We can get $$y+4(y-2)=12$$, $$y=4$$, $$x=y-2=2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6200", "queId": "bc956b71955f4367bb8ef5d275952b6d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\frac{1}{2}\\times \\frac{22}{7}\\div \\frac{11}{5}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{5}{7}$$ "}], [{"aoVal": "B", "content": "$$\\frac{4}{7}$$ "}], [{"aoVal": "C", "content": "$$\\frac{6}{7}$$ "}], [{"aoVal": "D", "content": "$$\\frac{3}{7}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$\\frac{1}{2}\\times \\frac{22}{7}\\div \\frac{11}{5}=\\frac{1}{2}\\times \\frac{22}{7}\\times \\frac{5}{11}=\\frac{5}{7}$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6203", "queId": "b8130b2c58a8487f9cea8266d53700b6", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the \\uline{\\textbf{average}} amount of sleep adults get each night? ", "answer_option_list": [[{"aoVal": "A", "content": "5 hours "}], [{"aoVal": "B", "content": "6 hours "}], [{"aoVal": "C", "content": "10 hours "}], [{"aoVal": "D", "content": "8 hours "}], [{"aoVal": "E", "content": "12 hours "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The average amount of sleep an adult gets is 8 hours. Everyone is different, however; where some adults function off of 6 hours, others need at least 9 hours or more to feel healthy and awake. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6205", "queId": "f31a001853074f3f8dad57d44226a08b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "(2016) A test has a mean of 80 with a standard deviation of 4. Which of the following scores is within one standard deviation of the mean? ", "answer_option_list": [[{"aoVal": "A", "content": "$$75$$ "}], [{"aoVal": "B", "content": "$$77$$ "}], [{"aoVal": "C", "content": "$$86$$ "}], [{"aoVal": "D", "content": "$$90$$ "}], [{"aoVal": "E", "content": "$$99$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["2016, Q 86 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6209", "queId": "dc4f5a695ade4404927b67f0050c9a69", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Cristi has to sell 10 glass bells that vary in price: 1 euro, 2 euro, 3 euro, 4 euro, 5 euro, 6 euro, 7 euro, 8 euro, 9 euro, 10 euro. In how many ways can Cristi divide all the grass bells in three packages so that all the packages have the same price? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "Such a division is not possible "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Distributive Law of Whole Numbers->Applying Distributive Law of Whole Numbers in Division"], "answer_analysis": ["1+2+3+4+5+6+7+8+9+10 = 55 is not divisible by 3. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6211", "queId": "ceacf946f0f847cf865322d455cb5633", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the solution of this equation: $$2^{2007}=4^{1003}\\cdot x$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "D", "content": "$$2^{2}$$ "}], [{"aoVal": "E", "content": "$$2^{2008}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable->Equations with Whole Number Coefficient"], "answer_analysis": ["$$2^{2007}=2^{2006}\\cdot x$$, $x=2$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6213", "queId": "b81f49ff92914d60a546bcd264ae17d1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is a solution of $$\\begin{cases}x-3=0 \\textbackslash\\textbackslash{} 3x-2y=7 \\end{cases}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "($x$,$y$)=($3$,$-1$) "}], [{"aoVal": "B", "content": "($x$,$y$)=($3$,$1$) "}], [{"aoVal": "C", "content": "($x$,$y$)=($-3$,$1$) "}], [{"aoVal": "D", "content": "($x$,$y$)=($-3$,$-1$) "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables"], "answer_analysis": ["$3-3=0$ $3\\cdot3-2\\cdot1=9-2=7$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6215", "queId": "aabc77a6b696449693caf26ef4f7e285", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$11+ 12 + 13 + 14 + 15 = 1 + 2 + 3 + 4 + 5 +$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$65$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$1+10 + 2+10 + 3+10 + 4+10 + 5+10 = 1+2+3+4+5 + 50$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6217", "queId": "e9ff0ff8143745a48685a33be20e4a7e", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "$$4\\times 9=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$16\\times 2$$ "}], [{"aoVal": "B", "content": "$$12\\times 3$$ "}], [{"aoVal": "C", "content": "$$7\\times 5$$ "}], [{"aoVal": "D", "content": "$$38\\times 1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$4\\times 9=36$$. $$\\text{A}$$: $$16\\times 2=32$$; $$\\text{B}$$: $$12\\times 3=36$$; $$\\text{C}$$: $$7\\times 5=35$$; $$\\text{D}$$: $$38\\times 1=38$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6228", "queId": "aac6735e17124f24938b982c9b2fd52f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{3}$ "}], [{"aoVal": "B", "content": "$\\dfrac{2}{5}$ "}], [{"aoVal": "C", "content": "$\\dfrac{3}{8}$ "}], [{"aoVal": "D", "content": "$\\dfrac{2}{9}$ "}], [{"aoVal": "E", "content": "$\\dfrac{5}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions"], "answer_analysis": ["$$\\frac{1}{2+\\dfrac{1}{2+\\dfrac{1}{2}}}=\\frac{1}{2+ \\dfrac{1}{ \\dfrac{5}{2}}}= \\frac{1}{2+ \\dfrac{2}{5}}= \\frac{1}{ \\dfrac{12}{5}}= \\frac{5}{12}$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6244", "queId": "c13f31ea3b4e4a8586ff33268f1195eb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many different three-digit numbers can we make using $6,7,8,$ and $9$? The digits can be repeated. ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$64$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Addition and Subtraction of Decimals"], "answer_analysis": ["$4\\times4\\times4=64$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6257", "queId": "e58110ad6e434e49be251600cce31ff5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the cost of eight mugs at £$$2.99$$ each? ", "answer_option_list": [[{"aoVal": "A", "content": "£$$23.92$$ "}], [{"aoVal": "B", "content": "£$$23.98$$ "}], [{"aoVal": "C", "content": "£$$24.00$$ "}], [{"aoVal": "D", "content": "£$$24.02$$ "}], [{"aoVal": "E", "content": "£$$24.08$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals->Multiplication of Decimals"], "answer_analysis": ["omitted "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6261", "queId": "c14aa2a065784bbd9b8aed2c0974ee35", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Given that $n!$ represent $n$ factorial, with $n!=1\\times 2\\times 3 \\times \\cdots \\times n$, then how many positive integer divisors of $12!$ are perfect squares? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$198$$ "}], [{"aoVal": "D", "content": "$$396$$ "}], [{"aoVal": "E", "content": "$$792$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6266", "queId": "c5cce67c900f474f9a1a66a4978addf4", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Happy Hotel is offering $$40 \\textbackslash\\%$$ off discount for any bookings. David booked a room, the new price is $$80$$ dollars cheaper than the original price, what was the original price． ", "answer_option_list": [[{"aoVal": "A", "content": "$$180$$ "}], [{"aoVal": "B", "content": "$$200$$ "}], [{"aoVal": "C", "content": "$$300$$ "}], [{"aoVal": "D", "content": "$$480$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$$80\\div40\\textbackslash\\%=200$$． so choose $$\\text{B}$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6267", "queId": "e58a0e9b6cc54573a4b08d515e689493", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is equivalent to $\\sqrt{16a^{16}}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$4a^{4}$ "}], [{"aoVal": "B", "content": "$4a^{8}$ "}], [{"aoVal": "C", "content": "$8a^{4}$ "}], [{"aoVal": "D", "content": "$8a^{8}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$sqrt{16a^{16}}=\\sqrt{16}\\sqrt{a^{16}}=4(a^{16\\times\\frac{1}{2}})=4a^{8}$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6272", "queId": "c5d5d834e1124ced992e9c50f3233792", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate: $$\\left(1+\\frac 12+\\frac 13+\\cdots +\\frac 1{149}\\right)\\times \\left(\\frac 12+\\frac 13+\\cdots +\\frac 1{149}+\\frac 1{150}\\right)$$$$-\\left(1+\\frac 12+\\frac 13+\\cdots +\\frac 1{149}+\\frac 1{150}\\right)\\times \\left(\\frac 12+\\frac 13+\\cdots +\\frac 1{149}\\right)=$$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{149}$ "}], [{"aoVal": "C", "content": "$\\dfrac{149}{150}$ "}], [{"aoVal": "D", "content": "$\\dfrac{1}{150}$ "}], [{"aoVal": "E", "content": "$$150$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Fast Calculation in Fractions"], "answer_analysis": ["Suppose $$\\left(\\frac 12+\\frac 13+\\cdots +\\frac 1{149}\\right)$$ as $$A$$, $$\\left(\\frac 12+\\frac 13+\\cdots +\\frac 1{150}\\right)$$ as $$B$$. $$(1+A)\\times B-(1+B)\\times A=B+AB-A-AB=B-A=\\frac 1{150}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6274", "queId": "af65b752133e4e088189a90fe2fce2de", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following is equal to the product shown below? $$\\frac{8}{4} \\cdot \\frac{12}{8} \\cdot \\frac{16}{12} \\cdot \\frac{20}{16} \\cdot \\cdot \\cdot \\frac{2024}{2020}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$253$$ "}], [{"aoVal": "B", "content": "$$503$$ "}], [{"aoVal": "C", "content": "$$1012$$ "}], [{"aoVal": "D", "content": "$$4048$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6276", "queId": "cede49b02b424488a9be3d092dbc7a4f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$6$$ pens cost as much as $$5$$ pencils, then $$36$$ pens cost as much as pencils. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$21$$ "}], [{"aoVal": "D", "content": "$$98$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Heuristics Skills-> Equivalent Substitution"], "answer_analysis": ["$$6$$ pens = $$5$$ pencils, we use $\\times6$ which give us $36$ pens = $30$ pencils "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6280", "queId": "b85c65b85f334568856bfd5a8fd989fe", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "What is the smallest whole number larger than the perimeter of any triangle with a side of length $12$ and a side of length $13$? (adapted from 2015 AMC8, Question 8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$51$$ "}], [{"aoVal": "D", "content": "$$49$$ "}], [{"aoVal": "E", "content": "$$33$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s\\textless12+13=25$. Adding $12+13$ to both sides of the inequality, we get $s+12+13\\textless25$, and because $s+12+13$ is the perimeter of our triangle, (B) 50 is our answer. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6282", "queId": "c5ddd90907f64da4a6030cb5ebfb7140", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "is a factor of $$1\\times2\\times3\\times4\\times5\\times6\\times7\\times8\\times9\\times10$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$71$$ "}], [{"aoVal": "B", "content": "$$73$$ "}], [{"aoVal": "C", "content": "$$75$$ "}], [{"aoVal": "D", "content": "$$77$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$1\\times2\\times3\\times4\\times5\\times6\\times7\\times8\\times9\\times10$$ is divisible by $$3$$ and $$25$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6287", "queId": "fc889c74107c461d8883f802f5ef7f6b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Simplify the expression: $4^{3}+4^{3}+4^{3}+4^{3}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$4^{12}$ "}], [{"aoVal": "B", "content": "$4^{27}$ "}], [{"aoVal": "C", "content": "$4^{3}$ "}], [{"aoVal": "D", "content": "$4^{4}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power"], "answer_analysis": ["omitted "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6291", "queId": "b3ede254e5f14843887e35b504133e10", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Teacher Nicole bought some badges and divided it equally among $8$ children. If everyone got $9$ badges, there would still be some badges remaining. What is the biggest possible and smallest possible number of badges Teacher Nicole could have bought? ", "answer_option_list": [[{"aoVal": "A", "content": "$$79$$，$$73$$ "}], [{"aoVal": "B", "content": "$$80$$，$$73$$ "}], [{"aoVal": "C", "content": "$$79$$，$$72$$ "}], [{"aoVal": "D", "content": "$$80$$，$$72$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["~\\uline{~~~~~~~~~~}~$\\div 8=9$ $\\text{R}$~\\uline{~~~~~~~~~~}~ Biggest possible remainder is $7$ while smallest possible remainder is $1$. Biggest possible number of badges is $$8\\times 9+7=79$$, while the least possible number of sweets is $$8\\times 9+1=73$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6292", "queId": "ab04909ac76146aebb86f0731624b045", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a rectangle, what is the ratio of one angle to the sum of all inner angles? ", "answer_option_list": [[{"aoVal": "A", "content": "1:2 "}], [{"aoVal": "B", "content": "1:3 "}], [{"aoVal": "C", "content": "1:4 "}], [{"aoVal": "D", "content": "2:5 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["$90:360=1:4$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6293", "queId": "d7f96e6ebf484e84a52d134e3044874a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Real numbers $x$ and $y$ satisfy $x^{3}+y^{3}=4$ and $xy = 2$. What is the value of $2xy+\\frac{x^{4}}{y^{2}}+\\frac{y^{4}}{x^{2}}$? (Adapted From 2020 AMC 10A Problem, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$-2$$ "}], [{"aoVal": "B", "content": "$$0$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$-4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$2xy+\\frac{x^{4}}{y^{2}}+\\frac{y^{4}}{x^{2}} = 2xy+\\frac{x^{6}+y^{6}}{x^{2}y^{2}} = \\frac{2xyx^{2}y^{2}+x^{6}+y^{6}}{x^{2}y^{2}}= \\frac{2x^{3}y^{3}+x^{6}+y^{6}}{x^{2}y^{2}} $ $= \\frac{(x^{3}+y^{3})^{2}}{x^{2}y^{2}} =\\frac{4^{2}}{4}= 4$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6298", "queId": "d3814d5ccfe1444cbd8d239ed3be08df", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Real numbers $x$ and $y$ satisfy $x+y=4$ and $x\\cdot y=-2$. What is the value of $x+\\frac{x^{3}}{y^{2}}+\\frac{y^{3}}{x^{2}}+y$? (2020 AMC 10A Problem, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$360$$ "}], [{"aoVal": "B", "content": "$$400$$ "}], [{"aoVal": "C", "content": "$$420$$ "}], [{"aoVal": "D", "content": "$$440$$ "}], [{"aoVal": "E", "content": "$$480$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$x+\\frac{x^{3}}{y^{2}}+\\frac{y^{3}}{x^{2}}+y=x+\\frac{y^{3}}{x^{2}}+y+ \\frac{x^{3}}{y^{2}}=\\frac{x^{3}}{x^{2}}+\\frac{y^{3}}{x^{2}}+\\frac{y^{3}}{y^{2}}+\\frac{x^{3}}{y^{2}}$ Continuing to combine $\\frac{x^{3}+y^{3}}{x^{2}}+\\frac{x^{3}+y^{3}}{y^{2}}=\\frac{\\left(x^{2}+y^{2}\\right)\\left(x^{3}+y^{3}\\right)}{x^{2} y^{2}}=\\frac{\\left(x^{2}+y^{2}\\right)(x+y)\\left(x^{2}-x y+y^{2}\\right)}{x^{2} y^{2}}$ From the givens, it can be concluded that $x^{2}y^{2}=4$. Also, $(x+y)^{2}=x^{2}+2 x y+y^{2}=16$ This means that $x^{2}+y^{2}=20$. Substituting this information into $\\frac{\\left(x^{2}+y^{2}\\right)(x+y)\\left(x^{2}-x y+y^{2}\\right)}{x^{2} y^{2}}$, we have $\\frac{20\\times 4\\times22}{4}=440$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6300", "queId": "b3fc95bb4edc48fabd61104bc8a55b91", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Given that $$a\\Phi b=2\\times a-b$$, for example, $$2\\Phi 1 = 2\\times2 -1$$, what is $$3\\Phi4$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition"], "answer_analysis": ["Nil "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6310", "queId": "e11bb62aeca44e8784adeb0b5cd02e08", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For how many integers $x$ is the number $x^{4}-51 x^{2}+50$ negative? ( 2014 AMC 10B Problems, Question \\#20) ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["First, note that $50+1=51$, which motivates us to factor the polynomial as $\\left(x^{2}-50\\right)\\left(x^{2}-1\\right)$. Since this expression is negative, one term must be negative and the other positive. Also, the first term is obviously smaller than the second, so $x^{2}-50\\textless0\\textless x^{2}-1$. Solving this inequality, we find $1\\textless x^{2}\\textless50$. There are exactly $12$ integers $x$ that satisfy this inequality, $\\pm\\textbackslash{2,3,4,5,6,7\\textbackslash}$. Thus our answer is $(\\mathbf{C}) 12$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6312", "queId": "cefc7e0f8a3942d4a6c66c503d262738", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many of the following options are equations? 1. $x = y$ 2. $x \\textgreater{} 1$ 3. $x \\geq x-1$ 4. $ 1 = 2$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["1 and 4 are equations. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6314", "queId": "dc9aaa0cb90e44348fa65ecdf7384677", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many sections will Linda get if she cuts a piece of wood $4$ times? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "It depends on how long the piece of wood is. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$4 + 1 = 5$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6315", "queId": "b87a6d0c2ea140c29cc42b6272f41d50", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "What is the product of $$628$$ and $$6$$?（) ", "answer_option_list": [[{"aoVal": "A", "content": "$$3628$$ "}], [{"aoVal": "B", "content": "$$3668$$ "}], [{"aoVal": "C", "content": "$$3728$$ "}], [{"aoVal": "D", "content": "$$3768$$ "}]], "knowledge_point_routes": ["Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Multiplication of Whole Numbers->Multiplication of Multi-Digit Numbers and 1-Digit Numbers->Multiplication of 3-Digit and 1-Digit (with regrouping for more than once)", "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["Stack the two numbers as shown below ,~ lining up the unit digits Remember that the 2 in 628 stands for 2 tens(20) ,the 6 in the 628 stands for 6 hundreds(600) First, multiply the ones~ $6\\times8=48$~, regroup the 4 tens to the tens column Write 8 in the ones place. Then,~ Multiply and add the tens .~$2\\times6+4=16$ Write 6 in the tens place and regroup the 1 hundred. Last, multiply and add the hundreds.~$6\\times6+1=37$ Write 7 in the hundreds place and write 3 in the thousands place. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6316", "queId": "ab1d072e77e24347b66e0a0c9ec58384", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $x+2y=3$, what is $2^{x}\\cdot 4^{}y$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$2^{}x \\cdot 4^{}y=2^{}x\\cdot 2^{2y}=2^{x+2y}=2^{3}=8$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6320", "queId": "f366fe8cf09147ac81fa860676b17f1b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In the animal school, some sheep are taking lessons. The teacher cow finds out that the sheep have $$24$$ legs altogether. How many sheep are there? (Adapted from 2012 Math Kangaroo Problem, Level 3-4, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$24 \\div 4 = 6$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6324", "queId": "bd082394cade401b86733ef37a182ce1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $1985^{}\\text{th}$ digit at the right of the decimal point in the decimal expression of $\\dfrac{1}{7}$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"], "answer_analysis": ["$$\\frac{1}{7}=0.\\overline{142857}$$, it is a decimal which repeats in cycles of $6$ digits. Every $6$\\textsuperscript{th}~digit is $7$. The $1986$\\textsuperscript{th} digit is $7$, so the $1985$\\textsuperscript{th} digit is $5$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6327", "queId": "dca47bcf3a0c47a6a6318a82786aef7a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$6.98-4.53+10.02-5.27=$$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$6.9$$ "}], [{"aoVal": "B", "content": "$$7.0$$ "}], [{"aoVal": "C", "content": "$$7.1$$ "}], [{"aoVal": "D", "content": "$$7.2$$ "}], [{"aoVal": "E", "content": "$$7.3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals"], "answer_analysis": ["$$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde6.98-4.53+10.02-5.27$$ $$=(6.98+10.02)-(4.53+5.27)$$ $$=17-9.8$$ $$=7.2$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6337", "queId": "d820c08fb333427d8f6516c97c7a2bd5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many different three-digit numbers can we make using $6,7,8,$ and $9$? The digits can be repeated. ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$64$$ "}], [{"aoVal": "E", "content": "$$72$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Addition and Subtraction of Decimals"], "answer_analysis": ["$4\\times4\\times4=64$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6338", "queId": "dcad602ca5034aa88013d8ab8138348d", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For how many values of $a$ is it true that the line $y=x+a^{2}-6$ passes through the vertex of the parabola $y=x^{2}-4x+a^{2}$? (Adapted From 2005 AMC 12B Problem, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "infinitely many "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["We see that the vertex of the quadratic function $y=x^{2}-4x+a^{2}$ is $\\left(2, a^{2}-4\\right)$. If $\\left(2, a^{2}-4\\right)$ will be on the line $y=x+a^{2}-6$, $a^{2} -4=2+a^{2}-6$. Solve for $a$, any value of $a$ will satisfy this equation. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6343", "queId": "ca95bd545dfa42a1b741bd45f970cc5b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Line $l\\_1$ has equation $2x-y=3$ and goes through $A=(1,-1)$. Line $l\\_2$ has equation $y=1$ and meets line $l\\_1$ at point $B$. Line $l\\_3$ has negative slope, goes through point $A$, and meets $l\\_2$ at point $C$. The area of $\\triangle A B C$ is $3$. What is the slope of $l\\_3$? (Adapted From 2013 AMC 12B Problems, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$-\\frac23$$ "}], [{"aoVal": "B", "content": "$$-\\frac34$$ "}], [{"aoVal": "C", "content": "$$-1$$ "}], [{"aoVal": "D", "content": "$$-\\frac43$$ "}], [{"aoVal": "E", "content": "$$-2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Line $l\\_1$ has the equation $y=2x-3$ when rearranged. Substituting $1$ for $y$, we find that line $l\\_2$ will meet this line at point $(2,1)$, which is point $B$. We call $\\overline{B C}$ the base and the altitude from $A$ to the line connecting $B$ and $C, y=1$, the height. The altitude has length $\\textbar-1-1\\textbar=2$. The area of $\\triangle A B C=3$. Since $A=\\frac{bh}{2}, b=3$. Points that are on the line $y= 1$ and has a distance of $3$ from $B$ are $(5,1)$ and $(-1,1)$. Since $l\\_3$ has negative slope, point $C$ is $(-1,1)$. $l\\_3$ passes through $(-1,1)$ and $(1,-1)$, and thus has slope $\\frac{1-(-1)}{-1-1}=(\\mathbf{C}) -1$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6344", "queId": "b896fa55f34f4f99abbbcea53f56cc0d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the median of the following distribution: 6, 2, 9, 4, 7, 3? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$5.5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$6.5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The median of the distribution is 5. The problem is easier if vou put the scores in order: 2, 3, 4, 6, 7, 9. Since the distribution has an even number of scores, there is no middle score and you must average the two middle scores, 4 and 6. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6345", "queId": "afa8f1055a15453b85fb2284e451cc28", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "26-18=． ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Addition and Subtraction of Whole Numbers->Adding and Subtracting within 10000->Subtraction of 3-digit Numbers", "Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$26-18=8$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6346", "queId": "e13a89fdc4984e218df401e79ca3f7a2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Find the missing number: $$512\\times2 = 32\\times $$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["$$512\\times2=1024=32\\times32$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6349", "queId": "c61d2b67feee4a7bbecdefc94c2000c1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alicia and Emily agreed to meet at the cinema at $3.55\\rm{pm}$. Emily left her house at $1.47\\rm{pm}$ but arrived at the cinema $17$ minutes late. How long was Emily\\textquotesingle s journey from her house to the cinema? ", "answer_option_list": [[{"aoVal": "A", "content": "$$189$$ minutes "}], [{"aoVal": "B", "content": "$$172$$ minutes "}], [{"aoVal": "C", "content": "$$216$$ minutes "}], [{"aoVal": "D", "content": "$$206$$ minutes "}], [{"aoVal": "E", "content": "None of the above. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion"], "answer_analysis": ["3: 55pm - 1: 47om + 15 minutes = 145 minutes. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6360", "queId": "afbabeab786049a187c9b2e0bee0dea0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate~ ~ ~$\\dfrac{2014}{2013-\\dfrac{2012}{2011-\\dfrac{2010}{5-\\dfrac{4}{3-\\dfrac{2}{1}}}}}$ After calculating, Chuan says that answer is D. Is he right or wrong? If not, choose the right option. ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{2014}$ "}], [{"aoVal": "B", "content": "$\\dfrac{1}{2013}$ "}], [{"aoVal": "C", "content": "$$2014$$ "}], [{"aoVal": "D", "content": "$$2013$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions"], "answer_analysis": ["$$3- \\frac{2}{1}=1$$ $$5- \\frac{4}{1}=1$$ $$\\cdots \\cdots$$ $$2013- \\frac{2012}{1}=1$$ $$\\frac{2014}{1}=2014$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6361", "queId": "fcc77df46ee542bbac5d46dfb7d59401", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which number has to be subtracted from $-17$ in order to obtain $-33$? (2017 Math Kangaroo Problem, Level 7-8, Question \\#3) ", "answer_option_list": [[{"aoVal": "A", "content": "$$-50$$ "}], [{"aoVal": "B", "content": "$$-16$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$40$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$(-17)-16=-33$, so the answer is $C$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6366", "queId": "afbcc8ffd87c4a63ac6327c2a3837274", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "If $$\\left\\textbar{} 5x+3 \\right\\textbar=8$$, $x=$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$-1$$ or $$\\frac{11}{5}$$ "}], [{"aoVal": "C", "content": "$$1$$ or $$\\frac{1}{5}$$ "}], [{"aoVal": "D", "content": "$$1$$ or $$-\\frac{11}{5}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities->Solving Inequalities"], "answer_analysis": ["$$5x+3=\\pm 8$$ $$x=1$$ or $$x=-\\frac{11}{5}$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6368", "queId": "b43857a54b7a42939e8af35d602fd625", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "The operator $$\\bigtriangleup$$ acts on two numbers to give the following outcomes: $$3 \\bigtriangleup 2 = 12$$ $$4 \\bigtriangleup 5 = 40$$ $$5 \\bigtriangleup 9 = 90$$ $$6 \\bigtriangleup 1 = 12$$ What is $$2 \\bigtriangleup 7$$ equal to? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition"], "answer_analysis": ["The pattern of the operation is $$a \\bigtriangleup b = a\\times b\\times2$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6369", "queId": "e5e5c86f83f44ec28ec8479ba6b94c7c", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Find the integer part of the following fractional expression: $$ \\frac{1}{\\frac{1}{50}+\\frac{1}{51} +\\frac{1}{52} +\\frac{1}{53} +\\frac{1}{54}} $$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$50$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6371", "queId": "e5e62635602944a8a1b5bf961ae0aa7f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Three football teams participate in a sport tournament. Each team plays the other two teams exactly once. In each game, the winner gets three points and the loser doesn\\textquotesingle t get any points. If the game ends in a tie, each team gets $1$ point. At the end of tournament, Which number of points is it impossible for any team to have? (2022 Math Kangaroo Problem, Level 3-4, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Each team plays $2$ games. $1$ points: a lost and a tie. $2$ points: two ties. $3$ points: a lost and a win. $4$ points: a win and a tie. $6$ points: two wins. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6373", "queId": "afc545fcfecc43eea647e128aa5deb3d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Suppose $5\\times8=\\triangle$, $4\\times7=\\angle$, $3\\times9=\\square$. Arrange the three shapes according to their values from smallest to largest. ", "answer_option_list": [[{"aoVal": "A", "content": "$\\angle$ $\\triangle$ $\\square$ "}], [{"aoVal": "B", "content": "$\\square$ $\\angle$ $\\triangle$ "}], [{"aoVal": "C", "content": "$\\triangle$ $\\angle$ $\\square$ "}], [{"aoVal": "D", "content": "$\\triangle$ $\\square$ $\\angle$ "}], [{"aoVal": "E", "content": "$\\square$ $\\triangle$ $\\angle$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$\\square=27$ $\\angle=28$ $\\triangle=40$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6374", "queId": "dcd1627cc09e4af99c42a95ee5679ece", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The students in Mr. Neatkin\\textquotesingle s class took a penmaship test. Two-thirds of the boys and~$\\dfrac{3}{4}$~of the girls passed the test, and an equal number of boys and girls passed the test. What is the minimum possible number of students in the class? (2008 AMC 8, 20) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$17$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["Let~$b$~be the number of boys and~$g$~be the number of girls. $\\dfrac{2}{3}b=\\dfrac{3}{4}g\\textbackslash{} \\Rightarrow\\textbackslash{} b=\\dfrac{9}{8}g$ For~$g$~and~$b$~to be integers,~~must cancel out with the denominator, and the smallest possible value is . This yields~~boys. The minimum number of students is~$8+9=\\boxed{\\left( B\\right)17}$ Solution 2 We know that~$\\dfrac{2}{3}B=\\dfrac{3}{4}G\\textbackslash{} or\\textbackslash{} \\dfrac{6}{9}B=\\dfrac{6}{8}G.$~So, the ratio of the number of boys to girls is~$9:8$. The So, the ratio of the number of boys to girls is~$8+9=\\boxed{\\left( B\\right)17}$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6375", "queId": "fcd1cde102c1495fba0d438fa0a3df51", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In how many different ways can Chloe select two digits out of $$ 0$$, $$1$$, $$ 2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, and $$9$$ and put into the two boxes to make the below equality correct? $$ 20- \\square =22-\\square $$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6379", "queId": "f83d59ccf5c04efda09f819e1180433b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I multiply a whole number by itself, then multiply that product by itself. The ones digit of my final product cannot be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["The ones digit of the product is the same as the ones digit of $$0^{4}$$, $$1^{4}$$, $$2^{4}$$, $$3^{4}$$, $$4^{4}$$, $$5^{4}$$, $$6^{4}$$, $$7^{4}$$, $$8^{4}$$, or $$9^{4}$$. The ones digit can be $$0$$, $$1$$, $$5$$, or $$6$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6383", "queId": "f3a2c3461c97422b90c154e478dc715c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of five consecutive whole numbers is $$280$$. What is the sum of the next five consecutive whole numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$285$$ "}], [{"aoVal": "B", "content": "$$305$$ "}], [{"aoVal": "C", "content": "$$405$$ "}], [{"aoVal": "D", "content": "$$425$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["Each whole number in the second sequence is $$5$$ more than the corresponding number in the first sequence. We have $$280 +5 \\times5 = 305$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6387", "queId": "c1c5d333928c44ceb0c183d45b862f3a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the range of the number in tens place? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0-5$$ "}], [{"aoVal": "B", "content": "$$1-5$$ "}], [{"aoVal": "C", "content": "$$0-9$$ "}], [{"aoVal": "D", "content": "$$1-9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6391", "queId": "d859f1b1062040bda5e450d5fa97a04f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For $\\triangle ABC$, all its side lengths are integers. The primeter of $\\triangle ABC$ with a side of length $25$ and a side length of $18$ is at least ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$52$$ "}], [{"aoVal": "D", "content": "$$51$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"], "answer_analysis": ["We know from the triangle inequality that the last side, $s$, fulfills $s+18\\textgreater25$. Therefore, $P\\textgreater25+25$. The least integer value of $P$ is $51$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6397", "queId": "fceaff9aa8b04b04b2f080ed6ace457f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$a$ and $$b$$ are reciprocals， $$\\frac{2}{a}\\div \\frac{b}{12}=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{24}$$ "}], [{"aoVal": "C", "content": "$$\\frac{b}{6a}$$ "}], [{"aoVal": "D", "content": "$$\\frac{a}{6b}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering->Comparing and Ordering Fraction by Comparing Its Reciprocal"], "answer_analysis": ["$$\\frac{2}{a}\\div \\frac{b}{12}= \\frac{2}{a}\\times \\frac{12}{b}= \\frac{24}{ab}=24 $$， "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6405", "queId": "cad9ec0c473a465d9ffd82a2f1b91986", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$x=120$$, what is the value of $$\\frac{x^{2}}{12^{2}}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$100$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$\\frac{x^{2}}{12^{2}}=\\left(\\frac{x}{12}\\right)^{2}=\\left(\\frac{120}{12}\\right)^{2}=\\left(10\\right)^{2}=100$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6410", "queId": "e60bfd12e66444c8a717c7866f8e1f26", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Let $Z$ be a $6$-digit positive integer, such as $247247$, whose first three digits are the same as its last three digits taken in the same order. Which of the following numbers must also be a factor of $Z$? (adapted from 2017 AMC 8 Problem, Question \\#$7$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$1001$$ "}], [{"aoVal": "D", "content": "$$111$$ "}], [{"aoVal": "E", "content": "$$1111$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"], "answer_analysis": ["chair number "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6415", "queId": "dcfaf7acc2d84fb4a30374f747c754f3", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following is neither a positive nor a negative number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$-23$$ "}], [{"aoVal": "C", "content": "$$0$$ "}], [{"aoVal": "D", "content": "$$-1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Knowing the Number Lines"], "answer_analysis": ["$$\\text{A}$$ is a positive number, $$\\text{B}$$ and $$\\text{D}$$ are two negative numbers, $$\\text{C}$$ is zero, which is neither positive nor negative. We choose $$\\text{C}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6425", "queId": "c1ec2b3aa244417898c19619cf7c6e5a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$$$Calculate$$$$ $$\\left (403 \\frac{3}{5}+183 \\frac{5}{11}+155 \\frac{3}{13}+118 \\frac{12}{17}\\right ) \\div$$$$ \\left~~( \\frac{1009}{15}+ \\frac{1009}{33}+ \\frac{1009}{39}+ \\frac{1009}{51}\\right )$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$5.5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$6.5$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Fast Calculation in Fractions"], "answer_analysis": ["$$\\left (403 \\frac{3}{5}+183 \\frac{5}{11}+155 \\frac{3}{13}+118 \\frac{12}{17}\\right ) \\div$$$$ \\left ( \\frac{1009}{15}+ \\frac{1009}{33}+ \\frac{10009}{39}+ \\frac{1009}{51}\\right )$$ $$=2018\\left ( \\frac{1}{5}+ \\frac{1}{11}+ \\frac{1}{13}+ \\frac{1}{17}\\right ) \\div \\frac{1000}{3}\\left ( \\frac{1}{5}+ \\frac{1}{11}+ \\frac{1}{13}+ \\frac{1}{17}\\right )$$ $=6$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6428", "queId": "c1f1d5711392441983087fcbea4d5003", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$(x+5)-(x+4)+(x+3)-(x+2)+(x+1)-(x+0)=$$~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$-3$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$3x+3$$ "}], [{"aoVal": "D", "content": "$$6x+3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["We can observe that when we remove the parentheses, all the $$x$$s are offset. $$5-4+3-2+1-0= 3$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6432", "queId": "f876f3e090ff46c3b9880059fd27f437", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Simplify the following expression: $$4a-3(a-b)$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$a-b$$ "}], [{"aoVal": "B", "content": "$$a+b$$ "}], [{"aoVal": "C", "content": "$$a+3b$$ "}], [{"aoVal": "D", "content": "$$a-3b$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Using a Letter to Represent an Unknown Number"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6439", "queId": "d4032f4f504e4feab356fc2493954e44", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There were $$9$$ pieces of paper. Some of them were cut into three pieces. As a result, there are now $$15$$ pieces of paper now. How many pieces of paper were cut? ($$2005$$ Math Kangaroo Problem, Level $$3-4$$, Question \\#$$17$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"], "answer_analysis": ["$15-9\\times1=6$ $6\\div(3-1)=3$ pieces of paper were cut. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6441", "queId": "cf7b2c3e74fe48d6858dcdad5950afe3", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For how many values of $a$ is it true that the line $y=x+a$ passes through the vertex of the parabola $y=x^{2}+a^{2}$? (2005 AMC 12B Problem, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "infinitely many "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["We see that the vertex of the quadratic function $y=x^{2}+a^{2}$ is $\\left(0, a^{2}\\right)$. The $y$-intercept of the line $y=x+a$ is $(0, a)$. We want to find the values (if any) such that $a=a^{2}$. Solving for $a$, the only values that satisfy this are 0 and 1, so the answer is $(\\text{C}) 2$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6442", "queId": "c677aeae71be49a3a1f00de87ecf8a3c", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Values for $A, B, C$, and $D$ are to be selected from $\\textbackslash{1,2,3,4,5,6\\textbackslash}$ without replacement (i.e. no two letters have the same value). How many ways are there to make such choices so that the two curves $y=A x^{2}+B$ and $y=C x^{2}+D$ intersect? (The order in which the curves are listed does not matter; for example, the choices $A=3, B=2, C=4, D=1$ is considered the same as the choices $ A=4, B=1, C=3, D=2 $.) ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$180$$ "}], [{"aoVal": "E", "content": "$$360$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Setting $y=A x^{2}+B=C x^{2}+D$, we find that $A x^{2}-C x^{2}=x^{2}(A-C)=D-B$, so $x^{2}=\\frac{D-B}{A-C} \\geq 0$ by the trivial inequality. This implies that $D-B$ and $A-C$ must both be positive or negative. If two distinct values are chosen for $(A, C)$ and $(B, D)$ respectively, there are 2 ways to order them so that both the numerator and denominator are positive/negative (increasing and decreasing). We must divide by 2 at the end, however, since the 2 curves aren\\textquotesingle t considered distinct. Calculating, we get $$ \\frac{1}{2} \\cdot\\left(\\begin{array}{l} 6 \\textbackslash\\textbackslash{} 2 \\end{array}\\right)\\left(\\begin{array}{l} 4 \\textbackslash\\textbackslash{} 2 \\end{array}\\right) \\cdot 2=(\\text { C) } 90 $$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6450", "queId": "dd19d414059b42e0a3a13ce1c308bbcf", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For how many integers $x$ is the number $x^{4}-7x^{2}+12$ negative? ( 2014 AMC 10B Problems, Question \\#20) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$0$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Factor the polynomial as $\\left(x^{2}-4\\right)\\left(x^{2}-3\\right)$. Since this expression is negative, one term must be negative and the other positive. Also, the first term is obviously smaller than the second, so $x^{2}-4\\textless0\\textless x^{2}-3$. Solving this inequality, we find $3\\textless x^{2}\\textless4$. There is no integer $x$ that satisfies this inequality. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6455", "queId": "c2044f97cec44f368936f656599a0f1a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Joe writes an expression $\\frac59\\times\\frac9{13}\\times\\frac{13}{17}\\cdots $ Following the pattern, he writes middle fraction is \\frac{45}{49}. What is the result of the expression? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac5{49}$ "}], [{"aoVal": "B", "content": "$\\frac5{89}$ "}], [{"aoVal": "C", "content": "$\\frac5{17}$ "}], [{"aoVal": "D", "content": "$\\frac1{31}$ "}], [{"aoVal": "E", "content": "$\\frac5{81}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["The last fraction should be $\\frac{85}{89}$, so the answer is $\\frac5{89}.$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6459", "queId": "c20bbf44110943ad8650b6d3675365f9", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "There were three color cups in the shop. At the beginning, there was only one cup of each kind. Later, there were five more blue cups, three more red cups, and one more yellow cup. How many cups were there in total at last?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition and Subtraction of Whole Numbers->Questions Involving Addition and Subtraction"], "answer_analysis": ["To calculate the total number of cups, do not need to consider the color of the cup. At the beginning, there were three cups. The number at last is $3+5+3+1=12$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6461", "queId": "bd937214b6494de599518518b6abfc70", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "One apple, one banana and two peaches together weigh $12$ lbs. One apple and one peach together weigh $5$ lbs. One banana and $2$ peaches together weigh $5$ lbs more than one apple and one peach weigh together. Each peach weighs the same. How many pounds does one banana weigh? ", "answer_option_list": [[{"aoVal": "A", "content": "$3$ lbs "}], [{"aoVal": "B", "content": "$4$ lbs "}], [{"aoVal": "C", "content": "$5$ lbs "}], [{"aoVal": "D", "content": "$6$ lbs "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution"], "answer_analysis": ["We can write their relationships as the equations below: $A+B+P+P=12$ $A+P=5$ $B+P+P=A+P+5$ So, $B+P+P=5+5=10$, $A=12-10=2$, $P=5-2=3$, $B=12-2-3-3=4$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6464", "queId": "c68d4d62c0434815b6073abd1e3783e2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Suppose that $x$ and $y$ are nonzero real numbers such that $\\frac{x+y}{x}=2$, what is the value of $\\frac{x}{y}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "B", "content": "$$-1$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Rearranging, we find $x+y=2x, -x=y, \\frac xy = -1$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6475", "queId": "cf98949b3d1f4f5894638e8ef3f3bcf3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Victor has $3$ siblings, and his mom is buying them chocolate cake for afternoon tea. His mom decides that all kids should receive the same amount of cake. What percent of the cake will Victor get? ", "answer_option_list": [[{"aoVal": "A", "content": "$33.3$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$25$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["$1\\div 4=25\\textbackslash\\%$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6479", "queId": "f89ff2d96572452d9bebb97b05f1c844", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is $$y$$ if $$56y=728$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$y = 728 \\div 56 = 13$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6481", "queId": "c21dc34692044b3292b0b395630c5aff", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$x-y = -2$$ and $$y+4x = 12$$, then $$x=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$x+2=y$$, then $$x=y-2$$. We can get $$y+4(y-2)=12$$, $$y=4$$, $$x=y-2=2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6486", "queId": "e6506a2c2cca4b91868e19bfab0efe12", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Think Store is selling boba plushies at $100$ dollars each. The plushies are so in demand that Think Store decides to increase the price of the plushies by $30\\textbackslash\\%$, but if a students buy $2$ boba plushies at the same time, there is a $40\\textbackslash\\%$ discount for the second plushie. How much does it costs to buy $2$ plushies? ", "answer_option_list": [[{"aoVal": "A", "content": "$$260$$ "}], [{"aoVal": "B", "content": "$$208$$ "}], [{"aoVal": "C", "content": "$$182$$ "}], [{"aoVal": "D", "content": "$$200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"], "answer_analysis": ["$100\\times (1+30\\textbackslash\\%)=130$ $130+130\\times (1-40\\textbackslash\\%)=130+78=208$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6489", "queId": "d42ba82202b34e13abb173d74824b28d", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "The sum of the repeating decimals~$0.\\overline{163}$~and~$0.\\overline{614}$~is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.7$$ "}], [{"aoVal": "B", "content": "$\\dfrac{777}{1000}$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$\\dfrac{7}{9}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals"], "answer_analysis": ["$0.163163163\\cdots+0.614614614\\cdots=0.777777777\\cdots=\\dfrac{7}{9}$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6490", "queId": "f40748be07574ba2a0f22ed11464b232", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Four numbers are written in a row. The average of the first two is $21$ , the average of the middle two is $26$ , and the average of the last two is $30$ . What is the average of the first and last of the numbers? (2022 AMC 8 Problems, Question \\#16) ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "$$28$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Note that the sum of the first two numbers is $21 \\cdot 2=42$, the sum of the middle two numbers is $26 \\cdot 2=52$, and the sum of the last two numbers is $30 \\cdot 2=60$. It follows that the sum of the four numbers is $42+60=102$, so the sum of the first and last numbers is $102-52=50$. Therefore, the average of the first and last numbers is $50 \\div 2=$ (B) $25$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6494", "queId": "ef74e2ea22774e13a6658606567910cf", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which expression has the same result as $1+2+3+4+2+4+6+8+3+6+9+12+4+8+12+16$? ", "answer_option_list": [[{"aoVal": "A", "content": "$(1+2+3+4)\\times 6$ "}], [{"aoVal": "B", "content": "$(1+2+3+4)$\\textsuperscript{2} "}], [{"aoVal": "C", "content": "$(16+1)\\times16\\div2$ "}], [{"aoVal": "D", "content": "$1\\times1+2\\times2+3\\times2+4\\times3+6+8\\times2+12\\times2+16$ "}], [{"aoVal": "E", "content": "$4\\times20$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$(1+2+3+4)\\times 1+(1+2+3+4)\\times 2+(1+2+3+4)\\times 3+(1+2+3+4)\\times 4=(1+2+3+4)\\times (1+2+3+4)$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6507", "queId": "ef815952705f47f78c4eaa9da6c459fd", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose? Meat: beef, chicken, pork Vegetables: baked beans, corn, potatoes, tomatoes Dessert: brownies, chocolate cake, chocolate pudding, ice cream~($2001$ AMC $8$ Problem, Question \\#$14$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$80$$ "}], [{"aoVal": "E", "content": "$$144$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$\\_3C\\_1\\times \\_4C\\_2\\times \\_4C\\_1=72$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6513", "queId": "ef8876a9440d432783b14e5a5140f50b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If the value of $$x+2y$$ is $$3$$, then what is the result of $$\\frac{1}{2}x+y-1$$?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{2}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$\\frac{1}{2}x+y-1=\\frac{1}{2}(x+2y)-1=\\frac{3}{2}-1=\\frac{1}{2}$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6516", "queId": "d8ceb2c2fec6460698cf83fc77917dfe", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of the digits in the number $$3567$$? (adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$7$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$3567$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$22$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$356$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"], "answer_analysis": ["$3+5+6+7=21$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6520", "queId": "cfc1f9547b134edbb55c5c7ec3ea82fd", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Which of the following is the largest fraction? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\dfrac{3}{5}$$ "}], [{"aoVal": "B", "content": "$$\\dfrac{3}{6}$$ "}], [{"aoVal": "C", "content": "$$\\dfrac{3}{7}$$ "}], [{"aoVal": "D", "content": "$$\\dfrac{3}{8}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["Same numerator, so smaller denominator means larger fraction. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6522", "queId": "eb03cb1626fd4055b3bc7442441da7da", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If I multiply $$333333333333333$$ by $$777777777777777$$ and add the first and last digits of the product, the sum is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["Just as for $$3\\times7$$, $$33\\times77$$, and $$333\\times777$$, the first digit is a $$2$$, the last digit is a $$1$$, and the sum is $$2+1=3$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6527", "queId": "e67a860ea37542eeb2c58fad90b27e5d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$5$$ apples cost as much as $$16$$ pineapples, then $$15$$ apples cost as much as pineapples. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$21$$ "}], [{"aoVal": "D", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"], "answer_analysis": ["$$5$$ apples = $$16$$ pineapples $$5\\times3$$ apples = $15$ apples $$16\\times3$$ pineapples = $48$ pineapples "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6535", "queId": "dd6d487fc83e475d82a2cda577e56c95", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Fill in the blank according to the pattern. $$1, 1, 2, 3, 5, 8, $$~\\uline{~~~~~~~~~~}~$$, 21, 34$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$17$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["Fibonacci number. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6552", "queId": "c6de9a3c418b49a388cc73dbf34e3389", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The outside temperature in a town is $-18$ $^{}o$$C$. What change in the temperature, would bring the outside temperature to $0$ $^{}o$$C$? ", "answer_option_list": [[{"aoVal": "A", "content": "$-19$ "}], [{"aoVal": "B", "content": "$-18$ "}], [{"aoVal": "C", "content": "$18$ "}], [{"aoVal": "D", "content": "$0$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Negative Numbers"], "answer_analysis": ["The opposite of $-18$ is $18$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6556", "queId": "eb258855bb7d4698ab49cdc0cb8eee4f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Suppose that $x$ and $y$ are nonzero real numbers such that $\\frac{5 x+y}{x-4y}=-1$. What is the value of $\\frac{x+3 y}{3 x-y}$? (Adapted From 2017 AMC 10B Problems, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Rearranging, we find $5 x+y=-x+4y$, or $6x=3 y \\Longrightarrow y=2x$. Substituting, we can convert the second equation into $$\\frac{x+6 x}{3 x-2x}=\\frac{7 x}{x}=\\text { (C) } 7$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6559", "queId": "cfed907132794e63ab56660c716a691b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Debbie spent $12$ dollars on a book and a volleyball. The volleyball costed $4$ dollars than the book. How many dollars did she spend on the volleyball? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$(12 + 4) \\div 2 = 8$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6574", "queId": "d90f402035474c86ab7475f508261b9a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Let $a, b$, and $c$ be three distinct one-digit numbers. What is the maximum value of the sum of the roots of the equation $(x-a)(x-b)+(x-b)(x-c)=0$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$15.5$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$16.5$$ "}], [{"aoVal": "E", "content": "$$17$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Unary Quadratic Equations"], "answer_analysis": ["Expanding the equation and combining like terms results in $2 x^{2}-(a+2 b+c) x+(a b+b c)=0$. By Vieta\\textquotesingle s formula the sum of the roots is $\\frac{-[-(a+2 b+c)]}{2}=\\frac{a+2 b+c}{2}$. To maximize this expression we want $b$ to be the largest, and from there we can assign the next highest values to $a$ and $c$. So let $b=9, a=8$, and $c=7$. Then the answer is $\\frac{8+18+7}{2}= 16.5$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6576", "queId": "e6b03156163c4220be5eed5f95011082", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "For how many integers $x$ is the number $x^{4}-7x^{2}+10$ negative? ( 2014 AMC 10B Problems, Question \\#20) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["Factor the polynomial as $\\left(x^{2}-5\\right)\\left(x^{2}-2\\right)$. Since this expression is negative, one term must be negative and the other positive. Also, the first term is obviously smaller than the second, so $x^{2}-5\\textless0\\textless x^{2}-2$. Solving this inequality, we find $2\\textless x^{2}\\textless5$. There are exactly $2$ integers $x$ that satisfy this inequality, $\\pm 2$. Thus our answer is $(\\mathbf{A}) 2$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6580", "queId": "d006192beabd499b8fa3c4474f907bf3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In how many different ways can you select two digits out of $$ 0$$, $$1$$, $$ 2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, and $$9$$ and put into the two boxes to make the below equality correct? $$ 20- \\square =22-\\square $$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6581", "queId": "eb47e0e082eb49788db74aa44daed86f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\left( {} \\right.$$The number of seconds in a week$$\\left. {} \\right)$$$$\\div$$$$\\left( {} \\right.$$the number of minutes in a week$$\\left. {} \\right)=$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$420$$ "}], [{"aoVal": "C", "content": "$$3600$$ "}], [{"aoVal": "D", "content": "$$7200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"], "answer_analysis": ["There are $$60$$ seconds in each minute, so the quotient of the two quantities is $$60$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6591", "queId": "f4741b6294b74f21b7a4756e97595942", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If I round $$1315$$ to the nearest ten, then multiply the result by $$3$$, then round to the nearest hundred, what is my final result? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3800$$ "}], [{"aoVal": "B", "content": "$$3900$$ "}], [{"aoVal": "C", "content": "$$3945$$ "}], [{"aoVal": "D", "content": "$$3960$$ "}], [{"aoVal": "E", "content": "$$4000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Estimating Large Numbers"], "answer_analysis": ["If I round $$1315$$ to the nearest ten, I get $$1320$$. Then, I multiply by $$3$$ to get $$3960$$. To the nearest hundred, this is $$4000$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6593", "queId": "e6c1e1e9acea4756aa7ce08908201586", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Denise fired a silver rocket and a gold rocket at the same time. The rockets exploded into $20$ stars in total. The gold rocket exploded into $6$ more stars than the silver one. How many stars did the gold rocket explode into? (2021 Math Kangaroo Problem, Level 3-4, Question \\#7) ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The silver rocket exploded $(20-6)\\div2=7$ stars, and the gold rocket exploded $20-7=13$ stars. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6601", "queId": "d92837bdc81d482a99fa414661c10c76", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the missing number in the box? $2:3=\\boxed{?}:12$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions"], "answer_analysis": ["$\\frac{2}{3}=\\frac{8}{12}$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6602", "queId": "cb9bb3d69d38481fad9ec5d5bda554a7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When the number $$789678567456$$ is added to the number $$987876765654$$, how many digits does the sum have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["The number $$789678567456$$ is added to the number $$987876765654$$. Since we carry a $$1$$ when adding the left-most digits, the sum has $$12+1$$ digits. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6604", "queId": "fdb96ff6015f46e0ad4b7467468d62aa", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two integers are inserted into the list $3,3,8,11,28$ to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers? (2023 AMC 8 Problems, Question \\#20) ", "answer_option_list": [[{"aoVal": "A", "content": "$$56$$ "}], [{"aoVal": "B", "content": "$$57$$ "}], [{"aoVal": "C", "content": "$$58$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$61$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["To double the range, we must find the current range, which is $28-3=25$, to then double to: $2(25)=50$. Since we do not want to change the median, we need to get a value less than $8$ (as $8$ would change the mode) for the smaller, making $53$ fixed for the larger. Remember, anything less than $3$ is not beneficial to the optimization. So, taking our optimal values of $7$ and $53$, we have an answer of $7+53=$ (D) $60$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6607", "queId": "e6d2b6efed4d49ef9ebb1298266827d0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the $5^{th}$ number in the $8^{th}$ row? ", "answer_option_list": [[{"aoVal": "A", "content": "$$53$$ "}], [{"aoVal": "B", "content": "$$54$$ "}], [{"aoVal": "C", "content": "$$69$$ "}], [{"aoVal": "D", "content": "$$70$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns of Number Tables->Triangle Number Table"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6611", "queId": "f9287e92518f4cc198e6f91398b92cb2", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "In a chinese chess competition, children would be awarded $$2$$ marks for every game won, $$1$$ mark will be awarded for every game that ended in a draw and $$0$$ marks will be awarded for every game that ended in a loss. $6$ students participated in the round robin and $5$ of the students\\textquotesingle{} scores are as follows: $$7$$, $$6$$, $$5$$, $$4$$, $$3$$. How many marks did the last place student score? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["$6$ students will play a total of $5+4+3+2+1=15$ games. Total score $=15\\times2=30$ Last student\\textquotesingle s score $=30-7-6-5-4-3=5$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6615", "queId": "d93a09698162477cb4c53b9a27c0d982", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Three (different) numbers are selected from $$0$$, $$1$$, $$3$$ and $$5$$ to form a three-digit number, find the difference between the smallest three-digit number and the largest three-digit number formed. ", "answer_option_list": [[{"aoVal": "A", "content": "$$401$$ "}], [{"aoVal": "B", "content": "$$455$$ "}], [{"aoVal": "C", "content": "$$428$$ "}], [{"aoVal": "D", "content": "$$431$$ "}], [{"aoVal": "E", "content": "$$530$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"], "answer_analysis": ["$$531-103=428$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6624", "queId": "e2583af7128c4ba99dbf97f583753ddf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following numbers is the multiple of $5$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$55$$ "}], [{"aoVal": "C", "content": "$$79$$ "}], [{"aoVal": "D", "content": "$$2022$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$55\\div 5 =11$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6626", "queId": "eb7b80758cd7402b859797664f643a6d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Usually, people spend $\\frac{1}{4}$ of their sleeping time dreaming. If Poole slept $8$ hours last night, how much time did he spend dreaming yesterday? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$$8\\times \\frac{1}{4}=2$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6630", "queId": "eb816d9f99ec4a2da6dd0b3bcc797a02", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The $$41^{}\\text{th}$$ number in the sequence $$7$$, $$11$$, $$15$$, $$19$$, $$\\cdots \\cdots $$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$171$$ "}], [{"aoVal": "B", "content": "$$167$$ "}], [{"aoVal": "C", "content": "$$164$$ "}], [{"aoVal": "D", "content": "$$160$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["$$7+4\\times (41-1)=167$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6634", "queId": "d957479f667d4cbc9b12657071838ae4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "This regression uses the number of times a new worker has spent practicing task (measured in Number Practice~Rounds) to predict how much time is needed to complete one round of the task (measured in Minutes). What is the equation of the least-squares regression line? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\overset{\\frown}{Rounds}=-0.6442+22.94\\textbackslash{} Minutes$ "}], [{"aoVal": "B", "content": "$\\overset{\\frown}{Rounds}=22.94+0.5466\\textbackslash{} Minutes$ "}], [{"aoVal": "C", "content": "$\\overset{\\frown}{Minutes}=22.94+2.866\\textbackslash{} Rounds$ "}], [{"aoVal": "D", "content": "$\\overset{\\frown}{Minutes}=22.94-0.6442\\textbackslash{} Rounds$ "}], [{"aoVal": "E", "content": "$\\overset{\\frown}{Minutes}=-0.6442+0.5466\\textbackslash{} Rounds$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["From Chapter 6, the correct answer is (d). The slope of the regression line, -0.6442, can be found under \"Coef\" to the right of \"Number of Rounds\" .The intercept of the regression line, 22.94, can be found under \"Coef\" to the right of \"Constant.\" Rounds is the explanatory variable (x) and Time is the response variable (y). "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6635", "queId": "f016486946b04aa2a4addd9770c873a7", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "$$$$Calculate$$$$ $$\\frac{1}{5^{5}+1}+ \\frac{1}{5^{5}+5}+ \\frac{1}{5^{5}+5^{2}}+ \\cdots$$$$ + \\frac{1}{5^{5}+5^{8}}+ \\frac{1}{5^{5}+5^{9}}+ \\frac{1}{5^{5}+5^{10}}$$． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{11}{6250}$$ "}], [{"aoVal": "B", "content": "$$\\frac{23}{12500}$$ "}], [{"aoVal": "C", "content": "$$\\frac{6}{3125}$$ "}], [{"aoVal": "D", "content": "$$\\frac{13}{6250}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions"], "answer_analysis": ["$$\\frac{1}{5^{5}+1}+ \\frac{1}{5^{5}+5}+ \\frac{1}{5^{5}+5^{2}}+ \\cdots + \\frac{1}{5^{5}+5^{8}}+ \\frac{1}{5^{5}+5^{9}}+ \\frac{1}{5^{5}+5^{10}}$$ $$=\\left ( \\frac{1}{5^{5}+1}+ \\frac{1}{5^{5}+5^{10}}\\right )+\\left ( \\frac{1}{5^{5}+5}+ \\frac{1}{5^{5}+5^{9}}\\right )$$$$+\\left ( \\frac{1}{5^{5}+5^{2}}+ \\frac{1}{5^{5}+5^{8}}\\right )+\\cdots+\\left (\\dfrac{1}{5^{5}+5^{5}}\\right )$$ $$=\\left ( \\frac{5^{5}+1}{5^{5}\\left (5^{5}+1\\right )}\\right )+\\left ( \\frac{5^{4}+1}{5^{5}(5^{4}+1)}\\right )$$$$+\\left ( \\frac{5^{3}+1}{5^{5}(5^{3}+1)}\\right )+ \\cdots +$$ $$\\left (\\frac{1}{2\\left (5\\right )^{5}}\\right )$$ $$= \\left (\\frac{5}{5^{5}}\\right )+\\left ( \\frac{1}{2(5)^{5}}\\right )= \\frac{11}{6250}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6636", "queId": "f94eaacae13c4b6bbcc56cf5e0a7e75f", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "\\textbf{Research indicates that the standard deviation of typical human body temperature is 0.4 degree Celsius (C). which of the following represents the standard deviation of typical human body temperature in degrees Fahrenheit (F), where $$F=\\frac{9}{5}C+32$$?} ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{9}{5}(0.4)+32$$ "}], [{"aoVal": "B", "content": "$$\\frac{9}{5}(0.4)$$ "}], [{"aoVal": "C", "content": "$$\\frac{9}{5}(0.4)^{2}$$ "}], [{"aoVal": "D", "content": "$$\\frac{9}{5}^{2}(0.4)$$ "}], [{"aoVal": "E", "content": "$$\\frac{9}{5}^{2}(0.4)^{2}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["\\textbf{Standard deviation for Y=ax+b is SD(Y)=\\textbar a\\textbar SD(x).} "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6639", "queId": "d4d7167d1d1947639a9b48232cbeb8d3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working $20$ days? ", "answer_option_list": [[{"aoVal": "A", "content": "$$39$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$210$$ "}], [{"aoVal": "D", "content": "$$400$$ "}], [{"aoVal": "E", "content": "$$401$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["On day $20$, she sold $1+2\\times(20-1)=39$ Sum of $20$ days: $(1+39)\\times 20\\div2=400$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6642", "queId": "d4d96ef43a9c4e4d83a5bd648084caf5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the value of $\\frac{1}{2}$~$\\cdot$~$\\frac{4}{2}$~$\\cdot$~$\\frac{3}{5}$ $\\ldots$~$\\frac{18}{20}$~$\\cdot$~$\\frac{19}{21}$~$\\cdot$ $\\frac{20}{22}$ ", "answer_option_list": [[{"aoVal": "A", "content": "$\\dfrac{1}{462}$ "}], [{"aoVal": "B", "content": "$\\frac{1}{231}$ "}], [{"aoVal": "C", "content": "$\\frac{1}{132}$ "}], [{"aoVal": "D", "content": "$\\frac{2}{213}$ "}], [{"aoVal": "E", "content": "$\\frac{1}{22}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6647", "queId": "fdfe5e92e07b4dc09fc8b132d40f974c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following fractions is the largest? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac13$ "}], [{"aoVal": "B", "content": "$\\frac34$ "}], [{"aoVal": "C", "content": "$$\\frac57$$ "}], [{"aoVal": "D", "content": "$\\frac79$ "}], [{"aoVal": "E", "content": "$\\frac8{11}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$\\frac 79 \\textgreater{} \\frac 34 \\textgreater{} \\frac 8{11}\\textgreater\\frac 57\\textgreater\\frac 13$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6658", "queId": "f03a851df00441979461ecbbcc4a43b9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$27+11+13$$=~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$31$$ "}], [{"aoVal": "B", "content": "$$41$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$51$$ "}], [{"aoVal": "E", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["$$27+11+13$$ $$=27+13+11$$ $$=40+11$$ $$=51$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6665", "queId": "e29251b27cac4490bd27e94509efc033", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Let $a, b$, and $c$ be positive integers with $a \\geq b \\geq c$ such that $a^{2}-b^{2}-c^{2}+a b=2011$ and $a^{2}+3 b^{2}+3 c^{2}-3 a b-2 a c-2 b c=-1997$. What is $a$ ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$249$$ "}], [{"aoVal": "B", "content": "$$250$$ "}], [{"aoVal": "C", "content": "$$251$$ "}], [{"aoVal": "D", "content": "$$252$$ "}], [{"aoVal": "E", "content": "$$253$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Addition and Subtraction of Equations"], "answer_analysis": ["Add the two equations. $$ 2 a^{2}+2 b^{2}+2 c^{2}-2 a b-2 a c-2 b c=14 . $$ Now, this can be rearranged and factored. $$ \\begin{aligned} \\&\\left(a^{2}-2 a b+b^{2}\\right)+\\left(a^{2}-2 a c+c^{2}\\right)+\\left(b^{2}-2 b c+c^{2}\\right)=14 \\textbackslash\\textbackslash{} \\&(a-b)^{2}+(a-c)^{2}+(b-c)^{2}=14 \\end{aligned} $$ $a, b$, and $c$ are all integers, so the three terms on the left side of the equation must all be perfect squares. We see that the only is possibility is $14=9+4+1$ $(a-c)^{2}=9 \\Rightarrow a-c=3$, since $a-c$ is the biggest difference. It is impossible to determine by inspection whether $a-b=1$ or 2 , or whether $b-c=1$ or 2 . We want to solve for $a$, so take the two cases and solve them each for an expression in terms of $a$. Our two cases are $(a, b, c)=(a, a-1, a-3)$ or $(a, a-2, a-3)$. Plug these values into one of the original equations to see if we can get an integer for $a$. $a^{2}-(a-1)^{2}-(a-3)^{2}+a(a-1)=2011$, after some algebra, simplifies to $7 a=2021$. 2021 is not divisible by 7 , so $a$ is not an integer. The other case gives $a^{2}-(a-2)^{2}-(a-3)^{2}+a(a-2)=2011$, which simplifies to $8 a=2024$. Thus, $a=253$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6667", "queId": "ebb8f1d63acb44579eacd33f31078d24", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the ones digit of the result of $3^{50}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers"], "answer_analysis": ["The ones digits of exponents based on $3$ follow the rule: $3, 9, 7, 1, 3, 9, 7, 1\\cdots $ $50\\div4=12R2$, which means the ones digit is $9$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6676", "queId": "de1fbafa4384498eab32d8d547354a34", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the result of $1\\div 1\\frac{2}{2001}\\div 1\\frac{2}{2003}\\cdots \\div 1\\frac{2}{2023}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$\\frac{2025}{2001}$ "}], [{"aoVal": "C", "content": "$\\frac{2021}{2025}$ "}], [{"aoVal": "D", "content": "$\\frac{2001}{2025}$ "}], [{"aoVal": "E", "content": "$\\frac{1}{2001}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Fractions"], "answer_analysis": ["$1\\div 1\\frac{2}{2001}\\div 1\\frac{2}{2003}\\cdots \\div 1\\frac{2}{2023}$ $=1\\div \\frac{2003}{2001}\\div \\frac{2005}{2003}\\cdots \\div \\frac{2025}{2023}$ $=1\\times \\frac{2001}{2003}\\times \\frac{2003}{2005}\\cdots \\times \\frac{2023}{2025}$ $=\\frac{2001}{2025}$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6677", "queId": "e7381f9699474c44b7bcbcb3482c7c65", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Which of the numbers below is greatest? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$22222$$ "}], [{"aoVal": "B", "content": "$2222^{2}$ "}], [{"aoVal": "C", "content": "$222^{22}$ "}], [{"aoVal": "D", "content": "$22^{222}$ "}], [{"aoVal": "E", "content": "$2^{2222}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"], "answer_analysis": ["$2^{2222}\\textgreater2^{2220}=\\left (2^{10}\\right )^{222}=1024^{222}\\textgreater22^{222}$. According to this rule, $\\text{E}\\textgreater\\text{D}\\textgreater\\text{C}\\textgreater\\text{B}\\textgreater\\text{A}$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6686", "queId": "ebd64b4dcea143058a36721d29fee0ed", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In an ice-cream shop there was some money in a drawer. After selling $6$ ice-cream cones, there are $70$ dollars in the drawer. After selling a total of $16$ ice-cream cones, there are $120$ dollars in the drawer. How many dollars were there in the drawer at the start? (2021 Math Kangaroo Problem, Level 3-4, Question \\#13) ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$50$$ "}], [{"aoVal": "E", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["The price of one ice-cream cone is $(120-70)\\div(16-6)=5$ dollars. The price of $6$ ice cream cones is $5\\times6=30$ dollars. There were $70-30=40$ dollars at the start. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6691", "queId": "e2ca796942454760a971eefc6c4644ca", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The next number in the sequence $$1$$, $$1$$, $$2$$, $$3$$, $$5$$, $$8$$, $$13$$, $$\\cdots$$ is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"], "answer_analysis": ["$$1+1= 2$$, $$1+2 = 3$$, $$\\cdots$$, $$5+8 = 13$$, $$8+13 = 21$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6693", "queId": "f9aad75d082641d7b1bcda776e25be9f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Susan participates a Math competition. In round one, she needs to solve $2$ problems. If she works out one problem successfully, she will get $1$ point. Otherwise, she will not lose any points. In round two, she also needs to solve $2$ problems. If she works out one problem successfully, she will get $3$ points. Otherwise, she will lose $1$ point. Which number of points is it impossible for her to have？ ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["After round one, she may have $0$ point, $1$ point, $2$points After two rounds, she may have $3$, $4$, $6$, $7$, $8$ points "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6694", "queId": "ebed60c10d834ff6b888c9f62d58c7b0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the next number below? 3, 5, 6, 10, 9, 15, 12,20,~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$25$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"], "answer_analysis": ["The numbers in the odd positions (1st, 3rd, 5th ,7th) are 3, 6, 9, 12. Each of these numbers is 3 more than the number before it. The numbers in the even positions (2nd, 4th, 6th, 8th) are 5, 10, 15, 20. Each of these numbers is 5 more than the number before it. Since the missing number is the gth position (odd), then the missing number is 12 + 3 = 15. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6696", "queId": "ebf0b4f454ea463c9075650896ca65a7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If a number is written as $2a+4$, then $3$ times the number is~\\uline{~~~~~~~~~~}~. (adapted from 1977 Math League.com contest problem, 8\\textsuperscript{th}~Grade, Question \\#31) ", "answer_option_list": [[{"aoVal": "A", "content": "$6a+4$ "}], [{"aoVal": "B", "content": "$2a+7$ "}], [{"aoVal": "C", "content": "$6a+12$ "}], [{"aoVal": "D", "content": "$32a+34$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Using a Letter to Represent an Unknown Number"], "answer_analysis": ["$3\\times (2a+4)=3(2a+4)=6a+12$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6700", "queId": "e768a8da7f4d44e49c651cc95a96eac0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the sum of the various numbers of Number $$1074$$? (adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$7$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"], "answer_analysis": ["Pay attention to the review questions and sum the numbers. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6704", "queId": "fe59c815fd50431cba386c9b72f519ad", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "What value of $a$ would make the solution to the equation, $$ 2 a+3-4 x+7=3\\left(-\\frac{4}{3} x+7\\right) $$,~\"infinitely many solutions\"?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$-5$ "}], [{"aoVal": "B", "content": "$\\frac{11}{2}$ "}], [{"aoVal": "C", "content": "$10.5$ "}], [{"aoVal": "D", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"], "answer_analysis": ["$2 a+10-4 x=-4 x+21$ $2 a=11 $ $a=\\frac{11}{2}$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6706", "queId": "e2e3a75d78de41468ab04806e0943018", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "15-9=, 29+7=． ", "answer_option_list": [[{"aoVal": "A", "content": "6, 36 "}], [{"aoVal": "B", "content": "4, 35 "}], [{"aoVal": "C", "content": "5, 36 "}], [{"aoVal": "D", "content": "8, 35 "}], [{"aoVal": "E", "content": "7, 39 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "], "answer_analysis": ["15-9=6, 29+7=36 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6720", "queId": "f9de8bf64b8941178d3f1e3c48cf8dcd", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Given that $x$ and $y$ are whole numbers such that $24x-25y =8$, find the smallest value of $x$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$42$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Indefinite Equations"], "answer_analysis": ["E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6722", "queId": "fe79c8e4cbe24ce6a74086a260787e4f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the result of $$\\frac{{{2}^{2}}}{{{2}^{2}}-1}\\times \\frac{{{3}^{2}}}{{{3}^{2}}-1}\\times \\cdots \\times \\frac{{{99}^{2}}}{{{99}^{2}}-1}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{99}{50}$$ "}], [{"aoVal": "B", "content": "$$\\frac{99}{100}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{99}$$ "}], [{"aoVal": "D", "content": "$$\\frac{99}{200}$$ "}], [{"aoVal": "E", "content": "$$\\frac{50}{99}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas"], "answer_analysis": ["$$=\\frac{2\\times 2}{(2+1)\\times (2-1)}\\times \\frac{3\\times 3}{(3+1)\\times (3-1)}\\times \\frac{4\\times 4}{(4+1)\\times (4-1)}\\times \\cdots \\times \\frac{98\\times 98}{(98+1)\\times (98-1)}\\times \\frac{99\\times 99}{(99+1)\\times (99-1)}$$ $$=\\frac{2\\times 2}{3\\times 1}\\times \\frac{3\\times 3}{4\\times 2}\\times \\frac{4\\times 4}{5\\times 3}\\times \\frac{5\\times 5}{6\\times 4}\\times \\cdots \\times \\frac{98\\times 98}{99\\times 97}\\times \\frac{99\\times 99}{100\\times 98}$$ $$=\\frac{2}{1}\\times \\frac{2}{3}\\times \\frac{3}{2}\\times \\frac{3}{4}\\times \\frac{4}{3}\\times \\frac{4}{5}\\times \\cdots \\times \\frac{98}{97}\\times \\frac{98}{99}\\times \\frac{99}{98}\\times \\frac{99}{100}$$ $$=\\frac{2}{1}\\times \\frac{99}{100}$$ $$=\\frac{99}{50}$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6723", "queId": "f9e461f9e32448059ae932f6f0cfc046", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Let $f(x)=a x^{2}+b x+c$, where $a$, $b$, and $c$ are integers. Suppose that $f(1)=0,20\\textless f(3)\\textless24,36\\textless f(4)\\textless40$, $10 k\\textless f(10)\\textless10(k+1)$ for some integer $k$. What is $k$? (Adapted From2011 AMC 12A Problems, Question 20) ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["From $f(1)=0$, we know that $a+b+c=0$. From the first inequality, we get $20\\textless9 a+3 b+c\\textless24$. Subtracting $a+b+c=0$ from this gives us $20\\textless8 a+2 b\\textless24$, and thus $10\\textless4 a+b\\textless12$. Since $4a+b$ must be an integer, it follows that $4 a+b=11$. Similarly, from the second inequality, we get $36\\textless16a+4 b+c\\textless40$. Again subtracting $a+b+c=0$ from this gives us $36\\textless15 a+3 b\\textless40$, or $12\\textless5 a+b\\textless\\frac{40}{3}$. It follows from this that $5 a+b=13$. We now have a system of three equations: $a+b+c=0,4a+b=11$, and $5a+b=13$. Solving gives us $(a, b, c)=(2,3,-5)$ and from this we find that $f(10)=2(10)^{2}+3(10)-5=225$. We find that $k=22 \\rightarrow(\\mathbf{B})22$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6726", "queId": "fe81c8466daa41e993117f5a1de33768", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the smallest three-digit numbers whose digits add up to $$8$$ and the largest three-digit numbers whose digits add up to $$8$$ is equal to~\\uline{~~~~~~~~~~}~. ($$2011$$ Math kangaroo Problems, Level $$7-8$$, Question \\#$$10$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$707$$ "}], [{"aoVal": "B", "content": "$$907$$ "}], [{"aoVal": "C", "content": "$$916$$ "}], [{"aoVal": "D", "content": "$$1000$$ "}], [{"aoVal": "E", "content": "$$1001$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"], "answer_analysis": ["The smallest three-digit number is $107$ and the largest one is $800$. $107+800=907$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6728", "queId": "ec29a9d1642d4e0e954bc8ec56846c29", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many whole numbers less than $$1000$$ can be written as the product of $$3$$ consecutive whole numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"], "answer_analysis": ["The whole numbers less than $$1000$$ that can be written as such a product are $$0\\times1\\times2$$, $$1\\times2\\times3$$, $$2\\times3\\times4$$, $$3\\times4\\times5$$, $$4\\times5\\times6$$, $$5\\times6\\times7$$, $$6\\times7\\times8$$, $$7\\times8\\times9$$, $$8\\times9\\times10$$, and $$9\\times10\\times11$$. In all, that\\textquotesingle s $$10$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6733", "queId": "f0c5c14a6416483094f4fb98add02366", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Let $f$ be a linear function for which $f(5)-f(2)=0$. What is $f(8)-f(2)$? ( Adapted From 2003 AMC 12B Problems, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$0$$ "}], [{"aoVal": "E", "content": "$$-3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules"], "answer_analysis": ["$f(5)-f(2)=0 \\Rightarrow f(5)= f(2)$; thus, $f(x)$ is a constant function. Then, $f(8) - f(2) = 0$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6737", "queId": "f0d4630d903749da9ed4cb67cd677ba0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Daniel had a package of $$36$$ pieces of candy. Without breaking any pieces of candy, he divided all the candy equally among his friends without remaining. Which of the following was definitely not the number of his friends? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders"], "answer_analysis": ["$$36 \\div 5 = 7R1$$, so the answer is $$5$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6740", "queId": "fa098283ff5647e1a99caf7db150ba34", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Evaluate$$\\left\\textbar{} 3-9 \\right\\textbar+\\left\\textbar{} 7-2 \\right\\textbar$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$-11$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$-2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"], "answer_analysis": ["$$\\left\\textbar{} 3-9 \\right\\textbar+\\left\\textbar{} 7-2 \\right\\textbar=\\left\\textbar{} -6 \\right\\textbar+\\left\\textbar{} 5 \\right\\textbar=6+5=11$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6751", "queId": "008bab8502ba425cb53caf894c517eca", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When William, Mark, Diana, and Jimmy checked their book bags, they found that Mark\\textquotesingle s books were fewer than Diana\\textquotesingle s and Jimmy\\textquotesingle s were more than William\\textquotesingle s. Mark\\textquotesingle s is not the least. Do you know who has the least books? (adapted from 2009 Math Kangaroo Problems, Level 1-2, Question \\#21) ", "answer_option_list": [[{"aoVal": "A", "content": "William "}], [{"aoVal": "B", "content": "Mark "}], [{"aoVal": "C", "content": "Diana "}], [{"aoVal": "D", "content": "Jimmy "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["Diana\\textgreater Mark, so it is not Diana. William \\textless{} Jimmy, so it is not Jimmy. We already know that Mark did not have the smallest number of books. So, it is William. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6757", "queId": "00f1a989bbeb47278f2b25864d1c9860", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many days are there in August?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$5$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$28$$ "}], [{"aoVal": "B", "content": "$$29$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$31$$ "}], [{"aoVal": "E", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Reading the Clock"], "answer_analysis": ["August have $31$ days. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6758", "queId": "2093112e13cb4f58a29d7a06e93bf9ec", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "If the day before yesterday was Sunday. How many days are there from today until Sunday? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["Before yesterday: Sunday Yesterday: Monday Today: Tuesday From Tuesday to Sunday, we have $$5$$ days based on the information given in the question. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6762", "queId": "0995d0865d1a410ab83ce64e3d94d7a7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $49$ matchsticks on the table. Kevin and Michael will take turns to take away the matchsticks from the first matchstick in order. Each person can take $1$ to $6$ matchsticks at a time. The person who takes the last matchstick on the table will win the game. If Kevin plays the game first, does he have the winning strategy? ", "answer_option_list": [[{"aoVal": "A", "content": "Yes, he has the winning strategy. "}], [{"aoVal": "B", "content": "No, he does not have the winning strategy. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["$49\\textbackslash{} \\div(1+6)=7$~groups, so the second mover will have the winning strategy. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6766", "queId": "2e8c56e0b21b48d1bf63833694d6ea7a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2015 P2 Q1 How many months of the year have 28 days? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["every month has 28 days. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6770", "queId": "09b096b4bc914e6f927080c808798415", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "While fishing, Pablo caught as many fish as his son Marco. Juan caught three times as much fish as his son. Altogether, they caught $$35$$ fish. What\\textquotesingle s the name of Juan\\textquotesingle s son? ", "answer_option_list": [[{"aoVal": "A", "content": "The described situation is impossible "}], [{"aoVal": "B", "content": "$$$$Juan "}], [{"aoVal": "C", "content": "$$$$Pablo "}], [{"aoVal": "D", "content": "$$$$Marco "}], [{"aoVal": "E", "content": "It cannot be determined from the information given "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions->Complex Reasoning "], "answer_analysis": ["Pablo is the name of his son. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6773", "queId": "01d8095c890046efb1ff7c5f718c2bfe", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Shawn is making a meal. It will cost $1$ minute for preparing the vegetables, $2$ minutes for washing the pan for oven, $6$ minutes for the oven roasting the meal, $2$ minutes for cleaning the table, and $1$ minute for putting the meal on the table. At least how long will it take for Shawn to finish the meal? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ minutes "}], [{"aoVal": "B", "content": "$$8$$ minutes "}], [{"aoVal": "C", "content": "$$9$$ minutes "}], [{"aoVal": "D", "content": "$$10$$ minutes "}], [{"aoVal": "E", "content": "$$12$$ minutes "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["Shawn can clean the table while the oven is working, so it will take $6$ minutes in total. So, he can finish the meal in $1+2+6+1=10$ minutes. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6778", "queId": "45cd174fa1654b23aea26641d2a25cf3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "\\textbf{In which place did each of the following shops come in the competition? Write the correct letter on the Prize list. What is the ranking of the pizza shop?} ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["nil "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6779", "queId": "059ab1499c3b480e9357df93d1cc7e09", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Eve arranged cards in a line as it is shown in the figure below. At each move Eve is allowed to interchange any two cards. What is the smallest number of moves Eve needs to get the word KANGAROO? insert pic ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["First, switch K and 1st O to make KANGONOA. Second, switch N and R to make KANGOROA. Third, switch the last A and the 2nd O to make KANGAROO. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6782", "queId": "05dae4e7e0144dc3ac9f95562a85c206", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "How many months of the year have exactly $$31$$ days? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["March, May, July, August, October and December. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6789", "queId": "03252e73c95a4cc1b418712fa21fd71a", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A certain play has three $30$-minute parts and two intermission among them. The play started at $8:30$ and ended at $10:15$. How many minutes long were the intermissions in total? (Adapted from 2010 Math Kangaroo Problem, Level 1-2, Question \\#19) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["From $8:30$ to $10:15$ = $1$ hr $45$ min, $1$ hr $45$ min = $105$ min, three $30$-minute parts = $90$ min, $105 - 90$ = $15$ min. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6801", "queId": "1c2b470a2e77436391f19d36256088b9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There were $$8$$ cups on the table with the sides up, If you can only turn $$6$$ at a time, Can it be done to make all the cups face down at the end? ", "answer_option_list": [[{"aoVal": "A", "content": "Yes, it can "}], [{"aoVal": "B", "content": "No, it can\\textquotesingle t "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Turning Mugs over"], "answer_analysis": ["To make all the $$8$$ cups face down, it only needs to turn them over with odd times, and 6 of them can be turned at a time, so it can be done. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6809", "queId": "413a589a3049465a85f0209cc6c22e74", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are two groups of flowers. Group $A$ has $17$ flowers and Group $B$ has $13$ flowers. Cathy and Ivy want to play a game with these flowers. They will take turns to take flowers from the two groups. Each person can take any number of flowers from a group at a time. The person who takes the last flower in two groups will win the game. If Ivy starts the game first, who has the winning strategy? ", "answer_option_list": [[{"aoVal": "A", "content": "Ivy has the winning strategy. "}], [{"aoVal": "B", "content": "Cathy has the winning strategy. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["Two groups of flowers are not equal. Thus, Ivy needs to take away 4 flowers from Group A and two groups will have the same amount of flowers. Then, Ivy will become the second mover and she has the winning strategy. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6836", "queId": "2a2dc71f2c1a48bdb5852cbd43eefbab", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A certain play has three $30$-minute parts and two intermissions among them. The play started at $8:30$ AM and ended at $10:15$ AM. How many minutes long were the intermissions in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["From $8:30$ to $10:15$ = $1$ hr $45$ min, $1$ hr $45$ min = $105$ min, three $30$-minute parts = $90$ min, $105 - 90$ = $15$ min. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6840", "queId": "a6951a561dbf4f2eac0fd764f33f2ec9", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Find the sum of all possible values of $x$ such that $\\textbar x-\\textbar{} x-1\\textbar\\textbar-x=1$ .~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"], "answer_analysis": ["We must check cases where $\\textbar x-\\textbar{} x-1\\textbar\\textbar$ is positive and cases where it is negative. $x\\textgreater1$ and $x\\textless1$ will cause different signs for $x-\\textbar x-1\\textbar$. Hence we must check both intervals. However, when $x\\textless1$, we see that when $x=\\frac{1}{2}$, the expression is equal to 0 , so we must also check the intervals $x\\textless\\frac{1}{2}$ and $\\frac{1}{2}\\textless x\\textless1$. Solving on the interval $x\\textless\\frac{1}{2}$, we get $\\textbar x+1+x\\textbar-x=1 \\Longleftrightarrow x=0$. Solving on the interval $\\frac{1}{2}\\textless x\\textless1$, we get $\\textbar x+1+x\\textbar-x=1 \\Longleftrightarrow x=0$. Solving on the interval $x\\textgreater1$, we get $\\textbar x-x+1\\textbar-x=1 \\Longleftrightarrow x=0$. Checking for extraneous solutions, we find that $x=0$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6848", "queId": "b926b2468261433bb567b86f298beebd", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In the calculation shown below, different letters represent different digits. $AA\\times AB\\times C=ADDA$ What is the sum of $A+B+C+D$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$16$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"], "answer_analysis": ["$11\\times13\\times7=1001$ $1+3+7+0=11$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6852", "queId": "08a395f687e84054a33cf0026b5e6d50", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Find the next number in the sequence below. $$1,4,10,22,46,94,\\cdots $$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$190$$ "}], [{"aoVal": "B", "content": "$$188$$ "}], [{"aoVal": "C", "content": "$$186$$ "}], [{"aoVal": "D", "content": "$$142$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Patterns of Figures"], "answer_analysis": ["The pattern is as follows: $1$ $\\xrightarrow{+3}$ $4$ $\\xrightarrow{+6}$ $10$ $\\xrightarrow{+12}$ $22$ $\\xrightarrow{+24}$ $46$ $\\xrightarrow{+48}$ $94$ $\\xrightarrow{+96}$ $190$ The differences start with 3 and double each time afterwards. The next number in the sequence is \\textbf{190.} "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6853", "queId": "211ea46e04444590ae8b7e75b5229c7f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the missing number in the sequence below? $1, 3, 7, 15, 31,$~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$63$$ "}], [{"aoVal": "B", "content": "$$47$$ "}], [{"aoVal": "C", "content": "$$57$$ "}], [{"aoVal": "D", "content": "$$59$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Patterns of Figures"], "answer_analysis": ["1, 3, 7, 15, 31, \\cdots .. 2. 4. 8.~ 16.~ 32 31+32 = 64 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6856", "queId": "0f738547d8d449439525e53a830abd79", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Rose and Kylie are playing a game. Here are the rules： 1. There are $$16$$ marbles placed in a row. 2. The players take turns removing either $1$ or $2$ marbles each turn. 3. Whoever picks the last marble wins the game. Rose starts first and is followed by Kylie. To ensure her victory, how many marbles must Rose take away in the first turn? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["If there are n marbles in total, the first player has a winning strategy for all $$n$$ that is not a multiple of $$3$$. For $$n$$ being a multiple of $$3$$, the second player can always win, regardless of what strategy the first player plays. $$16\\div (1+2)=5 \\textbackslash{} \\text{R} 1$$ Rose should take away the remainder, i.e. one marble, to make herself the second player when there is a multiple of $3$ marbles left. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6863", "queId": "0908eb283480427187488b2031b60932", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Chris, Molly, Sara, and Lynn each has some coins. Chris gives Molly $20$ coins, Molly gives Sara $25$ coins, Sara gives Lynn $30$ coins, and Lynn gives Chris $30$ coins. Now, which of the following is correct if they each wants to have the same number of coins as in the beginning? ", "answer_option_list": [[{"aoVal": "A", "content": "Lynn gives Sara $5$ coins, and Molly gives Sara $5$ coins. "}], [{"aoVal": "B", "content": "Chris gives Molly $5$ coins, and Chris gives Lynn $10$ coins. "}], [{"aoVal": "C", "content": "Chris gives Molly $5$ coins, and Chris gives Sara $5$ coins. "}], [{"aoVal": "D", "content": "Chris gives Lynn $10$ coins. "}], [{"aoVal": "E", "content": "Chris gives Sara $10$ coins. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["Chris gives Molly $20$ coins, and Lynn gives Chris $30$ coins. Now, Chris has $10$ more. Chris gives Molly $20$ coins, and Molly gives Sara $25$ coins. Now, Molly has $5$ less. Molly gives Sara $25$ coins, and Sara gives Lynn $30$ coins. Now, Sara has $5$ less. Sara gives Lynn $30$ coins, and Lynn gives Chris $30$ coins. Now, Lynn has the same as beginning. Thus, Chris can give Molly $5$ coins, and give Sara $5$ coins. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6879", "queId": "0c3999beea2e45b7ba94ee61738e01b1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the following column puzzle, different letters represent different one-digit numbers. Find the three-digit number represented by $$ABC$$. $$\\begin{matrix}\\& \\& 8 \\& 8\\& \\boxed C \\textbackslash\\textbackslash{} \\&\\&5\\& \\boxed B \\&4 \\textbackslash\\textbackslash{} + \\&\\&\\boxed A\\&1 \\&7 \\textbackslash\\textbackslash{} \\hline \\&2~\\&0 \\&2 \\&1\\textbackslash\\textbackslash{} \\end{matrix}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$625$$ "}], [{"aoVal": "B", "content": "$$620$$ "}], [{"aoVal": "C", "content": "$$602$$ "}], [{"aoVal": "D", "content": "$$260$$ "}], [{"aoVal": "E", "content": "$$206$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"], "answer_analysis": ["Start from the ones digit, $$4+7=11$$, $$0+1=1$$, so $$C=0$$. In the tens place, $$8+1+1=10$$, $$0+2=2$$, so $$B=2$$. In the hundreds place, $$8+5+1=14$$, $$14+6=20$$, so $$A=6$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6885", "queId": "1420194ae89e4c369a85b27ddfb32e40", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Tom wrote various words in code in such a way that different digits represent different letters and the same digit represents the same letter. For example, the word $BALL$ was coded as $$3488$$. One of the words below was coded as $$6155491$$. Which one? ", "answer_option_list": [[{"aoVal": "A", "content": "$$SURGEON$$ "}], [{"aoVal": "B", "content": "$$HARBORS$$ "}], [{"aoVal": "C", "content": "$SWEATER$ "}], [{"aoVal": "D", "content": "$MESSAGE$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions->Complex Reasoning "], "answer_analysis": ["According to the pattern: the same digit represents the same letter, the code $$6155491$$ should represent a word with two same letters at the third and fourth place. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6891", "queId": "4ac5e8dcbcd14ef0ad86b480ce29210e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The area of a square is $16$, its side length is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Magic Square"], "answer_analysis": ["$A=s^{2}$ $s^{2}=16$ $s=4$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6895", "queId": "9d6140e288404e148e41b2da42c832e4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "2 foxes and 2 rabbits want to cross a river. There is a boat that can hold 2 animals. When the number of fox is less than the number of rabbits, the rabbits fight with the foxes. For 2 foxes and 2 rabbits to cross the river safely, at least how many times does the boat need to cross the river? (count the round trip as twice and every trip need one animal row the boat)~\\uline{~~~~~~~~~~}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math->Fun Math Problems"], "answer_analysis": ["Assume the foxes as A, and the rabbits as B. The way they cross the river as following: $$AA\\xrightarrow{BB}$$ $$AA\\xleftarrow{B}B$$ $$B\\xrightarrow{AA}B$$ $$B\\xleftarrow{B}AA$$ $$\\xrightarrow{BB}AA$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6899", "queId": "3cf9d23869af42ea96eea397d6c5e2fb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are two groups of balls. Group $A$ has $585$ balls and Group $B$ has $590$ balls. DQ and Justin want to play a game with these balls. They will take turns to take balls from the two groups. Each person can take $1$ to $6$ balls from a group at a time. The person who takes the last ball in the two groups will win the game. If DQ starts the game first, does she have the winning strategy? ", "answer_option_list": [[{"aoVal": "A", "content": "Yes, she can take $5$ balls from group $A$ at first. "}], [{"aoVal": "B", "content": "Yes, she can take $3$ balls from group $B$ at first. "}], [{"aoVal": "C", "content": "Yes, she can take $6$ balls from group $A$ at first. "}], [{"aoVal": "D", "content": "Yes, she can take $5$ balls from group $B$ at first. "}], [{"aoVal": "E", "content": "No, she doesn\\textquotesingle t have winning strategy. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["DQ needs to take the $590-585=5$ balls in Group $B$ which will make the two groups have the same amount of balls. Then, no matter how many balls Justin takes in a group, DQ will take as many balls as Justin took before in the other group. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6900", "queId": "2a9893bcef9c4058bb99e82964b07539", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Jack and Edward want to take turns to count off numbers from $1$ to $124$ in order. Each person can count $1$ to $5$ numbers at a time. The person who counts off number $124$ will win the game. Does Jack have the winning strategy if he counts off numbers first? ", "answer_option_list": [[{"aoVal": "A", "content": "Yes, he has. "}], [{"aoVal": "B", "content": "No, he doesn\\textquotesingle t. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["$124\\div(1+5)=20R4$. So, Jack should count off $1$ to $4$ and there will be $120$ numbers left. Jack will become the second mover and he has the winning strategy. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6910", "queId": "0cffdaf96fa348be88665c267251792c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The ancient Romans used Roman numerals. We still use them today. Here are some examples: $$\\rm I=1$$, $$\\rm II=2$$, $$\\rm V=5$$, $$\\rm IX=9$$, $$\\rm X=10$$, $$\\rm XI=11$$, $$\\rm XX=20$$. This year($2022$) we celebrate Math Kangaroo number $$\\rm XX$$. What year was Math Kangaroo number $$\\rm XV$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2015$$ "}], [{"aoVal": "B", "content": "$$2016$$ "}], [{"aoVal": "C", "content": "$$2017$$ "}], [{"aoVal": "D", "content": "$$2018$$ "}], [{"aoVal": "E", "content": "$$2019$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions->Complex Reasoning "], "answer_analysis": ["According to the pattern, $$\\rm XX$$ is $$20$$, and $$\\rm XV$$ is $$15$$. So, Math Kangaroo number $$15$$ was $$5$$ less than real year, which was $$2017$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6911", "queId": "5d5022eeb6b1425faebca98a4dbe488c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If May $6$ falls on a Friday, what day of the week will it be in $25$ days? (Adapted from 2015 Math Kangaroo Problem, Level 3-4, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "Tuesday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Friday "}], [{"aoVal": "E", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$25\\div7=3R4$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6914", "queId": "21a6c44bb3e04e27b3f3b43a98f2f1ff", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If January $2$ falls on a Saturday, what day of the week will it be in $28$ days? ", "answer_option_list": [[{"aoVal": "A", "content": "Tuesday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Saturday "}], [{"aoVal": "E", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$28\\div7=4$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6916", "queId": "1490ccbcf9f747fb9b5e2389528941e3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "James starts classes at $9$ A.M. He has $2$ classes, each class $$45$$ minutes long. After each class, he will take a $$15$$-minute break. When will he finish all $$2$$ classes? ", "answer_option_list": [[{"aoVal": "A", "content": "$10:20$ A.M. "}], [{"aoVal": "B", "content": "$11:00$ A.M. "}], [{"aoVal": "C", "content": "$11:10$ A.M. "}], [{"aoVal": "D", "content": "$11:20$ A.M. "}], [{"aoVal": "E", "content": "$11:30$ A.M. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$$45+15+45+15=120$$ minutes = $2$ hours So, he will finish at $$11:00$$ A.M. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6920", "queId": "7dcf70fcce944457ad4f979411975a88", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "There are $13$ ping-pong players who will be divided into three teams, and they are going to have a men\\textquotesingle s singles. The rule is that the players in the same team will not play with each other, and each of them only plays one game with each player in other teams. What is the maximum number of games happened in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$23$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$56$$ "}], [{"aoVal": "E", "content": "$$72$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition"], "answer_analysis": ["Dividing the players into three teams as equally as possible can make the maximum number of games. So there are $4$, $4$, and $5$ players in the three teams and they will have $4\\times4+4\\times5+4\\times5=56$ games in total. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6921", "queId": "0d43d6d582ca4e669ae6250fb8183900", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "We left for a summer camp at $4:30$ PM and got to our destination at $6:40$ PM. How long did we travel?~ ", "answer_option_list": [[{"aoVal": "A", "content": "$1$ hour $40$ minutes "}], [{"aoVal": "B", "content": "$2$ hours $10$ minutes "}], [{"aoVal": "C", "content": "$2$ hours $20$ minutes "}], [{"aoVal": "D", "content": "$1$ hour $50$ minutes "}], [{"aoVal": "E", "content": "$50$ minutes "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$6:40$ - $4:30$ = $2$ hours $10$ minutes "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6938", "queId": "8adc7d54feae483486c067f661ff4001", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There are $5$ boxes on the table. From left to right, each of them has $8,$ $4,$ $2,$ $1,$ and $5$ balls of the same size, respectively. Every time, Judy can take one ball each from the other four boxes, and then put them into the box with the smallest number of balls. She follows the rules and operates $2023$ times. Now how many balls are there in the first box counting from the left? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"], "answer_analysis": ["Without operation: $$8$$, $$4$$, $$2$$, $$1$$, $$5$$ After the first operation: $$7$$, $$3$$, $$1$$, $$5$$, $$4$$ After the second operation: $$6$$, $$2$$, $$5$$, $$4$$, $$3$$ After the third operation: $$5$$, $$6$$, $$4$$, $$3$$, $$2$$ After the fourth operation: $$4$$, $$5$$, $$3$$, $$2$$, $$6$$ After the fifth operation: $$3$$, $$4$$, $$2$$, $$6$$, $$5$$ After the sixth operation: $$2$$, $$3$$, $$6$$, $$5$$, $$4$$ After the seventh operation: $$6$$, $$2$$, $$5$$, $$4$$, $$3$$ We can find that $6-2-5-4-3$ is repeating starting from the second operation. $$（2023-1）\\div5 R 2$$ Thus, after the $2023$\\textsuperscript{rd}~operation, the result will be the same as the third one, which means there are $5$ balls in the first box. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6952", "queId": "21f697b263e24e0d96aa94fdaf66bf24", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Alvin always tells the truth on Sundays, Tuesdays and Thursdays. He lies on every other days. One day he said, \"I told the truth yesterday.\" On which day of the week did he make this statement? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Friday "}], [{"aoVal": "E", "content": "Saturday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["If \"I told the truth yesterday\" is a true statement -\\/-\\textgreater{} mean today I am telling the truth. But, the day that Alvin tell the truth are not consecutive day. So, if \"I told the truth yesterday\" is not a true statement -\\/-\\textgreater{} mean yesterday I lie and today I am also lying. Alvin lies on Monday, Wednesday, Friday and Saturday. Friday and Saturday is consecutive day he lies, so it must be Saturday. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6961", "queId": "118d4c57e3aa4de5adcba25bead98ae6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are two groups of balls. Group $A$ has $50$ balls and Group $B$ has $40$ balls. Candy and Nini want to play a game with these balls. They will take turns to take balls from the two groups. Each person can take any number of balls from a group at a time, but they should take at least one ball at a time. The person who takes the last ball in the two groups will win the game. If Nini starts the game first, how many balls should she take to guarantee her success? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$10$ "}], [{"aoVal": "B", "content": "$8$ "}], [{"aoVal": "C", "content": "$6$ "}], [{"aoVal": "D", "content": "$4$ "}], [{"aoVal": "E", "content": "$2$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["Nini needs to take $$50-40=10$$ balls in Group A which will make the two groups have the same amount of balls. Then, no matter how many balls Candy takes in a group, Nini will take as many balls as Candy took before in the other group. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6968", "queId": "11c6a48d3f184775b789e7fbf078a94c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $7$ water glasses, all facing up. You need to turn exactly $2$ glasses over in each time. Is it possible to turn all $7$ of them upside down after several moves? ", "answer_option_list": [[{"aoVal": "A", "content": "Yes, it is possible. "}], [{"aoVal": "B", "content": "No, it is impossible. "}], [{"aoVal": "C", "content": "I have no idea. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Turning Mugs over"], "answer_analysis": ["You have to flip a cup an odd number of times to turn it over. To make all the $7$ cups face down, you have to make an odd number of flips. Each time you flip exactly $2$ cups, the total number of flips is an even number of times. Hence it is impossible. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6969", "queId": "11c9cb8f591140f7bf7316394da7eef9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$17$$ balls in a bag. Each ball has a number from $$1$$ to $$17$$ on it. We randomly pick a ball from the bag. What is the smallest number of balls we have to pick in order to be sure that we have at least one pair of balls with a difference equal to $$3$$? (adapted from $$2005$$ Math Kangaroo Problem, Level $$9-10$$, Question \\#$$15$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems"], "answer_analysis": ["We can create three drawers: $(1, 4, 7, 10, 13, 16)$. $(2, 5, 8, 11, 14, 17)$. $(3, 6, 9, 12, 15)$. At least $3\\times3+1=10$ numbers should be chosen. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6978", "queId": "41ffe4ba2e424a1d981a96d06870c1b6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Peter\\textquotesingle s father has $$4$$ sons and Peter has $$5$$ brother(s) and sister(s). How many daughter(s) does Peter\\textquotesingle s father have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["$$5+1-4=2$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "6994", "queId": "66db542ae0b2451996e7d61670fae50c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "John and Olivia exchanged sweets. First John gave Olivia as many sweets as Olivia had. Then Olivia gave John as many sweets as John had after the first exchange. After these two exchanges, each had $$4$$ sweets. How many sweets did John have at the beginning? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Planning->Simple Time Planning Problems->Working Simultaneously"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7002", "queId": "e7b93fb3665e46658355d2b3304c491d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2016 P2 Q2 How many hours are there in two weeks? ", "answer_option_list": [[{"aoVal": "A", "content": "7 x 12 "}], [{"aoVal": "B", "content": "7 x 2 x 12 "}], [{"aoVal": "C", "content": "2 x 7 x 2 x 12 "}], [{"aoVal": "D", "content": "(7+7) x 12 "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["Conversion of unit. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7009", "queId": "38fd235e627b41fda7c0e9d965196370", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Alice began reading a 400-page book at 8 am and had read 50 pages by 9:30. If she continues to read at the same rate, when can she finish reading this book? ", "answer_option_list": [[{"aoVal": "A", "content": "6 pm "}], [{"aoVal": "B", "content": "7 pm "}], [{"aoVal": "C", "content": "8 pm "}], [{"aoVal": "D", "content": "9 pm "}], [{"aoVal": "E", "content": "10 pm "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$$300\\div20-300\\div30=5$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7012", "queId": "7027ed4c9a10461eac1187cb28f88d0c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Lucy, Maria, and Anna have a meeting at $$12:30$$. Lucy\\textquotesingle s walk takes $$10$$ minutes, Maria\\textquotesingle s walk takes a quarter of an hour, and Anna\\textquotesingle s walk takes $$40$$ minutes. At what time must the person who needs the longest time to get to the meeting leave her house? (2006 Math Kangaroo Problem, Level 1-2, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12:00$$ "}], [{"aoVal": "B", "content": "$$12:10$$ "}], [{"aoVal": "C", "content": "$$12:15$$ "}], [{"aoVal": "D", "content": "$$12:20$$ "}], [{"aoVal": "E", "content": "$$11:50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$12:30$ - $40$ min = $11:50$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7028", "queId": "be0c928869ad4587828252e0ef1f407f", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A certain play has three $30$-minute parts and two intermissions among them. The play started at $8:30$ AM and ended at $10:15$ AM. How long did the commercials last for in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10 min$$ "}], [{"aoVal": "B", "content": "$$15 min$$ "}], [{"aoVal": "C", "content": "$$20 min$$ "}], [{"aoVal": "D", "content": "$$25 min$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["From $8:30$ to $10:15$ = $1$ hr $45$ min, $1$ hr $45$ min = $105$ min, three $30$-minute parts = $90$ min, $105 - 90$ = $15$ min. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7042", "queId": "62679f72f374442cb56a6063aff049ce", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are two containers, one with a capacity of 6 liters and the other with a capacity of 5 liters, and using them to get 1 liter of water from a bucket requires at leasttimes of operations. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Pouring Water Problems"], "answer_analysis": ["Fill the 6-liter container first, and then pour the water from the 6-liter container into the 5-liter container. After the 5-liter container is filled, there is 1 liter of water left in the 6-liter container. It takes two operations. So the answer is $$A$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7050", "queId": "34c816ff934748489f65811270c4a7d5", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A store opens at 9 a.m. and closes at 5p.m. each day. It is closed from 11.55 a.m. to 12.55 p.m. for a lunch break. How many hours does the store stay open each day? ", "answer_option_list": [[{"aoVal": "A", "content": "$8$ hours and $5$ minutes "}], [{"aoVal": "B", "content": "$$7$$ hours and $30$ minutes "}], [{"aoVal": "C", "content": "$8$ hours "}], [{"aoVal": "D", "content": "$7$ hours "}], [{"aoVal": "E", "content": "$6$ hours "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["NA "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7053", "queId": "8fc5afb639fd428389128f549b2a20c0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are two piles of matches. Each pile has $$6$$ matches. Cindy and Doris take turns to pick up matches from either pile. There is no limit to how many matches they can pick up, but they must pick up at least one match each turn. The person who picks up the last match will be the winner. If Cindy starts picking up matches first,~\\uline{~~~~~~~~~~}~will definitely be the winner (has a winning strategy). ", "answer_option_list": [[{"aoVal": "A", "content": "Cindy "}], [{"aoVal": "B", "content": "Doris "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["Doris will be the winner, since she can simply mirror the number of matches Cindy picks up every turn. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7063", "queId": "305f6a1cf4ee4e369faa3e83b12bb844", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Taylor has $2$ brothers and $3$ sisters. How many brothers and sisters does his sister Lucy have? ", "answer_option_list": [[{"aoVal": "A", "content": "3 brothers and 4 sisters "}], [{"aoVal": "B", "content": "2 brothers and 3 sisters "}], [{"aoVal": "C", "content": "3 brothers and 3 sisters "}], [{"aoVal": "D", "content": "2 brothers and 4 sisters "}], [{"aoVal": "E", "content": "3 brothers and 2 sisters "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["NA "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7064", "queId": "70550f4af1a64b4db77f34fb941d2c1a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Among $42$ people, at least how many people were born in the same month with the most births? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle"], "answer_analysis": ["There are $12$ months. Thus, $42 \\div 12 = 3R6$, $3+1 = 4$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7066", "queId": "2bfb196b1710475481304abe48ec99b5", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Teacher wrote $$10$$ non-zero natural numbers in order on the blackboard, where the $$1$$st number is $$16$$, and the sum of any $$3$$ adjacent numbers is $$100$$. The $$8$$th biggest number is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$81$$ "}], [{"aoVal": "B", "content": "$$82$$ "}], [{"aoVal": "C", "content": "$$83$$ "}], [{"aoVal": "D", "content": "$$84$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math"], "answer_analysis": ["Let first 10 numbers be $${{a}\\_{1}}$$、$${{a}\\_{2}}$$、$${{a}\\_{3}}$$、$${{a}\\_{4}}$$、$$\\ldots \\ldots $$、$${{a}\\_{10}}$$. $${{a}\\_{1}}+{{a}\\_{2}}+{{a}\\_{3}}={{a}\\_{2}}+{{a}\\_{3}}+{{a}\\_{4}}$$，$${{a}\\_{1}}={{a}\\_{4}}$$. Therefore, $${{a}\\_{1}}={{a}\\_{4}}={{a}\\_{7}}={{a}\\_{10}}=16$$，$${{a}\\_{8}}=100-{{a}\\_{10}}-{{a}\\_{9}}=100-16-{{a}\\_{9}}=84-{{a}\\_{9}}$$. The maximum value of $${{a}\\_{8}}$$ is $$83$$．$$For$$ example：$$16$$、$$83$$、$$1$$、$$16$$、$$83$$、$$1$$、$$16$$、$$83$$、$$1$$、$$16$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7074", "queId": "8fd4bc690ad043b79a7232ca2d0e6fa5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$25$$ matches on the table. John and James take turns to remove $$1$$ to $$3$$ matches each time. The person who removes the last match will be the winner. If both of them were to use the best method and John removes first, then~\\uline{~~~~~~~~~~}~will win.~ ", "answer_option_list": [[{"aoVal": "A", "content": "John "}], [{"aoVal": "B", "content": "James "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["$$25\\div 4=6\\ldots 1$$ John removes $$1$$ match and $$24$$ is a multiple of $$4$$. So, the first player will win the game. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7080", "queId": "54cba88f95334157ae1ae28dcb018080", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Light Bulb A lights up every $$15$$ minutes while Light Bulb B lights up every $$20$$ minutes. Both light bulbs lit up at the same time at $$8.30$$ a.m. By noon, how many more times would both light bulbs have lit up at the same time? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["The LCM of $$15$$ and $$20$$ is $$60$$. Both light bulbs will light up at the same time every $$60$$ minutes, at $$9.30$$ a.m., $$10.30$$ a.m. and $$11.30$$ a.m. (total of $$3$$ times). "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7092", "queId": "991da3afe3e94d6498c469293b4cd485", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Adam built fewer sandcastles than Martin but more than Susan. Lucy built more sandcastles than Adam and more than Martin. Dana built more sancastles than Martin but fewer than Lucy. Who of them built the most sandcastles? ", "answer_option_list": [[{"aoVal": "A", "content": "Martin "}], [{"aoVal": "B", "content": "Adam "}], [{"aoVal": "C", "content": "Susan "}], [{"aoVal": "D", "content": "Dana "}], [{"aoVal": "E", "content": "Lucy "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["L \\textgreater{} D\\textgreater{} M \\textgreater{} A \\textgreater{} S "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7099", "queId": "ababbc2496cf4ca299c7768e03f1f664", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The Gellers went on a trip. They left home at 9:15 in the morning and arrived at the hotel at 8:22 in the evening. How long did the journey take? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ hours $$22$$ minutes "}], [{"aoVal": "B", "content": "$$11$$ hours $$15$$ minutes "}], [{"aoVal": "C", "content": "$$11$$ hours $$7$$ minutes "}], [{"aoVal": "D", "content": "$$1$$ hours $$7$$ minutes "}], [{"aoVal": "E", "content": "$$12$$ hours $$7$$ minutes "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$3$h-$15$min + $8$h+$22$min = $11$h$7$min "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7101", "queId": "2c4bbbc9d76b4b24aa16563851ea3c68", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The first student wrote the number $1$ on the board, the second student wrote the number $2$, and the third one and each of the following students wrote a number that was the quotient of the number written just before the last number and the last number. What did the tenth student write? ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac1{2^{10}}$ "}], [{"aoVal": "B", "content": "$$256$$ "}], [{"aoVal": "C", "content": "$\\frac1{2^{13}}$ "}], [{"aoVal": "D", "content": "$$1024$$ "}], [{"aoVal": "E", "content": "$$2^{34}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"], "answer_analysis": ["The ten numbers are: $1(2^{0}), 2^{1}, \\frac1{2^{1}}, 2^{2}, \\frac1{2^{3}}, 2^{5} \\frac1{2^{8}}\\cdots$ Thus the tenth exponent is $34$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7103", "queId": "2c4d4abc52684d75a7de4d35aff58f34", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In Think Academy, there are $147$ students. Among these $147$ students, we can guarantee that at least~\\uline{~~~~~~~~~~}~students belong to the zodiac sign with the most students. ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$136$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle"], "answer_analysis": ["$147\\div12=12R3$, $12+1=13$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7107", "queId": "4bc51a0a3df5449581f73286be1ceaed", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "From $1$ to $23$, how many integers can be chosen at most to ensure that no two of chosen numbers differ by $4$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Constructing and Proving"], "answer_analysis": ["$1, 5, 9, 13, 17, 21$ $2, 6, 10, 14, 18, 22$ $3, 7, 11, 15, 19, 23$ $4, 8, 12, 16, 20$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7141", "queId": "79cafa9675da44d9a363bf7790d92680", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Rose and Kylie are playing a game. Here are the rules： 1. There are $$14$$ marbles placed in a row. 2. The players take turns removing either $1$ or $2$ marbles each turn. 3. Whoever picks the last marble wins the game. Rose starts first and is followed by Kylie. To ensure her victory, how many marbles must Rose take away in the first turn? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["If there are n marbles in total, the first player has a winning strategy for all $$n$$ that is not a multiple of $$3$$. For $$n$$ being a multiple of $$3$$, the second player can always win, regardless of what strategy the first player plays. $$14\\div (1+2)=4 \\textbackslash{} \\text{R} 2$$ Rose should take away the remainder, i.e. two marbles, to make herself the second player when there is a multiple of $3$ marbles left. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7145", "queId": "39eece3590a94e2f9b8f8ee3797e9e36", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The time shown on the electronic clock is $6:08$. How long before the numbers appear again? (adapted from 2007 Math Kangaroo Problem, Level 3 - 4, Question \\#16) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ h $$2$$ min "}], [{"aoVal": "B", "content": "$$3$$ h "}], [{"aoVal": "C", "content": "$$3$$ h $$2$$ min "}], [{"aoVal": "D", "content": "$$2$$ h $$12$$ min "}], [{"aoVal": "E", "content": "$$2$$ h "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$8:06$=$6:08$+$2$h$2$min "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7147", "queId": "47695b12320a4c328444a9e70bd97eaf", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "We are given a certain number. We double the number and then subtract $1$ from the result. We repeat this operation $4$ more times. If the end result is $2^{6}+1$, then what is the number that we started with? (Adapted from $2005$ Math Kangaroo Problems, Level $11-12$, Question \\#$29$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"], "answer_analysis": ["After repeating the operation $4+1=5$ times, the result is $2^{6}+1$. After repeating the operation $4$ times, the result is $(2^{6}+1+1)\\div2=2^{5}+1$. After repeating the operation $3$ times, the result is $2^{4}+1$. $$\\cdots $$ After doing the operation for the first time, the result is $2^{2}+1$. Before we do anything, the number is $2^{1}+1$, which is $3$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7161", "queId": "3e8ddf60b7314b48a659c2bbda5a703b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "When number $\\overline{OK}$ is divided by $K$, the result will give the same quotient as the divisor and leave the remainder of $O$. The same letter represents the same digit, and different letters represent different digits. Then, what is the product of the two digits, $O$ and $K$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$63$$ "}], [{"aoVal": "D", "content": "$$72$$ "}], [{"aoVal": "E", "content": "$$81$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"], "answer_analysis": ["$89\\div9=9R8$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7176", "queId": "b9aa2a9d45f44254b02d73bd48c76cf8", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "How many minutes are there in one week? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7\\times24$$ "}], [{"aoVal": "B", "content": "$$7\\times 2\\times 12$$ "}], [{"aoVal": "C", "content": "$$7\\times 12 \\times 60$$ "}], [{"aoVal": "D", "content": "$$7\\times 2 \\times 12 \\times 60$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["One week $$7$$ days. $$24$$ hours per day. $$60$$ minutes per hour. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7182", "queId": "2d17ec0b9ac9477abc3dfbc13e118f7d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "We left for a summer camp at $4:32$ PM and got to our destination at $6:11$ PM. How long did we travel? (Adapted from 2015 Math Kangaroo Problem, Level 1--2, Question \\#24) ", "answer_option_list": [[{"aoVal": "A", "content": "$1$ hour $39$ minutes "}], [{"aoVal": "B", "content": "$2$ hours $39$ minutes "}], [{"aoVal": "C", "content": "$2$ hours $21$ minutes "}], [{"aoVal": "D", "content": "$1$ hour $21$ minutes "}], [{"aoVal": "E", "content": "$39$ minutes "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$6:11$ - $4:43$ = $1$ hour $39$ minutes "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7183", "queId": "24af39fc66024042ab0d4bcec8dfd1fc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Apply this operation to $$(50, 20)$$. What are the last two numbers when the operation stops? ", "answer_option_list": [[{"aoVal": "A", "content": "$(2,2) "}], [{"aoVal": "B", "content": "$(3,3)$ "}], [{"aoVal": "C", "content": "$(5,5)$ "}], [{"aoVal": "D", "content": "$(7,7)$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Patterns of Figures->Special Changes"], "answer_analysis": ["E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7191", "queId": "47baf36c34bf45ba96ac9777f77a18f0", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Amy calculate $47\\times86$ wrong. Her teacher says her result which has a difference of $172$ from the correct one. After checking, Amy finds that she writes one of the four digits two multipliers the result as $9$. Which digits does she write incorrectly? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "It\\textquotesingle s impossible to determine. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"], "answer_analysis": ["The difference between the wrong answer and the correct one is $172$. $172\\div86=2$, $172\\div47=3R31$.That means Amy writes neither $ 8$ nor $6$ wrong. Then, compare $49\\times86$ and $97\\times86$, so we can get the correct answer. $49\\times86-47\\times86=172.$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7201", "queId": "28ff2dfc39b64e1189d663f735bfdd38", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Lucy, Maria, and Anna have a meeting at $$12:30$$. Lucy\\textquotesingle s walk takes $$10$$ minutes, Maria\\textquotesingle s walk takes a quarter of an hour, and Anna\\textquotesingle s walk takes $$30$$ minutes. At what time must the person who needs the longest time to get to the meeting leave her house? (Adapted from 2006 Math Kangaroo Problem, Level 1-2, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12:00$$ "}], [{"aoVal": "B", "content": "$$12:10$$ "}], [{"aoVal": "C", "content": "$$12:15$$ "}], [{"aoVal": "D", "content": "$$12:20$$ "}], [{"aoVal": "E", "content": "$$11:50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$12:30$ - $30$ min = $12:00$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7204", "queId": "8b8bbc1f779c4a1e916d7015410c2906", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "From Monday to Wednesday Mark always lies. For the rest of the week he tells the truth. One day, Mark said to Mary: $$1$$) \"Yesterday I lied.\" and $$2$$) \"Starting the day after tomorrow, I will be lying for two consecutive days.\" On what day of the week did Mark talk to Mary? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Wednesday "}], [{"aoVal": "D", "content": "Thurday "}], [{"aoVal": "E", "content": "Friday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions->Complex Reasoning "], "answer_analysis": ["It was on Monday, so the answer is A. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7210", "queId": "4c5b6cef26e840f69285cf974403a5b6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following month has $30$ days? (adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$5$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$February$ "}], [{"aoVal": "B", "content": "$$June$$ "}], [{"aoVal": "C", "content": "$$July$$ "}], [{"aoVal": "D", "content": "$$October$$ "}], [{"aoVal": "E", "content": "$$December$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Reading the Clock"], "answer_analysis": ["June has $30$ days. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7212", "queId": "6319041259e74549b3bccf638b9f9c5e", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A certain play has two $$45$$-minute parts and an intermission between them. The play started at $$10:50$$ and ended at $$12:40$$. How many minutes long was the intermission? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["From $$10:50$$ to $$12:40$$ = $$1$$ h $$50$$ min, $$1$$ h $$50$$ min = $$110$$ min, two $$45$$-minute parts = $$90$$ min, and $$110 - 90 = 20$$ min. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7216", "queId": "25146a5fc21041c5b0484c9f3e67789e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The distance between the school and the park is $$2400$$ $\\text{m}$. Lily and Candy depart from the school towards the park at the same time, and return immediately after arriving at the park. Lily travels $$47$$ $\\text{m/min}$, and Candy travels $$53$$ $\\text{m/min}$. They will meet each other for the first time after~\\uline{~~~~~~~~~~}~minutes. ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$96$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics"], "answer_analysis": ["$2400\\times2\\div(53+47)=48$min "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7219", "queId": "70e4d5d7ee9d43098a105e0d1b19928d", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "If $a,b,c,d,e,f,g,h,j$ represents different digits from $1$ to $9$ such that $a+\\frac{b}{c}+\\frac{d}{e}\\times f-\\left(g+\\frac{h}{j} \\right) = N$, where $N$ is a whole number. What is the value of $\\frac{d}{e}\\times f$ to maximize $N$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$56$$ "}], [{"aoVal": "C", "content": "$$63$$ "}], [{"aoVal": "D", "content": "$$72$$ "}], [{"aoVal": "E", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Forming a Maximum/Minimum Multi-Digit Numbers with Fixed Sums"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7221", "queId": "3efb8d77db7e4e87a8bd7c9b6fe95242", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "True or False: A number can\\textquotesingle t be equal to its opposite. ", "answer_option_list": [[{"aoVal": "A", "content": "True "}], [{"aoVal": "B", "content": "False "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"], "answer_analysis": ["$0$\\textquotesingle s opposite number is $0$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7246", "queId": "7a2e34fbae1e4194b2c2e2433ced2103", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are two groups of flowers. Group $A$ has $15$ flowers and Group $B$ has $13$ flowers. Cathy and Ivy want to play a game with these flowers. They will take turns to take flowers from the two groups. Each person can take any number of flowers from a group at a time. The person who takes the last flower in two groups will win the game. If Ivy starts the game first, who has the winning strategy? ", "answer_option_list": [[{"aoVal": "A", "content": "Ivy has the winning strategy. "}], [{"aoVal": "B", "content": "Cathy has the winning strategy. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["Two groups of flowers are not equal. Thus, Ivy needs to take away 2 flowers from Group A and two groups will have the same amount of flowers. Then, Ivy will become the second mover and she has the winning strategy. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7257", "queId": "5a33c86d6c42411aa78c85ca384bf674", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Bella got up at 8:10. It took 10 minutes to wash and 30 minutes to eat breakfast. At this moment, she began to read. After reading, she went out. She went out at 9:45. How long did she read? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ minutes "}], [{"aoVal": "B", "content": "$$15$$ minutes "}], [{"aoVal": "C", "content": "$$20$$ minutes "}], [{"aoVal": "D", "content": "$$25$$ minutes "}], [{"aoVal": "E", "content": "$$30$$ minutes "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$$8:10$$+$$10$$min+$$30$$min+reading=$$9:45$$ reading=$$25$$min "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7259", "queId": "5ec6441b45914f0f891da8db07e677d3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "London time is 7 hours behind of Hong Kong time. Mike is planning to have a flight to Hong Kong from London at $$1$$am of $$12$$th June. If the flight takes 13 hours. When will Mike arrive Hong Kong?(In Hong Kong time) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$am $$12$$th June "}], [{"aoVal": "B", "content": "$$9$$pm $$12$$th June "}], [{"aoVal": "C", "content": "$$8$$am $$12$$th June "}], [{"aoVal": "D", "content": "$$7$$am $$12$$th June "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["Because the flight takes 13 hours, Mike will arrive Hong Kong at $$2$$pm of $$12$$th June(London time). As london time is 7 hours behind Hong Kong time, it will be~$2+7=9$pm(Hong Kong time) "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7272", "queId": "9e348306d77e438d8dab7c6c0eb6da2d", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Grace was going to meet her friends at the bus station. Right now, it is $8:40$. Grace arrived at the bus station half an hour ago. The trip from her home to the station was $1$ hour long. What time did Grace depart toward the bus station? ", "answer_option_list": [[{"aoVal": "A", "content": "$7:20$ "}], [{"aoVal": "B", "content": "$7:10$ "}], [{"aoVal": "C", "content": "$7:50$ "}], [{"aoVal": "D", "content": "$8:10$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["Grace arrived at the bus station at $8:10$, and the trip was $1$ hour long, so she departed at $7:10$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7275", "queId": "95000a91fb5644d7983be7e73194ee33", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In the calculation shown below, different letters represent different digits. $AA\\times AB=5467$ What is the sum of $A+B$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"], "answer_analysis": ["$5467=77\\times71$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7278", "queId": "4cc989e4afa842ffa3b6887ed09cb5f5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following number is the opposite number of $-2022$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$-2022$$ "}], [{"aoVal": "B", "content": "$$2022$$ "}], [{"aoVal": "C", "content": "$\\frac{1}{2022}$ "}], [{"aoVal": "D", "content": "$-\\frac{1}{2022}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"], "answer_analysis": ["Opposite number is the number with opposite sign "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7291", "queId": "55e0b001051742dcb995d57203e107d3", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In a speed skating competition 10 racers reached in final. Tom overtook 3 racers more than those who overtook him. Which place did Tom end up in? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["9-3= 6/2=3. Tom ended up in 4th place. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7299", "queId": "440def6c64b648f28dadf550fd8188b1", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A certain play has three $30$-minute parts and two intermissions among them. The play started at $8:30$ AM and ended at $10:15$ AM. How long did the intermissions last for in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10 min$$ "}], [{"aoVal": "B", "content": "$$15 min$$ "}], [{"aoVal": "C", "content": "$$20 min$$ "}], [{"aoVal": "D", "content": "$$25 min$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["From $8:30$ to $10:15$ = $1$ hr $45$ min, $1$ hr $45$ min = $105$ min, three $30$-minute parts = $90$ min, $105 - 90$ = $15$ min. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7305", "queId": "ac238672079a4f3b8f371b43a3c8580b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate the following. $(220+130-310) \\div (99-89) \\times (2 \\times 3) =$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math"], "answer_analysis": ["$$NA.$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7307", "queId": "5a7dc26bff354dc8abd5201dea88e6a2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "When calculating $54\\times 96$, Judy fails to write the correct column multiplication. She writes one of the four digits as $7$ and gets a result which has a difference of $1920$ from the correct one. Which digit does she write incorrectly? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "It\\textquotesingle s impossible to determine. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"], "answer_analysis": ["The difference between the wrong answer and the correct one is $1920$, whose ones digit is $0$. That means Judy writes neither $4$ nor $6$ wrong. Then, compare $20\\times54$ and $20\\times96$, so we can get the correct answer. $74\\times96-54\\times96=1920.$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7325", "queId": "5f29d3bcb4664fa89f766454ecd494eb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When calculating $63\\times72$ , Judy fails to write the correct column multiplication. She writes one of the four digits as 9 and gets a result which has a difference of 432 from the correct one. Which digit does she write incorrectly? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "It\\textquotesingle s impossible to determine. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"], "answer_analysis": ["The difference between the wrong answer and the correct one is $432$, whose ones digit is $2$. That means Judy writes neither $2$ nor $3$ wrong. Then, compare $7\\times63$ and $6\\times72$, so we can get the correct answer. $69\\times72-63\\times72=432.$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7329", "queId": "9e628a2fc5f24d70bb2751113efbfdce", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Four friends are competing in a math competition. They are Andy, Bob, Cindy and Daisy. The organiser of the competition told you that: ($$1$$) Andy performed better than Bob. ($$2$$) Cindy\\textquotesingle s score is higher than Andy\\textquotesingle s score. ($$3$$) Daisy\\textquotesingle s score is lower than two of her friends. Arrange their scores in descending order. ", "answer_option_list": [[{"aoVal": "A", "content": "Andy, Bob, Cindy, Daisy "}], [{"aoVal": "B", "content": "Andy, Cindy, Daisy, Bob "}], [{"aoVal": "C", "content": "Cindy, Andy, Daisy, Bob "}], [{"aoVal": "D", "content": "Cindy, Andy, Bob, Daisy "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["The score from highest to lower: First -\\/-\\textgreater{} Cindy Second -\\/-\\textgreater{} Andy Thrid -\\/-\\textgreater{} Daisy Fourth -\\/-\\textgreater{} Bob "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7336", "queId": "3756a720bf354979bd3cb3de78c0f277", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There are $5$ boxes on the table. From left to right, each of them has $8,$ $4,$ $2,$ $1,$ and $5$ balls of the same size, respectively. Every time, Judy can take one ball each from the other four boxes, and then put them into the box with the smallest number of balls. She follows the rules and operates $2023$ times. Now how many balls are there in the first box counting from the left? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"], "answer_analysis": ["Without operation: $$8$$, $$4$$, $$2$$, $$1$$, $$5$$ After the first operation: $$7$$, $$3$$, $$1$$, $$5$$, $$4$$ After the second operation: $$6$$, $$2$$, $$5$$, $$4$$, $$3$$ After the third operation: $$5$$, $$6$$, $$4$$, $$3$$, $$2$$ After the fourth operation: $$4$$, $$5$$, $$3$$, $$2$$, $$6$$ After the fifth operation: $$3$$, $$4$$, $$2$$, $$6$$, $$5$$ After the sixth operation: $$2$$, $$3$$, $$6$$, $$5$$, $$4$$ After the seventh operation: $$6$$, $$2$$, $$5$$, $$4$$, $$3$$ We can find that $6-2-5-4-3$ is repeating starting from the second operation. $$（2023-1）\\div5$$R$$2$$ Thus, after the $2023$\\textsuperscript{rd}~operation, the result will be the same as the third one, which means there are $5$ balls in the first box. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7376", "queId": "c35aa0f7141841c688e903344eb9d06e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Lily walks to school every day. She leaves home at $7:15$ and arrives at the school at $7:50$. How many minutes does she spend? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$35$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$$7:50-7:15=35$$ min "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7380", "queId": "762b8b6abb0f47f7b0d91546faf67f18", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following number is the opposite number of $12$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$-12$$ "}], [{"aoVal": "C", "content": "$\\frac{1}{12}$ "}], [{"aoVal": "D", "content": "$-\\frac{1}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"], "answer_analysis": ["Opposite number is the number with opposite sign "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7381", "queId": "405fdabb9d1d4ef5924b50baae98cfcd", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There is a cube whose six faces are marked with $3$, $4$, $5$, $6$, $7$, and $8$. If the sum of every two numbers that are on the opposite faces are identical, the number on the opposite face of $4$ is~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math->Fun Math Problems->Dice"], "answer_analysis": ["$3+8=4+7=5+6=11$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7382", "queId": "887d626f08cb4b2a960096d277bd9ddc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Math workshops start at $5:00$ PM. Today Allan was $15$ minutes late to the workshop. What time did Allan come? ", "answer_option_list": [[{"aoVal": "A", "content": "$5:00$ PM "}], [{"aoVal": "B", "content": "$5:05$ PM "}], [{"aoVal": "C", "content": "$5:15$ PM "}], [{"aoVal": "D", "content": "$5:20$ PM "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$15$ minutes past $5:00$ PM is $5:15$ PM. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7388", "queId": "a7c40e109ddb444f91e03488ad86349f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "insert pic Seven children are standing in a circle. No two boys are standing next to each other. No three girls are standing next to each other. Which of these is true for the number of girls standing in the circle? ", "answer_option_list": [[{"aoVal": "A", "content": "only 3 is possible "}], [{"aoVal": "B", "content": "3 and 4 are possible "}], [{"aoVal": "C", "content": "only 4 is possible "}], [{"aoVal": "D", "content": "4 and 5 are possible "}], [{"aoVal": "E", "content": "only 5 is possible "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["\"No two boys stand next to each other\" meaning there are a maximum of 3 boys only. Hence, there are a minimum of 4 girls in the circle. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7395", "queId": "6d24a1659ead4b9e8e1f8a81eb9dff79", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Thirty apples are distributed among 4 children and each of them can get at least one apple. For the kid who gets the most apples, what\\textquotesingle s the least possible number of apples he or she can get? ", "answer_option_list": [[{"aoVal": "A", "content": "$7$ "}], [{"aoVal": "B", "content": "$8$ "}], [{"aoVal": "C", "content": "$9$ "}], [{"aoVal": "D", "content": "$10$ "}], [{"aoVal": "E", "content": "$11$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Simple Pigeonhole Principle Problems"], "answer_analysis": ["$$30\\div 4=7 \\textbackslash{} \\text{R}2$$, thus for the kid who gets the most apples, he or she can get $$7+1=8$$ apples at least. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7400", "queId": "5698ba755459432ba6b4989eeda8b325", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ivy, Vivian, and Candy are playing the truth or lie game. The rule is: the person who picks the truth card can only tell the truth, and the person who picks the lie card can only tell a lie. Ivy said: \"Vivian and Candy lied.\" Vivian said: \"I didn\\textquotesingle t lie.\" Candy said: \"Vivian lied.\" How many of them told the truth? How many of them told a lie?~\\hspace{0pt}~． ", "answer_option_list": [[{"aoVal": "A", "content": "$2$; $1$ "}], [{"aoVal": "B", "content": "$0$; $3$ "}], [{"aoVal": "C", "content": "$1$; $2$ "}], [{"aoVal": "D", "content": "$3$; $0$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["Vivian and Candy told contradictory information, so one of them told the truth and the other one told the lie. Therefore, Ivy has definitely told the lie. So two people told the lie, and one people told the truth. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7401", "queId": "5b12efa0a9614add892766ff17db9173", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are six balls numbered with $$1-6$$. Amy distributes them equally among three people and each time she needs the three people give her a digit from the two balls they got, then she will use the three digits to form a three$-$digit number. She does it three times, and the numbers are $$145$$, $$263$$, and $$651$$. Which two numbers below must belong to one person? ", "answer_option_list": [[{"aoVal": "A", "content": "$4$ and $5$ "}], [{"aoVal": "B", "content": "$2$ and $1$ "}], [{"aoVal": "C", "content": "$2$ and $5$ "}], [{"aoVal": "D", "content": "$$3$$ and $$4$$ "}], [{"aoVal": "E", "content": "$4$ and $6$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["According to $145$ and $651$, we can find that only $4$ and $6$ have changed with each other. So, they belong to one person. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7417", "queId": "bedc92899fa747a9a8a06fd7c4f109d5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are two piles of bananas, six in one pile and six in the other pile. Mia and Leo take turns to take the bananas from any one of the two piles. The number of bananas they can take is unlimited, but they have to take at least one each turn. Whoever picks the last banana is the winner. If Mia takes the first match, is guarantee to win. ", "answer_option_list": [[{"aoVal": "A", "content": "Mia "}], [{"aoVal": "B", "content": "Leo "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["The number of matches in the two piles is the same. No matter how many matches Andy takes from one pile, Bob just needs to take the same amount of matches from the other pile. As long as there are matches for Andy to take, Bob can definitely take away the same amount from the other pile. Therefore, Bob will take away the last match and he is guarantee to win. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7419", "queId": "40c340266cd9443bbce87ab9e7193d17", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Ken, Tom and Keven were playing a game together. At $1$ P.M., Ken got a score of $-75$, Tom got a score of $-32$, and Keven got a score of $3$. Half an hour later, Ken\\textquotesingle s score was $-1$, Tom\\textquotesingle s score was $41$, and Keven\\textquotesingle s score was $-62$. Who had the greatest change of score? ", "answer_option_list": [[{"aoVal": "A", "content": "Ken "}], [{"aoVal": "B", "content": "Tom "}], [{"aoVal": "C", "content": "Keven "}], [{"aoVal": "D", "content": "They had the same change. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts"], "answer_analysis": ["The changes of Ken\\textquotesingle s, Tom\\textquotesingle s and Keven\\textquotesingle s scores were $74$, $73$ and $65$, respectively. Ken had the greatest change. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7424", "queId": "958c26347a1e420d8377c5555fac0186", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A certain movie is $$90$$ minutes long. It started at $$5:10\\textasciitilde\\text{PM}$$. During the movie, there were two commercial breaks, one lasting $$8$$ minutes and one lasting $$5$$ minutes. At what time did the movie finish? (2009 Math Kangaroo Problem, Level 3-4, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "At $$6:13\\textasciitilde\\text{PM}$$ "}], [{"aoVal": "B", "content": "At $$6:27\\textasciitilde\\text{PM}$$ "}], [{"aoVal": "C", "content": "At $$6:47\\textasciitilde\\text{PM}$$ "}], [{"aoVal": "D", "content": "At $$6:53\\textasciitilde\\text{PM}$$ "}], [{"aoVal": "E", "content": "At $$7:13\\textasciitilde\\text{PM}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$90+8+5=103$ min=$1$ h $43$ min $5:10+$ $1$ h $43$ min $=6:53$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7431", "queId": "6d68357893a744e9831f02817afc6474", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "From City A to City B, the train passes through three other stations besides the starting and ending stations.~~The train leaves at 8:10 and arrives at the third station at 13:25. It will run for 45 minutes. How long does it take to reach the terminal? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$hours $$15$$minutes "}], [{"aoVal": "B", "content": "$$5$$hours $$15$$minutes "}], [{"aoVal": "C", "content": "$$5$$hours "}], [{"aoVal": "D", "content": "$$4$$hours $$45$$minutes "}], [{"aoVal": "E", "content": "$$5$$hours $$45$$minutes "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$$13:25$$-$$8:10$$=$4$h $15$min $4$h $15$min+$$45$$min=$5$h "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7440", "queId": "910417331009438495b590c77f4e9fd2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$3$$ matches on the table. Andy and Bob take turns to pick up $$1$$ to $$2$$ matches each time. The person who picks up the last match will be the winner. If both Andy and Bob were to use the best method and Andy wants to win, he should pick up the matches~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "First "}], [{"aoVal": "B", "content": "Second "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["Andy should go second. Since Bob must pick up either $1$ or $2$ matches when he begins, there will be either $2$ or $1$ match(es) left. Both results lead to Andy\\textquotesingle s victory "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7446", "queId": "df2bc983deba4329aaf02e56888db07c", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "How many real solutions does $\\textbar x+\\textbar{} x+2\\textbar x\\textbar\\textbar\\textbar=1$ have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"], "answer_analysis": ["We have to go through slowly and case by case in order to get every solution, then check for extraneous ones. First, we take off the outermost set of absolute value bars, leaving the equations $$ \\left\\textbackslash{\\begin{array}{c} x+\\textbar x+2\\textbar{} x\\textbar\\textbar=1 \\textbackslash\\textbackslash{} x+\\textbar x+2\\textbar{} x\\textbar\\textbar=-1 \\end{array}\\right. $$ Now, moving the $x$ over and taking off the outermost absolute value bars on both equations leaves us with the equations $$ \\left\\textbackslash{\\begin{array}{c} x+2\\textbar x\\textbar=1-x \\textbackslash\\textbackslash{} x+2\\textbar x\\textbar=-1+x \\textbackslash\\textbackslash{} x+2\\textbar x\\textbar=-1-x \\textbackslash\\textbackslash{} x+2\\textbar x\\textbar=1+x \\end{array}\\right. $$ Moving the $x$ over in every equation gives $$ \\left\\textbackslash{\\begin{array}{c} 2\\textbar x\\textbar=1-2 x \\textbackslash\\textbackslash{} 2\\textbar x\\textbar=-1 \\textbackslash\\textbackslash{} 2\\textbar x\\textbar=-1-2 x \\textbackslash\\textbackslash{} 2\\textbar x\\textbar=1 \\end{array}\\right. $$ Obviously, $2\\textbar x\\textbar=-1$ cannot happen, so we can throw out that equation. Now, removing the absolute value bars on the three remaining equations gives us $$ \\left\\textbackslash{\\begin{array}{c} 2 x=1-2 x \\textbackslash\\textbackslash{} 2 x=-1+2 x \\textbackslash\\textbackslash{} 2 x=-1-2 x \\textbackslash\\textbackslash{} 2 x=1+2 x \\textbackslash\\textbackslash{} 2 x=1 \\textbackslash\\textbackslash{} 2 x=-1 \\end{array}\\right. $$ Obviously, $2 x=-1+2 x$ and $2 x=1+2 x$ are not real equations, so we can throw those out leaving us with four final equations. Solving each one, we get that $x=\\frac{1}{2},-\\frac{1}{2}, \\frac{1}{4}$, and $-\\frac{1}{4}$. Plugging in all those values to the original equation tells us that only $\\frac{1}{4}$ is a real solution while the others are all extraneous, so there is only one real solution. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7453", "queId": "6d8e4deaa3124fa2aa967253f581f186", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Fill in the blanks with $$+$$, $$-$$, $$\\times$$ or $$\\div$$. $$(13-2)$$~\\uline{~~~~~~~~~~}~$$4=7$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$+$$ "}], [{"aoVal": "B", "content": "$$-$$ "}], [{"aoVal": "C", "content": "$$\\times$$ "}], [{"aoVal": "D", "content": "$$\\div$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Filling the Symbol in the Equations"], "answer_analysis": ["$$Nil$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7460", "queId": "da9df4a69bdc460e92b74dc208e97e40", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Mr. John plays a game with his two smart students. He says: \"I have a $2-$digit prime number. But I tell Andy only the ones digit and tell Fiona only the tens digit.\" A few moments later, Andy says: \"I don\\textquotesingle t know what the number is, neither do you.\" Fiona says: \"I didn\\textquotesingle t know what the number was before, but now I know it.\" What is the ones digit of the prime number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["Andy knows neither of them know the number, which means the ones digit could not be $7.$ Then using elimination, Fiona knows it, which means the tens digit could be $3$ or $6.$ But no matter what it is, the ones digit will always be $1.$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7471", "queId": "4a2600a01d1c41ec8682fad1e82866c0", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Teacher wrote $$10$$ non-zero natural numbers in sequence on the blackboard, where the $$1$$st number is $$16$$, and the sum of any $$3$$ adjacent numbers is $$100$$. The biggest possibility of the $$8$$th number is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$81$$ "}], [{"aoVal": "B", "content": "$$82$$ "}], [{"aoVal": "C", "content": "$$83$$ "}], [{"aoVal": "D", "content": "$$84$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math"], "answer_analysis": ["Let first 10 numbers be $${{a}\\_{1}}$$、$${{a}\\_{2}}$$、$${{a}\\_{3}}$$、$${{a}\\_{4}}$$、$$\\ldots \\ldots $$、$${{a}\\_{10}}$$. $${{a}\\_{1}}+{{a}\\_{2}}+{{a}\\_{3}}={{a}\\_{2}}+{{a}\\_{3}}+{{a}\\_{4}}$$，$${{a}\\_{1}}={{a}\\_{4}}$$. Therefore, $${{a}\\_{1}}={{a}\\_{4}}={{a}\\_{7}}={{a}\\_{10}}=16$$，$${{a}\\_{8}}=100-{{a}\\_{10}}-{{a}\\_{9}}=100-16-{{a}\\_{9}}=84-{{a}\\_{9}}$$. The maximum value of $${{a}\\_{8}}$$ is $$83$$. For example：$$16$$、$$83$$、$$1$$、$$16$$、$$83$$、$$1$$、$$16$$、$$83$$、$$1$$、$$16$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7476", "queId": "4a3217a4f1c945dbad62c5bf02b6ed16", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Bud played basketball for half an hour and stopped at 10:15. When did Bud start to play basketball？ ", "answer_option_list": [[{"aoVal": "A", "content": "10:45 "}], [{"aoVal": "B", "content": "9:45 "}], [{"aoVal": "C", "content": "9:30 "}], [{"aoVal": "D", "content": "110:30 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["10:15 - 30 minutes = 9:45 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7480", "queId": "4a3cfc0219f145f7a6c5bcd825fb7823", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are two piles of matches, seven in one pile and seven in the other pile. JoJo and Kevin take turns to take the matches from any pile. The number of matches they can take is unlimited, but they have to take at least one each turn. Whoever picks the last match is the winner. If JoJo takes the first match, is guarantee to win. ", "answer_option_list": [[{"aoVal": "A", "content": "JoJo "}], [{"aoVal": "B", "content": "Kevin "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["The number of matches in the two piles is the same. No matter how many matches JoJo takes from one pile, Kevin just needs to take the same amount of matches from the other pile. As long as there are matches for JoJo to take, Kevin can definitely take away the same amount from the other pile. Therefore, Kevin will take away the last match and he is guarantee to win. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7485", "queId": "76df50ddc9b8400ebfb9b7572cff4906", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "It is Thursday today. Mary\\textquotesingle s birthday was sixteen days ago. On what day of the week was Mary\\textquotesingle s birthday? ", "answer_option_list": [[{"aoVal": "A", "content": "Tuesday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Friday "}], [{"aoVal": "E", "content": "Saturday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["Fourteen days ago, it was Thursday again. Then, two days before Thursday was Tuesday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7491", "queId": "4ebdc6ed66474df8be8e12002703e636", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following number is the opposite number of $-5$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$-5$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$\\frac{1}{5}$ "}], [{"aoVal": "D", "content": "$-\\frac{1}{5}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"], "answer_analysis": ["Opposite number is the number with opposite sign "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7492", "queId": "696152aaea4c456487583359e0445b64", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The time in Thornsburg is $$6$$ hours ahead of London. The current time in London is $$8:27$$pm of $$15$$th April. What is the time in Thornsburg currently? Choose the answer. ", "answer_option_list": [[{"aoVal": "A", "content": "$$8:27$$pm $$15$$th April "}], [{"aoVal": "B", "content": "$$14:27$$ $$15$$th April "}], [{"aoVal": "C", "content": "$$2:27$$pm $$15$$th April "}], [{"aoVal": "D", "content": "$$2:27$$am $$16$$th April "}], [{"aoVal": "E", "content": "$$14:27$$am $$15$$th April "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$6$ hours ahead of $08:27$pm is $02:27$am. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7500", "queId": "4ecf165342224a40a4175b574d9d7c8a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy has $$18$$ boxes of clay. Bala has $$9$$ boxes of clay. Cindy has $$6$$ boxes of clay. How many boxes of clay do they have altogether? ", "answer_option_list": [[{"aoVal": "A", "content": "$$35$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$34$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math"], "answer_analysis": ["\\textbf{[Solution]} $$18 + 9 + 6 = 23$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7523", "queId": "7291e285338a46cea0f2db5b9ca4439b", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Four friends are competing in a math competition. They are Andy, Bob, Cindy and Daisy. The organiser of the competition told you that: ($$1$$) Andy performed better than Bob. ($$2$$) Cindy\\textquotesingle s score is higher than Andy\\textquotesingle s score. ($$3$$) Daisy\\textquotesingle s score is lower than two of her friends. Rank them from the highest to the lowest. ", "answer_option_list": [[{"aoVal": "A", "content": "Andy, Bob, Cindy, Daisy "}], [{"aoVal": "B", "content": "Andy, Cindy, Daisy, Bob "}], [{"aoVal": "C", "content": "Cindy, Andy, Daisy, Bob "}], [{"aoVal": "D", "content": "Cindy, Andy, Bob, Daisy "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["The score from highest to lower: First -\\/-\\textgreater{} Cindy Second -\\/-\\textgreater{} Andy Thrid -\\/-\\textgreater{} Daisy Fourth -\\/-\\textgreater{} Bob "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7529", "queId": "5376ee7c5acd4a00b17c7dfcb2e892b0", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "$$100$$ squares are placed in a row, each filled up with a digit among $$0$$, $$1$$, $$2$$, $$\\cdots $$, $$9$$. Now if a digit appears $$5$$ times or more, all the squares filled up with that digit will be painted red. Find the smallest possible number of red squares. ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$64$$ "}], [{"aoVal": "C", "content": "$$68$$ "}], [{"aoVal": "D", "content": "$$72$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7531", "queId": "e404d8f83eee406799672dc0d4716f25", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ivy, Vivian, and Candy are playing the truth or lie game. The rule is: the person who picks the truth card can only tell the truth, and the person who picks the lie card must tell a lie. \\textbf{Ivy said: \"Vivian and Candy lied.\"} \\textbf{Vivian said: \"I didn\\textquotesingle t lie.\"} \\textbf{Candy said: \"Vivian lied.\"} How many of them told the truth? How many of them told a lie?~\\hspace{0pt} ", "answer_option_list": [[{"aoVal": "A", "content": "$2$; $1$ "}], [{"aoVal": "B", "content": "$0$; $3$ "}], [{"aoVal": "C", "content": "$1$; $2$ "}], [{"aoVal": "D", "content": "$3$; $0$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["Vivian and Candy told contradictory information, so one of them told the truth and the other one told the lie. Therefore, Ivy has definitely told the lie. So two people told the lie, and one people told the truth. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7543", "queId": "d1a30fcf1ad94fc4843c709480ef0ba4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Students $$A$$, $$B$$, $$C$$, $$D$$, $$E$$ and $$F$$ are standing in a row. We know that: $$\\quad \\quad \\quad 1$$) $$D$$ is standing between $$E$$ and $$F$$; $$\\quad \\quad \\quad 2$$) $$C$$ is standing between $$D$$ and $$E$$; $$\\quad \\quad \\quad 3$$) $$B$$ is standing between $$C$$ and $$D$$; and $$\\quad \\quad \\quad 4$$) $$A$$ is standing between $$B$$ and $$C$$. Which of the folowing statements is true? ", "answer_option_list": [[{"aoVal": "A", "content": "$$A$$ is positioned either at the right end of the row or the left end of the row. "}], [{"aoVal": "B", "content": "$$A$$ is second from one of the ends of the row. "}], [{"aoVal": "C", "content": "$$A$$ is third from one of the ends of the row. "}], [{"aoVal": "D", "content": "The situation described in the problem is impossible. "}], [{"aoVal": "E", "content": "$$E$$ and $$F$$ are right next to $$A$$. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions->Complex Reasoning "], "answer_analysis": ["The only true statement here is that $A$ is the third from one of the ends of the row, which is $C$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7547", "queId": "9ab535bf3efb4456808f664dde7a53e2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Two sixth-grade students play chess with at least $$10$$ fifth-grade students, and each of the two men plays exactly one game against each other. There are three results: $$2$$ points for winning, $$1$$ point for drawing, and $$0$$ point for losing. After the competition, it is known that the sum of the two sixth grade students is $$20$$ points, and each fifth grader has scored $$N$$ points. $$N$$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition"], "answer_analysis": ["The number of the fifth-grade student is $$n$$. $$N=[(n+2)\\times(n+1)-20]\\div n= (n^{2}+3n-18)\\div n = n+3-\\frac{18}{n}$$ $$n=18$$ $$N=18+3-1=20$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7555", "queId": "72d29d8d091447d6b30932fc7eae339e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Lucy, Maria and Anna have a meeting at $$12:30$$. Lucy\\textquotesingle s walk takes $$10$$ minutes, Maria\\textquotesingle s a quarter of an hour, and Anna\\textquotesingle s $$40$$ minutes. At what time must the person who needs the longest time to get to the meeting leave her house? (2006 Math Kangaroo Problem, Level 1-2, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12:00$$ "}], [{"aoVal": "B", "content": "$$12:10$$ "}], [{"aoVal": "C", "content": "$$12:15$$ "}], [{"aoVal": "D", "content": "$$12:20$$ "}], [{"aoVal": "E", "content": "$$11:50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$12:30-40 min=11:50$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7560", "queId": "df78d39d224144ea95717e47a4850603", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "If you need $$6$$ minutes to cook $$2$$ eggs, you will need minutes to cook $$4$$ eggs in a pot. (The pot can hold $$4$$ eggs.) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Planning"], "answer_analysis": ["It takes $$6$$ minutes to cook a $$2$$ raw egg, and of course a $$4$$ raw egg will be cooked in a pot, and it will still take $$6$$ minutes to cook. So choose $$\\text{B}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7562", "queId": "dae4734d9c524fc3b94ea6d4f53205c6", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Four friends are competing in a math competition. They are Andy, Bob, Cindy and Daisy. The organiser of the competition told you that: ($$1$$) Andy performed better than Bob. ($$2$$) Cindy\\textquotesingle s score is higher than Andy\\textquotesingle s score. ($$3$$) Daisy\\textquotesingle s score is lower than two of her friends. Rank them from the highest to the lowest. ", "answer_option_list": [[{"aoVal": "A", "content": "Andy, Bob, Cindy, Daisy "}], [{"aoVal": "B", "content": "Andy, Cindy, Daisy, Bob "}], [{"aoVal": "C", "content": "Cindy, Andy, Daisy, Bob "}], [{"aoVal": "D", "content": "Cindy, Andy, Bob, Daisy "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["The score from highest to lower: First -\\/-\\textgreater{} Cindy Second -\\/-\\textgreater{} Andy Thrid -\\/-\\textgreater{} Daisy Fourth -\\/-\\textgreater{} Bob "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7564", "queId": "7761fd864ef3449d9cfd19bf18d677df", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Two men and two boys are planning to cross a river using a small boat that can only hold either one man or two boys. What is the least possible number of times the boat needs to cross the river in order to bring all four of them to the other side? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$9$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"], "answer_analysis": ["Two boys cross the river and one of them goes back. A man crosses the river and the other boy goes back. Two boys cross the river and one of them goes back. The other man crosses the river and the other boy goes back. Two boys cross the river. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7567", "queId": "72e90114736b4c97b05adaa3a6e28963", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Math workshop starts at $5:00$ PM. Today Allan was $15$ minutes late to the workshop. What time did Allan come?~ ", "answer_option_list": [[{"aoVal": "A", "content": "$5:00$ PM "}], [{"aoVal": "B", "content": "$5:05$ PM "}], [{"aoVal": "C", "content": "$5:15$ PM "}], [{"aoVal": "D", "content": "$5:20$ PM "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$15$ minutes past $5:00$ PM is $5:15$ PM. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7583", "queId": "9adfadec6e7b498ba30884abe3916430", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Andrea needs an hour to get to the shopping center. If she leaves at $4$, she gets there half an hour after the store closes. When does the shopping center close? ", "answer_option_list": [[{"aoVal": "A", "content": "$3:30$ "}], [{"aoVal": "B", "content": "$5:30$ "}], [{"aoVal": "C", "content": "$5:00$ "}], [{"aoVal": "D", "content": "$4:00$ "}], [{"aoVal": "E", "content": "$4:30$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["If Andrea leaves at $4$ PM, she arrives at the store when it is $5$ PM, and the store closes at $4:30$ PM. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7608", "queId": "89c746b6d3a940419c94774445d47fd4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following numbers is the opposite of $-2$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$-2$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$\\frac{1}{2}$ "}], [{"aoVal": "D", "content": "$-\\frac{1}{2}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"], "answer_analysis": ["Opposite number is the number with opposite sign "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7610", "queId": "80c86721f64545a4abcd3e716244048b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following calculations shows how to work out the number of seconds in~~24 days? ", "answer_option_list": [[{"aoVal": "A", "content": "24 \\times 24~ "}], [{"aoVal": "B", "content": "24 \\times 60 "}], [{"aoVal": "C", "content": "24 \\times 24 \\times 60 "}], [{"aoVal": "D", "content": "24 \\times 60 \\times 60 "}], [{"aoVal": "E", "content": "24 \\times 24 \\times 60 \\times 60 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["1 day = 24 hours，$$1$$ hour = 60 minutes，$$1$$ minute = 60 seconds，$$24$$ days = (24 \\times 24) hours = [(24\\times 24) \\times 60] minutes = 24\\times 24\\times 60\\times 60 seconds "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7613", "queId": "9b1018648d354477b1bf219f22788ce5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Jacob writes down a three-digit number on a piece of paper. Lisa, Mike, and Henry are guessing the number Jacob writes down. Lisa: \"The number is $473$.\" Mike: \"The number is $623$.\" Henry: \"The number is $428$.\" Among the three digits, each person guesses two of them correctly for both digits and their positions. What is the number Jacob writes down? ", "answer_option_list": [[{"aoVal": "A", "content": "$$678$$ "}], [{"aoVal": "B", "content": "$$428$$ "}], [{"aoVal": "C", "content": "$$623$$ "}], [{"aoVal": "D", "content": "$$478$$ "}], [{"aoVal": "E", "content": "$$423$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["In the hundreds place, $4$ appears twice, so $4$ is in the hundreds place. In the tens place, $2$ appears twice, so $2$ is in the tens place. In the ones place, $3$ appears twice, so $3$ is in the ones place. Thus, the number Jacob writes down is $423$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7614", "queId": "a8bef60f903e469ca1c1c6956334b29d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The math workshop started at $5:00$. Today Leo was $15$ minutes late to the workshop. What time did Leo arrive? ", "answer_option_list": [[{"aoVal": "A", "content": "$5:00$ "}], [{"aoVal": "B", "content": "$5:05$ "}], [{"aoVal": "C", "content": "$5:15$ "}], [{"aoVal": "D", "content": "$5:20$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$15$ minutes past $5:00$ ~is $5:15$ . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7618", "queId": "6197d451b812429e854c567d682bb904", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following number is the opposite number of $12$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$-12$$ "}], [{"aoVal": "C", "content": "$\\frac{1}{12}$ "}], [{"aoVal": "D", "content": "$-\\frac{1}{12}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"], "answer_analysis": ["Opposite number is the number with opposite sign "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7621", "queId": "7c51eea30ea1493abb337515da4bba3f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "What is the missing number in the sequence below? 1, 3, 7, 15, 31,~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$63$$ "}], [{"aoVal": "B", "content": "$$47$$ "}], [{"aoVal": "C", "content": "$$57$$ "}], [{"aoVal": "D", "content": "$$59$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Patterns of Figures"], "answer_analysis": ["1, 3, 7, 15, 31, \\cdots .. 2. 4. 8.~ 16.~ 32 31+32 = 64 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7632", "queId": "9220b5b802044337852c68fe46e8298e", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Grace was going to meet her friends at the bus station. Right now, it is $8:20$. Grace arrived at the bus station half an hour ago. The trip from her home to the station was $1$ hour long. What time did Grace depart toward the bus station? ", "answer_option_list": [[{"aoVal": "A", "content": "$7:20$ "}], [{"aoVal": "B", "content": "$6:50$ "}], [{"aoVal": "C", "content": "$7:50$ "}], [{"aoVal": "D", "content": "$8:50$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["Grace arrived at the bus station at $7:50$, and the trip was $1$ hour long, so she departed at $6:50$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7633", "queId": "b1f3e4f2d0b943058ba679107675e64d", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "There are $1000$ students in Grade $3$ in Think Academy. Among these $1000$ students, at least how many students were born in the month with the most births? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$82$$ "}], [{"aoVal": "C", "content": "$$83$$ "}], [{"aoVal": "D", "content": "$$84$$ "}], [{"aoVal": "E", "content": "$$1000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle"], "answer_analysis": ["$1000\\div 12=83R4$, $83+1=84$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7635", "queId": "9225431446224ef3b0279551616551b7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Fill in the blanks with $$+$$, $$-$$, $$\\times$$ or $$\\div$$. $$(9+6)$$~\\uline{~~~~~~~~~~}~$$7=8$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$+$$ "}], [{"aoVal": "B", "content": "$$-$$ "}], [{"aoVal": "C", "content": "$$\\times$$ "}], [{"aoVal": "D", "content": "$$\\div$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Filling the Symbol in the Equations"], "answer_analysis": ["$$Nil$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7640", "queId": "810772db20954a2199211d0cc1360072", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In the calculation shown below, different letters represent different digits. $AA\\times BC\\times ABC=ABCABC$ What is the product of $A\\times B\\times C$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$21$$ "}], [{"aoVal": "D", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"], "answer_analysis": ["$AA\\times BC=77\\times13=11\\times91$ $A=7, B=1, C=3$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7654", "queId": "73bcab869f0b4bfca174a206a74e5a7b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "About the number 325, five boys said: Andrei: \"This is a 3-digit number\" Boris: \"All digits are distinct\" Vick: \"The sum of the digits is 10\" Greg: \"The unit digits is 5\" Danny: \"All digits are odd\" Which of the boys was wrong? ", "answer_option_list": [[{"aoVal": "A", "content": "Andrei "}], [{"aoVal": "B", "content": "Boris "}], [{"aoVal": "C", "content": "Vick "}], [{"aoVal": "D", "content": "Greg "}], [{"aoVal": "E", "content": "Danny "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["2 is not odd. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7668", "queId": "a48b341d0e194ece93f480ac24ca84ab", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A certain play has two $30$-minute parts and one intermission among them. The play started at $8:00$ and ended at $9:15$. How many minutes long were the intermission? (Adapted from 2010 Math Kangaroo Problem, Level 1-2, Question \\#19) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["From $8:00$ to $9:15$ = $1$ h $15$ min, $1$ h $15$ min = $75$ min, two $30$-minute parts = $60$ min, $75 - 60$ = $15$ min. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7675", "queId": "85d1a59f332e48fab3f4da5ecbbc64ae", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Math workshops start at $5:00$ PM. Today Allan was $15$ minutes late to the workshop. When did Allan come? ", "answer_option_list": [[{"aoVal": "A", "content": "$5:00$ PM "}], [{"aoVal": "B", "content": "$5:05$ PM "}], [{"aoVal": "C", "content": "$5:15$ PM "}], [{"aoVal": "D", "content": "$5:20$ PM "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$15$ minutes past $5:00$ PM is $5:15$ PM. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7678", "queId": "9278bd8836594889b36535a8562e84fa", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A school has two classes in the morning, each class continues $$45$$ minutes, and there is a break between classes. The first class starts at $$10:00$$, and the second class ends at $$12:00$$. How long does the courseware rest? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["From $$10:00$$ to $$12:00$$ = $$2$$ h = $$120$$ min, two $$45$$-minute parts = $$90$$ min, and $$120 - 90 = 30$$ min. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7685", "queId": "b6c8616bb96e4d50b484be3fb2b964b8", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Joseph has $$100$$ mice. Each of them is either white or grey. At least one of the mice is grey, and out of any seven of Joseph\\textquotesingle s mice at least four are white. How many grey mice does Joseph have at the most? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$93$$ "}], [{"aoVal": "D", "content": "$$97$$ "}], [{"aoVal": "E", "content": "$$99$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems"], "answer_analysis": ["The maximum is $3$ since any group of $7$ at most $3$ are grey. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7686", "queId": "e91d78a07ae3423a956836feea512e55", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$25$$ matches on the table. John and James take turns to remove $$1$$ to $$3$$ matches each time. The person who removes the last match will be the winner. If both of them were to use the best method and John removes first, then~\\uline{~~~~~~~~~~}~will win.~ ", "answer_option_list": [[{"aoVal": "A", "content": "John "}], [{"aoVal": "B", "content": "James "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["$$25\\div 4=6\\ldots 1$$ John removes $$1$$ match and $$24$$ is a multiple of $$4$$. So, the first player will win the game. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7695", "queId": "97183c487a584339ada9ef0e646c8d4f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following number is the opposite number of $-5$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$-5$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$\\frac{1}{5}$ "}], [{"aoVal": "D", "content": "$-\\frac{1}{5}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"], "answer_analysis": ["Opposite number is the number with opposite sign "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7702", "queId": "a4c11c820b124473b45673c8ee3e4dba", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following calculations shows how to work out the number of seconds in~~24 days? ", "answer_option_list": [[{"aoVal": "A", "content": "24 x24~ "}], [{"aoVal": "B", "content": "24 x~60 "}], [{"aoVal": "C", "content": "24 x~24 x~60 "}], [{"aoVal": "D", "content": "24 x~60 x~60 "}], [{"aoVal": "E", "content": "24 x~24 x~60 x~60 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["1 day = 24 hours，$$1$$ hour = 60 minutes，$$1minute$$ = 60 seconds，$$24$$ days = (24 x 24) hours = [(24x 24) x 60] minutes = 24x 24x 60x 60 seconds "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7708", "queId": "78d21d6d8ae242c2afb74bdfd2c4dfd2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The numbers $$1$$, $$2$$, $$4$$, $$5$$, $$8$$, $$9$$, $$10$$, $$13$$ and $$16$$ are divided into groups of one or more numbers. The sum of the numbers in each group is the same. What is the largest possible number of groups? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"], "answer_analysis": ["$1+2+4+5+8+9+10+13+16=68$ $2$ groups: sum of each group is $34$, $34=1+16+2+5+10=4+13+8+9$ $4$ groups: sum of each group is $17$, $17=1+16=2+5+10=4+13=8+9$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7712", "queId": "9bd479bde3f541e1ab16904524b04139", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When calculating $63\\times72$ , Judy fails to write the correct column multiplication. She writes one of the four digits as $9$ and gets a result which has a difference of $432$ from the correct one. Which digit does she write incorrectly? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "It\\textquotesingle s impossible to determine. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"], "answer_analysis": ["The difference between the wrong answer and the correct one is $432$, whose ones digit is $2$. That means Judy writes neither $2$ nor $3$ wrong. Compare $7\\times63$ and $6\\times72$, and we can get the correct answer. $69\\times72-63\\times72=432.$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7719", "queId": "cdc8d08ff4184caca59072ad8e3219fe", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Given that $$2a+3b=84$$, the largest possible value of $$a\\times b$$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$270$$ "}], [{"aoVal": "B", "content": "$$272$$ "}], [{"aoVal": "C", "content": "$$294$$ "}], [{"aoVal": "D", "content": "$$296$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Forming a Maximum/Minimum Multi-Digit Numbers with Fixed Sums"], "answer_analysis": ["Given that an unchanged sum, the smaller the difference the larger the product. $84=42+42$$$\\Rightarrow (2a) \\times (3b)=6ab\\leqslant {{42}^{2}}\\Rightarrow ab\\leqslant 294$$. Thus, the largest possible value of $ab$ is $294$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7720", "queId": "edda09bd011c45b48a1617c95f18d1c6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There is a cube whose six faces are marked with $3$, $4$, $5$, $6$, $7$, and $8$. If the sum of every two numbers that are on the opposite faces are the same, the number on the opposite face of $4$ is~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math->Fun Math Problems->Dice"], "answer_analysis": ["$3+8=4+7=5+6=11$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7723", "queId": "bb94c184371e4737b58cc207cf6e3279", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Bob constructs a rectangular building by many $1\\times1\\times1$ cubes. The volume of the rectangular building is $210$. What is the least sum of all edges of the rectangular building? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$80$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$210$$ "}], [{"aoVal": "E", "content": "$$116$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Problems of Extreme Value with Fixed Products"], "answer_analysis": ["Given the product, the smaller the difference, the smaller the sum. $210=2\\times3\\times5\\times7$, so the length, the width, and the height are $5,$ $6,$ and $7$. $(5+6+7)\\times4=72.$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7728", "queId": "7d894810f54c420e9e1c34d42d040529", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Apply this operation to $$(7, 28)$$. What are the last two numbers when the operation stops? ", "answer_option_list": [[{"aoVal": "A", "content": "$(2,2)$ "}], [{"aoVal": "B", "content": "$(3,3)$ "}], [{"aoVal": "C", "content": "$(5,5)$ "}], [{"aoVal": "D", "content": "$(7,7)$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Patterns of Figures->Special Changes"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7737", "queId": "a08aa7ef26c94c0ca4b5d61fe44e4018", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Lucy, Maria and Anna have a meeting at $$12:30$$. Lucy\\textquotesingle s walk takes $$10$$ minutes, Maria\\textquotesingle s walk takes a quarter of an hour, and Anna\\textquotesingle s walk takes $$40$$ minutes. At what time must the person who needs the longest time to get to the meeting leave her house? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12:00$$ "}], [{"aoVal": "B", "content": "$$12:10$$ "}], [{"aoVal": "C", "content": "$$12:15$$ "}], [{"aoVal": "D", "content": "$$12:20$$ "}], [{"aoVal": "E", "content": "$$11:50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$12:30$ - $40$ min = $11:50$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7743", "queId": "a514b68ee2974f5d862b1faf47b024b5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A talk show has two $$30$$-minute parts and has few commercials between them. The TV show started at $$1:50$$ and ended at $$3:00$$. How many minutes long were the commercials in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ min "}], [{"aoVal": "B", "content": "$$20$$ min "}], [{"aoVal": "C", "content": "$$15$$ min "}], [{"aoVal": "D", "content": "$$10$$ min "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["From $$1:50$$ to $$3:00$$ is $$1$$ h $$10$$ min, and two $$30$$-minute parts = $$60$$ min. $$1$$ hr $$10$$ min = $$70$$ min, and $$70 - 60 = 10$$ min. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7744", "queId": "e95baf5c19084439a9756d333322b356", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Vera leaves home at $$9.15$$ a.m. to walk to Derek's house, which takes her $$25$$ minutes. Carl leaves his house $$5$$ minutes after Vera but only takes $$6$$ minutes to get to Derek's house. When Carl arrives, how long will he and Derek have to wait for Vera to arrive? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ min "}], [{"aoVal": "B", "content": "$$14$$ min "}], [{"aoVal": "C", "content": "$$21$$ min "}], [{"aoVal": "D", "content": "$$24$$ min "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["Vera will arrive at $$9.40$$ a.m. Carl will leave at $$9.20$$ a.m. and arrive at $$9.26$$ a.m. So, Carl and Derek will have to wait for $$14$$ min. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7758", "queId": "f297eaf3b38b4bb7998925a448a0546a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The numbers $$1$$, $$5$$, $$8$$, $$9$$, $$10$$, $$12$$, and $$15$$ are divided into groups of one or more numbers. The sum of the numbers in each group is the same. What is the largest possible number of groups? (2016 Math Kangaroo Problem, Level 1-2, Question \\#24) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"], "answer_analysis": ["$1+5+8+9+10+12+15=60$ $2$ groups: sum of each group is $30$, $30=15+5+10=1+8+9+12$ $3$ groups: sum of each group is $20$, $20=15+5=12+8=10+9+1$ $4$ groups: sum of each group is $15$, $15-12=3$, but there is no $3$ in given numbers Thus, the largest possible number of groups is $3$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7759", "queId": "f29bb177737a48cb9e356b22515fd819", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Andrea needs an hour to get to the shopping center. If she leaves at $4$ PM, she gets there half an hour after the store closes. If she leaves at $8$ AM, she gets there half an hour before the store opens. What hours is the shopping center open? (2007 Math Kangaroo Problem, Level 1-2, Question \\#24) ", "answer_option_list": [[{"aoVal": "A", "content": "$7:30$ to $4:30$ "}], [{"aoVal": "B", "content": "$8:30$ to $5:30$ "}], [{"aoVal": "C", "content": "$7:30$ to $5:30$ "}], [{"aoVal": "D", "content": "$8:30$ to $4:30$ "}], [{"aoVal": "E", "content": "$9:30$ to $4:30$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["If Andrea leaves at $4$ PM, she arrives at the store when it is $5$ PM, and the store closes at $4:30$ PM. If Andrea leaves at $8$ AM, she arrives at the store when it is $9$ AM, and the store opens at $9:30$ AM. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7763", "queId": "f742f5395e1a4c6f8cb4569902f7375c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are two piles of matches, six in one pile and six in the other pile. Andy and Bob take turns to take the matches from any one of the two piles. The number of matches they can take is unlimited, but they have to take at least one each turn. Whoever picks the last match is the winner. If Andy takes the first match, is guarantee to win. ", "answer_option_list": [[{"aoVal": "A", "content": "Andy "}], [{"aoVal": "B", "content": "Bob "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["The number of matches in the two piles is the same. No matter how many matches Andy takes from one pile, Bob just needs to take the same amount of matches from the other pile. As long as there are matches for Andy to take, Bob can definitely take away the same amount from the other pile. Therefore, Bob will take away the last match and he is guarantee to win. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7772", "queId": "97f0e8ab3f3e4780aeeb0e313ec8e2c9", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "All numbers that are divisible by neither $$5$$ nor $$11$$ were removed from a sequence of consecutive natural numbers from $$1$$ to $$5500$$. A new sequence was formed. How many terms are there in this new sequence? (Adapted from $$2004$$ Math Kangaroo Problems, Level $$9-10$$, Question \\#$$30$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1000$$ "}], [{"aoVal": "B", "content": "$$1500$$ "}], [{"aoVal": "C", "content": "$$2500$$ "}], [{"aoVal": "D", "content": "$$3300$$ "}], [{"aoVal": "E", "content": "$$4400$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Number Operation"], "answer_analysis": ["Method $1$: $5500\\div5=1100$; $5500\\div11=500$; $5500\\div(5\\times11)=100$. $1100+500-100=1500$. Method $2$: In each group formed by $55$ consecutive numbers, $55-(11+5-1)=40$ numbers will be removed. $5500\\div55\\times(55-40)=1500$ numbers will remain in this new sequence. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7773", "queId": "f753eab2cf60498295be31efd71e9e21", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A tortoise is running along a $$5$$ metre track. It can run either half a metre or a metre every second. How many different ways can the tortoise finish the track? ", "answer_option_list": [[{"aoVal": "A", "content": "$$72$$ "}], [{"aoVal": "B", "content": "$$89$$ "}], [{"aoVal": "C", "content": "$$91$$ "}], [{"aoVal": "D", "content": "$$56$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Inductive Recursion"], "answer_analysis": ["$$1$$,$$2$$,$$3$$,$$5$$,$$8$$,$$13$$,$$21$$,$$34$$,$$55$$,$$89$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7781", "queId": "fbfc1e1271cd49c1916e4a65f18d0204", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A cat divides $$24$$ cans of tuna into $$4$$ groups. Each group has at least $$1$$ can of tuna, and the number of cans in each group \\uline{cannot be the same}. There are at mostcans of tuna in the group that has the largest number of cans. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$21$$ "}], [{"aoVal": "D", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Obtaining Maximum/Minimum Values "], "answer_analysis": ["$$ 1 + 2+3 + 18 = 24$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7782", "queId": "9c8769716d3244b98fd33b96529a612d", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "Basil has several domino tiles, as shown in the figure. He wants to arrange them in a line according to the well-known \"domino rules\": in any two tiles that are next to each other, the squares that touch must have the same number of points. What is the largest number of tiles he can arrange in this way? [insert picccc] ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["One possible configuration for 5 dominoes is shown. [pic] "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7783", "queId": "ffe5dfecf5fa4c55a1dc51dcb5a20b4b", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A school has three classes in the morning, and there is a $$15$$-minutes break between each two classes. Each class is of the same length. The first class starts at $$9:45 $$, and the third class ends at $$12:00 $$. How long is each class? ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$35$$ "}], [{"aoVal": "D", "content": "$$40$$ "}], [{"aoVal": "E", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["From $$9:45$$ to $$12:00$$ = $$2$$ h $$15$$m = $$135$$ min, two $$15$$-minute parts = $$30$$ min, and $$135 - 30 = 105$$ min. $$105\\div3=35$$min "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7791", "queId": "982bfbf3b11d4e64b9aea0ddc80d49f2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The weights of four boys are 45kg, 48kg, 52kg and 53kg. Mason\\textquotesingle s weight is an even number. Joshua\\textquotesingle s weight is a multiple of 5. Christopher is not the heaviest and Mateo is not the lightest. Who is the heaviest among the four boys? ", "answer_option_list": [[{"aoVal": "A", "content": "Mason "}], [{"aoVal": "B", "content": "Joshua "}], [{"aoVal": "C", "content": "Christopher "}], [{"aoVal": "D", "content": "Mateo "}], [{"aoVal": "E", "content": "Impossible to determine "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["Mason\\textquotesingle s weight is an even number = 48kg / 52kg. Joshua\\textquotesingle s weight is a multiple of 5 = 45kg. Christopher is not the heaviest = x 53kg. Mateo is not the lightest = x 45kg Jason - \\textgreater{} either Mason or Christpoher is 28/52kg -\\textgreater{} Mateo. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7793", "queId": "9ca7cf140328497b98122848bf76a11e", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "From $1$ to $45$, how many numbers must be chosen at least to ensure that there are two of chosen numbers sum to $30$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$31$$ "}], [{"aoVal": "D", "content": "$$32$$ "}], [{"aoVal": "E", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Constructing and Proving"], "answer_analysis": ["$$16+1+14+1=32$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7796", "queId": "e517a849e66442fea50288d5d850b461", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Teacher James distributes $82$ apples to $12$ students. At least how many apples can the student with the most apples get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle"], "answer_analysis": ["$82\\div12=6R10$, $6+1=7$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7803", "queId": "aebca65fe557477eac922bcb94429f7a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$A$ and $B$ play a game as follows. First $A$ says $1, 2$ or $3$. Then $B$ can add $1, 2$ or $3$ to the number the first player said. The game continues with the players playing alternately, in each turn adding $1, 2$ or $3$ to the previous number. For example, A can say $2$, then B can say $5$, then A could say $6$, and so on. The player who says $100$ wins. Who has the winning strategy? ", "answer_option_list": [[{"aoVal": "A", "content": "A "}], [{"aoVal": "B", "content": "B "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations"], "answer_analysis": ["Observe that B can always say a multiple of 4 in his turn. For example, consider the following sequence of moves: A-1; B-4; A-6; B-8 and so on. Regardless of what A says, B can always say a multiple of 4. Hence B will say 100 and will win "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7813", "queId": "dc1416d88f1643fca435b690b39ad738", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2016 P2 Q7 It takes 5 mintues to boil an egg. What is the least amount of time it takes to boil 3 eggs? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$minutes "}], [{"aoVal": "B", "content": "$$12$$minutes "}], [{"aoVal": "C", "content": "$$15$$minutes "}], [{"aoVal": "D", "content": "$$18$$minutes "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["5 minutes, boil together. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7817", "queId": "dc1c33e698aa483792fa273b1c66f0ea", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $9$ water glasses, all facing up. You need to turn exactly $2$ glasses over in each time. Is it possible to turn all $9$ of them upside down after several moves? ", "answer_option_list": [[{"aoVal": "A", "content": "Yes, it is possible. "}], [{"aoVal": "B", "content": "No, it is impossible. "}], [{"aoVal": "C", "content": "I have no idea. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Turning Mugs over"], "answer_analysis": ["You have to flip a cup an odd number of times to turn it over. To make all the $9$ cups face down, you have to make an odd number of flips. Each time you flip exactly $2$ cups, the total number of flips is an even number of times. Hence it is impossible. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7819", "queId": "e53cd3db96b54eb1b9a196eca73619ee", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "David went to watch $Spider Man$ at the cinema on June $25$\\textsuperscript{th}. The movie started at $6 : 32$ P.M. and finished at $7 : 54$ P.M.. On the same day, Mary needed to go abroad by plane. The plane took off at $11 : 40$ P.M., and the time she spent on plane was $2$ hours and $11$ minutes longer than that David spent at the cinema. When would Mary get off the plane? ", "answer_option_list": [[{"aoVal": "A", "content": "$3 : 23$ P.M. on June $25$\\textsuperscript{th} "}], [{"aoVal": "B", "content": "$3 : 13$ A.M. on June $25$\\textsuperscript{th} "}], [{"aoVal": "C", "content": "$3 : 13$ P.M. on June $26$\\textsuperscript{th} "}], [{"aoVal": "D", "content": "$3 : 13$ A.M. on June $26$\\textsuperscript{th} "}], [{"aoVal": "E", "content": "$3 : 23$ A.M. on June $26$\\textsuperscript{th} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["From $6 : 32$ P.M. to $7 : 54$ P.M., it lasted $1$ hour and $22$ minutes. The time Mary spent on plane: $1$ hour and $22$ minutes $+$ $2$ hours and $11$ minutes $=$ $3$ hours and $33$ minutes. Thus, Mary would get off the plane at $3 : 13$ A.M. on June 26\\textsuperscript{th}. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7824", "queId": "d311b61d546a40b780d83ca5753e68d4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Cindy and Chloe are siblings. Each of them have $$2$$ brothers and $$2$$ sister in. How many children are there in the family? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["Cindy is sister to Chloe and Chloe is sister to Cindy. Thus, they have one more common sister. There are a total of $$3$$ girls in the family. Their brother are the same, thus $$2$$ boys in the family. In total $$5$$ children. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7826", "queId": "aef6ddcbe2464c3681fafc4a14abf013", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Jacky wants to insert the digit 3 somehwere in the number 2014. Where should she insert digit 3 if she wants her five digit number to be as small as possible? ", "answer_option_list": [[{"aoVal": "A", "content": "in front of 2014 "}], [{"aoVal": "B", "content": "between the 2 and the 0 "}], [{"aoVal": "C", "content": "between the 0 and the 1 "}], [{"aoVal": "D", "content": "between the 1 and the 4 "}], [{"aoVal": "E", "content": "behind 2014. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Forming a Maximum/Minimum Multi-Digit Numbers with Fixed Sums"], "answer_analysis": ["3 is a digit between 1 and 4. Try to put into and see which number is the smallest. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7828", "queId": "c577f21c39b6449c9c83f3cf13fe61d1", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Jack, Rebecca, Dustin and Steve write down one number, respectively, which are $44$, $85$, $72$ and $39$.Both Jack\\textquotesingle s and Dustin\\textquotesingle s numbers are odd. Both Jack\\textquotesingle s and Steve\\textquotesingle s numbers are more than $60$. What number is written by Rebecca? ", "answer_option_list": [[{"aoVal": "A", "content": "$$44$$ "}], [{"aoVal": "B", "content": "$$85$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$39$$ "}], [{"aoVal": "E", "content": "Impossible to determine "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["Eliminate odd numbers and numbers more than $60$, so the only number left is $44$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7830", "queId": "b7f588e52ccd4fd985b6d78e3df0841e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In class, Anna, Bell, and Julie are doing math homework at school. Among them, Anna took $$18$$ minutes and $$25$$ seconds. Bell took $$19$$ minutes and $$36$$ seconds, and Julie took $$20$$ minutes and $$15$$ seconds. How long did the three take in total? (adapted from 2008 Math Kangaroo Problem, Level 3 - 4, Question \\#15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$57$$ minutes $$16$$ seconds "}], [{"aoVal": "B", "content": "$$58$$ minutes $$16$$ seconds "}], [{"aoVal": "C", "content": "$$58$$ minutes $$26$$ seconds "}], [{"aoVal": "D", "content": "$$58$$ minutes $$6$$ seconds "}], [{"aoVal": "E", "content": "$$57$$ minutes $$26$$ seconds "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$18$ minutes + $19$ minutes + $20$ minutes + $25$ seconds $+$ $36$ seconds + $15$ seconds = $57$ minutes $76$ seconds = $58$ minutes $16$ seconds "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7831", "queId": "9d1da5d5bdf24b01ae0600d065e7fbe1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The time in Thornsburg is $$6$$ hours ahead of London. The time in London is $$8.27$$ pm. What is the time in Thornsburg? Choose the answer. ", "answer_option_list": [[{"aoVal": "A", "content": "$$02.27$$ pm "}], [{"aoVal": "B", "content": "$$14.27$$ pm "}], [{"aoVal": "C", "content": "$$02.27$$ pm "}], [{"aoVal": "D", "content": "$$02.27$$ am "}], [{"aoVal": "E", "content": "$$14.27$$ am "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$6$ hours ahead of $08:27$ pm is $02:27$ am. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7833", "queId": "c58278d1722a49f582032d973b65db1b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Suppose $a, b$, and $c$ are nonzero real numbers, and $a+b+c=0$. What are the possible value(s) for $\\frac{a}{\\textbar a\\textbar}+\\frac{b}{\\textbar b\\textbar}+\\frac{c}{\\textbar c\\textbar}+\\frac{a b c}{\\textbar a b c\\textbar} ?$ (2017 AMC 8 Problem, Question \\#21) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$1$ and $-1$ "}], [{"aoVal": "C", "content": "$2$ and $-2$ "}], [{"aoVal": "D", "content": "$0,2$ and $-2$ "}], [{"aoVal": "E", "content": "$0,1$ and $-1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"], "answer_analysis": ["There are 2 cases to consider: \\textbf{Case 1:} 2 of $a, b$, and $c$ are positive and the other is negative. WLOG, we can assume that $a$ and $b$ are positive and $c$ is negative. In this case, we have that $$ \\frac{a}{\\textbar a\\textbar}+\\frac{b}{\\textbar b\\textbar}+\\frac{c}{\\textbar c\\textbar}+\\frac{a b c}{\\textbar a b c\\textbar}=1+1-1-1=0 \\text {. } $$ \\textbf{Case 2}: 2 of $a, b$, and $c$ are negative and the other is positive. Without loss of generality, we can assume that $a$ and $b$ are negative and $c$ is positive. In this case, we have that $$ \\frac{a}{\\textbar a\\textbar}+\\frac{b}{\\textbar b\\textbar}+\\frac{c}{\\textbar c\\textbar}+\\frac{a b c}{\\textbar a b c\\textbar}=-1-1+1+1=0 \\text {. } $$ Note these are the only valid cases, for neither 3 negatives nor 3 positives would work, as they cannot sum up to 0 . In both cases, we get that the given expression equals $(\\mathbf{A}) 0$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7846", "queId": "a1b82e06aaae4bd794bea2357cfb6047", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The numbers $$2$$, $$4$$, $$6$$, $$8$$, $$9$$ and $$11$$ are divided into groups of one or more numbers. The sum of the numbers in each group is the same. Which number must be in the group with the number $$11$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"], "answer_analysis": ["$2+4+6+8+9+11=40$ $2$ groups: sum of each group is $20$, $20=9+11=2+4+6+8$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7851", "queId": "d33adfc876df4f4b93bfbc5358322a96", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Joy writes a four-digit number on a piece of paper and let Sandy guess. $\\textasciitilde$ Sandy asks: \"Is it $$6031$$?\" Joy says: \"You guess $1$ digit correct and it\\textquotesingle s in the correct place.\" Sandy asks: \"Is it $$5672$$?\" Joy says: \"You guess $2$ digits correct and they\\textquotesingle re in the wrong places.\" Sandy asks: \"Is it $$4796$$?\" Joy says: \"You guess $4$ digits correct and they\\textquotesingle re in the wrong places.\" $\\textasciitilde$ According to the conversation above, what number does Joy write? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4967$$ "}], [{"aoVal": "B", "content": "$$9764$$ "}], [{"aoVal": "C", "content": "$$9647$$ "}], [{"aoVal": "D", "content": "$$6497$$ "}], [{"aoVal": "E", "content": "$$6947$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["The number is formed by $4,7,9,6$ according to last question. Thus, according to the first question, $6$ should be in the thousands place. From the second and last question, $7$ is in ones place, $4$ is in tens place, and $9$ is in hundreds place. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7864", "queId": "eea5f58127d04072a1e0f8dcad0c8ecb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Thirty apples are distributed among 4 children and each of them can get at least one apple. For the kid who gets the most apples, what\\textquotesingle s the least possible number of apples he or she can get? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$7$ "}], [{"aoVal": "B", "content": "$8$ "}], [{"aoVal": "C", "content": "$9$ "}], [{"aoVal": "D", "content": "$10$ "}], [{"aoVal": "E", "content": "$11$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Simple Pigeonhole Principle Problems"], "answer_analysis": ["$$30\\div 4=7 \\textbackslash{} \\text{R}2$$, thus for the kid who gets the most apples, he or she can get $$7+1=8$$ apples at least. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7867", "queId": "d36ea5f7c22442c58ab13b4e2ee01e6c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Let\\textquotesingle s convert! $$1$$ hour $$45$$ minutes $$=$$~\\uline{~~~~~~~~~~}~minutes ", "answer_option_list": [[{"aoVal": "A", "content": "$$145$$ "}], [{"aoVal": "B", "content": "$$105$$ "}], [{"aoVal": "C", "content": "$$95$$ "}], [{"aoVal": "D", "content": "$$75$$ "}], [{"aoVal": "E", "content": "$$65$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$60+45=105$ minutes. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7889", "queId": "cf4243d0f1cb4474bc033bc8118047c8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following calculations shows how to work out the number of seconds in~~24 days? ", "answer_option_list": [[{"aoVal": "A", "content": "24 x~24~ "}], [{"aoVal": "B", "content": "24 x~60 "}], [{"aoVal": "C", "content": "24 x 24 x 60 "}], [{"aoVal": "D", "content": "24 x 60 x 60 "}], [{"aoVal": "E", "content": "24 x~24 x~60 x~60 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["1 day = 24 hours，$$1$$ hour = 60 minutes，$$1$$ minute = 60 seconds，$$24$$ days = (24 \\times 24) hours = [(24\\times 24) \\times 60] minutes = 24\\times 24\\times 60\\times 60 seconds "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7891", "queId": "ef11f5ae9d5f4934aedaabeb5d05d0a8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "For any two numbers $$x$$ and $$y$$, the special operation $$^{}\\otimes$$ is defined as follow $$x^{}\\otimes y=x+y-\\frac {2012}{335}$$. Calculate $$\\frac {2^{}\\otimes 4^{}\\otimes 6^{}\\otimes \\cdots ^{}\\otimes 2010^{}\\otimes 2012}{2012}$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1006$$ "}], [{"aoVal": "B", "content": "$$1005$$ "}], [{"aoVal": "C", "content": "$$503$$ "}], [{"aoVal": "D", "content": "$$502$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Patterns of Figures->Special Changes"], "answer_analysis": ["E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7896", "queId": "d3dc8a20dc884659a4f2b2c1645c42ba", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A train started from the starting station at 7:30, it takes 8 hours and 37 minutes to arrive at the terminal station. When will it arrive? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3:30$$ A.M. "}], [{"aoVal": "B", "content": "$$3:37$$ P.M. "}], [{"aoVal": "C", "content": "$$4:37$$ P.M. "}], [{"aoVal": "D", "content": "$$4:07$$ P.M. "}], [{"aoVal": "E", "content": "$$4:37$$ A.M. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["$$7:30$$+$$8$$h$$37$$m=$$16:07$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7912", "queId": "ef3edca139b24b908536f5ce722676ce", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The weights of four boys are $45\\rm{kg}$, $48\\rm{kg}$, $52\\rm{kg}$ and $53\\rm{kg}$. Mason\\textquotesingle s weight is an even number. Joshua\\textquotesingle s weight is a multiple of $5$. Christopher is not the heaviest and Mateo is not the lightest. Who is the heaviest among the four boys? ", "answer_option_list": [[{"aoVal": "A", "content": "Mason "}], [{"aoVal": "B", "content": "Joshua "}], [{"aoVal": "C", "content": "Christopher "}], [{"aoVal": "D", "content": "Mateo "}], [{"aoVal": "E", "content": "Impossible to determine "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["Mason\\textquotesingle s weight is an even number = 48kg / 52kg. Joshua\\textquotesingle s weight is a multiple of 5 = 45kg. Christopher is not the heaviest = x 53kg. Mateo is not the lightest = x 45kg Jason - \\textgreater{} either Mason or Christpoher is 28/52kg -\\textgreater{} Mateo. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7923", "queId": "c6918d40841c418fabc414dbdb8fa0c8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Math workshop starts at $5:00$ PM. Today Allan was $15$ minutes late to the workshop. What time did Allan come? (2010 Math Kangaroo Problem, Level 1--2, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$5:00$ PM "}], [{"aoVal": "B", "content": "$5:05$ PM "}], [{"aoVal": "C", "content": "$5:15$ PM "}], [{"aoVal": "D", "content": "$5:20$ PM "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["$15$ minutes past $5:00$ PM is $5:15$ PM. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7927", "queId": "eaee82725b3447859c92e1e3077451c1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Peter can draw a cartoon in $30$ minutes. How many hours does it take to paint four cartoons?~(adapted from 2011 Math kangaroo Problems, Level 1-2, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["There are $60$ minutes in an hour. It will take $120$ minutes to draw $4$ cartoons.~ $120$ minutes=$2$ hours. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7928", "queId": "c6ac83fc0e1f43aa88b2e376d15fde98", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Bob and Linda went mountain climbing together. They climbed the mountain from $8$:$30$. Bob reached the top at $14$:$00$, and Linda was $1$ hour and $40$ minutes behind him. How long did it take Linda climb?~(adapted from 2003 Math Kangaroo Problem, Level 3 - 4, Question \\#10) ", "answer_option_list": [[{"aoVal": "A", "content": "$3$ hr $30$ min "}], [{"aoVal": "B", "content": "$4$ hr $30$ min "}], [{"aoVal": "C", "content": "$7$ hr $10$ min "}], [{"aoVal": "D", "content": "$6$ hr $20$ min "}], [{"aoVal": "E", "content": "$8$ hr $40$ min "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"], "answer_analysis": ["It lasted $3$ hours and $30$ minutes from $8$:$30$ to $12$:$00$. It lasted $2$ hours from $12$:$00$ to $14$:$00$. So Bob took $5$ hours and $30$ minutes. Linda was $1$ hour and $40$ minutes behind Bob. Linda\\textquotesingle s time was $7$ hours and $10$ minutes. Bob: $3$h+$30$min+$2$h=$5$h$30$min Linda:$3$h+$30$min+$2$h+$1$h+$40$min=$7$h$10$min "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7936", "queId": "f425c85b93394731a1d7b6b7b063df1c", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A certain play has three $30$-minute parts and two intermission among them. The play started at $8:30$ and ended at $10:15$. How many minutes long were the intermissions in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Time Problem"], "answer_analysis": ["From $8:30$ to $10:15$ = $1$ hr $45$ min, $1$ hr $45$ min = $105$ min, three $30$-minute parts = $90$ min, $105 - 90$ = $15$ min. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7950", "queId": "dd99e23150a54cf9b5d1d6e958ee1f87", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are two piles of matches. Each pile has $$6$$ sticks. Cindy and Doris take turns to pick up matches from either pile. There is no limit to how many matches they can pick up, but they must pick up at least one match each turn. The person who picks up the last match will be the winner. If Cindy starts picking up matches first,~\\uline{~~~~~~~~~~}~will be the winner (has a winning strategy). ", "answer_option_list": [[{"aoVal": "A", "content": "Cindy "}], [{"aoVal": "B", "content": "Doris "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"], "answer_analysis": ["Doris will be the winner, since she can simply mirror the number of matches Cindy picks up every turn. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7962", "queId": "f4aa7d6c44594caaac75e8b80c0511dd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Two cups with capacities of 9 liters and 3 liters, respectively, have different diameters at the top and bottom and are unmarked. If water can be taken arbitrarily, how many operations are required at least to pour out 6 liters of water? (Filling the cup is counted as one operation, pouring the water out is counted as another operation.) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Pouring Water Problems"], "answer_analysis": ["2 operations at least. 1. Fill the 9 liter cup to the top. 2. Pour water from the 9 liter cup into the 3 liter cup until the 3 liter cup is full, leaving 6 liters of water in the 9 liter cup. The answer is B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7966", "queId": "f94e5095fed648a0af370b4e2e6c710d", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "From $1$ to $30$, how many integers can be chosen at most to ensure that no two of chosen numbers sum to $36$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$19$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Constructing and Proving"], "answer_analysis": ["1, 2, 3, 4, 5, 18→ 6 $30-5-1=24$, $24\\div2=12$ $$6+12=18$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7969", "queId": "de07443fc5504a5f8a30d5c4e7d4cb80", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Out of 8 bottles of sugar, 1 bottle has a lighter mass than the other 7. How many times can the balance be used to ensure that the lighter one is found? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math"], "answer_analysis": ["omit "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7989", "queId": "f57d1581f15740f5ad444a74793bbd89", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ivy, Vivian, and Candy are playing the truth or lie game. The rule is: the person who picks the truth card can only tell the truth, and the person who picks the lie card must tell a lie. \\textbf{Ivy said: \"Vivian and Candy lied.\"} \\textbf{Vivian said: \"I did\\textquotesingle t lie.\"} \\textbf{Candy said: \"Vivian lied.\"} How many of them told the truth? How many of them told a lie?~\\hspace{0pt} ", "answer_option_list": [[{"aoVal": "A", "content": "$2$; $1$ "}], [{"aoVal": "B", "content": "$0$; $3$ "}], [{"aoVal": "C", "content": "$1$; $2$ "}], [{"aoVal": "D", "content": "$3$; $0$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"], "answer_analysis": ["Vivian and Candy told contradictory information, so one of them told the truth and the other one told the lie. Therefore, Ivy has definitely told the lie. So two people told the lie, and one people told the truth. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "7994", "queId": "00437161c674491894df0e1c19c954c8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If the exam lasts for two days and ends on Wednesday, what day does the exam start?~(adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$4$$) ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Friday "}], [{"aoVal": "D", "content": "Saturday "}], [{"aoVal": "E", "content": "Thursday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["Tuesday to Wednesday is exactly two days. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8001", "queId": "00c41d59a843421c99cf0a9310b7997b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The number of apples in basket $$A$$ was $$\\frac{13}{19}$$ of that in basket $$B$$. After $$10$$ apples were taken out from basket $$A$$ and were put in basket $$B$$, the number of apples in basket $$A$$ became $$\\frac{1}{3}$$ of that in basket $$B$$. How many apples were there in basket $$A$$ and basket $$B$$, respectively, in the beginning? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ apples in basket $$A$$; $$19$$ apples in basket $$B$$ "}], [{"aoVal": "B", "content": "$$26$$ apples in basket $$A$$; $$19$$ apples in basket $$B$$ "}], [{"aoVal": "C", "content": "$$26$$ apples in basket $$A$$;~$$38$$ apples in basket $$B$$ "}], [{"aoVal": "D", "content": "$$19$$ apples in basket $$A$$; $$13$$ apples in basket $$B$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"], "answer_analysis": ["The total number of apples in basket $$A$$ and basket $$B$$ is constant. In the beginning, $$A: B=13:19$$; now, $$A: B=1:3=8:24$$ (the total number of portions is still $$32$$). By comparison, the number of portions in basket $$A$$ decreases by $$5$$, and the number of portions in basket $$B$$ increases by $$5$$, so each portion is $$10\\div5=2\\text{kg}$$. Formerly, there were $$13\\times2=26$$ apples in basket $$A$$ and $$19\\times2=38$$ apples in basket $$B$$. So, the answer is $$C$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8003", "queId": "00dda9f02ca64cb292cd2a8564138558", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The average cost of a long-distance call in the USA in 1985 was 50 cents per minute, and the average cost of a long-distance call in the USA in 2008 was 5 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (adapted from 2007 AMC 8, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$80$$ "}], [{"aoVal": "E", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $50-5=45$ so the percent decrease is $\\frac{45}{50}$ which is ~$ 90 \\textbackslash\\%$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8004", "queId": "097e549b99444475b22e74850de5ceba", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My mom\\textquotesingle s birthday is on Sunday, and my dad\\textquotesingle s birthday is $$55$$ days later. On what day of the week will my dad\\textquotesingle s birthday be? ", "answer_option_list": [[{"aoVal": "A", "content": "$$ $$Sunday$$ $$ "}], [{"aoVal": "B", "content": "$$ $$Monday$$ $$ "}], [{"aoVal": "C", "content": "$$ $$Tuesday$$ $$ "}], [{"aoVal": "D", "content": "$$ $$Thursday$$ $$ "}], [{"aoVal": "E", "content": "$$ $$Saturday$$ $$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["After $$1$$ day, it is Monday; after $$2$$ days, it is Tuesday; after $$3$$ days, it is Wednesday $$\\cdots$$ After $$8$$ days, it is still Monday, and the period is $$7$$ days. $$55\\div 7=7$$(weeks) $$\\rm R$$ $$6$$ (days). The birthday is Saturday. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8006", "queId": "12a44af54376463da580ed205dd44ec5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$10$$ February $$2013$$ falls on Friday, which day of the week will $$10$$ February $2014$ fall on? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday "}], [{"aoVal": "B", "content": "Monday "}], [{"aoVal": "C", "content": "Tuesday "}], [{"aoVal": "D", "content": "Wednesday "}], [{"aoVal": "E", "content": "Thursday "}], [{"aoVal": "F", "content": "Friday "}], [{"aoVal": "G", "content": "Saturday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["No leap year, 365 days "], "answer_value": "G"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8012", "queId": "1bf06eab37644b91be0d58bc2c525830", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "On a map of England and Wales the distance between St Ives in Cornwall and St Ives in Cambridgeshire measures $$18\\text{cm}$$. In reality the distance between the two towns is about $$450\\text{km}$$. Which of the options below is the scale of the map? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1:2500000$$ "}], [{"aoVal": "B", "content": "$$1:1000000$$ "}], [{"aoVal": "C", "content": "$$1:750000$$ "}], [{"aoVal": "D", "content": "$$1:500000$$ "}], [{"aoVal": "E", "content": "$$1:250000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["The scale of the map is $$18\\text{cm} : 450\\text{km}$$; converting the actual distance to centimetres, this is equivalent to $$18 : 450 \\times 1000 \\times 100 = 18 : 45 000 000$$. Simplifying gives a scale of $$1 : 2 500 000$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8013", "queId": "0129abdaa0db4312ac58082b33476cce", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A mixture of $$30$$ litres of paint is $$25\\textbackslash\\%$$ red tint, $$30\\textbackslash\\%$$ yellow tint and $$45\\textbackslash\\%$$ water. Five litres of yellow tint are added to the original mixture. What is the percentage of yellow tint in the new mixture? ", "answer_option_list": [[{"aoVal": "A", "content": "$$25\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$35\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$40\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$45\\textbackslash\\%$$ "}], [{"aoVal": "E", "content": "$$50\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["Since $$30\\textbackslash\\%$$ of the original $$30$$ liters of paint was yellow, and $$5$$ liters of yellow paint were added to make the new mixture, there are $$9+5=14$$ liters of yellow tint in the new mixture. Since only $$5$$ liters of paint were added to the original $$30$$, there are a total of $$35$$ liters of paint in the new mixture. This gives $$40\\textbackslash\\%$$ of yellow tint in the new mixture, which is $$40$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8015", "queId": "013029d4f788492fa90c125bc4baf373", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Rick and Roy each stands at different ends of a straight road that is $$2021$$m long. They run toward each other. Rick\\textquotesingle s speed is $$21\\text{m/s}$$ and Roy\\textquotesingle s speed is $$22\\text{m/s}$$. They will meet in~\\uline{~~~~~~~~~~}~seconds. ($$2016$$ Math League.com contest problem, $$5$$th Grade, Question \\#$$26$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$35$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$47$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$2021\\div (21+22)=47$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8020", "queId": "01513e9d25f246f9960e3d25c02db5af", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$13^{}\\text{th}$$February is Friday, what day of the week is $$1$$\\textsuperscript{st~}February? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday　 "}], [{"aoVal": "B", "content": "Monday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Thursday　 "}], [{"aoVal": "E", "content": "Saturday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["We can count backward by days or by weeks. Count a few weeks back to find that February $$6$$ is a Friday. Then count a few days back to find that February $$1$$ is a Sunday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8021", "queId": "2098f3c77dac4765aea3be75e95c88d7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "To defeat a dragon, Matthias has to cut off all the dragon\\textquotesingle s heads. If he can cut off $$3$$ of the dragon\\textquotesingle s heads, one new head immediately grows. Matthias defeats the dragon by cutting off $$17$$ heads in total. How many heads did the dragon have at the beginning? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Including and Excluding "], "answer_analysis": ["$17\\div3=5R2$, so Matthias has $5$ groups of $3$ cuts, which means $5$ new heads grew. Thus, there are $17-5=12$ heads originally. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8023", "queId": "1bf74c5b01e746029d25880f2313247c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Gabriel wrote his name $$100$$ times in the sand. What was the $$100\\text{th}$$ letter he wrote? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$a$$ "}], [{"aoVal": "B", "content": "$$b$$ "}], [{"aoVal": "C", "content": "$$r$$ "}], [{"aoVal": "D", "content": "$$i$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"], "answer_analysis": ["The $$1\\text{st}$$ letter Gabriel wrote was $$G$$, and every $$7\\text{th}$$ letter after was $$G$$. The $$99\\text{th}$$ letter he wrote was $$G$$, and the $$100\\text{th}$$ was an\"$$a$$.\" "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8024", "queId": "01783de305314dc7ba5d87cc1dc397db", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "At the $2018$ Tompkins County Fair a vendor is offering a \"fair special\" on hats. If you buy one hat at the regular price of $\\textbackslash$ 30$, you get a second hat at a $40\\textbackslash\\%$ discount, and a third pair at half the regular price. James took advantage of the \"fair special\" to buy three hats. What percentage of the $\\textbackslash$ 90$ regular price did he save? (adapted from 2013 AMC 8, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$25$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["First, the amount of money one will pay for three hats without the discount $=\\textbackslash$ 90$. Then, find the amount of money using the discount: $30+0.6 \\times 30+\\frac{1}{2} \\times 30=\\textbackslash$ 63$. Finding the percentage yields $\\frac{63}{90}=70\\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-70\\textbackslash\\%= 30\\textbackslash\\%$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8027", "queId": "019224a476eb40419f76370b179c20f8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sales tax rate in Bergville is $$6\\textbackslash\\%$$. During a sale at the Bergville Coat Closet, the price of a coat is discounted $$20\\textbackslash\\%$$ from its ＄$$90.00$$ price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up ＄$$90.00$$ and adds $$6\\textbackslash\\%$$ sales tax, then subtracts $$20\\textbackslash\\%$$ from this total. Jill rings up ＄$$90.00$$, subtracts $$20\\textbackslash\\%$$ of the price, then adds $$6\\textbackslash\\%$$ of the discounted price for sales tax. What is Jack's total minus Jill's total? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$-1.06$$ "}], [{"aoVal": "B", "content": "＄$$-0.53$$ "}], [{"aoVal": "C", "content": "＄$$0$$ "}], [{"aoVal": "D", "content": "＄$$0.53$$ "}], [{"aoVal": "E", "content": "＄$$1.06$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"], "answer_analysis": ["The price Jacks rings up is $$(90.00)(1.06)(0.80)$$. The price Jill rings up is $$(90.00)(0.80)(1.06)$$. By the commutative property of multiplication, these quantities are the same, and the difference is $$(\\text{C})$$＄$$0$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8039", "queId": "3c80e363215c4e2092e2d3873e641db4", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The distance between Exeter and London is $$175$$ miles. Sam left Exeter at $$10:00$$ on Tuesday for London. Morgan left Exeter~ for London at $$13:00$$ the same day. They travelled on the same road. Sam\\textquotesingle s average speed was $$25$$ miles per hour, and Morgan\\textquotesingle s average speed was $$50$$ miles an hour. At what time did Sam and Morgan meet? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16:00$$ "}], [{"aoVal": "B", "content": "$$15:55$$ "}], [{"aoVal": "C", "content": "$$15:30$$ "}], [{"aoVal": "D", "content": "$$15:00$$ "}], [{"aoVal": "E", "content": "$$14:40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$25\\times3=75$miles $75\\div (50-25)=3$h $13+3=16$ They meet at $16:00$. revise from ($$2017$$ Junior Mathematical Challenge Question \\#$$25$$) "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8041", "queId": "3337a0520fa449f0ac9b992628ee44b1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There were $$31$$ runners competing in a race. The number of runners who finished before John is four times smaller than the number of runners who finished later than John. At what place did John finish? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["Before is ``$$1$$'', so after is ``$$4$$'', Before: $$(31-1) \\div (4+1) = 6$$, and John: $$6+1=7$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8043", "queId": "058a929170a4407cbbefa0e9be4c7f66", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Gary will be three times as old as Harry $$4$$ years from now. If Harry is $$5$$ years old now, how old will Gary be in $$4$$ years? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$23$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$31$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["Harry is $$5$$ years old now; he\\textquotesingle ll be $$9$$ in $$4$$ years. Gary is thus $$3\\times9=27$$ years old "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8044", "queId": "058d22cc76eb4bff836858ecf11fa6ff", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Bowen has $$40$$ grams of a $$25\\textbackslash\\%$$ sugar solution. After~\\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of the solution is $$40\\textbackslash\\%$$. (Evaporate: the water turns from liquid into vapor and is no longer in the solution anymore.) ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ grams "}], [{"aoVal": "B", "content": "$$12$$ grams "}], [{"aoVal": "C", "content": "$$9$$ grams "}], [{"aoVal": "D", "content": "$$6$$ grams "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"], "answer_analysis": ["$$40-40\\times25\\textbackslash\\%\\div40\\textbackslash\\%=40-25=15$$ ounces. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8045", "queId": "0205c319805f4938a574d5dd9f5c727d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mike makes $5$ cakes every minute. He works for $16$ minutes. How many cakes does he make altogethe? ", "answer_option_list": [[{"aoVal": "A", "content": "$$80$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$70$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"], "answer_analysis": ["$$16\\times 5 = 80$$ ~ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8054", "queId": "024d959f3f824a3ab90354b8e95efb48", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Luis has 7 apples and 2 bananas. He gives 2 apples to Yuri who, in return gives bananas to Luis. Then Luis has as many apples as bananas. How many bananas did Yuri give to Luis? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"], "answer_analysis": ["$$7-2=5$$ $$5-2=3.$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8057", "queId": "05b67ba0dfcb444fa1ae089f5f1e0f2b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alice\\textquotesingle s first day in Caterpillar Club was Tuesday. She wants to throw a party on her 40th day in the club. If Alice attends the club everyday, on which day of the week will the party be? ", "answer_option_list": [[{"aoVal": "A", "content": "Friday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Sunday "}], [{"aoVal": "D", "content": "Monday "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["40th day = 39th day after first day joining. 39 days/7 = 5 weeks R 4 days. 4 days after Tues is Saturday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8058", "queId": "025b8851af974508a90f60e2c9275f2a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A fifth-grade class has $8$ boys and $10$ girls. What is the ratio of boys to girls?. ", "answer_option_list": [[{"aoVal": "A", "content": "$8:10$ "}], [{"aoVal": "B", "content": "$10:8$ "}], [{"aoVal": "C", "content": "$4:5$ "}], [{"aoVal": "D", "content": "$5:4$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["Simplify $8:10$ to $4:5$, or $\\text{C}$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8063", "queId": "2e99a27703e94c19a675a14ed25fc891", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Emily was $$6$$ years old last year, and her sister was $$6$$ years old six years ago. What is the age difference between Emily and her sister today? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages"], "answer_analysis": ["Emily was $$6$$ years old last year , which means Emily is $7$ years old this year. Her sister was~ $$6$$ years old six years ago, which tells us her sister is~ $12$ years old this year, so the age difference is $5$ today. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8066", "queId": "028868fac05b42c6802aa97c4ccf38bb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Gill is now 27 and has moved into a new flat. She has four pictures to hang in a horizontal row on a wall which is 4800 mm wide. The pictures are identical in size and are 420 mm wide. Gill hangs the first two pictures so that one is on the extreme left of the wall and one is on the extreme right of the wall. She wants to hang the remaining two pictures so that all four pictures are equally spaced. How far should Gill place the centre of each of the two remaining pictures from a vertical line down the centre of the wall? ", "answer_option_list": [[{"aoVal": "A", "content": "$$210mm$$ "}], [{"aoVal": "B", "content": "$$520mm$$ "}], [{"aoVal": "C", "content": "$$730mm$$ "}], [{"aoVal": "D", "content": "$$840mm$$ "}], [{"aoVal": "E", "content": "$$1040mm$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8067", "queId": "028967df4030433b910b34f63ed4bd61", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "David and Billy are on the bus together. They sit in the same column. There are $5$ people in front of David, Billy is in the middle. There are $10$ people behind Billy, and David is in the middle. How many people in this column? (adapted from2004 Math Kangaroo Problem, Level 3 - 4, Question \\#19) ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line"], "answer_analysis": ["$5 + 10 - 2 = 13$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8068", "queId": "09e29390f8544d238200f3f59870f9ce", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many pieces can we get if we break a wooden stick in $8$ places? (Adapted from 1999 Math Kangaroo Problem, Level 3-4, Question \\#3) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Planting no Trees on either Side (straight line type)->Sawing Woods"], "answer_analysis": ["$8+1=9$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8070", "queId": "c2663bc98b5846eea1da2771587378b3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There were $$27$$ children in a class. There were twice as many boys as girls. How many boys were there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ boys "}], [{"aoVal": "B", "content": "$$18$$ boys "}], [{"aoVal": "C", "content": "$$16$$ boys "}], [{"aoVal": "D", "content": "$$14$$ boys "}], [{"aoVal": "E", "content": "$$9$$ boys "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["$$\\dfrac{27}{(2+1)}=9$$, $$9\\times2=18$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8072", "queId": "02a4749306bd4a8b9cf07c36debaade2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are twice as many boys in a room as girls. If $$5$$ boys leave the room, there would be an equal number of boys and girls in the room. How many boys were in the room at first? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Difference and Multiple"], "answer_analysis": ["The number of boys that leave the room must equal the number of boys that remain. Since $$5$$ boys leave, there are $$5$$ boys still in the room for a total of $$10$$ boys. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8073", "queId": "0e4e05f173f54207ae66a4357a5f29d3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are twelve rooms in a building and each room has two windows and one light. Last evening, eighteen windows were lit. In how many rooms was the light off? (2016 Math Kangaroo Problem, Level 1-2, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$18\\div2=9$, $12-9=3$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8083", "queId": "53bda166eaeb4de180072d3fadab501e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There were $$31$$ runners competing in a race. The number of runners who finished before John is $18$ less than the number of runners who finished later than John. At what place did John finish? (Adapted from 1998 Math Kangaroo Problem, Level 3 - 4, Question \\#13) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["Before: $$(31-1-18) \\div 2 = 6$$, and John: $$6+1=7$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8086", "queId": "3c899876d4434a43ab94cea802694831", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A basket with $$5$$ watermelons weighs $$3250$$ grams. If $$3$$ of the watermelons were taken out, the remaining weight would be $$1510$$ grams. What is the weight (in grams) of the basket? ", "answer_option_list": [[{"aoVal": "A", "content": "$$350$$ grams "}], [{"aoVal": "B", "content": "$$1160$$ grams "}], [{"aoVal": "C", "content": "$$1740$$ grams "}], [{"aoVal": "D", "content": "$$870$$ grams "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Equivalent Substitution in Equation Word Problems->Replacement of Equivalent Substitution"], "answer_analysis": ["$$NA.$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8088", "queId": "031405a4a395494e8ec510a2d8c30626", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a magic land, a monkey wants to climb a tree of $180$ m. The monkey can make one of the two kinds of climb each day: $6$ m up or $10$ m up. Beginning at the ground , at least how many days will the monkey need in order to rest on the branch of $108$ m high? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value"], "answer_analysis": ["$10 \\times 9 + 6 \\times 3 = 108$ $9 + 3 = 12$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8093", "queId": "03504ffde2d4458bb0a086c175b201ad", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$4$ years gao, the sum of Cathy\\textquotesingle s and Larry\\textquotesingle s ages was $$20$$. What is the sum of their ages this years? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$28$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$36$$ "}], [{"aoVal": "E", "content": "$$38$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$20 + 4 + 4 = 28$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8094", "queId": "0a1465c41f524726bf1fcdd08b0d5106", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$75$$ out of $$100$$ apples are \\textbf{not} rotten. What percentage of the apples are rotten? ", "answer_option_list": [[{"aoVal": "A", "content": "75\\% "}], [{"aoVal": "B", "content": "100\\% "}], [{"aoVal": "C", "content": "25\\% "}], [{"aoVal": "D", "content": "50\\% "}], [{"aoVal": "E", "content": "175\\% "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["$$\\frac{75}{100}=75 \\textbackslash\\%$$, $$100\\textbackslash\\%-75\\textbackslash\\%=25\\textbackslash\\%$$, $$25\\textbackslash\\%$$ of the apples are rotten. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8095", "queId": "86e12cc4a2204e229c11663b0558beec", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Find the exact number of minutes after $3.00 \\text{pm}$ when the minute and hour hands are first at $90^{\\circ}$ to each other. ", "answer_option_list": [[{"aoVal": "A", "content": "$$31 \\frac{2}{11}$$ "}], [{"aoVal": "B", "content": "$$31 \\frac{3}{11}$$ "}], [{"aoVal": "C", "content": "$$32 \\frac{8}{11}$$ "}], [{"aoVal": "D", "content": "$$33 \\frac{3}{11}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8097", "queId": "6fa3d07122024f82a3903e98aaf8ec6f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many times does it take to cut a rope into $$5$$ pieces? The rope can\\textquotesingle t be folded. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "It depends on how long the rope is. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$$5 - 1 = 4$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8098", "queId": "064fbdccba4a49ad854ca364681b3bf1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Amy has $12$ candies and Nancy has $33$ candies. How many candies do they have in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$33$$ "}], [{"aoVal": "C", "content": "$$44$$ "}], [{"aoVal": "D", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$12+33=45$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8100", "queId": "29fda63f65c64ee58c40dffe55e85719", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Paul was going to buy $$4$$ servings of ice cream, but he was $$80$$ pence short. So, he bought $$3$$ servings and had $$30$$ pence left. What was the price of one serving of ice cream? ", "answer_option_list": [[{"aoVal": "A", "content": "$$70$$ pence "}], [{"aoVal": "B", "content": "$$80$$ pence "}], [{"aoVal": "C", "content": "$$90$$ pence "}], [{"aoVal": "D", "content": "$$100$$ pence "}], [{"aoVal": "E", "content": "110 pence "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems"], "answer_analysis": ["$$(80+30)\\div (4-3)=110$$ pence. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8104", "queId": "06590ff09c274ceba9e8a7894fbf117d", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Luke and Matthew ran a lemonade stand on Saturday. They agreed that Matthew would get $65$\\% of the profit because the lemonade stand was his idea. They made a profit of $60$ dollars. How much money did Luke make? ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$39$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$60 \\times 65$\\%=$39$, $60-39=21$, Luke made $21$ dollars. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8106", "queId": "03c6ab73b39e41dcb5c43c6429a9a46a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Alan is $5$ years old, his mother is $18$ years older than him, and his father is $2$ years older than his mother. How old is his father?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$7$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages"], "answer_analysis": ["Alans\\textquotesingle{} mother is $18$ years older than him, his mother is $23$ years old. His father is two years older than his mother, so he is $25$ years old. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8116", "queId": "04300e2d3c1646b8b230770b596978fa", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "On Monday morning, a snail fell down a well which is $$5$$ metres deep. During the day, it climbs up $$2$$ metres, and during the night it slides down $$1$$ metre. On what day of the week will the snail get out of the well? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$Tuesday "}], [{"aoVal": "B", "content": "$$$$Wednesday "}], [{"aoVal": "C", "content": "$$$$Thursday "}], [{"aoVal": "D", "content": "$$$$Friday "}], [{"aoVal": "E", "content": "$$$$Monday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems->Snail Climbing out of Well (completed)"], "answer_analysis": ["Nil "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8122", "queId": "6afde6f03ce14fdb8799de8411707621", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$37$$ sakura trees were planted along one side of the road. The trees were planted at $$4m$$ intervals. After drivers complained the road was too pink, pineapple trees were planted on the other side of the road at $$6m$$ intervals. If there were sakura and pineapple trees at both ends of the road, how many pineapple trees were planted? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$144$$ "}], [{"aoVal": "D", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["Number of sakura intervals = $$37-1 = 36$$ Length of road = $$36 \\times 4 = 144m$$ Number of pineapple intervals = $$144m \\div 6m = 24$$ Number of pineapple trees = $$24 + 1 = 25$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8123", "queId": "0a5475e16c9f416494e261766197a564", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Fatimah has $$3$$ bags of marbles. There are $$291$$ marbles in each bag. How many marbles does Fatimah have in all? ", "answer_option_list": [[{"aoVal": "A", "content": "$$97$$ "}], [{"aoVal": "B", "content": "$$294$$ "}], [{"aoVal": "C", "content": "$$582$$ "}], [{"aoVal": "D", "content": "$$873$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$$3\\times291=873$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8124", "queId": "2eadd69c9425495ca68a939822878f57", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I ate lunch every day of my $$12$$-week summer break. I ate lunch out-doors only on every Saturday, Sunday, and Tuesday. I ate lunch in-doors ondays. ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["I ate lunch every day of my $$12$$-week summer break. I ate lunch out-doors only on every Saturday, Sunday, and Tuesday. I ate lunch in-doors $$4$$ days each week. In $$12$$ weeks, that\\textquotesingle s $$12\\times 4=48$$ days. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8127", "queId": "53c6cb79db614be89558f79509c017c8", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Bella and her brother agreed to share a pizza which was cut into $15$ slices. Bella ate $40$\\% of the pizza. How many slices did she eat? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$15 \\times 40$\\%=$6$, She ate $6$ slices. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8130", "queId": "0486b1fbf39e418c9804273217989ce9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a jar of red, green, and blue marbles, all but $$6$$ are red marbles, all but $$8$$ are green, and all but $$4$$ are blue. How many marbles are in the jar? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems"], "answer_analysis": ["Suppose there are $$x$$ red marbles, $$y$$ green marbles and $$z$$ blue marbles. Thus, we can get $$\\begin{cases} x+y=4① \\textbackslash\\textbackslash{} y+z=6②\\textbackslash\\x+z=8③\\end{cases}$$, ①$$+$$②$$+$$③: $$2x+2y+2z=18$$, $$x+y+z=9$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8132", "queId": "048aba6a7bd14f23a83ceadf07f21bf6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Cecilia and her dad are climbing stairs from the first floor. They start at the same time, and each of them keeps her or his speed of climbing unchanged. When Cecilia arrives at the third floor, her dad arrives at the fifth floor. When Cecilia arrives at the eighth floor, which floor does her dad arrive at? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$\\textsuperscript{th} "}], [{"aoVal": "B", "content": "$$15$$\\textsuperscript{th} "}], [{"aoVal": "C", "content": "$$10$$\\textsuperscript{th} "}], [{"aoVal": "D", "content": "$$13$$\\textsuperscript{th} "}], [{"aoVal": "E", "content": "$$16$$\\textsuperscript{th} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$(5-1) \\div(3-1)=2$. $(8-1) \\times 2+1=15$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8140", "queId": "6b026e80bf1e487a8637003d3039ada4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "After Sally takes 20 shots, she has made $50 \\textbackslash\\%$ of her shots. After she takes 5 more shots, she raises her percentage to $60 \\textbackslash\\%$. How many of the last 5 shots did she make? (adapted from 2004 AMC 8, Question\\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Sally made $0.5\\times 20=10$ shots originally. Letting $x$ be the number of shots she made, we have $\\frac{10+x}{25}=0.60$. Solving for $x$ gives us $x=$ $(E)5$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8143", "queId": "072e63fc31c04c10a581a7f99d871ce8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Irene mixes $$100$$ grams of dogfood that contains $$50\\textbackslash\\%$$ rice with $$400$$ grams of dogfood that contains $$80\\textbackslash\\%$$ rice. Find the percent concentration of the rice in the new mixture. ", "answer_option_list": [[{"aoVal": "A", "content": "$$70\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$72\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$75\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$74\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$\\dfrac{100\\times50\\textbackslash\\%+400\\times80\\textbackslash\\%}{100+400}=74\\textbackslash\\%$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8148", "queId": "3ca008279c6240388e135d83fccacd3d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The average cost of a long-distance call in the USA in 1985 was 41 cents per minute, and the average cost of a long-distance call in the USA in 2005 was 7 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (2007 AMC 8, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$17$$ "}], [{"aoVal": "C", "content": "$$34$$ "}], [{"aoVal": "D", "content": "$$41$$ "}], [{"aoVal": "E", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $41-7=34$ so the percent decrease is $\\frac{34}{41}$ which is about $(\\mathbf{E}) 80 \\textbackslash\\%$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8155", "queId": "744eb4d9cfd44941b4668c2f224a1207", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mike has $$160$$ grams of a $$3\\textbackslash\\%$$ salt solution and Danni has an $$8\\textbackslash\\%$$ salt solution. If Danni gives $$200$$ grams of her solution to Mike, they will have the same amount of pure salt in their solutions. How many grams of solution did Danni have in the beginning? ", "answer_option_list": [[{"aoVal": "A", "content": "$400$ "}], [{"aoVal": "B", "content": "$450$ "}], [{"aoVal": "C", "content": "$460$ "}], [{"aoVal": "D", "content": "$480$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"], "answer_analysis": ["$$160\\times3\\textbackslash\\%+200\\times8\\textbackslash\\%=20.8$$ ounces. $$20.8\\div8\\textbackslash\\%+200=260+200=460$$ ounces. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8156", "queId": "0761893e09464f8d9ba99347521683a9", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "At the 2017 King County Fair a vendor is offering a \"fair special\" on hats. If you buy one hat at the regular price of $40$ dollars, you get a second hat at a $10 \\textbackslash\\%$ discount, and a third pair at half the regular price. James took advantage of the \"fair special\" to buy three hats. What percentage of the $120$ dollars regular price did he save? (adapted from 2013 AMC 8, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$25$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["First, find the amount of money one will pay for three hats without the discount. We have $\\textbackslash$ 40 \\times 3$ hats $=\\textbackslash$ 120$. Then, find the amount of money using the discount: $40+0.9 \\times 40+\\frac{1}{2} \\times 40=\\textbackslash$ 96$. Finding the percentage yields $\\frac{96}{120}=80 \\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-80 \\textbackslash\\%=(\\text{B}) 20$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8165", "queId": "17bdd4b62c4d44b4ae0c7314e7eee864", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My aunt can fold $$16$$ paper cranes in $$4$$ minutes. My uncle can fold $$15$$ paper cranes in $$5$$ minutes. How long would it take them to fold $$42$$ cranes if they work together at those rates?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ minutes "}], [{"aoVal": "B", "content": "$$9$$ minutes "}], [{"aoVal": "C", "content": "$$12$$ minutes "}], [{"aoVal": "D", "content": "$$13$$ minutes "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"], "answer_analysis": ["My aunt can fold $$4$$ paper cranes in $$1$$ minute. My uncle can fold 3 paper cranes in $$1$$ minute. Together they fold $$7$$ paper cranes in $$1$$ minute. It takes them $$42\\div7 = 6$$ minutes to fold $$42$$ paper cranes. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8172", "queId": "3808f854e18248dcb53e5d5917034ff4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "On the farm, there are $$5$$ sheep, $$5$$ hens, $$2$$ dogs, $$2$$ cats, and the farmer. How many legs are there altogether? (2006 Math Kangaroo Problem, Level 1-2, Question \\#15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$48$$ "}], [{"aoVal": "E", "content": "$$46$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"], "answer_analysis": ["$5\\times4+5\\times2+2\\times4+2\\times4+2=48$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8175", "queId": "58731479c7c9412db282d3d519e30879", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If $$11$$th November 2031 is a Tuesday, what day of the week will $$11$$th November 2032 be? ", "answer_option_list": [[{"aoVal": "A", "content": "Tuesday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Friday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["$$1$$ leap year, so $$2$$ days shifted. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8187", "queId": "07c5f4cf9e7545529e14a00ac089da46", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "An average of $$40$$ campers sign up for each of the $$6$$ sports at camp. If each camper signs up for exactly $$3$$ sports, how many campers are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$80$$ "}], [{"aoVal": "B", "content": "$$120$$ "}], [{"aoVal": "C", "content": "$$160$$ "}], [{"aoVal": "D", "content": "$$180$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["Since $$40\\times 6=240$$, $$240$$ campers have signed up for the $$6$$ sports, and each camper is counted $$3$$ times. There are $$240\\div 3=80$$ campers in all. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8191", "queId": "0efb74891373421e8d0147802e56a726", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Al ran twice as far as Bob ran. They ran a total off $$18\\rm km$$. How far did Al run? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3\\rm km$$ "}], [{"aoVal": "B", "content": "$$6\\rm km$$ "}], [{"aoVal": "C", "content": "$$9\\rm km$$ "}], [{"aoVal": "D", "content": "$$12\\rm km$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["Al ran twice as far as Bob. Split $$18\\rm km$$ into two parts, one twice the other, to see that Bob ran $$6\\rm km$$ and Al ran twice as far, $$12\\rm km$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8200", "queId": "17dc38aa5551484c95c8f281e7bd5404", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "David has $$15$$ more candies than Andy at the beginning. David has $$3$$ candies more than Andy after giving some candies to Andy. How many candies does Debbic give to Aiden? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples"], "answer_analysis": ["$$15-3=12$, $$8\\div 2=4$$. $$\\text{D}$$． "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8203", "queId": "2a32777a3f294c3db19c96bcc6f40345", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Adam paid ＄$$6$$ for $$15$$ buns. How many dollars did Tom pay for the same kind of buns if he bought $$5$$ more of them? (2008 Math Kangaroo Problem, Level 1-2, Question \\#13) ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["There are $$3$$ groups of $$5$$ buns in $$15$$ buns: $$15\\div 5=3$$, so $$5$$ buns cost $$6\\div 3=$$＄$$2$$. In total, Tom bought $$15 + 5 = 20$$ buns, which is $$4$$ groups of $$5$$ buns. So, Tom paid $$4\\times 2 =$$＄$$8$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8208", "queId": "080fc4c0106943e99c5c7510e03e431e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$20$$ years ago Allen was half as old as he is today, how old was he $$10$$ years ago? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->When..., When... Type Age Problems"], "answer_analysis": ["If $$20$$ years ago Allen was half as old as he is today, then today he is $$40$$. Thus, $$10$$ years ago he was $$30$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8209", "queId": "1c6f60eea57d4b6b9420726a56c8f0a4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A teacher distributes scorecards equally to students, and there is a surplus of $8$ cards. If $2$ more cards are given to each student, all the cards will be distributed. Then there arestudents in the class in total. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["If $2$ more scorecards are given to each student, all the cards are distributed. Therefore, the class has $8\\div2=4$ students. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8211", "queId": "53daf37c5f9c4d8bac1a46ec688117cb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ryan buys a watch on sale for $$20\\textbackslash\\%$$ off in a shopping mall. He has an additional $$200-$$dollar coupon since he is a member of this shopping mall. The sales tax in his city is $$5\\textbackslash\\%$$, and he paid $$\\textbackslash$2730$$ for this watch. What was the original price of the watch? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$2600$$ "}], [{"aoVal": "B", "content": "＄$$2800$$ "}], [{"aoVal": "C", "content": "＄$$3200$$ "}], [{"aoVal": "D", "content": "＄$$3500$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Tax Problems"], "answer_analysis": ["$$\\dfrac{2730}{1+5\\textbackslash\\%}=2600$$, $$\\dfrac{2600+200}{1-20\\textbackslash\\%}=3500$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8215", "queId": "0f28a2ee525d4883921c8c7d065b5c21", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Workers want to plant some trees between houses. There are $17$ houses on one side of a road. Workers want to plant three trees between every two adjacent houses. How many trees do they need to plant? ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$51$$ "}], [{"aoVal": "D", "content": "$$54$$ "}], [{"aoVal": "E", "content": "$$57$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$(17 - 1）\\times 3 = 48$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8218", "queId": "4158c9ed7cd1486abe8c31a7aabc6b3d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A sum of $$\\textbackslash$459$$ was shared among $$5$$ boys and $$14$$ girls. Each girl received $$\\textbackslash$16$$. How much did each boy get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$38$$ "}], [{"aoVal": "B", "content": "$$$47$$ "}], [{"aoVal": "C", "content": "$$$52$$ "}], [{"aoVal": "D", "content": "$$$56$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["Girls $=14\\times\\textbackslash$16=\\textbackslash$224$ Boys $=\\textbackslash$459-\\textbackslash$224=\\textbackslash$235$ Each boy $=\\textbackslash$235\\div5=\\textbackslash$47$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8225", "queId": "824cc608e403425ab5229c62b26a91b9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The radius of a coin is $$3\\text{cm}$$. When $$4000$$ of these coins are placed side by side in a straight line, how long would this line be? ", "answer_option_list": [[{"aoVal": "A", "content": "$$240\\text{cm}$$ "}], [{"aoVal": "B", "content": "$$12\\text{m}$$ "}], [{"aoVal": "C", "content": "$$240\\text{m}$$ "}], [{"aoVal": "D", "content": "$$1.2\\text{km}$$ "}], [{"aoVal": "E", "content": "$$2.4\\text{km}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["The length of the line is $$4000\\times 2\\times 3\\text{cm=}24000\\text{cm=}240\\text{m}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8226", "queId": "25a71039e2d649ea95715815053dd12c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alicia, Bryant, and Charles work for a software company and they want to write a particular computer program. Alicia and Bryant first write $\\frac{1}{3}$ of the program in $6$ days. Then Bryant and Charles write $\\frac{1}{4}$ of the remaining program in $2$ days. In the end three of them work together to finish the program in $5$ days. How many days will it take if Alicia works on the program by herself? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$75$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["In the second part, Bryant and Charles can write $\\left( 1-\\frac{1}{3} \\right) \\times \\frac{1}{4}=\\frac{1}{6}$ of the program in 2 days. Therefore, they can write $\\frac{1}{6} \\div 2 =\\frac{1}{12}$ in one day. There is still $1-\\frac{1}{3}-\\frac{1}{6}=\\frac{1}{2}$ left. Now in the last part, they work together and finish in $5$ days. They can write $\\frac{1}{2} \\div 5=\\frac{1}{10}$ in one day. Therefore, Alicia can write $\\frac{1}{10}-\\frac{1}{12}=\\frac{1}{60}$ in one day, which means she needs $60$ days to complete. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8229", "queId": "08668fdb94c74452ac365f111e2e8e33", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A gardener has a box of bulbs to plant in a garden. The garden has three sections. She plants 1/2~of the bulbs in the first section. She plants 3 /4~of the remaining bulbs in the second section. She has 6 bulbs left, which she plants in the third section. How many bulbs were in the box at the start? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$32$$ "}], [{"aoVal": "E", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["1- 1/2 - 1/2 x 3/4=1/8，1/8 means 6 bulbs, so in total there are 6~$\\div$~1/8=48 bulbs. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8236", "queId": "139128ca94ae4d4bab6367b96fcccc3b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "John is 8 years and 3 months old. Alice is 102 months old. Cindy has been alive for 4380 days. Who is the oldest? ", "answer_option_list": [[{"aoVal": "A", "content": "John "}], [{"aoVal": "B", "content": "Alice "}], [{"aoVal": "C", "content": "Cindy "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8240", "queId": "0b750c016aa84b1e98d018a58e707e55", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "As a Grade 1 student, Jenny saw thirteen seats in a row in the class, and she didn\\textquotesingle t know which one belonged to her. The teacher told her that there were seven students behind her seat. So which seat should she sit?(Adapted from 2015 Math Kangaroo Problem, Level 1-2, Question \\#18) ~\\hspace{0pt}\\hspace{0pt}\\hspace{0pt}\\hspace{0pt} ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$\\textsuperscript{th} "}], [{"aoVal": "B", "content": "$$6$$\\textsuperscript{th} "}], [{"aoVal": "C", "content": "$$7$$\\textsuperscript{th} "}], [{"aoVal": "D", "content": "$$8$$\\textsuperscript{th} "}], [{"aoVal": "E", "content": "$$9$$\\textsuperscript{th} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$13-7=6$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8245", "queId": "53e3e22d97e4474ebe87536c3dd401b6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A clothing store bought some shirts at＄$$96$$ each. It wants to earn＄$$24 $$ for each shirt after a discount of $$20 \\textbackslash\\% $$. What is the selling price before the discount for each shirt? ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ dollars "}], [{"aoVal": "B", "content": "$$120$$ dollars "}], [{"aoVal": "C", "content": "$$150$$ dollars "}], [{"aoVal": "D", "content": "$$180$$ dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["$$\\left( 96+24 \\right)\\div \\left( 1-20 \\textbackslash\\% \\right)=150$$ dollars. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8248", "queId": "2a4ab6b22dbb42d2acba2ab7d637ea6c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Iate half an apple pie on Saturday and two thirds of the remainder on Sunday. What fraction of the pie was left for Monday?　 ", "answer_option_list": [[{"aoVal": "A", "content": "None　 "}], [{"aoVal": "B", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "D", "content": "$$\\frac{2}{3}$$ "}], [{"aoVal": "E", "content": "$$\\frac{1}{6}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Understanding the Base"], "answer_analysis": ["After I eat one half, half of the apple pie is left. Eating two thirds of this half leaves one third of one half of the pie, which is one sixth, for Monday. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8254", "queId": "1c95f2d788a44a0a8ed82d16803d46c0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$1$$ similar skirt and $$3$$ similar blouses cost $$$75$$. If each skirt costs twice as much as each blouse, how much will each skirt cost? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$30$$ "}], [{"aoVal": "B", "content": "$$$25$$ "}], [{"aoVal": "C", "content": "$$$20$$ "}], [{"aoVal": "D", "content": "$$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Equivalent Substitution in Equation Word Problems"], "answer_analysis": ["1S + 3B = 75; 1S = 2B; 2B + 3B = 75; 5B = 75; B = 75~$\\div$~5 = 15 1S = 2~$\\times$~15 = 30 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8259", "queId": "21266173baf7469e9bee26a3e9ae65a8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Felix and Marmalade are two cats. Together they weigh $$10\\text{kg}$$. Felix weighs $$4\\text{kg}$$ less than Marmalade. How much does Marmalade weigh? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3\\text{kg}$$ "}], [{"aoVal": "B", "content": "$$6\\text{kg}$$ "}], [{"aoVal": "C", "content": "$$7 \\text{kg}$$ "}], [{"aoVal": "D", "content": "$$9\\text{kg}$$ "}], [{"aoVal": "E", "content": "$$14 \\text{kg}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["$$F=M-4$$ $$M-4+M=10$$ $$M=7$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8264", "queId": "588855bcd03447e88d1daf4ad16d17cc", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Six friends went to hike together and agreed to share the bill equally. However, James forgot to bring his wallet, so each of his five friends paid an extra of $10.2$ dollars to cover James\\textquotesingle~portion. How much did they have to pay in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$51$$ "}], [{"aoVal": "B", "content": "$$58.4$$ "}], [{"aoVal": "C", "content": "$$255$$ "}], [{"aoVal": "D", "content": "$$306$$ "}], [{"aoVal": "E", "content": "$$308.8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Everyone should pay $10.2\\times5=51$ dollars. $51\\times 6=306$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8273", "queId": "1ca6dcd8190744809dae4ca77c8e3ff1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Of $$60$$ people at a school board meeting, $$24$$ are men. The ratio of women to men at the meeting is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$3:2$$ "}], [{"aoVal": "B", "content": "$$2:3$$ "}], [{"aoVal": "C", "content": "$$11:6$$ "}], [{"aoVal": "D", "content": "$$6:11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["Women: $$60-24=36$$, Women: Men$$=36:24=3:2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8275", "queId": "09004cc948254e26b202b6f15a77439e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Water from the first faucet fills the swimming pool in $36$ hours. Water from each of the two other faucets fills the same swimming pool $4$ times faster. In how many hours will the swimming pool be filled if all three faucets are opened? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems"], "answer_analysis": ["The efficiency of the first faucet is $\\frac1{36}$ and that of the other two is $\\frac4{36}$. Thus it takes $1\\div (\\frac1{36}+\\frac4{36}\\times2)=4$ hours to fill the pool. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8277", "queId": "38314d3b528d47faaf826ea1d042c051", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My vacation will start three weeks and two days after yesterday. If today is Tuesday, my vacation will start on what day? ", "answer_option_list": [[{"aoVal": "A", "content": "　Monday "}], [{"aoVal": "B", "content": "　Tuesday "}], [{"aoVal": "C", "content": "　Wednesday "}], [{"aoVal": "D", "content": "　Thursday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Three weeks after yesterday, which was a Monday, is a Monday also. Two days after a Monday is a Wednesday. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8278", "queId": "3ccca4d0dc2b471ba6804ad1a7b3477c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Mina put $12$ potted plants in a row from one end to the other end of the corridor. They were placed at an equal distance from one another. The distance between the first and the fifth potted plant was $28$ m. Mina went along the corridor from the first pot to the last pot. How many meters did she walk? ", "answer_option_list": [[{"aoVal": "A", "content": "$$70$$ "}], [{"aoVal": "B", "content": "$$77$$ "}], [{"aoVal": "C", "content": "$$84$$ "}], [{"aoVal": "D", "content": "$$91$$ "}], [{"aoVal": "E", "content": "$$98$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$28 \\div (5 - 1) = 7$ $7 \\times (12 - 1) = 77$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8279", "queId": "4aabdcd39fee461c871204349348ace2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $6$ boxes each contains only oranges, apples, or pears. The boxes weigh $$15$$, $$16$$, $$18$$, $$19$$, $$20$$, and $$31$$ kg, respectively. If the total weight of apples is half of that of pears, and there is only one box of oranges, what is the weight of the box of oranges. ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$31$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["The total weight of all the boxes is $15+16+18+19+20+31=119$ kg. The weight of pears is twice that of apples, so excluding the box of orange, the weight of the remaining boxes should be divisible by $3$. Only removing $20$, the remaining weight is divisible by $3$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8284", "queId": "091ccf07e9e5422c866e46852d21566f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A shop purchased some basketballs at ＄$$60$$ each. It then sold them at ＄$$75$$ each. How much did the shopkeeper earn for $$10$$ basketballs? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$150$$ "}], [{"aoVal": "B", "content": "＄$$200$$ "}], [{"aoVal": "C", "content": "＄$$250$$ "}], [{"aoVal": "D", "content": "＄$$300$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$$(75-60)\\times 10 = 150$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8285", "queId": "4f4e73d048684215b7878bb5954e4999", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Some students are going to an amusement park. If each student carries $9$ bottles of water in his or her backpack, there will be $2$ students left carrying nothing; if one of the students carries $2$ bottles of water and the rest students carry $8$ bottles each, all the bottles of water can be carried to the park. There are~\\uline{~~~~~~~~~~}~bottles of water in total that need to be carried. ", "answer_option_list": [[{"aoVal": "A", "content": "$$80$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$92$$ "}], [{"aoVal": "D", "content": "$$102$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Distribution Conversion Problems"], "answer_analysis": ["Solve the problem as a problem of surplus and shortage. If each student carries $9$ bottles, there will be a shortage of $9\\times2=18$ bottles; if each student carries $8$ bottles, there will be a shortage of $8-2=6$ bottles. Therefore, there are $(18-6)\\div(9-8)=12$ students and $12\\times9-18=90$ bottles of water. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8289", "queId": "0beee3702e83476cb1b9b3d152e4dd48", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Seventh grade students from a school line up and form a square array. There are $196$ students in the outermost layer. How many students in total are there in this array? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1960$$ "}], [{"aoVal": "B", "content": "$$2401$$ "}], [{"aoVal": "C", "content": "$$2000$$ "}], [{"aoVal": "D", "content": "$$2601$$ "}], [{"aoVal": "E", "content": "$$2500$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares"], "answer_analysis": ["The number of students on each side of the outermost layer was $$196\\div 4+1=50$$ students. The total number of students in the array was $$50\\times 50=2500$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8290", "queId": "13da29d05739453685a5e973d6e8abb5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given March $$25$$ of a certain year is Monday, what day of the week would May $$1$$ fall on this year? ． ", "answer_option_list": [[{"aoVal": "A", "content": "Tuesday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Friday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$(31-25+30+1=37$ $37\\div7=5R2$ Exactly $5$ weeks from $25$ Mar, it will also be a Monday; another $2$ days later will be a Wednesday "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8293", "queId": "86ff87ef3f684b42b57e7217153535aa", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A mixture of 45 liters of paint is $20 \\textbackslash\\%$ red tint, $30 \\textbackslash\\%$ yellow tint and $50 \\textbackslash\\%$ water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (2007 AMC 8, Question \\#17 ) ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$37$$ "}], [{"aoVal": "D", "content": "$$39$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Since $30 \\textbackslash\\%$ of the original 45 liters of paint was yellow, and 5 liters of yellow paint were added to make the new mixture, there are $13.5+5=18.5$ liters of yellow tint in the new mixture. Since only 5 liters of paint were added to the original 45 , there are a total of 50 liters of paint in the new mixture. This gives $ 37\\textbackslash\\%$ of yellow tint in the new mixture, which is (C) 37 . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8295", "queId": "cbc4085e95ab419f9450c3d6429f0e33", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A ship is being attacked by pirates. One by one the pirates climb a rope to get on the ship. The pirate captain is the $$8$$\\textsuperscript{th} in line, and there are as many pirates in front of him as there are behind him. How many pirates are in line to climb the rope?（）($$2015$$ Math Kangaroo Problem, Levels $$1-2$$, Question \\#$$18$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line"], "answer_analysis": ["The $$8$$\\textsuperscript{th} means there are $$7$$ people in front of him. So there are also $$7$$ people behind him. The total number of pirates can be calculated: $$7+7+1=15$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8296", "queId": "13e67e76f839419e9e4c2a599e3c4a61", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A $$12$$-metre long steel pipe was cut into few pieces. The length of each piece is $$3$$ metres. It takes $$18$$ minutes to complete the whole process. How long does it take to cut a $$12$$-metre pipe into $$6$$-metre sections? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ minutes "}], [{"aoVal": "B", "content": "$$9$$ minutes "}], [{"aoVal": "C", "content": "$$12$$ minutes "}], [{"aoVal": "D", "content": "$$18$$ minutes "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$$18\\div3=6$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8302", "queId": "383f11d2185e41a4b853ed963165ffee", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A city council decided to put lanterns on both sides of a river. The distance between any two neighbouring lanterns on each side must be $11$ metres. The length of the river is $132$ metres. The distance between the first and the last lantern on each side must be also $132$ metres. How many lanterns will there be in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$26$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division"], "answer_analysis": ["132/11 = 12 lanterns 12 lanterns + 1 = 13 lanterns 13 x 2 = 26 lanterns. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8304", "queId": "98adf9ae2e9c4217b6d0d5825a45b724", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Nine bus stops are equally spaced along a certain bus route. The distance between the first stop and the third stop is $$600$$ m. How long is the bus route? ($$2004$$ Math kangaroo Problem, Level $$5-6$$, Question \\#$$9$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1800$$ m "}], [{"aoVal": "B", "content": "$$2100$$ m "}], [{"aoVal": "C", "content": "$$2400$$ m "}], [{"aoVal": "D", "content": "$$2700$$ m "}], [{"aoVal": "E", "content": "$$3000$$ m "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Straight Line Type with Objects on Both Sides->Planting Trees on Both Sides"], "answer_analysis": ["Each interval is $600\\div2=300$ m. There are $9-1=8$ intervals in total, so the bus route\\textquotesingle s length is $300\\times8=2400$ m. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8313", "queId": "0fd8e98372b940de8eb81f7650ae3c5b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A ship is being attacked by pirates. One by one the pirates climb a rope to get on the ship. The pirate captain is the $$8$$\\textsuperscript{th} in line, and there are as many pirates in front of him as there are behind him. How many pirates are in line to climb the rope?（） ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line"], "answer_analysis": ["The $$8$$\\textsuperscript{th} means there are $$7$$ people in front of him. So there are also $$7$$ people behind him. The total number of pirates can be calculated: $$7+7+1=15$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8314", "queId": "61e2632143ff445e81fd07db73cdc90e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Students in the third grade lined up and formed a square array to perform a dance. Each side of the outermost layer had $37$ students. How many students in total are there in the outermost layer? ", "answer_option_list": [[{"aoVal": "A", "content": "$$148$$ "}], [{"aoVal": "B", "content": "$$152$$ "}], [{"aoVal": "C", "content": "$$144$$ "}], [{"aoVal": "D", "content": "$$140$$ "}], [{"aoVal": "E", "content": "$$156$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares"], "answer_analysis": ["$$36\\times 4=144$$, or $$37\\times 4-4=144$$ students. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8315", "queId": "0c318f65b6b54a00ba2fa37cb6396fc6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "On Think Planet, each Thinkyear has $8$ Thinkmonths and each Thinkmonth has $6$ Thinkweeks. How many Thinkweeks are there in one quarter of a Thinkyear? ", "answer_option_list": [[{"aoVal": "A", "content": "$$48$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$8\\times6\\div4=12$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8317", "queId": "bddb5a5878d74530b8e30637f6320c71", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When asked about his age, my uncle said \"If you multiply my current age by $2$, then subtract the product by $6$, divide the answer by $2$ and then add $8$, the final answer is $38$.\" My uncle\\textquotesingle s age isyears old． ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$33$$ "}], [{"aoVal": "C", "content": "$$38$$ "}], [{"aoVal": "D", "content": "$$43$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems->Finding the Working Hours"], "answer_analysis": ["$$[（38-8）\\times2+6]\\div2=33$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8334", "queId": "141febd5ea234b20a670950d830d44d3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alex, John and Sam went to buy oranges. Alex paid $\\textbackslash$20$, John paid $\\textbackslash$15$, and Sam only paid $\\textbackslash$5$. They bought 120 oranges altogether. They divided them in proportion to the amount of money each of them had paid. How many oranges did John get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division"], "answer_analysis": ["A: J: S 20:15:5 = 40 120/40 = 3 oranges per person 3*15= 45 oranges "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8342", "queId": "bddee69baaec485cb151f8064140edbe", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "After a test, teacher Valeria collects the data of the scores. Given that: The average score of class $A$ is $76$. The average score of class $B$ is $84$. The average score of class $C$ is $89$. The average score of class $A$ and $B$ is $79$. The average score of all the three classes is $81$. There are $40$ students in class $A.$ What is the ratio of number of students of class $B$ to that of $C$? ", "answer_option_list": [[{"aoVal": "A", "content": "$3:2$ "}], [{"aoVal": "B", "content": "$1:1$ "}], [{"aoVal": "C", "content": "$4:1$ "}], [{"aoVal": "D", "content": "$5:2$ "}], [{"aoVal": "E", "content": "$2:3$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"], "answer_analysis": ["There are $40\\div\\frac{84-79}{79-76}=24$ students in class $B.$ There are $(40+24)\\div\\frac{89-81}{81-79}=16$ students in class $C.$ $24:16=3:2$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8353", "queId": "1038d05552044ecbb56c355533cfe882", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ala, Lenka and Miso went out for dessert. Lenka paid $$4$$ dollars and $$50$$ cents for three scoops of ice cream. Miso paid $$3$$ dollars and $$60$$ cents for two cookies. How much did Ala pay for one scoop of ice cream and one cookie? (2011 Math Kangaroo Problem, Level 3 - 4, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$3$~dollars and~$30$~cents "}], [{"aoVal": "B", "content": "$4$~dollars and~$80$~cents "}], [{"aoVal": "C", "content": "$5$~dollars and~$10$~cents "}], [{"aoVal": "D", "content": "$6$~dollars and~$30$~cents "}], [{"aoVal": "E", "content": "$8$~dollars and~$10$~cents "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems->Basic Problems of Distribution"], "answer_analysis": ["$4$ dollars and $50$ cents are equal to $450$ cents, so one scoop of ice cream costs $450 \\div 3 = 150$ cents. $$3$$ dollars and $$60$$ cents are equal to $360$ cents, so one cookie costs $360 \\div 2 = 180$ cents. Thus, Ala should pay $ 150 + 180 = 330$ cents for one scoop of ice cream and one cookie. $330$ cents are equal to $3$ dollars and $30$ cents, so the answer is $A$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8354", "queId": "2f2c2f36bb2042b5b9cdf436ae4e15a8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Danni bought a painting for £$$42$$ last year. She sold it this year for £$$55$$. How much did she earn? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["$$55-42=13$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8355", "queId": "0cb3c33218ca46cc9c92568107be9867", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $38$ chickens and rabbits in a farm in total. The number of ducks is $2$ more than five times that of rabbits. How many ducks are there in the farm? ", "answer_option_list": [[{"aoVal": "A", "content": "$$32$$ "}], [{"aoVal": "B", "content": "$$33$$ "}], [{"aoVal": "C", "content": "$$29$$ "}], [{"aoVal": "D", "content": "$$26$$ "}], [{"aoVal": "E", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["$$(38-2)\\div (1+5)=36\\div 6=6$$ $$6\\times 5+2=32$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8357", "queId": "7dc422666dc645f8907f39a5af379082", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A fruit shop brought in some fruit. A quarter of them were sold last week. This week another $120$ kilograms were sold. One third of the original fruit is left now. How many kilos of fruit did the fruit shop buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$150\\text{kg}$$ "}], [{"aoVal": "B", "content": "$$190\\text{kg}$$ "}], [{"aoVal": "C", "content": "$$240\\text{kg}$$ "}], [{"aoVal": "D", "content": "$$288\\text{kg}$$ "}], [{"aoVal": "E", "content": "$$324\\text{kg}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["$$1-\\frac{1}{4}-\\frac{1}{3} =\\frac{5}{12}$$, $$120\\div\\frac{5}{12}=288\\text{kg}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8361", "queId": "c72768ba139a4b3e9f55e05e7f6efa5c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Nicole has a $$500$$ ml bottle of mouthwash. Every morning, she uses two capfuls of mouthwash. Each capful contains $$4$$ ml of mouthwash. If Nicole open a new bottle of mouthwash on $$12$$ April, on which of these dates will she use up the whole bottle of mouthwash? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ June "}], [{"aoVal": "B", "content": "$$13$$ June "}], [{"aoVal": "C", "content": "$$14$$ August "}], [{"aoVal": "D", "content": "$$15$$ August "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Nicole uses $$4\\times2=8$$ ml of mouthwash every day. $$500\\div8=62$$ R $$4$$ So, $$62$$ days after $$12$$ April, the bottle of mouthwash will become empty. There are $$18$$ remaining days in April and $$31$$ days in May. $$62-18-31=13$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8363", "queId": "3860eb31081a4647823a9071d078c222", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A bag of toffee is $5$ dollars, a bag of cotton candy is $3$ dollars, and a bag of orange candy is $12$ dollars. Now, the candy shop decides to mix $25$ bags of toffee, $60$ bags of cotton candy, and $15$ bags of orange candy for $100$ bags of assorted candy. What should be the price of the assorted candy in dollars to keep the total revenue unchanged? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$3.5$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$4.85$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Total revenue: $25\\times 5+60\\times 3+15\\times 12=485$ dollars A bag of assorted candy: $$485\\div 100=4.85$$ dollars "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8364", "queId": "189b3ff6a22f4ac7922c877858d546f0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jill is now $$14$$ years old. Jack is now $$6$$ years older than Jill was $$2$$ years ago. How old is Jack now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["Jill is now $$14$$. Two years ago, she was $$12$$. Since Jack is now $$6$$ years older than Jill was $$2$$ years ago, Jack is now $$12 + 6= 18$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8366", "queId": "145797913373474090dd53511cdc3bc0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mr. Ronald sold $$300$$ burgers on Monday. He sold $$133$$ fewer burgers on Tuesday. How many burgers did he sell on Tuesday? ", "answer_option_list": [[{"aoVal": "A", "content": "$$167$$ "}], [{"aoVal": "B", "content": "$$133$$ "}], [{"aoVal": "C", "content": "$$166$$ "}], [{"aoVal": "D", "content": "$$433$$ "}], [{"aoVal": "E", "content": "$$177$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["$$300-133=167$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8368", "queId": "2f3234d5d01a44f9bc4b5a5c41371aa0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "To make coleslaw Cathy uses twice as much carrot (by weight) as cabbage. She then adds half as much yoghurt as cabbage. A pot of Cathy\\textquotesingle s coleslaw weighs $$175\\text{g}$$. How many pots of coleslaw can she make with a $$2 \\text{kg}$$ cabbage? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["The ratio by weight of carrot: cabbage:yoghurt$$=2:1:0.5$$ which we can double to give $$4:2:1$$. We can see that here $$2$$ represents the amount of cabbage and we want $$2 \\text{kg}$$ of cabbage, so there will be $$4+2+1=7\\text{kg}$$ of coleslaw altogether. Therefore the number of pots is $$7000\\div 175 =40$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8370", "queId": "386449a6d0cc49f0a871679377c09b44", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a traditional Chinese novel, there are $108$ heroes, three of whom are women. How many male heroes are there in this novel？(adapted from $$2007$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$105$$ "}], [{"aoVal": "B", "content": "$$98$$ "}], [{"aoVal": "C", "content": "$$96$$ "}], [{"aoVal": "D", "content": "$$94$$ "}], [{"aoVal": "E", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["There are $108$ heroes in total. Subtract three heroines to get the number of male heroes. That is $108-3=105$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8372", "queId": "4ad0a93e0367427491eda6e6bbc5a25c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A total of $$46$$ bicycles and tricycles are in the garage. If there are $$100$$ wheels in total, there should be~\\uline{~~~~~~~~~~}~tricycles in the garage. ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$38$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"], "answer_analysis": ["$(100-2\\times46)\\div(3-2)=8$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8373", "queId": "33ca829cbfd8476d923ee8f264b1553e", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Amanda is $$7$$ years old last year. In $$2$$ years times, she is double of her sister\\textquotesingle s age. What is the sum of their age this year? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$13$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["$$2$$ years time, Amanda $$10$$ and sister $$5$$. Total $$15$$. This year, $$15-2-2=11$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8374", "queId": "3865cdd8cbf34d679de8e27172ea628a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If I have $$2500$$ quarters, then I have． ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$100$$ "}], [{"aoVal": "B", "content": "＄$$500$$ "}], [{"aoVal": "C", "content": "＄$$625$$ "}], [{"aoVal": "D", "content": "＄$$1000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["Every $$4$$ quarters is ＄$$1$$; the number of dollars I have is $$2500\\div 4=$$＄$$625$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8379", "queId": "fa3ad7645a2c414487ddfc6de4532e28", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Bud needs to recite 120 words for a dictation in a week (7 days). She plans to recite 15 words everyday. Can she be fully prepared for the test? ", "answer_option_list": [[{"aoVal": "A", "content": "Yes, she can. "}], [{"aoVal": "B", "content": "No, she can\\textquotesingle t. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division"], "answer_analysis": ["$$15\\times7=105$$，$$105\\textless120$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8381", "queId": "cbcd99dcc0fa4466b0fe6b6ef19da33f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Two plums and one cherry weigh $$80\\text{g}$$. One cherry and one plum weigh $$50\\text{g}$$. What is the weight of four plums? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30\\text{g}$$ "}], [{"aoVal": "B", "content": "$$40\\text{g}$$ "}], [{"aoVal": "C", "content": "$$50\\text{g}$$ "}], [{"aoVal": "D", "content": "$$120\\text{g}$$ "}], [{"aoVal": "E", "content": "$$160\\text{g}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Equivalent Substitution in Equation Word Problems"], "answer_analysis": ["Let the mass of one plum and the mass of one cherry be $$p \\text{g}$$ and $$c\\text{g}$$ respectively. Then $$2p +c=80$$ and $$p+c=50$$. We can deduce that $$p=80-50= 30$$, and so four plums weigh $$120 \\text{g}$$. Revise from ($$2017$$ Primary Mathematics Challenge-February, Question \\#$$18$$) "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8383", "queId": "747b9eb27e0c4e3eb6d7f66ce3e615b4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a mathematics contest with ten problems, a student gains $$5$$ points for a correct answer and loses $$2$$ points for an incorrect answer. If Olivia answered every problem and her score was $$29$$, how many correct answers did she have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Suppose Olivia has $$x$$ correct answers. $$5x-2(10-x)=29$$, $$x=7$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8384", "queId": "b938868d547b40808b18445880172bd5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "On Kellin\\textquotesingle s $$13$$th birthday, Allen was four times her age. On Kellin\\textquotesingle s $$24$$st birthday, how old was Allen? ", "answer_option_list": [[{"aoVal": "A", "content": "$$39$$ "}], [{"aoVal": "B", "content": "$$44$$ "}], [{"aoVal": "C", "content": "$$ 52 $$ "}], [{"aoVal": "D", "content": "$$ 63 $$ "}], [{"aoVal": "E", "content": "$$ 74$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["On Kellin\\textquotesingle s $$13$$th birthday, Allen was four times her age, that is $$52$$. It is then eleven years until Kellin\\textquotesingle s $$24$$st birthday, so Allen\\textquotesingle s age at that time was $$52 +11 =63$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8386", "queId": "0cfedf7223b74db6866b1f5cf2e722a5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a jar of red, green, and blue marbles, all but $$6$$ are red marbles, all but $$8$$ are green, and all but $$4$$ are blue. How many marbles are in the jar? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems"], "answer_analysis": ["Suppose there are $$x$$ red marbles, $$y$$ green marbles and $$z$$ blue marbles. Thus, we can get $$\\begin{cases} x+y=4① \\textbackslash\\textbackslash{} y+z=6②\\textbackslash\\x+z=8③\\end{cases}$$, ①$$+$$②$$+$$③: $$2x+2y+2z=18$$, $$x+y+z=9$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8387", "queId": "0cffa9b6a24147f2a5e74a7e3fcf3b6f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Hailey is $$6$$ years old and Xavier is $$7$$ years old this year. What is the sum of their ages after $$10$$ years? ", "answer_option_list": [[{"aoVal": "A", "content": "$$23$$ "}], [{"aoVal": "B", "content": "$$26$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$35$$ "}], [{"aoVal": "E", "content": "$$43$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$6+7+10\\times2=33$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8389", "queId": "98bceddc353440969b58bca62b72c0bd", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Water from the first faucet fills the swimming pool in $20$ hours. Water from each of the three other faucets fills the same swimming pool $3$ times faster. In how many hours will the swimming pool be filled if all three faucets are opened? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems"], "answer_analysis": ["The efficiency of the first faucet is $\\frac1{20}$ and that of the other two is $\\frac3{20}$. Thus it takes $1\\div (\\frac1{20}+\\frac3{20}\\times3)=2$ hours to fill the pool. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8392", "queId": "33d789a3b9324a2b953f6e2656593255", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A red kangaroo and a gray kangaroo weigh $$139\\textasciitilde\\text{kg}$$ altogether. The red kangaroo weighs $$35\\textasciitilde\\text{kg}$$ less than the gray kangaroo. How much does the gray kangaroo weigh? ", "answer_option_list": [[{"aoVal": "A", "content": "$$104\\text{kg}$$ "}], [{"aoVal": "B", "content": "$$52\\text{kg}$$ "}], [{"aoVal": "C", "content": "$$87\\text{kg}$$ "}], [{"aoVal": "D", "content": "$$96\\text{kg}$$ "}], [{"aoVal": "E", "content": "$$53\\text{kg}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["$$139-35=104$$ Red kangaroo: $$104 \\div2 = 52$$ Gray kangaroo: $$52+35=87$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8398", "queId": "21a6cba8db2744f8b26bec95227941fc", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "I ate half of an apple pie on Saturday and two-thirds of the remainder on Sunday. What fraction of the pie was left for Monday? ", "answer_option_list": [[{"aoVal": "A", "content": "None "}], [{"aoVal": "B", "content": "$\\frac12$ "}], [{"aoVal": "C", "content": "$\\frac13$ "}], [{"aoVal": "D", "content": "$\\frac23$ "}], [{"aoVal": "E", "content": "$\\frac16$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages"], "answer_analysis": ["$(1-\\frac12)\\times(1-\\frac23)=\\frac12\\times\\frac13=\\frac16$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8401", "queId": "0d2a54beb7c844a18c9c3f355cbaf1b9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a group of $$48$$ children, the ratio of boys to girls is $$3:5$$. How many boys must join the group to make the ratio of boys to girls $$5:3$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$48$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"], "answer_analysis": ["Initially there are $$48$$ children of whom $$\\frac{3}{8}$$ are boys and $$\\frac{5}{8}$$ are girls, so there are $$18$$ boys and $$30$$ girls. When more boys join, there are still $$30$$ girls but now they form $$\\frac{3}{8}$$ of the total. So the total number of pupils is now $$\\frac{8}{3}\\times30= 80$$, of whom $$80-30=50$$ are boys. Hence the number of boys joining is $$50-18=32$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8403", "queId": "f0ef346ae36c469390642bbd4608b607", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Lucy joined a math test which had the scoring rules below: for any correct answer, she got $5$ points; for any skipped or wrong answer, she lost $7$ points. There were $20$ problems in total. When she finished the test, she got only $4$ points. How many problems did she answer correct? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$16$$ "}], [{"aoVal": "E", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems"], "answer_analysis": ["The total points is $20\\times5=100.$ If there was one wrong anwser, she would lose $5+7=12$ points. $(20\\times5-4)\\div(7+5)=8$, so she got $20-8=12$ problems correct. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8405", "queId": "61fbe7fa0a0044f6b0081d5f72e9963e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Nathan has $$4$$ red shirts, $$6$$ yellow shirts and $$8$$ white shirts. What fraction of his shirts are white? Give your answer in its simplest form. ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{8}{18}$$ "}], [{"aoVal": "B", "content": "$$\\frac{3}{9}$$ "}], [{"aoVal": "C", "content": "$$\\frac{4}{9}$$ "}], [{"aoVal": "D", "content": "$$\\frac{4}{5}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["White shirts $$=8$$ Total shirts $$=4+6+8=18$$ Fraction of shirts that are white $$=\\frac{8}{18}=\\frac{4}{9}$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8419", "queId": "10b43c01039a4fe488befcd4dcb673ff", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "An empty truck weighs $$2000$$ kg. After the truck was loaded, the freight (that is, the load) made up $$80\\textbackslash\\%$$ of the weight of the loaded truck. At the first stop one fourth of the freight was unloaded. What percent of the loaded truck\\textquotesingle s weight did the freight make up after that? ($$2003$$ Math Kangaroo Problem, Level $$7-8$$, Question \\#$$17$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$20\\textbackslash\\% $$ "}], [{"aoVal": "B", "content": "$$25\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$55\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$ 60\\textbackslash\\%$$ "}], [{"aoVal": "E", "content": "$$75\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["Actually, we don\\textquotesingle t need the weight of the empty truck. Suppose the weight of the loaded truck before the first stop is $5x$ kg, and the weight of the feight is $4x$ kg. After the first stop, $4x \\times \\frac14=x$ kg of freight is unloaded. Now, the freight weighs $4x-x=3x$ kg, and the loaded truck weighs $5x-x=4x$ kg. Thus, the percent is $\\frac{3x}{4x}=\\frac34=75\\textbackslash\\%$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8422", "queId": "263e1caecbc34394bf18332e4fc412ab", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jodie has just begun to read a $$160$$-page book. If she reads $$20$$ pages every day, she will finish the book in ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ days "}], [{"aoVal": "B", "content": "$$18$$ days "}], [{"aoVal": "C", "content": "$$20$$ days "}], [{"aoVal": "D", "content": "$$80$$ days "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["Jodie has just begun to read a $$160$$-page book. If she reads $$20$$ pages every day, she will finish the book in $$160 \\div 20 =8$$ days. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8423", "queId": "ab5c19be74d84d5796e7561f934aa7e5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Tadek has $$7$$ zloty (unit of money) more than Witek. Witek has $$10$$ zloty less than Karol. Witek and Karol have $$28$$ zloty together. How much money does Tadek have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$16$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference->Sum and Differences Problems with multiple Variables"], "answer_analysis": ["Witek has $$(28 - 10) \\div 2 = 9$$ zloty, so Tadek has $$9 + 7 = 16$$ zloty. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8428", "queId": "14b508470c974f929e8d7286bdaf3571", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Ben and Ken have some books. After Ben sends $4$ books to Ken, he has $1$ book less than Ken. Which of the following is true? ", "answer_option_list": [[{"aoVal": "A", "content": "Originally, Ben had $3$ books more than Ken. "}], [{"aoVal": "B", "content": "Originally, Ben had $4$ books more than Ken. "}], [{"aoVal": "C", "content": "Originally, Ben had $1$ books less than Ken. "}], [{"aoVal": "D", "content": "Originally, Ben had $9$ books more than Ken. "}], [{"aoVal": "E", "content": "Originally, Ben had $7$ books more than Ken. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$4+4-1=7$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8430", "queId": "21be02cb035c482ca156bbe82db297e7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "David and Billy are on the bus together. They sit in the same column. There are $5$ people in front of David, Billy is in the middle. There are $10$ people behind Billy, and David is in the middle. How many people in this column? (adapted from2004 Math Kangaroo Problem, Level 3 - 4, Question \\#19) ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line"], "answer_analysis": ["$5 + 10 - 2 = 13$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8431", "queId": "10c388fcb7144749814a0028bff06f7a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Chloe and Zoe are both students in Ms. Demeanor\\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to $90\\textbackslash\\%$ of the problems she solved alone, but overall $60\\textbackslash\\%$ of her answers were correct. Zoe had correct answers to $70\\textbackslash\\%$ of the problems she solved alone. What was Zoe\\textquotesingle s overall percentage of correct answers? (adapted from 2017 AMC 8, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$65$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Assume the total amount of problems is $100$ per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got $90$ problems correct by herself, and got $120$ problems correct overall. We also know that Zoe had $70$ problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $120-90=30$. Therefore Zoe has $30+70=100$ problems out of $200$ problems correct. Thus $\\frac{100}{200} = 50$ percent. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8434", "queId": "264680a72d1f46adb950229b84ce6cca", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the enchanted garden of the Green King, there are apple trees that grow golden apples. Every day, $$5$$ golden apples become ripe on each tree, and at the end of each day they fall from the trees. Today, the Green Gardener has picked up $$20$$ ripe apples that fell under the trees last night. How many enchanted trees are there in the garden?（$$2005$$ Math Kangaroo Problem, Levels $$1-2$$, Question \\#$$1$$） ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["$$5$$ apples fall down from each trees. \"Each\"~is a sign of division. So, the answer is $$20\\div5=4$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8435", "queId": "14bce265dfb3480fa9646d89089b9c5a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Add the number of days in January March, April, May, June, July, August, September, October, November and December. ", "answer_option_list": [[{"aoVal": "A", "content": "$$334$$ "}], [{"aoVal": "B", "content": "$$335$$ "}], [{"aoVal": "C", "content": "$$336$$ "}], [{"aoVal": "D", "content": "$$337$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["The only missing month is February. The sum will be either $$365$$ - $$28$$ or (in leap years) $$366$$ - $$29$$. Both are equal to $$337$$． "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8438", "queId": "264ad7501c054932860b13501bab59ec", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Some cows live on a grassland. $10$ cows can eat all grass in $9$ days. $12$ cows can eat all grass in $7$ days. The amount of new grass that grows each day is constant. $24$ cows can eat all grass in~\\uline{~~~~~~~~~~}~days. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$4.5$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Newton's Problem of Cows and Fields"], "answer_analysis": ["Suppose a cow can eat $1$ m\\textsuperscript{2}~of grass each day. The amount of new grass that grows each day: $(9\\times10-12\\times7)\\div(9-7)=3$ m\\textsuperscript{2}. The amount of grass originally: $$90-9\\times 3=63$$ m\\textsuperscript{2}. $$24$$ cows can eat all grass in $$63\\div \\left( 24\\times1-3 \\right)=3$$ days. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8439", "queId": "1d579d0ef9e8461f9a79f95890b36514", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The distance between Exeter and London is $$175$$ miles. Sam left Exeter at $$10:00$$ on Tuesday for London. Morgan left London for Exeter at $$13:00$$ the same day. They travelled on the same road. Up to the time when they met, Sam\\textquotesingle s average speed was $$25$$ miles per hour, and Morgan\\textquotesingle s average speed was $$35$$ miles an hour. At what time did Sam and Morgan meet? ", "answer_option_list": [[{"aoVal": "A", "content": "$$17:00$$ "}], [{"aoVal": "B", "content": "$$15:55$$ "}], [{"aoVal": "C", "content": "$$15:30$$ "}], [{"aoVal": "D", "content": "$$15:00$$ "}], [{"aoVal": "E", "content": "$$14:40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Sam left Exeter three hours before Morgan left London, and travelled $$3\\times 25$$ miles $$=75$$ miles in the three hours to $$13:00$$. So at $$13:00$$, the distance between Sam and Morgan was $$ \\left( {175-75} \\right) $$ miles $$=100$$ miles. Let the time in hours between $$13:00$$ and the time at which Sam and Morgan met be $$t$$. Then $$25t+35t=100$$. So $$t=\\frac{{100}}{{60}}$$ hours $$=100$$ minutes $$=1$$ hour $$40$$ minutes. So Sam and Morgan met at $$14:40$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8441", "queId": "c28b62fc73ef462da79ce767eaa2e7ca", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Some students are lining up at the cafeteria. Ellie is the third from the back and the seventh from the front. How many students are there lining up in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$3+7-1=9$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8442", "queId": "14cd4c6e7f2e4b28b3aa7b6e6f0e7c9f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A bridge is built across a river. One quarter of the bridge is over the left bank of the river and one third of the bridge is over the right bank. The river is $$120\\text{m}$$ wide. How long is the bridge? ", "answer_option_list": [[{"aoVal": "A", "content": "$$150\\text{m}$$ "}], [{"aoVal": "B", "content": "$$190\\text{m}$$ "}], [{"aoVal": "C", "content": "$$240\\text{m}$$ "}], [{"aoVal": "D", "content": "$$288\\text{m}$$ "}], [{"aoVal": "E", "content": "$$324\\text{m}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["The river is $$120\\text{m}$$ wide and represents $$\\left( 1-\\frac{1}{4}-\\frac{1}{3} \\right)=\\frac{5}{12}$$ of the length of the bridge. Therefore $$\\frac{1}{12}$$ of the length of the bridge is $$24\\text{m}$$. Hence the total length of the bridge is $$12\\times 24\\text{m}=288\\text{m}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8446", "queId": "0d9658f9cd054d6081c837d2d16e56d9", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There are $$40$$ guests queueing to enter a party. Every $$4^{\\rm th}$$ guest in the queue receives a balloon and every $$6^{\\rm th}$$ guest in the queue receives a mask. How many guests receive both a balloon and a mask?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems"], "answer_analysis": ["Every 12th guest receives both a mask and a balloon. Hence, the 12th, 24th and 36th guest receive both. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8448", "queId": "b940442870d34766bd321afbd92de2c2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Daniel raises some ducks and dogs. All the ducks and dogs have $18$ legs and $5$ pairs of wings in total. How many ducks and dogs are there in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems"], "answer_analysis": ["$5$ pairs of wings means there are $5$ ducks, so there are $18-5\\times2=8$ legs for dogs, which is $8\\div4=2$. Thus, there are $2+5=7$ animals. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8449", "queId": "21d00abfc3dd489d8c167dc9e09f6f56", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There were $$31$$ runners competing in a race. The number of runners who finished before John is four times smaller than the number of runners who finished later than John. At what place did John finish? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["Before is ``$$1$$'', so after is ``$$4$$'', Before: $$(31-1) \\div (4+1) = 6$$, and John: $$6+1=7$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8456", "queId": "1d694293ea634a02b259aa5073b6aea2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The number of ounces of water needed to reduce $$9$$ ounces of shaving lotion containing $$50\\textbackslash\\%$$ alcohol to a lotion containing $$30\\textbackslash\\%$$ alcohol is: ($$1953 $$ AHSME Problem, Question \\#$$9$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Solving Concentration Problems with Equations"], "answer_analysis": ["Solution $$1$$. Say we add $$N$$ ounces of water to the shaving lotion. Since half of an $$9$$ ounce bottle of shaving lotion is alcohol, we know that we have $$\\dfrac{9}{2}$$ ounces of alcohol. We want $$\\dfrac{9}{2}=0.3(9+N)$$ (because we want the amount of alcohol, $$\\dfrac{9}{2}$$, to be $$30\\textbackslash\\%$$, or $$0.3$$, of the total amount of shaving lotion, $$9+N$$). Solving this, we find that $$9=0.6(9+N)\\Rightarrow9=5.4+0.6N\\hspace{0pt}\\Rightarrow3.6=0.6N\\hspace{0pt}\\Rightarrow6=N$$. So, the total amount of water we need to add is $$6$$. Solution $$2$$. The concentration of alcohol after adding $$n$$ ounces of water is $$\\dfrac{4.5}{9+n}$$. To get a solution of $$30\\textbackslash\\%$$ alcohol, we solve $$\\dfrac{4.5}{9+n}=\\dfrac{3}{10}$$ $$45=27+3n$$ $$18=3n$$ $$6=n\\Rightarrow6$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8457", "queId": "a6b9f4460acb4f4aa34afc80021e2ec4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In the Adventure Park, 30 children took part in two of the adventures. 15 of them participated in the \"moving bridge\" contest, and 20 of them went down the zip-wire. How many of the children took part in both adventures? ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"], "answer_analysis": ["There are 30 children. 15 of them participated in the \"moving bridge\" contest. This means that the other 15, who did not participate in the \"moving bridge\" surely went down the zip-wire. In fact 20 went down the zip-wire; therefore, 20-15=5 of the 15 \"moving bridges\\textquotesingle{} \" participants must have also gone down the zip-wire. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8459", "queId": "11049f33a15e4414ba18712a8abded66", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When Lucy was born, Cathy was $23$ years old. The sum of their ages $3$ years later will be $45$. How old will be Cathy $3$ years later? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$28$$ "}], [{"aoVal": "D", "content": "$$33$$ "}], [{"aoVal": "E", "content": "$$34$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["Suppose that Lucy will be $x$ years old $3$ years later, Cathy will be $$(x+23)$$ years old. $x+(x+23)=45$, so $x=11$. Thus, Cathy will be $11+23=34$ years old $3$ years later. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8460", "queId": "2f6ed7ccbbc34762915343faff39bc88", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When Kerr was born, Barry was $13$ years old. The sum of their ages $5$ years later will be $51$. How old will be Barry $5$ years later? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$33$$ "}], [{"aoVal": "E", "content": "$$34$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["Suppose that Lucy will be $x$ years old $5$ years later, Cathy will be $$(x+13)$$ years old. $x+(x+13)=51$, so $x=19$. Thus, Cathy will be $13+19=32$ years old $5$ years later. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8463", "queId": "14ee35a7009e4252b39c4e924d643d7b", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "A store sells cakes for $10 each, at the following discounts. \\textbf{① $1 off each every Wednesday.} \\textbf{② Buy three or more, $1 off each.} If both rules are met at same time, the price can be reduced together. How much will Tracy pay for 4 cakes at this store on Tuesday? ", "answer_option_list": [[{"aoVal": "A", "content": "$36 "}], [{"aoVal": "B", "content": "$40 "}], [{"aoVal": "C", "content": "$34 "}], [{"aoVal": "D", "content": "$44 "}], [{"aoVal": "E", "content": "$30 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Money Calculation"], "answer_analysis": ["40-1*4=36 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8464", "queId": "191ddbbf6b3f4378a5a32d0a13e964df", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $2\\text{cm}$ represents $50\\text{km}$ on a map and the distance between two towns on this map is $7.5\\text{cm}$, then their actual distance apart is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$375\\text{km}$ "}], [{"aoVal": "B", "content": "$275\\text{km}$ "}], [{"aoVal": "C", "content": "$187.5\\text{km}$ "}], [{"aoVal": "D", "content": "$75\\text{km}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["If $$2\\textasciitilde\\text{cm}$$ represents $$50\\textasciitilde\\text{km}$$, $$1\\textasciitilde\\text{cm}$$ represents $$25\\textasciitilde\\text{km}$$. So, their actual distance apart is $$7.5\\times 25=187.5\\textasciitilde\\text{km}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8467", "queId": "1117a435af6f476ca0364b4e5071ef83", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $10$ benches on one side of a road. Brown wants to put $1$ pot of flowers between every two adjacent benches. How many pots of flowers does he need to prepare? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$10 - 1 = 9$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8470", "queId": "0dde5cc69dbb450d8f4542d600e60f89", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Cagney can frost a cupcake every $$30$$ seconds and Lacey can frost a cupcake every $$60$$ seconds. Working together, how many cupcakes can they frost in $$5$$ minutes? (Adapted from $$2012$$ AMC $$10\\rm A$$ Problem, Question \\#$$11$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$25$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"], "answer_analysis": ["In $$300$$ seconds ($$5$$ minutes), Cagney will frost $$\\dfrac{300}{30}=10$$ cupcakes, and Lacey will frost $$\\dfrac{300}{60}=5$$ cupcakes. Therefore, working together they will frost $$10+5=\\boxed{(\\text{B})15}$$ cupcakes. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8482", "queId": "21f9a290dc5c49c7ad429a395c56ad9a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Owen attends a basketball shooting game. He gets $70 \\textbackslash\\%$ on $10$ one-point shots , $80 \\textbackslash\\%$ on $10$ two-points shots and $90 \\textbackslash\\%$ on $10$ three-points shots. Compare Owen\\textquotesingle s score with the total points possible, which percent is closest to his overall score? (Adapted from 2006 AMC 8, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$77$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$83$$ "}], [{"aoVal": "E", "content": "$$87$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$70 \\textbackslash\\% \\cdot 10=7$ $80 \\textbackslash\\% \\cdot 20=16$ $90 \\textbackslash\\% \\cdot 30=27$ Adding them up gets $7+16+27=50$. The overall percentage correct would be $\\frac{50}{60}=\\frac{5}{6}=5 \\cdot 16 . \\overline{6}=83 . \\overline{3} \\approx(\\mathbf{D}) 83$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8490", "queId": "7de2775f644946d3b624a66768409ff7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are five kangaroo mothers, six kangaroo babies, and one kangaroo father. Each kangaroo mother should take care of the same number of kangaroo babies. How many kangaroo babies should kangaroo father take care of? (adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Including and Excluding "], "answer_analysis": ["The key point is that each kangaroo mother needs to take care of the same number of kangaroo babies. So $6$ (number of kangaroo baby) $$\\div$$ $5$ (number of kangaroo mother)$=1\\ldots\\ldots1$, and the remaining one is taken care of by kangaroo father. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8491", "queId": "3417f8f710f64fdbbcba14996ce02a94", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are twice as many boys in a room as girls. If $$5$$ boys leave the room, there would be an equal number of boys and girls in the room. How many boys were in the room at first? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Difference and Multiple"], "answer_analysis": ["The number of boys that leave the room must equal the number of boys that remain. Since $$5$$ boys leave, there are $$5$$ boys still in the room for a total of $$10$$ boys. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8500", "queId": "220ec0ae082a4045a146c089b89e7568", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Pamela, Pearl, and Polly went to buy some toys. Pamela paid $$2$$ dollars and $$70$$ cents for three identical dolls. Pearl paid $$3$$ dollars and $$40$$ cents for two identical toy cars. How much did Polly pay for one doll and one toy car? (Adapted from 2011 Math Kangaroo Problem, Level 3-4 , Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$2$ dollars and $80$ cents "}], [{"aoVal": "B", "content": "$2$ dollars and $70$ cents "}], [{"aoVal": "C", "content": "$2$ dollars and $60$ cents "}], [{"aoVal": "D", "content": "$2$ dollars and $50$ cents "}], [{"aoVal": "E", "content": "$2$ dollars and $40$ cents "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems->Basic Problems of Distribution"], "answer_analysis": ["$$2$$ dollars and $$70$$ cents=$270$ cents $$3$$ dollars and $$40$$ cents=$340$ cents One doll costs $270\\div3=90$ cents. One toy car costs $340\\div2=170$ cents. $170+90=260$ cents = $2$ dollars $60$ cents. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8506", "queId": "66be19db9494482dadf60b633102e78d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A police spotted a burglar from $$100\\text{m}$$ apart. The burglar immdiately runs away at a speed of $$4\\text{m/s}$$ and the police starts chasing him at $$8\\text{m/s}$$ at the same time. At this rate, how long will it take the police to catch the burglar? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1 $$ minute "}], [{"aoVal": "B", "content": "$$25 $$ seconds "}], [{"aoVal": "C", "content": "$$30$$ seconds "}], [{"aoVal": "D", "content": "$$15$$ seconds "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"], "answer_analysis": ["The distance between them is $$100$$ m, and the difference between their speeds is $$12-8=4000$$ m/h. It takes $$100\\div4000\\times60=1.5$$minutes to catch the burglar, which is $$90$$ seconds "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8512", "queId": "2697f0682d664f249b5865823a52b3dc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A sugar solution is made by mixing $$7$$ grams of sugar and $$21$$ grams of water. Find the percent concentration of the solution. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$\\% "}], [{"aoVal": "B", "content": "$25$\\% "}], [{"aoVal": "C", "content": "$30$\\% "}], [{"aoVal": "D", "content": "$33.3$\\% "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$7\\div(7+21)=25\\textbackslash\\%$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8519", "queId": "6b6325982a944ffdb9c8517a874a986e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Two plums and one cherry weigh $$80\\text{g}$$. Two cherries and one plum weigh $$70\\text{g}$$. What is the weight of four plums? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30\\text{g}$$ "}], [{"aoVal": "B", "content": "$$40\\text{g}$$ "}], [{"aoVal": "C", "content": "$$50\\text{g}$$ "}], [{"aoVal": "D", "content": "$$120\\text{g}$$ "}], [{"aoVal": "E", "content": "$$160\\text{g}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Equivalent Substitution in Equation Word Problems"], "answer_analysis": ["Let the mass of one plum and the mass of one cherry be $$p \\text{g}$$ and $$c\\text{g}$$ respectively. Then $$2p +c=80$$ and $$2c+p=70$$. Hence $$3p +3c=150$$, and $$p+c=50$$. But since $$2p+c=80$$, we can deduce that $$p=80-50= 30$$, and so four plums weigh $$120 \\text{g}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8523", "queId": "4b16ab49ec4d43a89eed0c9e8cc62c03", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A total of $$32$$ chickens and rabbits are caged together. If there are $$90$$ legs in total, how many chickens and rabbits are in the cage, respectively? ", "answer_option_list": [[{"aoVal": "A", "content": "$20$; $12$ "}], [{"aoVal": "B", "content": "$13$; $19$ "}], [{"aoVal": "C", "content": "$18$; $14$ "}], [{"aoVal": "D", "content": "$19$; $13$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"], "answer_analysis": ["Suppose all the animals in the cage are chickens: there should be $$2\\times 32=64$$ legs. However, $$90-64=26$$ legs are missing because we counted $$26\\div2=13$$ rabbits as chickens. Hence, there are $$13$$ rabbits and $$32-13=19$$ chickens. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8525", "queId": "4fafa47a38464c2f8761f34cd7ec2a5d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Anna is $$10$$ years old and the age of her mother is $$4$$ times that of Anna. How old will Anna\\textquotesingle s mother be when Anna\\textquotesingle s mother is twice as old as Anna? (Adapted from $$2007$$ Math kangaroo Problem, Level $$5-6$$, Question \\#$$20$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$70$$ "}], [{"aoVal": "E", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Varying Multiples in Age Problems"], "answer_analysis": ["The age difference between them is $(4-1)\\times10=30$, which stays the same forever. Then, when Anna\\textquotesingle s mother is twice as old as Anna, Anna should be $30$ years old, then her mom should be $30\\times2=60$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8529", "queId": "4fb1533375584a0c8adf7a5d0aa3cb11", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Some students are buying a boardgame together. If each person pays $$$60$$, they need another $$$60$$ for payment. If each person pays $$$70$$, they will have $$$10$$ left. How much is the boardgame? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$600$$ "}], [{"aoVal": "B", "content": "$$$480$$ "}], [{"aoVal": "C", "content": "$$$690$$ "}], [{"aoVal": "D", "content": "$$$550$$ "}], [{"aoVal": "E", "content": "$$$720$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Number of students: $$(60+10)\\div (70-60)=7$$ Price of boardgame: $$60\\times7+60=480$$． "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8532", "queId": "41f082de42c341629bcc82594b86ed9a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In a speed skating competition, $$10$$ skaters reached the finish line. The number of skaters that came in before Tom was $$3$$ less than the number of skaters who came in after him. Which place did Tom end up in? (2015 Math Kangaroo Problem, Level 3 - 4, Question \\#13) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Order of one Character"], "answer_analysis": ["The sum of the number of skaters that came in before Tom and the number of skaters that came in after him is $10 - 1 = 9$. The number of skaters that came in before Tom was $(9 - 3) \\div 2 = 3$, so Tom was the fourth one. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8533", "queId": "343aca92b3e84de184f0b111600485d8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There is a tournament at the pool, First, $$13$$ children signed up and then another $$19$$ children signed up, Six teams with an equal number of members each are needed for the tournament, At least how many more children need to sign up so that,the six teams can be formed． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["The total number of children is $$13+19=32$$, To form six teams with the same number of children in each team, we divide $$32$$ by $$6$$, $$32\\div6=5$$$$\\rm R$$$$2$$, The remaining $$2$$ children will need $$4$$ more children to form the sixth team. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8535", "queId": "2b268da3c71a4bcfa32f46935aad025c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Bob and Wilson are standing in line. Bob knows that there are $$5$$ people in front of him. Wilson knows that there is a total of $$12$$ people in the line. If Bob is just in front of Wilson, how many of the people in the line are behind Wilson? (Adapted from 2017 Math Kangaroo Problem, Level 1-2, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$12-5-2=5$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8537", "queId": "b4b00e785c14437ba4617facc409cdcc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mother\\textquotesingle s Day in $$2020$$ was May $$10^{\\rm th}$$, which was a Sunday. Father\\textquotesingle s Day in $$2020$$ was June $$21^{\\rm st}$$. On what day of the week did Father\\textquotesingle s Day fall? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Wednesday "}], [{"aoVal": "D", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["There are in total $$21 + 21 = 42$$ days from May $$11$$ to June $$21$$. Since $$42 \\div 7 = 6$$, with no remainder, the Father\\textquotesingle s Day falls on Sunday as well. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8542", "queId": "11dcb7ce71be47d9bef00b9ef338fd9c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If today is Monday, then $63$ days from today will be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$Monday "}], [{"aoVal": "B", "content": "$$$$Tuesday "}], [{"aoVal": "C", "content": "$$$$Friday "}], [{"aoVal": "D", "content": "$$$$Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["If today is Monday, every $$7$$ days is another Monday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8545", "queId": "3d62a87a37cb43d0be834b7f03b739cc", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "A store sells cakes for $10 each, at the following discounts. \\textbf{① $1 off each every Wednesday.} \\textbf{② Buy three or more, $1 off each.} If both conditions are met at same time, the price can be reduced together. How much will Tracy pay for 4 cakes at this store on Tuesday? ", "answer_option_list": [[{"aoVal": "A", "content": "$36 "}], [{"aoVal": "B", "content": "$40 "}], [{"aoVal": "C", "content": "$34 "}], [{"aoVal": "D", "content": "$44 "}], [{"aoVal": "E", "content": "$30 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Money Calculation"], "answer_analysis": ["40-1*4=36 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8551", "queId": "19afd7d3f4c0416998d98cb29508ec57", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A balloon ride can take at most $$3$$ people at a time. If $$41$$ people want to fly in the balloon, the least number of rides needed is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["A balloon ride can take \\emph{at most}~$$3$$ people at a time. If $$41$$ people want to fly in the balloon, the least number of rides needed is $$41 \\div3$$, rounded \\emph{up} to $$14$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8552", "queId": "19afe9be9fff4e23a3eec804d608e0eb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Andy spent $$5$$ dollars on $$15$$ biscuits. How much would it cost if Andy bought six more of them? (adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$13$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["Fifteen cookies for five dollars means three cookies for one dollar. Six more cookies cost $$2$$ dollars. $$5+2=7$$~ dollars in total. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8561", "queId": "70153cc3fb404602a432fb572ad1d24f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy mixes $$10$$ grams of a $$20\\textbackslash\\%$$ sugar solution and $$40$$ grams of a $$25\\textbackslash\\%$$ sugar solution together. After~\\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of solution is $40\\textbackslash\\%$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ grams "}], [{"aoVal": "B", "content": "$$18$$ grams "}], [{"aoVal": "C", "content": "$$20$$ grams "}], [{"aoVal": "D", "content": "$$25$$ grams "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"], "answer_analysis": ["$$10\\times20\\textbackslash\\%+40\\times 25\\textbackslash\\%=12$$ ounces. $$(10+40)-12\\div40\\textbackslash\\%=20$$ ounces. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8562", "queId": "e312ac4ffbaa47c58d2d70c41679ca21", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "One of my two brothers is $$4$$ years older than the other. If the sum of their ages is $$38$$, the older brother isyears old. ", "answer_option_list": [[{"aoVal": "A", "content": "$$17$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "$$42$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["One of my two brothers is $$4$$ years older than the other. If they were the same age, they\\textquotesingle d each be $$19$$. Thus, one is $$17$$ and the other is $$21$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8566", "queId": "4205f91673fe4cc4ab15fc1c83adf5b7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Lee is $14$ years old and Lay is $41$ years old. How many years ago, Lay\\textquotesingle s age is exactaly $4$ times Lee\\textquotesingle s age? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"], "answer_analysis": ["Let the year be $x$ years ago. $14-x=(41-x)\\div 4$ $4(14-x)=41-x$ $56-4x=41-x$ $15=3x$ $3x=15$ $x=5$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8568", "queId": "4fc487c7cfce47a98498d99956c1164b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Which of the following equations represents the situation: John drinks $x$ cups of boba everyday on weekdays and $2$ cups of boba everyday on the weekends. ", "answer_option_list": [[{"aoVal": "A", "content": "$x+2$ "}], [{"aoVal": "B", "content": "$5x+2$ "}], [{"aoVal": "C", "content": "$5x+4$ "}], [{"aoVal": "D", "content": "$5x-4$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"], "answer_analysis": ["The boba that John drinks during weekdays: $$5x$$ The boba that John drinks during weekends: $$2\\times 2 =4$$ The total boba that John drinks during a week: $$5x+4$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8572", "queId": "fa4d815096fe42d2b713efbf644dbd18", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Granny and the triplets Cara, Cate and Chris all have their birthdays today. The ages of all four of them total $$120$$ years. Granny is $$5$$ times as old as each of the triplets. When were the triplets born? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2000$$ "}], [{"aoVal": "B", "content": "$$2002$$ "}], [{"aoVal": "C", "content": "$$2004$$ "}], [{"aoVal": "D", "content": "$$2007$$ "}], [{"aoVal": "E", "content": "$$2009$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Sums and Multiples in Age Problems"], "answer_analysis": ["Given that Granny is $$5$$ times older than each of the three triplets, we know that the age of each triplet is $$120\\div (5+3)= 15$$. So Cara, Cate and Chris were born in $$2007$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8573", "queId": "15c8bb8ac0c14cdab3c54e540b236e0d", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Nick has $83$ books and Steven has $140$ books. Starting from tomorrow, Nick will buy $8$ books and Steven will buy $5$ books every day. How many days later will they have the same number of books? ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$19$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "Never "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$(140-83) \\div (8-5)=19$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8579", "queId": "345be9ef3467416d95c524ee771b1cd5", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "In a basket, there are $60$ bananas. $20$\\% of them are rotten. How many bananas are in good condition? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$1-20$\\%=$80$\\%, $60 \\times 80$\\%=$48$. $48$ bananas are in good condition. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8581", "queId": "d08737d93b2b41ed9298f8915af81512", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$7$$ numbers with an average of $$79$$. After eliminating a number, the average of the remaining numbers is $$84$$. What is the eliminated number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$19$$ "}], [{"aoVal": "C", "content": "$$29$$ "}], [{"aoVal": "D", "content": "$$49$$ "}], [{"aoVal": "E", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$(84-79)\\times6=30$, $79-30=49$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8582", "queId": "58fb8c4ab631401194650e84f747171f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If today is Saturday, what day of the week will be 100 days later? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday "}], [{"aoVal": "B", "content": "Friday "}], [{"aoVal": "C", "content": "Monday "}], [{"aoVal": "D", "content": "Thursday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["$$100\\div7=14$$$$\\cdots \\cdots 2$$, So 2 days later is Monday. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8587", "queId": "66db6d3a0b37432cb8b42618d93c7b0c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Some zoo animals are standing in an array to prepare for the Zoo Olympics. The fox, Bob, finds that no matter whether he counts from front to back, back to front, left to right, or right to left, he is always the $$3$$\\textsuperscript{rd} in line. How many animals are there in the array?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$25$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number of People in a Rectangular Array"], "answer_analysis": ["$$3+3-1=5$$. Since each row and column has $$5$$ animals, there are $$5\\times5=25$$ animals in total. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8590", "queId": "26e63fc0e4b240e4b73ae972e71fa5d9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of two natural numbers is equal to $$77$$. If the first number is multiplied by $$8$$ and the second by $$6$$, then those products are equal. The larger of these numbers is~\\uline{~~~~~~~~~~}~. ($$2004$$ Math Kangaroo Problems, Level $$5-6$$, Question \\#$$20$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$23$$ "}], [{"aoVal": "B", "content": "$$33$$ "}], [{"aoVal": "C", "content": "$$43$$ "}], [{"aoVal": "D", "content": "$$44$$ "}], [{"aoVal": "E", "content": "$$54$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple->Problems of Sum and Multiplication with Indirect Multiples"], "answer_analysis": ["Suppose one of the numbers is $x$. $8x=6(77-x)$, $x=33$. Thus, these two numbers are $33$ and $44$. The larger one is $44$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8591", "queId": "38ef70c334a54280af6dab68b62e158b", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Mother\\textquotesingle s Day in $$2020$$ was May $$10$$\\textsuperscript{th}, which was Sunday. Father\\textquotesingle s Day in $$2020$$ was June $$21$$\\textsuperscript{st}. On what day did Father\\textquotesingle s Day fall? ", "answer_option_list": [[{"aoVal": "A", "content": "Thursday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Sunday "}], [{"aoVal": "D", "content": "Tuesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["It passed $$31-10 + 21 = 42$$ days in total. Since $$42 \\div 7 = 6$$, which means the Father\\textquotesingle s Day fell on Sunday as well. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8593", "queId": "1e1f6144fc514493aaf2b483c05bdd63", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Zosia is drawing kangaroos.The first one is blue, the next one green, the one after it red, the fourth one yellow, and then again blue, green, red, yellow, and so on, in the same order. What color will the seventeenth kangaroo be? (2003 Math Kangaroo Problem, Level 3-4, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$Blue "}], [{"aoVal": "B", "content": "$$$$Green "}], [{"aoVal": "C", "content": "$$$$Red "}], [{"aoVal": "D", "content": "$$$$Black "}], [{"aoVal": "E", "content": "$$$$Yellow "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"], "answer_analysis": ["$17\\div4=4R1$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8594", "queId": "12494b0fc0de4222a618734a6f9671e1", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Ella says:\" I can run $18\\text{km}$ every hour.\" Vivian says: \" Haha, I am the faster runner because I can run $100\\text{m}$ every $21\\text{s}$.\" Vivian\\textquotesingle s statement is~\\uline{~~~~~~~~~~}~because it only takes Ella~\\uline{~~~~~~~~~~}~$\\text{s}$ to run $100\\text{m}$. ", "answer_option_list": [[{"aoVal": "A", "content": "correct, 200 "}], [{"aoVal": "B", "content": "correct, 60 "}], [{"aoVal": "C", "content": "wrong, 20 "}], [{"aoVal": "D", "content": "wrong, 10 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["$\\frac{18km}{1h}=\\frac{18000m}{3600s}=5m/s$ $100\\div 5=20s$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8598", "queId": "15f4f028d9094418b3fc16298497248a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Anna, Bridgit and Carol run in a $$100\\text{m}$$ race. When Anna finishes, Bridgit is $$16\\text{m}$$ behind her and when Bridgit finishes, Carol is $$25\\text{m}$$ behind her. The girls run at constant speeds throughout the race. How far behind was Carol when Anna finished? ", "answer_option_list": [[{"aoVal": "A", "content": "$$37\\text{m}$$ "}], [{"aoVal": "B", "content": "$$41\\text{m}$$ "}], [{"aoVal": "C", "content": "$$50\\text{m}$$ "}], [{"aoVal": "D", "content": "$$55\\text{m}$$ "}], [{"aoVal": "E", "content": "$$60\\text{m}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Carol finishes $$25$$ metres behind Bridgit, so she travels $$75$$ metres while Bridgit runs $$100$$ metres. Therefore she runs $$3$$ metres for every $$4$$ metres Bridgit runs. When Anna finishes, Bridgit has run $$84$$ metres, so that at that time Carol has run $$\\frac{3}{4}\\times 84$$ metres $$=63$$ metres. Hence Carol finishes $$\\left( 100-63 \\right)$$ metres $$= 37$$ metres behind Anna. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8607", "queId": "160a7249c2ea427ca24a5587eac0136c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There were $$31$$ runners competing in a race. The number of runners who finished before John is four times smaller than the number of runners who finished later than John. At what place did John finish? ($$1998$$ Math Kangaroo Problem, Level $$3-4$$, Question \\#$$13$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["$$(31-1) \\div (4+1) = 6$$ $$6+1=7$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8608", "queId": "1a04c9c5940547c1b91c4482af09cf9b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mike has a bookcase with three layers, and the ratio of books placed on the upper, middle and lower layers is $$5:6:4$$. Given that there are $$240$$ books on the middle level, books should be removed from middle level and added to the lower level so that the number of books on each level can be exactly the same. ", "answer_option_list": [[{"aoVal": "A", "content": "$$48$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with an Invariant Part"], "answer_analysis": ["Lower level: $$240\\div6\\times4=160$$, The number of books to be added to the lower level: $$(240-160)\\div2=40$$. So, the answer is $$\\text{B}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8610", "queId": "702400ac7e094faa81be58f565c29a72", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Tom and Jerry have to mail $$2000$$ envelopes for a new marketing campaign. Jerry can mail $$120$$ envelopes per hour. With Tom\\textquotesingle s help, they can get the job done in $$10$$ hours. How long will it take Tom to finish the job by himself? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"], "answer_analysis": ["Working together: $$2000\\div10=200$$ envelopes per hour. Tom: $$200-120=80$$ envelops per hour, $$2000\\div80=25$$ hours. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8612", "queId": "d08b0be5df684e91b08def2b9c5b3777", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A series of colored lanterns are arranged in the pattern: red, red, red, yellow, yellow, red, red, red, yellow, yellow $\\cdots$ The $$50$$\\textsuperscript{th} lantern is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "red "}], [{"aoVal": "B", "content": "yellow "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"], "answer_analysis": ["Since $$50\\div(3+2)=10$$ which has no remainder, the $$50^{\\text{th}}$$ colored lantern is yellow. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8613", "queId": "b4bb2b59517c4a359cc2511ef9f09d2a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a farm, there is an equal number of cows, sheep, and chickens. These animals have $250$ legs in total. How many sheep are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$23$$ "}], [{"aoVal": "C", "content": "$$25$$ "}], [{"aoVal": "D", "content": "$$33$$ "}], [{"aoVal": "E", "content": "$$38$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems"], "answer_analysis": ["Group $1$ of each kind of animals together, and there are $4+4+2=10$ legs in each group. There are $250\\div10=25$ groups, so there are $25$ sheep. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8616", "queId": "8748f948746249edbf509ecce70d72e7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If Kelly was 12 years old 4 years ago, how old will she be 8 years from now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$26$$ "}], [{"aoVal": "D", "content": "$$22$$ "}], [{"aoVal": "E", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["$$12+4+8=24$$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8617", "queId": "2290ac52a3ed4007a91061996bb73f93", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$20$$ students in a class lining up for recess. Mike is the $$7$$\\textsuperscript{th} counting from front to back. How many students are behind Mike? What is his position counting from back to front? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$, $$13^{\\rm th}$$ "}], [{"aoVal": "B", "content": "$$13$$, $$14^{\\rm th}$$ "}], [{"aoVal": "C", "content": "$$13$$, $$12^{\\rm th}$$ "}], [{"aoVal": "D", "content": "$$14$$, $$13^{\\rm th}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Order of one Character"], "answer_analysis": ["The number of students behind Mike plus the position of Mike equals the total number of students in the class. So there are $$13$$ students behind Mike: $$20-7=13$$. However Mike is not included in these $$13$$ students, which means Mike is the $$14$$\\textsuperscript{th} student counting from back to front. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8621", "queId": "a2374a895c0d4c5189040a6113355cd0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The ratio of your pears to oranges is $$3:7$$, and you have $$15$$ pears. How many oranges do you have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$21$$ "}], [{"aoVal": "D", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"], "answer_analysis": ["$$3:7=15:x→\\dfrac{3}{7}=\\dfrac{15}{x}→3x=105→x=35$$ or $$3$$ multiply by $$5$$ equals $$15$$, so if we multiply $$5$$ by $$7$$, we get $$35$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8622", "queId": "79692c6b3fc3484c957827b9cabc2191", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$10$$ trees are planted at equal distance along a river. The distance between the $$1^{st}$$ and the $$3^{rd}$$ tree is $$20$$ metres. What is the distance between the $$7^{th}$$ and $$9^{th}$$ tree? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$70$$ "}], [{"aoVal": "E", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["They are having the same number of intervals. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8625", "queId": "1e4e6ba34d3c4a658aafadb081495651", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The average of John and Leo's ages is Kelly's age. The average of Kelly and Mila's ages is Leo's age. Of the four children, John is the youngest and Mila the oldest. The average of John and Mila's ages is 11. What is the total of the ages of Kelly and Leo? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["PMC 2019 21 "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8636", "queId": "b4bf9149351d4af181eb7f29fcc16013", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Marcus has $$75$$ toy cars. $$\\frac{1}{5}$$ of his toy cars are black, $$\\frac{2}{15}$$ of the remainder are white, and the rest are grey. He hasmore black toy cars than white toy cars. ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["$75\\div5=15$ toy cars are black. $15\\times4=60$ toy cars are white or grey. $60\\div15\\times2=8$ toy cars are white. He has $15-8=7$ more black toy cars than white toy cars. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8641", "queId": "300193aecaa64ec08f681325c9b5554d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Miya is $3$ years old this year, and her brother is $3$ years older than her. How old her brother will be $2$ years later?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$7$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages"], "answer_analysis": ["When Miya is $3$, her brother is $6$, so $2$~years later, her brother is $8$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8643", "queId": "6b8d401afae44216a0c8d5f60573fc7a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Five years ago, Jennifer\\textquotesingle s age was five times Jason\\textquotesingle s age. Now, Jennifer\\textquotesingle s age is four times Jason\\textquotesingle s age. How old is Jennifer now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$100$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["Let Jason\\textquotesingle s age five years ago be 1 unit. Then Jennifer\\textquotesingle s age was 5 units. Now, Jason\\textquotesingle s age is 1 unit + 5 and Jennifer\\textquotesingle s age is 5 units + 5. We also know that Jennifer\\textquotesingle s age is four times Jason\\textquotesingle s age or 4 x (1 unit + 5) = 4 units + 20. Then:~ 5 units + 5 = 4 units + 20 5 units - 4 units = 20 - 5 1 unit = 15 Jennifer is 5 units + 5 = 5x15 + 5 = 80 years old now. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8646", "queId": "165075983eeb4c76bb07e2b043a909c7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The number of weeks in $$139$$ days is most nearly equal to． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["The number of weeks in $$139$$ days is most nearly $$140\\div 7=20$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8653", "queId": "272937053dac4edc9665c283ce65b173", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When Patience asked her Granddad how old he was, he answered, \"I am $$34$$ now and will be $$33$$ on my birthday.\" She looked confused so he added, \"After being $$50$$ for a year I started counting backwards on each birthday. \" How old will he actually be on his birthday?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$33$$ "}], [{"aoVal": "B", "content": "$$34$$ "}], [{"aoVal": "C", "content": "$$56$$ "}], [{"aoVal": "D", "content": "$$67$$ "}], [{"aoVal": "E", "content": "$$83$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["When Granddad would have claimed to be $$49$$ he was actually $$51$$, $$48$$ when he was actually $$52$$- in every case his claimed age and his real age have a total of $$100$$. So this year his age is $$100-33=67$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8654", "queId": "1a54dc2d189d470ebfb5f48a48505e88", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Calculate: $1^{2}+2^{2}+3^{2}+\\cdots +20^{2}+21^{2}$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$231$$ "}], [{"aoVal": "B", "content": "$$2870$$ "}], [{"aoVal": "C", "content": "$$3311$$ "}], [{"aoVal": "D", "content": "$$53361$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8655", "queId": "625a19f4d2c14ff0ab7eae0950403c2d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In the window of Bradley\\textquotesingle s Bicycle Bazaar there are some unicycles, some bicycles and some tricycles. Laura sees that there are seven saddles in total, thirteen wheels in total and more bicycles than tricycles. How many unicycles are in the window? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems"], "answer_analysis": ["JMC 2017 22 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8656", "queId": "1a56e8d7729b4ea69eac40eb4a08eb24", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Red and green dragons lived in a cave. Each red dragon had $$6$$ heads, $$8$$ legs, and $$2$$ tails. Each green dragon had $$8$$ heads, $$6$$ legs, and $$4$$ tails. There were $$44$$ tails altogether, and there were $$6$$ less green legs than red heads. How many red dragons lived in the cave? ($$2003$$ Math Kangaroo Problems, Level $$5-6$$, Question \\#$$29$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis->Basic Type->Non-typical Types"], "answer_analysis": ["Suppose there are $x$ red dragons and $y$ green dragons. $2x+4y=44$ and $6x-6y=6$. We can get that $y=7$ and $x=8$. Thus, there are $8$ red dragons. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8663", "queId": "4ff3b135fecb4c29a98ff609e49247fe", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$20$$ students in a class lining up for recess. Mike is the $$7$$\\textsuperscript{th} counting from front to back. How many students are behind Mike? What is his position counting from back to front? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$, $$13$$ "}], [{"aoVal": "B", "content": "$$13$$, $$14$$ "}], [{"aoVal": "C", "content": "$$13$$, $$12$$ "}], [{"aoVal": "D", "content": "$$14$$, $$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Order of one Character"], "answer_analysis": ["The number of students behind Mike plus the position of Mike equals the total number of students in the class. So there are $$13$$ students behind Mike: $$20-7=13$$. However Mike is not included in these $$13$$ students, which means Mike is the $$14$$\\textsuperscript{th} student counting from back to front. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8667", "queId": "f5b4f2b295d244909283349d8c038fe2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A bookstore purchases $$20$$ story books for ＄$$820$$. If the bookstore wants to earn ＄$$12$$ for each book, what is the selling price of each book? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$50$$ "}], [{"aoVal": "B", "content": "＄$$51$$ "}], [{"aoVal": "C", "content": "＄$$52$$ "}], [{"aoVal": "D", "content": "＄$$53$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["$$\\frac{820}{20}+12=41+12=53$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8670", "queId": "4b6592860cc547908160da24dfd2a2c5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Henry starts to read a $$290$$-page book on a Monday. He reads four pages every day except on Sundays when he reads $$25$$ pages. He will read the book starting from page~\\uline{~~~~~~~~~~}~next Monday. ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$49$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$240$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["$$25+6\\times 4=49$$，$$49+1=50$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8671", "queId": "1e978c774dbc4d6e94ac3df23435c53c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$10$$ blind boxes on the desk, and each blind box contains two toys. Now there are $$16$$ toys in hands. How many blind boxes remain？(adapted from $$2010$$ Math Kangaroo Problem, Level $$1-2$$, Question \\#$$15$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$$16$$ toys means $$8$$ blind boxes are opened. There are $$10$$-$$8$$=$$2$$ blind boxes that have not been opened. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8674", "queId": "3db2ae7af8ff459987310c5c5b2539d8", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "A salt solution is made by mixing $$8$$ ounces of pure salt and $$32$$ ounces of water. Find the percent concentration of the solution. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$15\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$20\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$25\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$8\\div(8+32)=20\\textbackslash\\%$$. ~~ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8675", "queId": "66fb9f92550b4d94af78dd64ca55fddf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The speed of high-speed train is approximately $$350$$ kilometers per hour, while the walking speed of a person is approximately $$5$$ meters per second. Approximately, how many times is the speed of a high-speed train faster than the walking speed of a person?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2 $$ "}], [{"aoVal": "B", "content": "$$20 $$ "}], [{"aoVal": "C", "content": "$$70 $$ "}], [{"aoVal": "D", "content": "$$200 $$ "}], [{"aoVal": "E", "content": "$$700$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"], "answer_analysis": ["The speed of high-speed train is approximately $$350$$ kilometers per hour, which is approximately $$100$$ meters per second. So its speed is roughly $$20$$ times faster than $$5$$ $$ meters per second. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8676", "queId": "34a7f96474264c658adb82fcc362cb8f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If February is a month that contains Friday $$13^{}\\text{th}$$, what day of the week is February $$1$$st?． ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday　 "}], [{"aoVal": "B", "content": "Monday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Thursday　 "}], [{"aoVal": "E", "content": "Saturday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["We can count backward by days or by weeks. Count a few weeks back to find that February $$6$$ is a Friday. Then count a few days back to find that February $$1$$ is a Sunday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8677", "queId": "1ea0df171d7a49d2a7463b2af7d41c84", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Grandpa suggested dividing all the peanuts between the family members in the following way: one person would get $5$ kilos, two people would get $4$ kilos each, four people would get $2$ kilos each, one person would get $6$ kilos, and one person would not get any peanuts. Grandma suggested dividing the peanuts equally among all of the family members. How many people would get more peanuts in grandma\\textquotesingle s suggestion than grandpa\\textquotesingle s? (adapted from 2005 Math Kangaroo Problem, Level 5-6, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Grandma\\textquotesingle s suggestion: $(1\\times 5 + 2\\times 4+4\\times 2+1\\times 6+1\\times 0)\\div(1+2+4+1+1) = 27\\div9=3$ Thus, there are $4+1=5$ people get more peanuts. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8678", "queId": "6b9d71feffca4bfe8c4e21f51a4a31be", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Study the pattern below. The $$100^{}\\rm {th}$$ letter is . $$A A B B C A A B B C A A B B C A A \\cdots$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$A$$ "}], [{"aoVal": "B", "content": "$$B$$ "}], [{"aoVal": "C", "content": "$$C$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"], "answer_analysis": ["$$100$$~$\\div$ $$5$$ = $$20$$ $$R0$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8679", "queId": "59279935ffd3426bb4136d25d0df86f3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Given that May $2$nd of a given year is a Thursday, what day is May $29$th of the same year? ", "answer_option_list": [[{"aoVal": "A", "content": "Saturday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Tuesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems"], "answer_analysis": ["$29-2=27$ days later, it will be May $29$th. $27\\div7=3R6$, which means May $29$th is Wednesday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8680", "queId": "16a25ba9f8e04f189f791913f6b471b6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $$16$$-quart radiator is filled with water.Four quarts are removed and replaced with pure antifreeze liquid.Then four quarts of the mixture are removed and replaced with pure antifreeze.This is done a third and a fourth time.The fractional part of the final mixture that is water is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{81}{256}$$ "}], [{"aoVal": "B", "content": "$$\\frac{27}{64}$$ "}], [{"aoVal": "C", "content": "$$\\frac{37}{64}$$ "}], [{"aoVal": "D", "content": "$$\\frac{175}{256}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"], "answer_analysis": ["After the first time:$$1\\times \\frac{12}{16}+0\\times \\frac{4}{16}=\\frac{3}{4}$$. After the second time:$$\\frac{3}{4}\\times \\frac{12}{16}+0 \\times \\frac{4}{16}= \\frac{9}{16}$$. After the third time:$$\\frac{9}{16}\\times \\frac{12}{16}+0 \\times \\frac{4}{16}= \\frac{27}{64}$$. After the fourth time:$$\\frac{27}{64}\\times \\frac{12}{16}+0 \\times \\frac{4}{16}= \\frac{81}{256}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8685", "queId": "3dbde30796f94c44b2e263b5bea67847", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "On a map of the Andes, if $2$ $\\text{cm}$ represents $6000$ $\\text{km}$, then ~represents $300$ $\\text{km}$ . ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.1$$ "}], [{"aoVal": "B", "content": "$$0.5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["If $2$ $\\text{cm}$ represents $6000\\text{km}$, $1\\text{cm}$ represents $3000\\text{km}$, and $0.1\\text{cm}$ represents $300\\text{km}$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8692", "queId": "a24849a03db44c7f8821c2ead15a0ecd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My sister runs $$10\\text{km}$$ per hour, and I run $$2\\text{km}$$ in $$15$$ minutes. If we both run for $$2$$ hours, my sister will run$$\\text{km}$$ farther than I will. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["I run $$2\\text{km}$$ in $$15$$ minutes, or $$8\\text{km}$$ in $$1$$ hour. In $$2$$ hours, I will run $$16\\text{km}$$ and my sister will run $$20\\text{km}$$. She will run $$4\\text{km}$$ farther than I will. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8694", "queId": "2bc19d01cb93432f890d95c6f9355ccd", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In 2010 about 120 million digital still cameras were sold worldwide. By 2018 this number had decreased by 85\\%. About how many million digital still cameras were sold in 2018? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$28$$ "}], [{"aoVal": "C", "content": "$$38$$ "}], [{"aoVal": "D", "content": "$$48$$ "}], [{"aoVal": "E", "content": "$$58$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["$120\\times（1-85\\textbackslash\\%）=18$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8700", "queId": "2bc5b05b78b54e47b3e54627d8cb3978", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Monica arrived in the Kangaroo Camp on July 25th in the morning and left the camp on August 3rd in the afternoon. How many nights did she sleep in the camp? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["July has 31 days. She arrive on morning of July 25. From July 25 to 31, there are 7 nights that she slept in the camp. Then she slepft for 2 days in August, since she left on the afternoon Aug 3 already. Hence, 2=7=9 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8701", "queId": "d099cad18be84975900c73c05f9e8596", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "There are three books Chinese, Math, and English. Sissy wants to put them in the bookcase. How many ways are there for the three books to put? List out all the ways. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["List out all the possible ways in order. $C A E$ $C E A$ $A C E$ $A E C$ $E C A$ $E A C $ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8703", "queId": "4b76669ce26f4c83b9cf2b166fd049e1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a fruit stall, there are 25 apples. There are 9 fewer apples than oranges. How many oranges are there in the fruit stall? ", "answer_option_list": [[{"aoVal": "A", "content": "$$17$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$34$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$25+9=34$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8706", "queId": "2306531494994d67b8623f7603101c79", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "On a map of the Andes, if $2$ $\\text{cm}$ represents $6000$ $\\text{km}$, then ~represents $300$ $\\text{km}$ . ", "answer_option_list": [[{"aoVal": "A", "content": "$$0.1$$ "}], [{"aoVal": "B", "content": "$$0.5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["If $2$ $\\text{cm}$ represents $6000\\text{km}$, $1\\text{cm}$ represents $3000\\text{km}$, and $0.1\\text{cm}$ represents $300\\text{km}$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8707", "queId": "de8086cc231940be9a4c3751f6365733", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Chloe has＄$$7$$. She is going to buy $$6$$ pens, and each costs $90$ cents. She also buys a certain number of pencils, and each costs $$50$$ cents. How many pencils at most can she buy? (Adapted from 2007 Math Kangaroo Problem, Level 3-4, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$7$ dollars =~ $700$ cents $(700-6\\times90)\\div50=3R10$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8714", "queId": "ab912e8d10d44ea89d0e2d0eef45faf5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Isabella must take four $100$-point tests in her math class. Her goal is to achieve an average grade of $95$ on the tests. Her first two test scores were $97$ and $91$. After seeing her score on the third test, she realized she can still reach her goal. What is the lowest possible score she would have made on the third test? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ "}], [{"aoVal": "B", "content": "$$92$$ "}], [{"aoVal": "C", "content": "$$95$$ "}], [{"aoVal": "D", "content": "$$96$$ "}], [{"aoVal": "E", "content": "$$97$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Isabella wants an average grade of $95$ on her $4$ test; this also means that she wants the sum of her test scores to be at least $95\\times 4=380$ (if she goes over this number, she\\textquotesingle ll be over the goal!). She\\textquotesingle s already taken two tests, which sum to $97+91=188$, which means she needs $380-188=192$ more points to achieve her desired average. In order to minimize the score on the third test, we assume that Isabella will receive all $100$ points on the fourth test. Therefore, the lowest score on the third test would be $192-100=92$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8717", "queId": "1ab92ac7213c4fed915c07d69575af43", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "\\textbf{In the setting of the previous problem, about what percent of the variation in the number of service calls is explained by the linear relation between number of service calls and number of machines?~} ", "answer_option_list": [[{"aoVal": "A", "content": "86\\% "}], [{"aoVal": "B", "content": "93\\% "}], [{"aoVal": "C", "content": "74\\% "}], [{"aoVal": "D", "content": "None of the above "}], [{"aoVal": "E", "content": "\\textbf{Can't tell from the information given} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$R^{2} = r^{2} = 0.86^{2} = 0.7396$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8725", "queId": "5010dd64822146b69b2a5055c3572558", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Otto the octopus needs $$2$$ tentacles to juggle up to $$3$$ balls. If Otto uses all $$8$$ tentacles, Otto can juggle up to balls. ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["Otto needs $$2$$ tentacles to juggle up to $$3$$ balls. Using $$8=4\\times2$$ tentacles, Otto can juggle up to $$4\\times3 = 12$$ balls. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8737", "queId": "2be566b670084b3fba84deaddf00ce87", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Lucy was $$20$$ years old when Bill was $$12$$. Now, Bill is $$17$$ years old. How old is Lucy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$21$$ "}], [{"aoVal": "D", "content": "$$23$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["The age difference between Lucy and Bill is $$20~-- 12 = 8$$, which will not change. Thus, Lucy is $$17 + 8 = 25$$ years old. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8745", "queId": "b9749b14654d47afb8ff37b26d113196", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Olivia has $32$ clothes, $4$ of them are yellow, $10$ are blue, $13$ are purple, and the others are white. Suddenly the power is off, and it is all black in the room. At least how many clothes should Olivia pick in order to guarantee that she gets $8$ clothes in the same color? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$4+5+7+7+1=24$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8746", "queId": "9470b5e9b9f141ecaddfddd41f59334c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jack mixed $20$ grams of sugar with $30$ grams of water. What is the percent concentration of the sugar solution? Then Jack added $50$ grams of water. What is the percent concentration the sugar solution? ", "answer_option_list": [[{"aoVal": "A", "content": "$$40 \\textbackslash\\% $$; $$20\\textbackslash\\% $$. "}], [{"aoVal": "B", "content": "$$40 \\textbackslash\\% $$; $$25 \\textbackslash\\% $$. "}], [{"aoVal": "C", "content": "$$50 \\textbackslash\\% $$; $$20 \\textbackslash\\% $$. "}], [{"aoVal": "D", "content": "$$50 \\textbackslash\\% $$;~$$25 \\textbackslash\\% $$. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems->Calculating Solvent from Solution and Solute"], "answer_analysis": ["$n\\_1=\\frac{20}{20+30}\\times100\\textbackslash\\%=40\\textbackslash\\%$; $n\\_2=\\frac{20}{20+30+50}\\times100\\textbackslash\\%=20\\textbackslash\\%$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8748", "queId": "1af51f519342449c9e0685e658bbc883", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Colin has $$70$$ stamps. He has $$7$$ times as many stamps as Ben. How many more stamps does Colin have than Ben? ", "answer_option_list": [[{"aoVal": "A", "content": "$$73$$ "}], [{"aoVal": "B", "content": "$$70$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems"], "answer_analysis": ["$$70 \\div10 = 7$$ $$70-10=60$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8749", "queId": "82ce579b479f4a579f72930e17ba5628", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a certain year, June $$24$$\\textsuperscript{th}~is Thursday. What day is August $$27$$\\textsuperscript{th~}in this year? $\\textasciitilde$ ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Friday "}], [{"aoVal": "E", "content": "Saturday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Counting from June $$24$$\\textsuperscript{th}, after $30-24=6$ days it is June $$30$$\\textsuperscript{st}. After $58$ days it is August $$27$$\\textsuperscript{th}. In total, there are $6+58=64$ days. $64\\div 7 =9R1$, which means August $$27$$\\textsuperscript{th~}is Friday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8750", "queId": "990de1b72a4646019e3b400f1d95497c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A tank filled with 200 litres of water weighs 350kg. The same tank filled with 150 litres of water weighs 315kg. What is the weight of the empty tank? ", "answer_option_list": [[{"aoVal": "A", "content": "$$120$$kg "}], [{"aoVal": "B", "content": "$$150$$kg "}], [{"aoVal": "C", "content": "$$165$$kg "}], [{"aoVal": "D", "content": "$$210$$kg "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"], "answer_analysis": ["T + 200L = 350kg $\\cdots $ ① -) T + 150L = 315kg $\\cdots $ ② \\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_ (50L = 35kg) x3 = 150L = 105kg 315kg - 105kg = 210kg "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8751", "queId": "594713f4e0a54955bbbc177e8ebb4478", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Esther made $$8$$ paper stars. Faiza made $$4$$ times as many paper stars as Esther did. Gurmit made $$5$$ times as many paper stars as Esther did, How many paper stars did the three boys make altogether? ", "answer_option_list": [[{"aoVal": "A", "content": "$$64$$ "}], [{"aoVal": "B", "content": "$$80$$ "}], [{"aoVal": "C", "content": "$$144$$ "}], [{"aoVal": "D", "content": "$$152$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"], "answer_analysis": ["omitted "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8754", "queId": "172a6dbdb43948c794e913ba773dbe50", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Debbie bought a loaf of bread for $$$4$$. She paid for the bread with a $$$10$$ note. How much change did Debbie receive? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$$4$$ "}], [{"aoVal": "B", "content": "$$$6$$ "}], [{"aoVal": "C", "content": "$$$14$$ "}], [{"aoVal": "D", "content": "$$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["$$10-4=6$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8755", "queId": "877194e213ef49bb85a4188c792afc5d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Six rectangles each with a common base width of $2$ have lengths of $1,4,9,16,25$, and 36 . What is the sum of the areas of the six rectangles? (2014 AMC 8, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$91$$ "}], [{"aoVal": "B", "content": "$$93$$ "}], [{"aoVal": "C", "content": "$$162$$ "}], [{"aoVal": "D", "content": "$$182$$ "}], [{"aoVal": "E", "content": "$$202$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["The sum of the areas is equal to $2 \\cdot 1+2 \\cdot 4+2 \\cdot 9+2 \\cdot 16+2 \\cdot 25+2 \\cdot 36$. This is equal to $2(1+4+9+16+25+36)$, which is equal to $2 \\cdot 91$. This is equal to our final answer of (D) 182 . "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8756", "queId": "4701f0a24cb44deb958dd0da2441fe6f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My old printer printed $$13$$ pages in $$3$$ seconds. My new printer prints $$21$$ pages in $$2$$ seconds. In $$6$$ seconds my new printer printsmore pages than my old one could have. ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$27$$ "}], [{"aoVal": "D", "content": "$$37$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["My old printer printed $$13$$ pages in $$3$$ seconds or $$26$$ pages in $$6$$ seconds. My new printer prints $$21$$ pages in $$2$$ seconds or $$63$$ pages in $$6$$ seconds. The difference is $$63 - 26=37$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8780", "queId": "397ac5a098ae4c5dac1059df62e3d786", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "March $$12$$th, $$2012$$ was a Monday. What day was May $$1$$st, $$2015$$? ", "answer_option_list": [[{"aoVal": "A", "content": "Tuesday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Friday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["March $$12$$th, $$2013$$: Tuesday March $$12$$th, $$2014$$: Wednesday March $$12$$th, $$2014$$: Thursday $(31-12)+30+1=50$, $50\\div 7=7\\textbackslash{} \\rm r \\textasciitilde1$, so it was Friday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8785", "queId": "a25b23b388c744a6afa341d8d1a09bed", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2014 P2 Q10 Tim is 8 years old and Sally is 4 years old. How old will Sally be when Tim is 14 years old? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["8 + 6 = 14 4 + 6 = 10 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8788", "queId": "a25bd2d10423408bbc69d70d7673969b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Pip is 10 years and 2 months old. Bud is 124 months old. Bob has been alive for 3660 days. Who is the oldest? ", "answer_option_list": [[{"aoVal": "A", "content": "Pip "}], [{"aoVal": "B", "content": "Bud "}], [{"aoVal": "C", "content": "Bob "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["omitted "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8792", "queId": "8b363b447f464faba7b50d1941060b6a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "There are some ducks and chickens in a farm. The number of chickens is $10$ more than ducks.The number of ducks is half the number of chicken. How many ducks and chickens are there in the farm? ~ ", "answer_option_list": [[{"aoVal": "A", "content": "$26$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$39$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$10+10+10=30$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8795", "queId": "350e77ab80a84b6ea8f872e947a0badc", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "I ate half of an apple pie on Saturday and two thirds of the remainder on Sunday. What fraction of the pie was left for Monday? ", "answer_option_list": [[{"aoVal": "A", "content": "None "}], [{"aoVal": "B", "content": "$\\frac12$ "}], [{"aoVal": "C", "content": "$\\frac13$ "}], [{"aoVal": "D", "content": "$\\frac23$ "}], [{"aoVal": "E", "content": "$\\frac16$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["$(1-\\frac12)\\times(1-\\frac23)=\\frac12\\times\\frac13=\\frac16$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8800", "queId": "67301634161942b49134ba39bd5b96ae", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There were some cupcakes in a bakery. First, Jade ate half of the cupcakes. Then, Neil ate half of the remaining cupcakes. Finally, Terry ate $6$ and there were $$2$$ cupcakes left. At beginning, how many cupcakes were there in the bakery? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$6+2=8$$ $$8+8=16$$ $$16+16=32$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8821", "queId": "b044bdc50e6948c2939430d6f499c1db", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If today is Tuesday, what day was it $$76$$ days ago? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$Monday "}], [{"aoVal": "B", "content": "$$$$Tuesday "}], [{"aoVal": "C", "content": "$$$$Wednesday "}], [{"aoVal": "D", "content": "$$$$Thursday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Today is Tues. $$77$$ days ago was Tues. $$76$$ days ago was Wed. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8822", "queId": "35258801683b477b94c336af438813b8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There is a piece of wire. First, half of the piece is used. Then, half of the remaining piece is used. Next, $$16$$ meters are used. Finally, $$9$$ meters are left. The original piece of the wire is~\\uline{~~~~~~~~~~}~meters long. ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$64$$ "}], [{"aoVal": "D", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$16 + 9 = 25$$ $$25 + 25 =50$$ $$50 + 50 =100$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8827", "queId": "c2cc718040e04ca4a0c83b743af94a37", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Karl is now $10$ years old, and Ala is $3$ years old. How many years from now will Karl be twice as old as Ala? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$1$$ "}], [{"aoVal": "E", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["The age difference is equal to $10-3=7$. When the age of Karl is twice the age of Ala, the age of Ala will be equal to the age difference which is $7$. Thus, it will pass $7-3 = 4$ years. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8828", "queId": "1b7ffadac1ea48809002660767616994", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a certain year, March $$27$$\\textsuperscript{th}~is Friday. What day is April $$24$$\\textsuperscript{th~}in this year? $\\textasciitilde$ ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Friday "}], [{"aoVal": "E", "content": "Saturday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Counting from March $$27$$\\textsuperscript{th}, after $31-27=4$ days it is March $$31$$\\textsuperscript{st}. After $24$ days it is April $$24$$\\textsuperscript{th}. In total, there are $4+24=28$ days. $28\\div 7 =4$, which means April $$24$$\\textsuperscript{th~}is Friday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8830", "queId": "23a915e78ec143738053a03e90547b02", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "How many digits have to be written in order to write down every number from $$1$$ to $$100$$ inclusive? ($$2007$$ Math Kangaroo Problem, Level $$3-4$$, Question \\#$$23$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$150$$ "}], [{"aoVal": "C", "content": "$$190$$ "}], [{"aoVal": "D", "content": "$$192$$ "}], [{"aoVal": "E", "content": "$$200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem->Correspondence between Numbers and Page Numbers->Applying the Total Number of Numbers"], "answer_analysis": ["$1$-digit numbers: $9\\times1=9$ digits. $2$-digit numbers: $90\\times2=180$ digits. $3$-digit numbers: $1\\times3=3$ digits. Total: $9+180+3=192$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8833", "queId": "1b8a0463db0c4bebaeef07997eace089", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ten years ago, the sum of the ages of my mother and father was $$71$$. What is the sum of their ages today? ", "answer_option_list": [[{"aoVal": "A", "content": "$$51$$ "}], [{"aoVal": "B", "content": "$$61$$ "}], [{"aoVal": "C", "content": "$$81$$ "}], [{"aoVal": "D", "content": "$$91$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["Ten years ago, the sum of the ages of my mother and father was $$71$$. Each has aged $$10$$ years, so the sum of their ages is now $$91$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8836", "queId": "30bf13245023460e8997d7111f174a8d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The triplets Adam, Jan and Stas and their sister Marysia who is four years older than them were $24$ years old together three years ago. How old is Marysia today? (2001 Math Kangaroo Problem, Level 5-6, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["Adam, Jan and Stas were $(24-4)\\div4=5$ years old three years ago. Marysia was $5+4=9$ years old. Thus, Marysia is $9+3=12$ years old. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8838", "queId": "50527e768fc64e4a8028f90a9868ed8b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A mother cut a cake into $$12$$ equal slices. Her four children had a slice each and she had one too. Later, a neighbour ate four slices. What percentage of the cake was left at the end of the day? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$10\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$25\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$35\\textbackslash\\%$$ "}], [{"aoVal": "E", "content": "$$50\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["$12-(4\\times1)-1-4=3$ $\\frac{3}{12}\\times100\\textbackslash\\%=25\\textbackslash\\%$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8839", "queId": "30bf68fb808c4f1b8110a71bc503371d", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A worm is staying at the bottom of a well with a depth of $$13$$ metres. If it climbs up $$4$$ metres in the daytime and slips down $$1$$ metre at night, which day will it climb up to the ground? ", "answer_option_list": [[{"aoVal": "A", "content": "The $$4$$th day "}], [{"aoVal": "B", "content": "The $$5$$th day "}], [{"aoVal": "C", "content": "The $$6$$th day "}], [{"aoVal": "D", "content": "The $$7$$th day "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"], "answer_analysis": ["It climbs up $$4$$ metres in the day time and slips down $$1$$ metre at night, so it climbs up $$3$$ metres in a whole day. For the first $$3$$ days, it climbs $$9$$ metres. During the day time of the forth day, it climbs $$4$$ metres and reaches the ground. Then it needs four days to climb up to the ground. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8854", "queId": "b4ece9a28c0f4c7693d6b175f6dd1203", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A bag of toffee is $7$ dollars, a bag of cotton candy is $6$ dollars, and a bag of orange candy is $15$ dollars. Now, the candy shop decides to mix $40$ bags of toffee, $50$ bags of cotton candy, and $10$ bags of orange candy for $100$ bags of assorted candy. What should be the price of the assorted candy in dollars to keep the total revenue unchanged? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7.3$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9.5$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Total revenue: $40\\times 7+50\\times 6+10\\times 15=730$ dollars A bag of assorted candy: $$730\\div 100=7.3$$ dollars "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8860", "queId": "8791404a6c9247669ac325195ce17039", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A drawer contains $10$ yellow socks, $8$ blue socks and $4$ pink socks. Bella picks socks from the drawer without looking. What is the smallest number of socks she must pick to make sure she has at least one sock of each colour? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$19$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Extreme Value of Average"], "answer_analysis": ["$10+8+1=19$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8861", "queId": "b04cc06ceb2f45bcb14bc873262b6eca", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Peter has some toy cars, and Paul has $$4$$ more toy cars than Peter. Altogether they have $$36$$ toy cars. How many toy cars does Paul have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference->Sum and Differences Problems with multiple Variables"], "answer_analysis": ["Paul has $$(36 + 4) \\div 2 = 20$$ toy cars. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8864", "queId": "6749543a4c4e483eaa09c7465aa1dfba", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "There is an equation with all integers in the upper squares, and the answer on the right side is only the approximation of $$\\frac{\\square }{3}+\\frac{\\square }{5}+\\frac{\\square }{7}\\approx 1.16$$ after rounding off. The numbers in each of the three upper squares of the equation are~\\uline{~~~~~~~~~~}~in order. ", "answer_option_list": [[{"aoVal": "A", "content": "$1,2,3$ "}], [{"aoVal": "B", "content": "$1,3,5$ "}], [{"aoVal": "C", "content": "$1,4,3$ "}], [{"aoVal": "D", "content": "$2,1,2$ "}], [{"aoVal": "E", "content": "$2,3,5$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"], "answer_analysis": ["NA "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8869", "queId": "39c3062b5afa4c81857a43ad5d4e3b72", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Nancy has $23$ donuts. She gives one donut to Sana, and then Nancy has $10$ more donuts than Sana. At beginning, how many donuts does Sana have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$23-1=22$$ $$22-10=12$$ $$12-1=11$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8871", "queId": "1fbd323f929a46cf8b4ae86af94d47e5", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Joann\\textquotesingle s birthday in $$2020$$ was May $$10$$\\textsuperscript{th}, which was Sunday. Elizabeth\\textquotesingle s birthday in $$2020$$ was June $$21$$\\textsuperscript{st}. What day of the week is Elizabeth\\textquotesingle s birthday on? ", "answer_option_list": [[{"aoVal": "A", "content": "Thursday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Sunday "}], [{"aoVal": "D", "content": "Tuesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["It passed $$31-10 + 21 = 42$$ days in total. Since $$42 \\div 7 = 6$$, it was Sunday. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8882", "queId": "2c848cf8a3684a8fbbbdb0b22ade62d0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A sugar solution is made by mixing $$7$$ ounces of sugar and $$21$$ ounces of water. Find the percent concentration of the solution. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$\\% "}], [{"aoVal": "B", "content": "$25$\\% "}], [{"aoVal": "C", "content": "$30$\\% "}], [{"aoVal": "D", "content": "$33.3$\\% "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$7\\div(7+21)=25\\textbackslash\\%$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8885", "queId": "8b52eb5b2f384128a9beecce5b84956b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ellis\\textquotesingle s Eel Emporium contains a large tank holding three different types of eel: electric eels, moray eels and freshwater eels. A notice on the tank reads as follows: All the eels are electric eels except for $$12$$ All the eels are moray eels except for $$14$$ All the eels are freshwater eels except for $$16$$ How many eels are in the tank? ", "answer_option_list": [[{"aoVal": "A", "content": "$$42$$ "}], [{"aoVal": "B", "content": "$$33$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems"], "answer_analysis": ["Let the number of electric eels be $$x$$, the number of moray eels be $$y $$ and the number of freshwater eels be $$z$$. The information on the notice tells us that $$y + z = 12$$, $$x + z = 14$$ and $$x + y = 16$$. When you add these three equations, you obtain $$2x + 2y + 2z = 42$$ and hence $$x + y + z = 21$$. Therefore the number of eels in the tank is $$21$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8886", "queId": "2c85f85b43c547aa8b4c3517991676de", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Tom and Ben played a quiz game. $$2$$ points for a correct answer. Tom got $$5$$ questions right, Ben got $$8$$ questions right. How many more points than Ben did Tom get?~(adapted from $$2021$$ Math kangaroo, Level $$1-2$$, Question \\#$$14$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["August got $$5\\times2=10$$ points, and Ben got $$8\\times2=16$$ points. $$16-10=6$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8887", "queId": "2c86d070ab8c45b991b7bdfde4be189b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Farmer Baar has 36 sheep, some pink and the rest white. There are twice as many pink sheep as white sheep. How many of the sheep are pink? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple->Sum and Multiple of Two Variables"], "answer_analysis": ["$36\\div (1+2)=12, 12\\times2=24$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8888", "queId": "6755c48c72454835b9e9b7c4fbca6f8a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "John is 33 years old. His three sons are 5, 6 and 10 years old. In how many years will the three sons together be as old as their father? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["Let x be the number of years needed for the ages of the three sons sum up to be equal to their dad\\textquotesingle s age. Their dad\\textquotesingle s age is then 33+x, while the sum of the sons\\textquotesingle{} age is (5+x) x (6+x)+(10+x)=21+3x. We have the following equation: 21+3x = 33+x 2x = 12 x = 6 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8892", "queId": "67572310a8bb4d58bf7d1502b5e12761", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In Grade $3$, Amy\\textquotesingle s height was $136$ cm. When she was Grade $4$, the doctor said that her height was $15$cm taller than last year. What was her height in Grade $4$? (adapted from $$2019$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$3$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$15$ cm "}], [{"aoVal": "B", "content": "$137$ cm "}], [{"aoVal": "C", "content": "$151$ cm "}], [{"aoVal": "D", "content": "$161$ cm "}], [{"aoVal": "E", "content": "$167$ cm "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"], "answer_analysis": ["$136+15=151$ cm "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8897", "queId": "5e26fa34813e424e8e6ee5a179f75bb9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Blii and Elsa went to see a movie together and sat in the same row. Ela was in the sixth row counting from the front of the room and Elsa was seated in the fourteenth counting from the end. How many rows in their room? (Adapted from 2001 Math Kangaroo Problem, Level 3-4, Question \\#13) ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line"], "answer_analysis": ["$6 + 14 - 1 = 19$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8901", "queId": "5074192cee714c75a3a52358dd875594", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Several people buy a boardgame together. If each person pays $60$ dollars, $60$ more dollars are needed for the payment. If each person pays $70$ dollars, $10$ dollars are remaining. How much is the boardgame in dollars? ", "answer_option_list": [[{"aoVal": "A", "content": "$$600$$ "}], [{"aoVal": "B", "content": "$$480$$ "}], [{"aoVal": "C", "content": "$$690$$ "}], [{"aoVal": "D", "content": "$$550$$ "}], [{"aoVal": "E", "content": "$$720$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems"], "answer_analysis": ["$$(60+10)\\div (70-60)=7$$ $$60\\times7+60=480$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8905", "queId": "9936982de95b4611810f791046ef4c13", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Farmer Dunphy has $$100$$ metres of fencing. He wants to make a closed rectangular pen. He uses a long wall for one of the sides. Each side of the pen is a whole number in metres. What is the largest area that the pen can be? ", "answer_option_list": [[{"aoVal": "A", "content": "$$125\\text{m}^{2}$$ "}], [{"aoVal": "B", "content": "$$625\\text{m}^{2}$$ "}], [{"aoVal": "C", "content": "$$1000\\text{m}^{2}$$ "}], [{"aoVal": "D", "content": "$$1250\\text{m}^{2}$$ "}], [{"aoVal": "E", "content": "$$2500\\text{m}^{2}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems Combined with Geometry->Tile Word Problems"], "answer_analysis": ["$a+2b=100$, when $$a=2b=50$$, the largest area is $$50\\times (50\\div 2)=1250$$ m\\textsuperscript{2}. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8906", "queId": "f5d48c82aee34181ac89ab558e8f39c8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many fingers are there on a dozen pairs of gloves if each glove has $$5$$ fingers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["There are $$2\\times5 =10$$ fingers on a pair of gloves. $$\\text{A}$$ dozen pairs have $$12 \\times 10 = 120$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8908", "queId": "5e2d2c0604854be086310a7e2f2d567f", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Kevin got $$80\\textbackslash\\%$$ of the problems correct on a $$25-$$problem test, $$ 90\\textbackslash\\%$$ on a $$40-$$problem test, and $$70\\textbackslash\\%$$ on a $$10-$$problem test. What percent of all the problems did Kevin answer correctly? (2010 AMC8 Problem, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$64$$ "}], [{"aoVal": "B", "content": "$$75$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$84$$ "}], [{"aoVal": "E", "content": "$$86$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["Ryan answered $$(0.8)(25)=20$$ problems correct on the first test, $$(0.9)(40)=36$$ on the second, and $$(0.7)(10)=7$$ on the third. This amounts to a total of $$ 20+36+7=63$$ problems correct. The, total number of problems is $$25+40+10=75$$.Therefore, the percendage is $$\\frac {63}{75}\\to(\\rm D)84$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8912", "queId": "3100e88ffd7d4d76a81d65e1707a67e5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A teacher distributes scorecards to students. If everyone gets $3$ cards, there will be a shortage of $12$ cards. If everyone gets $2$ cards, all these cards will just be divided. Then, how many students are there in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems"], "answer_analysis": ["If $2-1=1$ fewer card is given to students, the situation would transfer from \\textquotesingle a shortage of $12$ cards\\textquotesingle~ to \\textquotesingle all cards are just divided\\textquotesingle. So, there are in total $12$ students. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8915", "queId": "f5d5e3d976c0471a8ee7c4fe0438c3d3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2015 P2 Q5 Today, Wednesday, 8th of April 2015, is the day of the SASMO competition and your friend says tha the Singapore Math Kangaroo Contest was 14 days ago. On which day was the SMKC? ", "answer_option_list": [[{"aoVal": "A", "content": "23rd of March, Monday "}], [{"aoVal": "B", "content": "24th of March, Tuesday "}], [{"aoVal": "C", "content": "25th of March, Wednesday "}], [{"aoVal": "D", "content": "26th of March, Thursday "}], [{"aoVal": "E", "content": "27th of March, Friday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Draw table. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8920", "queId": "cc1ff60502104a48a1354527311ba3b2", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Suppose $20 \\textbackslash\\%$ of $x$ equals $30 \\textbackslash\\%$ of $y$. What percentage of $y$ is $x$ ? (adapted from 2020 AMC 8, Question 15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$75$$ "}], [{"aoVal": "D", "content": "$150$ "}], [{"aoVal": "E", "content": "$$300$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Since $20 \\textbackslash\\%=\\frac{1}{5}$, multiplying the given condition by 5 shows that $x$ is $30 \\cdot 5=(\\mathbf{C}) 150$ percent of $y$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8922", "queId": "2caaf37b6b6642b4acbdbc5ada15bccd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A shop purchased some tennis rackets at ＄$$100$$ each, and then sold them at ＄$$150$$ each. How much did the shopkeeper earn for $$10$$ rackets? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$200$$ "}], [{"aoVal": "B", "content": "＄$$250$$ "}], [{"aoVal": "C", "content": "＄$$300$$ "}], [{"aoVal": "D", "content": "＄$$500$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$$(150-100)\\times 10 = 500$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8923", "queId": "50802ffd15ed4c4ba440f0fa2e601176", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jack bought a batch of goods that he hoped to earn a $$50\\textbackslash\\%$$ profit after selling them. On the first day, he sold $$60\\textbackslash\\%$$ of his goods at a profit of $$50\\textbackslash\\%$$. On the second day, he sold all remaining goods for a discount. If the total profit is $$76\\textbackslash\\%$$ of the planned profit, what was the discount rate? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$21\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$22\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$24\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"], "answer_analysis": ["Let the cost for the batch of goods be $$m$$ dollars. Jack finally earned: $$m\\times 50\\textbackslash\\%\\times 92\\textbackslash\\%=0.38m$$. On the first day he earned: $$m\\times 60\\textbackslash\\%\\times 50\\textbackslash\\%=0.30m$$. Profit for the second day: $$0.38m-0.30m=0.08m$$. Profit rate for the second day: $$\\frac{0.08m}{\\left( m-0.6m \\right)}=20\\textbackslash\\%$$. Percentage discount: $$1-\\frac{\\left( 1+20\\textbackslash\\% \\right)}{\\left( 1+50\\textbackslash\\% \\right)}=20\\textbackslash\\%$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8925", "queId": "310dda11c52c4ce5a97b92e7a7b2bdf7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Paul has $13$ books, and Jenny has $6$ more books than Paul. How many books do Paul and Jenny have together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$22$$ "}], [{"aoVal": "D", "content": "$$23$$ "}], [{"aoVal": "E", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Jenny has $$13 + 6 = 19$$ books. So, there are $13 + 19 = 32$ books in total. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8926", "queId": "c7804702c9c1402f9634b0e57b1d60d5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the land of Seuss, a plate of green eggs costs twice as much as a plate of ham. If a plate of ham costs $$5$$￠, how much would $$1$$ pay for $$2$$ plates of green eggs and $$3$$ plates of ham? ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$￠ "}], [{"aoVal": "B", "content": "$$35$$￠ "}], [{"aoVal": "C", "content": "$$30$$￠ "}], [{"aoVal": "D", "content": "$$25$$￠ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"], "answer_analysis": ["Since a plate of green eggs costs twice as much as a plate of ham, a plate of the eggs costs $$10$$￠. The cost of $$2$$ plates of eggs and $$3$$ plates of ham is $$2\\times 10$$￠$$+3\\times 5$$￠$$=20$$￠$$+15$$￠$$=35$$￠. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8930", "queId": "59a124cef42d4c94b831ab0e07e1a800", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of $$2$$ positive whole numbers is $$3$$ times their difference. When the larger is divided by the smaller, the quotient is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Difference and Multiple"], "answer_analysis": ["The sum must be a multiple of $$3$$. There are many examples, e.g., $$2\\And 1$$, $$4\\And 2$$, $$10\\And 5$$, etc. The quotient is always $$2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8933", "queId": "39ffe4f8bfe241af94c729249f49caca", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a mathematics contest with ten problems, a student gains $$5$$ points for a correct answer and loses $$2$$ points for an incorrect answer. If Olivia answered every problem and her score was $$29$$, how many correct answers did she have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Suppose Olivia has $$x$$ correct answers. $$5x-2(10-x)=29$$, $$x=7$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8937", "queId": "c2e27acf781747ed887f201c3f1902eb", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "At the 2018 Tompkins County Fair a vendor is offering a \"fair special\" on shoes. If you buy one pair of shoes at the regular price of $\\textbackslash$ 80$, you get a second pair at a $34\\textbackslash\\%$ discount, and a third pair at half the regular price. James took advantage of the \"fair special\" to buy three pairs. What percentage of the $\\textbackslash$ 240$ regular price did he save? (adapted from 2013 AMC 8, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$28$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$38$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["First, the amount of money one will pay for three hats without the discount $=\\textbackslash$ 240$. Then, find the amount of money using the discount: $80+0.66\\times 80+\\frac{1}{2} \\times 80=\\textbackslash$ 172.8$. Finding the percentage yields $\\frac{172.8}{240}=72\\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-72\\textbackslash\\%= 28\\textbackslash\\%$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8942", "queId": "2032f7b96fcf4f2c8499a135043eda25", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I had $$3$$ dozen socks in my drawer, but I lost $$2$$ pairs. How many socks do I now have in my drawer? ", "answer_option_list": [[{"aoVal": "A", "content": "$$32$$ "}], [{"aoVal": "B", "content": "$$34$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["I had $$3$$ dozen socks in my drawer, which is $$36$$ socks. When I lost $$2$$ pairs, I lost $$4$$ socks, so I had $$32$$ socks left. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8944", "queId": "2880102c561847a79d4d988e65715c64", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mike and Jack compete in the long jump. Mike jumps twice as far as Jack once. Mike jumps three times. How many times can jack jump the distance equal to Mike？(adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["We can imagine the distance of Jack\\textquotesingle s long jump as $1$, and the distance of Mike\\textquotesingle s long jump as $2$. The distance that Mike jumps three times is $2$$\\times$$3$=$6$. ~Jack needs to jump $6$$\\div$$1=$$6$ times. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8945", "queId": "5e435ff9ea0444c4b3ad0e90a8861aef", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "NBA playoffs are held annually. The $62$\\textsuperscript{nd~}NBA playoffs were held in $2008$. When Cindy was $7$ years old, the $66$\\textsuperscript{th}~NBA playoffs were held. How old is Cindy in $2022$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$17$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$66-62+2008=2012$ $7+(2022-2012)=17$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8955", "queId": "20475d6f4e4947128f5e7cd35367a37f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Rina bought a handbag for＄$$60$$ at a discount of $$20\\textbackslash\\%$$. Ana paid＄$$67.5$$ for the same handbag. What was the discount rate given to Ana? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$12\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$15\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$18\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["Original price: $$60\\div \\left( 1-20\\textbackslash\\% \\right)=75$$. Discount for Ana: $$\\left( 75-67.5 \\right)\\div 75=10\\textbackslash\\%$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8956", "queId": "677587cf2d7f445d86998360b3f47c1a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2014 P2 Q5 What number between 37 and 47 is exactly divisible by both 2 and 3? ", "answer_option_list": [[{"aoVal": "A", "content": "$$38$$ "}], [{"aoVal": "B", "content": "$$39$$ "}], [{"aoVal": "C", "content": "$$42$$ "}], [{"aoVal": "D", "content": "$$44$$ "}], [{"aoVal": "E", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division"], "answer_analysis": ["6 x 7 = 42 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8957", "queId": "4784020f2a3e4415885b7617f7078071", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If each fork costs ＄$$6$$, each spoon costs ＄$$7$$, and each knife costs ＄$$8$$, what is the total cost of $$3$$ forks, $$4$$ spoons, and $$5$$ knives? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$40$$ "}], [{"aoVal": "B", "content": "＄$$46$$ "}], [{"aoVal": "C", "content": "＄$$80$$ "}], [{"aoVal": "D", "content": "＄$$86$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$$3$$ forks cost ＄$$6\\times3 =$$＄$$18$$. $$4$$ spoons cost ＄$$7\\times4 =$$＄$$28$$. $$5$$ knives cost ＄$$8\\times5 = $$＄$$40$$. They cost a total of ＄$$18+$$＄$$28+$$＄$$40 =$$＄$$86$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8966", "queId": "289af981df934f3d9d58674d7c64a6f4", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A given month has $$31$$ days, and it has four Mondays and four Thursdays. What day of the week is the $$20^{\\rm th}$$ of this month? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$Wednesday$$$$. "}], [{"aoVal": "B", "content": "Thursday "}], [{"aoVal": "C", "content": "Friday "}], [{"aoVal": "D", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["It implies that there are four Mondays, four Tuesdays, four Wednesdays, and four Thursdays. Similarly, there are five Fridays, five Saturdays, and five Sundays. The first day of the month therefore must be a Friday. $$20\\div7=2\\text{ R }6$$. The $$20^{\\rm th}$$ day of this month is a Wednesday, which is the $$6^{\\rm th}$$ day after Friday, inclusive. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8973", "queId": "677f5e71abcc4006a14a6ee86b9457de", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Grandpa suggested dividing all the peanuts between the family members in the following way: one person would get $5$ kilos, two people would get $4$ kilos each, four people would get $2$ kilos each, one person would get $6$ kilos, and one person would not get any peanuts. Grandma suggested dividing the peanuts equally among all of the family members. How many people would get more peanuts in grandma\\textquotesingle s suggestion than grandpa\\textquotesingle s? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Grandma\\textquotesingle s suggestion: $(1\\times 5 + 2\\times 4+4\\times 2+1\\times 6+1\\times 0)\\div(1+2+4+1+1) = 27\\div9=3$ Thus, there are $4+1=5$ people get more peanuts. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8976", "queId": "2070e8e9ad71476dbea8bb6468c3e317", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Anna is $$10$$ years old and the age of her mother is $$4$$ times that of Anna. How old will Anna\\textquotesingle s mother be when Anna\\textquotesingle s mother is twice as old as Anna? (Math kangaroo Problem, Level $$5-6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$70$$ "}], [{"aoVal": "E", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Varying Multiples in Age Problems"], "answer_analysis": ["The age difference between them is $(4-1)\\times10=30$, which stays the same forever. Then, when Anna\\textquotesingle s mother is twice as old as Anna, Anna should be $30$ years old, then her mom should be $30\\times2=60$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8977", "queId": "4c2228c414cf4507a3502274c27fd237", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$2$$ watermelons can serve $$15$$ people, I need watermelons for $$60$$ people. ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"], "answer_analysis": ["If $$2$$ melons can serve $$15$$ people, I need $$4\\times2=8$$ melons for $$4\\times15=60$$ people. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8978", "queId": "b50af7cb22704ba892f668c342921d09", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "On Kellin\\textquotesingle s $$13$$th birthday, Allen was four times her age. On Kellin\\textquotesingle s $$24$$th birthday, how old was Allen? ", "answer_option_list": [[{"aoVal": "A", "content": "$$39$$ "}], [{"aoVal": "B", "content": "$$44$$ "}], [{"aoVal": "C", "content": "$$ 52 $$ "}], [{"aoVal": "D", "content": "$$ 63 $$ "}], [{"aoVal": "E", "content": "$$ 74$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["On Kellin\\textquotesingle s $$13$$th birthday, Allen was four times her age, that is $$52$$. It is then eleven years until Kellin\\textquotesingle s $$24$$th birthday, so Allen\\textquotesingle s age at that time was $$52 +11 =63$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8979", "queId": "20791ee4e06a4edeb45dba05f9d73b43", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A glass contains $$240$$ $$\\rm ml$$ of water. The water takes up $$\\frac 23$$ of the volume of the glass. What is the volume of the glass, in milliliters? ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$100$$ "}], [{"aoVal": "C", "content": "$$120$$ "}], [{"aoVal": "D", "content": "$$270$$ "}], [{"aoVal": "E", "content": "$$360$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["$$240\\div \\frac 23=360$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8980", "queId": "2cfb178f3aaa4fada6f4dd78cc5ecbfe", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "At the pumpkin festival, Mike brought a $10$ pounds pumpkin. Mary\\textquotesingle s pumpkin weighed $5$ pounds more than Mike\\textquotesingle s. How many pounds is Mary\\textquotesingle s pumpkin？(adapted from $$2009$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$28$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["Mary\\textquotesingle s pumpkin weighs $5$ pounds more than Mike\\textquotesingle s, so it\\textquotesingle s $10 + 5 = 15$ pounds. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8986", "queId": "20804e21e09e41e2a1f201f42c1be6b1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Water makes up $$84\\textbackslash\\%$$ of the weight of Kubus the Camel when he is thirsty. After he drinks, Kubus weighs $$800$$ kg and water makes up $$85\\textbackslash\\%$$ of his weight. What is the weight of Kubus the Camel when he is thirsty? ($$2001$$ Math Kangaroo Problem, Level $$9-10$$, Question \\#$$16$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$672$$ kg "}], [{"aoVal": "B", "content": "$$680$$ kg "}], [{"aoVal": "C", "content": "$$715$$ kg "}], [{"aoVal": "D", "content": "$$720$$ kg "}], [{"aoVal": "E", "content": "$$750$$ kg "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["The ratio between the thirsty Kubus and the water he drank: $$(100-85):(85-84)=15:1$$. So, the weight of the thirsty Kubus is: $$800 \\times \\frac{15}{15+1}=750$$ kg. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8988", "queId": "abd318c6c36b4d00b6031180aefc4c83", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Arthur decided to lose weight. On the first month, he lost $2$ kg. He decided that each month he would be losing twice as much kilograms as the month before. How many kilograms did Arthur lose in total in the first three monthes? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Geometric Progression"], "answer_analysis": ["$2 + 4 + 8 = 14$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "8991", "queId": "35c5f540168c42ddb87900669a7fbb40", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many tens must be added to $$215$$ to make $$985$$?~\\uline{~~~~~~~~~~}~tens ", "answer_option_list": [[{"aoVal": "A", "content": "$$770$$ "}], [{"aoVal": "B", "content": "$$77$$ "}], [{"aoVal": "C", "content": "$$120$$ "}], [{"aoVal": "D", "content": "$$1200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with Invariant Sums", "Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Addition and Subtraction of Whole Numbers->Adding and Subtracting within 10000->Subtraction of 3-digit Numbers"], "answer_analysis": ["$$985-215=770$$ $$770\\div 10=77$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9000", "queId": "50b5773e9ccb47b2ae6a76de4e2c1136", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Determine whether 2008 is a common year or a leap year. ", "answer_option_list": [[{"aoVal": "A", "content": "a common year "}], [{"aoVal": "B", "content": "a leap year "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["$2008\\div4=502$, so 2008 is a leap year. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9003", "queId": "995395a086b94524b656f12ccfb2ecb1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $$15\\textbackslash\\%$$ sugar solution contains $$18$$ grams of pure sugar. How many grams of solution are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ grams "}], [{"aoVal": "B", "content": "$$100$$ grams "}], [{"aoVal": "C", "content": "$$120$$ grams "}], [{"aoVal": "D", "content": "$$150$$ grams "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$18\\div15\\textbackslash\\% = 120$$ grams. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9005", "queId": "3a4302374beb4b9bb287f025c6c9b910", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$19^{}\\text{th}$$March is Monday, what day of the week is $$1$$\\textsuperscript{st~}March ? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday　 "}], [{"aoVal": "B", "content": "Monday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Thursday　 "}], [{"aoVal": "E", "content": "Saturday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["There are 19 days between $$19^{}\\text{th}$$March and~ $$1$$\\textsuperscript{st~}March. Apart from $19$\\textsuperscript{th} March itself, there are $18$ days, 18 days = 2 week and 4 days. Therefore,~~$$1$$\\textsuperscript{st~}March is Thursday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9010", "queId": "75545ef04b054c9d9bb0a3389f39b2f4", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Elsa started to raise some chicken in her farm in January. The number of chicken triples every month, while she goes to the market to sell $81$ chicken every month. On April when she came back from the market, she found she had no chicken left. How many chicken did she raise in January? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$45$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems"], "answer_analysis": ["$81 \\div 3 = 27$ $(81 + 27) \\div 3 = 36$ $(36 + 81) \\div 3 = 39$ $(39 + 81) \\div 3 = 40$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9015", "queId": "554dcd8cf4db44bba1c2c303814e25c1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mariam had ＄$$4y$$. After buying some cloth at ＄$$7$$ per metre, she had ＄$$y$$ left. How many metres of cloth did she buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3y}{7}$$ "}], [{"aoVal": "B", "content": "$$\\frac{5y}{7}$$ "}], [{"aoVal": "C", "content": "$21y$ "}], [{"aoVal": "D", "content": "$$35y$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["Amount of money she spent to buy the cloth $$\\rightarrow$$＄$$4y-$$＄$$y$$ $$=$$＄$$3y$$, Length of cloth she bought $$\\rightarrow$$＄$$3y\\div $$＄$$7/\\text{m}$$ $$= \\frac{3y}{7}\\text{m}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9016", "queId": "755716b534644524b64070f2d8e89dd2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A pencil is one dollar, and a pencil box is two dollars more expensive than a pencil. Jimmy has seven dollars and bought a pencil box. How many pencils can Jimmy buy？(adapted from $$2009$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$1$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["A pencil box costs two dollars more than a pencil, so it\\textquotesingle s $1+2=3$ dollars. $7-3=4$. So~He can buy $4\\div1=4$~pencils. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9019", "queId": "b9ae7f6da3644676a43ed238be442a9b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The February of a given year has five Fridays. What day of the week was January $$31$$\\textsuperscript{th~}of that year? ", "answer_option_list": [[{"aoVal": "A", "content": "Friday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Wednesday "}], [{"aoVal": "D", "content": "Thursday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["There are seven days in a week. In order to have five Fridays, a month has at least $$4\\times 7+1=29$$ days. Since February has at most $$29$$ days, the $$1$$\\textsuperscript{st} and $$29$$\\textsuperscript{th} days of this February must be Friday, which means that January $$31$$ is Thursday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9023", "queId": "35e07a8c8c474bb2a06eab793f4ba4e7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "George takes 4 minutes to go from 1st floor to 3rd floor. He just realised that he forgot his water bottle on the 5th floor. He is now on the 2nd floor. How long would it take him to get his watter bottle? ", "answer_option_list": [[{"aoVal": "A", "content": "4 minutes "}], [{"aoVal": "B", "content": "5 minutes "}], [{"aoVal": "C", "content": "6 minutes "}], [{"aoVal": "D", "content": "8 minutes "}], [{"aoVal": "E", "content": "None of the above. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications"], "answer_analysis": ["2 gaps between 1st to 3rd floor. hence, 4/2=2 minutes per gap. Moving from 2nd to 5th floor, 3 gaps -\\textgreater{} 3 gaps x 2 minutes per gap = 6 minutes. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9027", "queId": "35e3d08db3384991b74d8f9237c114bf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Billy has three times as many llamas as lambs. Milly has twice as many lambs as llamas. They have $$17$$ animals in total. How many of the animals are llamas? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Indefinite Equation Word Problems"], "answer_analysis": ["Let Billy have $$b$$ lambs and $$3b$$ llamas. Let Milly have $$m$$ llamas and $$2m$$ lambs. Therefore, as they have $$17$$ animals in total, $$4b + 3m= 17$$. The only positive integer solution of this equation is $$b= 2$$, $$m= 3$$. So the number of llamas is $$3b + m = 3 \\times 2 + 3 = 6 + 3 = 9$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9033", "queId": "28ebd08f7b9a4fd2b5a29dba55cdf4fc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$15^{}\\text{th}$$March is Monday, what day of the week is $$26$$\\textsuperscript{th} March ? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday　 "}], [{"aoVal": "B", "content": "Monday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Friday　 "}], [{"aoVal": "E", "content": "Saturday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["There are 11 days between $$15^{}\\text{th}$$March and~ $$26$$\\textsuperscript{th} March. 11 days = 1 week and 4 days. Therefore,~~$$26$$\\textsuperscript{th} March is Friday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9041", "queId": "b517757aafc849dbb93583a85b080fcc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sarah is $$1.14\\text{m}$$ tall. Benny is $$0.23\\text{m}$$ taller than Sarah. What is the total height of the $$2$$ children? Round off your answer to $$1$$ decimal place. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1.4\\text{m}$$ "}], [{"aoVal": "B", "content": "$$2.1\\text{m}$$ "}], [{"aoVal": "C", "content": "$$2.5\\text{m}$$ "}], [{"aoVal": "D", "content": "$$2.6\\text{m}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["Benny\\textquotesingle s height $$=1.14+0.23=1.37\\text{m}$$ Total heights of the $$2$$ children $$=1.14+1.37=2.51=2.5\\text{m}$$ (rounded to $$1$$ d.p.) "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9042", "queId": "28f475c9f7064d948dbcba7b4fd41806", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are~ $$30$$ students in Pat\\textquotesingle s math class. If there are twice as many girls as boys in the class, how many boys are in the class? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"], "answer_analysis": ["There are $$30$$ students in Pat\\textquotesingle s math class. With twice as many girls as boys, the class has $$20$$ girls and $$10$$ boys. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9046", "queId": "b078bb4dea3142b3bf27f3707db62f84", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Lily\\textquotesingle s family used $$21$$ tons of water in the first two months, and an average of $$31$$ tons of water on the remaining three tests. The average tons of water for the five months was~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$120$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$23$$ "}], [{"aoVal": "D", "content": "$$27$$ "}], [{"aoVal": "E", "content": "$$25$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Total tons of water: $$21\\times 2+31\\times 3=135$$ Average tons of water: $$135\\div 5=27$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9051", "queId": "24dccd6fe9dd4c5fa0cc77f021a04cd3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Mr.Smith wants to cut a wood into $5$ pieces. It takes him $2$ minutes to cut a piece. How many minutes will he use to cut? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Mr.Smith needs to cut $5-1=4$ times, which means he needs to use $4 \\times 2 = 8$ minutes to cut. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9057", "queId": "70d29f5e0a8140f88ef9becfaac2134f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Paul had eight $$\\textbackslash$5$$-notes at first. He exchanged all his money for $$\\textbackslash$2$$-notes only. How many notes did he have in the end? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["He has $=\\textbackslash$5\\times8=\\textbackslash$40$ Number of $\\textbackslash$2$-notes $=\\textbackslash$40\\div\\textbackslash$2=20$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9060", "queId": "b07b758fc37a43aa9d4d5e8bdd4b1a62", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Farmer Dunphy has $$16$$ metres of fencing. He wants to make a closed rectangular pen. He uses a long wall for one of the sides. Each side of the pen is a whole number in metres. What is the largest area that the pen can be? ", "answer_option_list": [[{"aoVal": "A", "content": "$$25\\text{m}^{2}$$ "}], [{"aoVal": "B", "content": "$$27\\text{m}^{2}$$ "}], [{"aoVal": "C", "content": "$$30\\text{m}^{2}$$ "}], [{"aoVal": "D", "content": "$$28\\text{m}^{2}$$ "}], [{"aoVal": "E", "content": "$$32\\text{m}^{2}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems Combined with Geometry->Tile Word Problems"], "answer_analysis": ["$a+2b=16$, when $$a=2b=8$$, the largest area is $$8\\times (8\\div 2)=32$$ m\\textsuperscript{2}. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9061", "queId": "3a6defe4b99d44a5a66f0b24ebb999cc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In how many places do we need to break a wooden stick in order to get $$5$$ pieces? (1999 Math Kangaroo Problem, Level 3-4, Question \\#3) ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "It depends on how long the stick is. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Planting no Trees on either Side (straight line type)->Sawing Woods"], "answer_analysis": ["$5-1=4$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9063", "queId": "5563eea1e50e4ccf8b4987951670c614", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Tom starts a savings account with ＄$$4,000$$ at a bank. The interest rate is $$2\\textbackslash\\%$$ per year. How much interest will he earn in his savings account at the end of the second year? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$160$$ "}], [{"aoVal": "B", "content": "＄$$161.6$$ "}], [{"aoVal": "C", "content": "＄$$4,160$$ "}], [{"aoVal": "D", "content": "＄$$4,161.6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Interest Problems"], "answer_analysis": ["$$4000\\times \\left( 1+2\\textbackslash\\% \\right)\\times \\left( 1+2\\textbackslash\\% \\right)-4000=161.6$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9069", "queId": "3a738576173341b9950fffbfcfd02524", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If there are $$8$$ pencils in each box, how many pencils are in $$80$$ boxes?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$88$$ "}], [{"aoVal": "C", "content": "$$640$$ "}], [{"aoVal": "D", "content": "$$808$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["There are $$80 \\times8 = 640$$ pencils in $$80$$ boxes. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9075", "queId": "2d5ac1ffd2554acda68a9b3ace5b117c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "At which of~ these times is the angle between the minute hand and the hour hand of a clock equal to $$150^{}\\circ$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9\\text{pm}$$ "}], [{"aoVal": "B", "content": "$$8\\text{pm}$$ "}], [{"aoVal": "C", "content": "$$6\\text{pm}$$ "}], [{"aoVal": "D", "content": "$$5\\text{pm}$$ "}], [{"aoVal": "E", "content": "$$4\\text{pm}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems"], "answer_analysis": ["At all the times given, the minute hand is pointing to $$12$$. When the minute hand is pointing to $$12$$ and the angle between the hands is $$150^{}\\circ$$, the hour hand has turned $$\\frac{150}{360}= \\frac{5}{12}$$ of a complete turn. Therefore the hour hand will point at $$5$$ and the time will be $$5\\text{pm}$$. (There are other times when the angle between the hands is $$150^{}\\circ$$ but, of these, only at $$7\\text{pm}$$ does the minute hand point to $$12$$ and $$7\\text{pm}$$ is not one of the times given.) "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9076", "queId": "3608fd0cae9f4f0db6c5f54de02cf476", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Lisa is buying potatoes at a grocery store. She can either spend $10$ dollars on a $25\\text{-lb}$ bag or $15$ dollars on a $35\\text{-lb}$ bag. Whic is the cheaper one? ", "answer_option_list": [[{"aoVal": "A", "content": "The $25\\text{-lb}$ bag "}], [{"aoVal": "B", "content": "The $35\\text{-lb}$ bag "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"], "answer_analysis": ["$$\\frac{10}{25}\\textasciitilde\\textbackslash$ \\text{/lb}=0.4\\textasciitilde\\textbackslash$ \\text{/lb}$$ $$\\frac{15}{35}\\textasciitilde\\textbackslash$ \\text{/lb}=0.43\\textasciitilde\\textbackslash$ \\text{/lb}$$ $$\\frac{10}{25}\\textless\\frac{15}{35}$$ So, the answer is $$A$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9077", "queId": "3ee1252200a043d69102ff1f19852b07", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ali is arranging the books on his bookshelves. He puts half his books on the bottom shelf and two-thirds of what remains on the second shelf. Finally he splits the rest of his books over the other two shelves so that the third shelf contains four more books than the top shelf. There are three books on the top shelf. How many books are on the bottom shelf？ ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["Since Ali places half his books on the bottom shelf and $$\\frac{2}{3}$$ of the remainder on the second shelf, he places $$\\frac{2}{3}\\times\\frac{1}{2}=\\frac{1}{3}$$ of his books on the second shelf, leaving $$\\left(1-\\frac{1}{2}-\\frac{1}{3}\\right) =\\frac{1}{6}$$~ of his books for the top two shelves. There are three books on the top shelf and four more, so seven books, on the third shelf. Therefore these $$10$$ books represent $$\\frac{1}{6}$$ of the total number of books on the bookshelves. Hence there are $$60$$ books on the bookshelves and half of these, or $$30$$ books, on the bottom shelf. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9082", "queId": "50e2bc1b9981451da4850b2d0760b083", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Given that May $2$nd of a given year is a Thursday, what day is May $29$th of the same year? ", "answer_option_list": [[{"aoVal": "A", "content": "Saturday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Tuesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems"], "answer_analysis": ["$29-2=27$ days later, it will be May $29$\\textsuperscript{th}. $27\\div7=3R6$, which means May $29$\\textsuperscript{th}~is Wednesday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9084", "queId": "31ade8e5fd1f4d89b81e3361fb8b5d2c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that August $$15$$th of a given year is a Friday, What day is June $$10$$th of the same year? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Friday "}], [{"aoVal": "D", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$$30-10+31+15=$$ $66\\div7=9r3$ $$$$Tuesday$$$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9088", "queId": "ff313a6edc9f448b9cc424174c60b323", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The selling price of a television is＄$$4800$$ and its profit percentage is $$20\\textbackslash\\%$$. If the cost of the television is not changed, how much should it be sold for if the profit percentage has to be $$75\\textbackslash\\%$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6000$$ dollars "}], [{"aoVal": "B", "content": "$$6500$$ dollars "}], [{"aoVal": "C", "content": "$$7000$$ dollars "}], [{"aoVal": "D", "content": "$$8000$$ dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["$$\\frac{4800}{\\left( 1+20\\textbackslash\\% \\right)}=4000$$ dollars, $$4000\\times \\left( 1+75\\textbackslash\\% \\right)=7000$$ dollars. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9101", "queId": "a2ad6165be134ef2875c1798789d5958", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The upper shelf of a bookshelf has $$143$$ books. The lower shelf has $$39$$ books. How many books should be taken from the upper shelf to the lower shelf so that both shelves will have the same number of books? ", "answer_option_list": [[{"aoVal": "A", "content": "$$52$$ "}], [{"aoVal": "B", "content": "$$104$$ "}], [{"aoVal": "C", "content": "$$91$$ "}], [{"aoVal": "D", "content": "$$46$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["$$143-39=104$$, $$104$$~$\\div$ $$2$$ = $$52$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9106", "queId": "252a169e54b4429abc423fb95a4c13c2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If Pip was 18 years old 5 years ago, how old will he be 7 years from now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$22$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["$$18+5+7=30$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9107", "queId": "632a2a9dfa734f2097ac608766cdd02f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My dad, Burly Ird, says he has to moan at me two school mornings in every three to get me out of bed. In a twelve-week term, with five schooldays each week, on how many mornings will he moan at me? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$40$$ "}], [{"aoVal": "E", "content": "$$42$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["The number of moaning mornings is $$\\frac{2}{3}\\times 12 \\times 5 = 40$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9109", "queId": "2949882443274602ad9ff0fffe5be4cb", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "In one year, there were 5 Sundays in February. What day of the week was 3\\textsuperscript{rd~}Feb ? ", "answer_option_list": [[{"aoVal": "A", "content": "Saturday "}], [{"aoVal": "B", "content": "Monday "}], [{"aoVal": "C", "content": "Tuesday "}], [{"aoVal": "D", "content": "Wednesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["Normally, there are 28 days in February, which has 4 Sundays at most. Therefore, it could be the leap year with 29 days in February. If there are 5 Sundays, the first day in Februray should be Sunday, so Feb 3rd is Tuesday. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9116", "queId": "6c5027bfc900405a96a3262d907d3162", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The cost of a computer is $3500$ dollars and the profit percentage is $12\\textbackslash\\%$ for each computer. Find the price of the computer. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3850$$ dollars "}], [{"aoVal": "B", "content": "$$3920$$ dollars "}], [{"aoVal": "C", "content": "$$4200$$ dollars "}], [{"aoVal": "D", "content": "$$4550$$ dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts->Calculating Price from Cost and Profit"], "answer_analysis": ["The price of the computer is: $3500\\times(1+12\\textbackslash\\%)=3920$ dollars. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9119", "queId": "9972583aedc84488b67fca5cb1ffab6a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that March $$26$$\\textsuperscript{th}, $$2021$$ was Friday, what day was April $$20$$\\textsuperscript{th}, $$2021$$? $\\textasciitilde$ ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Wednesday "}], [{"aoVal": "E", "content": "Friday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Counting from March $$26$$\\textsuperscript{th}, $$2021$$, after $31-26=5$ days it was March $$31$$\\textsuperscript{st}, $$2021$$. After $20$ days it was April $$20$$\\textsuperscript{th}, $$2021$$. In total, there were $5+20=25$ days. $25\\div 7 =3R4$, which means April $$20$$\\textsuperscript{th}, $$2021$$ was Tuesday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9124", "queId": "757d78c55cce4dec843aca99df10cd82", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Tom, Joanna and Jacky each come up with a number. The sum of the three numbers is $$360$$. Tom\\textquotesingle s number is twice Joanna\\textquotesingle s number, and Joanna\\textquotesingle s number is three times Jacky\\textquotesingle s number. What are these three numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$108$$ "}], [{"aoVal": "C", "content": "$$216$$ "}], [{"aoVal": "D", "content": "$$360$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["Jacky\\textquotesingle s number is ``$$1$$'', so Joanna\\textquotesingle s number is ``$$3$$'', and Tom\\textquotesingle s number is ``$$6$$''. Jacky\\textquotesingle s number: $$360 \\div (6 +3+1) =36$$. Joanna\\textquotesingle s number: $$36 \\times 3=108$$. Tom\\textquotesingle s number: $$36 \\times 6 =216$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9132", "queId": "47f70782f7f14c2baa01838dc586e7da", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "( $$2004$$ AMC $$8$$ Problem, Question \\#$$12$$) Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for $$24$$ hours. If she is using it constantly, the battery will last for only $$3$$ hours. Since the last recharge, her phone has been on $$9$$ hours, and during that time she has used it for $$60$$ minutes. If she doesn\\textquotesingle t use it any more but leaves the phone on, how many more hours will the battery last? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Simple Work Word Problems"], "answer_analysis": ["When not being used, the cell phone uses up $$\\dfrac{1}{24}$$ of its battery per hour. When being used, the cell phone uses up $$\\dfrac{1}{3}$$ of its battery per hour. Since Niki\\textquotesingle s phone has been on for $$9$$ hours, of those $$8$$ simply on and~~being used to talk, $$8\\left(\\dfrac{1}{24}\\right)+1\\left(\\dfrac{1}{3}\\right)=\\dfrac{2}{3}$$ of its battery has been used up. To drain the remaining $$\\dfrac{1}{3}$$ the phone can last for $$\\dfrac{\\dfrac{1}{3}}{\\dfrac{1}{24}}=\\boxed{(\\text{B})8}$$ more hours without being used. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9137", "queId": "31de0d7a18ae4cf68af276242e97c24c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mike bought five ice creams. He had three brothers and he gave each brother an ice cream. How many ice creams was left?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$3$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["Each brother gets one ice cream, and three brothers need three ice cream, so Mike has $5-3=2$~ice cream left. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9138", "queId": "70f10ebca60b4f78b3596722ccc3a9d5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Elmp visits the Sesame Street Park every Wednesday. If the 1st of January 2017 was Sunday and February has 28 days, what was the last date in March 2017 in which Elmo visited Sesame Street Park? ", "answer_option_list": [[{"aoVal": "A", "content": "28th March "}], [{"aoVal": "B", "content": "29th March "}], [{"aoVal": "C", "content": "30th March "}], [{"aoVal": "D", "content": "31st March "}], [{"aoVal": "E", "content": "None of the above. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems"], "answer_analysis": ["Draw the calendar out. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9139", "queId": "633400457b2a47cfa9363f17f1286353", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A construction team is going to build a road of $50$ miles. The plan is that it finishes $30$\\% of the road in the first month, $40$\\% of the road in the second month and $30$\\% of the road in the third month. How many miles can be built after two months? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$30$\\%+$40$\\%=$70$\\%, $50 \\times 70$\\%=$35$ After two months, $35$ miles of road can be built. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9140", "queId": "7a1e1572638c473891ceef59b339554f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Kate bought $$2$$ apple pies and Lucy bought $$4$$ cupcakes. They each paid the same amount of money and together they paid $$16$$ dollars. How many dollars does $$1$$ cupcake cost? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Applying Division"], "answer_analysis": ["$4$ cupcakes cost $16\\div2=8$ dollars, so one cupcake cost $8\\div4=2$ dollars. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9144", "queId": "31e38582c22d45a8b73fdd680db87bbc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Esther made $$18$$ paper stars and she made $$3$$ times as many paper stars as Amy. How many paper stars did Amy make? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"], "answer_analysis": ["omitted "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9152", "queId": "3ab230920c8a448a935224efb4bbd275", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "In a class of pupils, $80\\textbackslash\\%$ participated in basketball, $85\\textbackslash\\%$ participated in football, $74\\textbackslash\\%$ participated in softball and $68\\textbackslash\\%$ participated in squash. Find the minimum percentage of pupils who participated in all the four sports events. ", "answer_option_list": [[{"aoVal": "A", "content": "$7\\textbackslash\\%$ "}], [{"aoVal": "B", "content": "$10\\textbackslash\\%$ "}], [{"aoVal": "C", "content": "$12\\textbackslash\\%$ "}], [{"aoVal": "D", "content": "$15\\textbackslash\\%$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["Least percentage of pupils who participated in both basketball and football $=80\\textbackslash\\%+ 85\\textbackslash\\%-100\\textbackslash\\% =65\\textbackslash\\%$, Least percentage of pupils who participated in basketball, football and softball $=65\\textbackslash\\%+74\\textbackslash\\%-100\\textbackslash\\% =39\\textbackslash\\%$, Least percentage of pupils who participated in basketball, football, softball and squash $=39\\textbackslash\\%+ 68\\textbackslash\\%-100\\textbackslash\\% = 7\\textbackslash\\%$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9156", "queId": "e368d6c3bc1b423a838f92958f48a055", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Simon has two identical aquariums. There are $$26$$ quarts of water in one, and $$42$$ quarts of water in the other. How many quarts of water does Simon need to pour from the second aquarium into the first in order to have the same amount of water in both? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Giving and Receiving"], "answer_analysis": ["Difference: $42-26=16$ Move: Half of $16=8$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9157", "queId": "2974fbb221394803aa3e2851d02d7c6a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In $$20$$ years, Li will be $$3$$ times as old as he is now. How old will he be in $$10$$ years? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->When..., When... Type Age Problems"], "answer_analysis": ["In $$20$$ years, Li will be $$3$$ times his age now, so $$20$$ must be twice his age now. Thus, Li is $$10$$ now and will be $$20$$ in $$10$$ years. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9160", "queId": "c30d76211ffc4b33b74ecb40481a3f80", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When Paul is $$4$$ years old, his brother Peter is $$7$$ years old. How old is Paul when Peter is $$10$$ years old? Paul is~\\uline{~~~~~~~~~~}~years old. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["We can find their age difference is $$7-4=3$$. It will never change. So when Peter is $$10$$ years old, Paul is $$10-3=7$$ years old. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9175", "queId": "2dcf32ee240746e991d76e0c3e410ed7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If Paul gives $$6$$ candies to Billy, they will have the same number of candies. At beginning, Paul has $$17$$ candies. How many candies does Billy have, originally? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Their difference: $$6+6=12$$ Billy: $$17-12=5$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9177", "queId": "7ec7203e832d43a4ae2c712cd4fd38c3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Su Li has the same number of ten-cent and fifty-cent coins. The total value is ＄$$6$$. How many coins does she have in all? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$$10u + 50u = 600$$ Thus, $$1u = 10$$, in total we have $$2u=20$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9180", "queId": "366ebcb8e901438dbcaab7f7eae8fb50", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Andy is $18$ years old and his mother is $$54$$ years old now. In how many years\\textquotesingle{} time will the sum of their ages be $$90$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$28$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["$$18+54 = 72$$ $$90-72 = 18$$ $$18\\div2=9$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9191", "queId": "8bb83ae894e1479cae8a829f26b30e09", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Together, Mom Kangaroo and her son Jumper weigh $60$ kilograms. Mom Kangaroo alone weighs $52$ kilograms. How much does Jumper weigh? ($$2019$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$3$$) ", "answer_option_list": [[{"aoVal": "A", "content": "2 kilograms "}], [{"aoVal": "B", "content": "4 kilograms "}], [{"aoVal": "C", "content": "8 kilograms "}], [{"aoVal": "D", "content": "30 kilograms "}], [{"aoVal": "E", "content": "46 kilograms "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"], "answer_analysis": ["Jumper\\textquotesingle s weight is Mom Kangaroo and Jumper\\textquotesingle s weight minus the mom\\textquotesingle s weight. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9195", "queId": "da31826157214798804ddb8fa2daadca", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "There are three books, Chinese, Math, and English. Sissy wants to put them in bookcase. How many ways are there for three books to put? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["List out all the possible ways in order. $C A E$ $C E A$ $A C E$ $A E C$ $E C A$ $E A C $ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9198", "queId": "67e89215e9c9426f941e2f128e8d0841", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alex had $76. He spent some of it in a shop. Then he gave half of what he had left to Charlie. Charlie spent a quarter of what Alex gave him on lunch. Charlie spent $9 on lunch. How much did Alex spend in the shop? ", "answer_option_list": [[{"aoVal": "A", "content": "$4 "}], [{"aoVal": "B", "content": "$12 "}], [{"aoVal": "C", "content": "$14 "}], [{"aoVal": "D", "content": "$36 "}], [{"aoVal": "E", "content": "$40 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Charlie\\textquotesingle s 1/4 is 9, so Charlie gets 4\\times 9=36 dollars, and Alex is left with 36+36=72 dollars, so he spends 76-72=4 dollars "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9204", "queId": "3aef27b0617f40e3abdf060f4491b2df", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Min Ho deposited ＄$$20 000$$ into a bank at the beginning of the year. The annual interest for depositing money into the bank was $$5\\textbackslash\\%$$. How much did Min Ho have in the bank at the end of the year if he did not take out any money from the bank?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\textbackslash$1000$$ "}], [{"aoVal": "B", "content": "$$\\textbackslash$19 000$$ "}], [{"aoVal": "C", "content": "$$\\textbackslash$21 000$$ "}], [{"aoVal": "D", "content": "$$\\textbackslash$31 000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["He has $20000 \\times 1.05 = \\textbackslash$21000$ at the end of the year. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9206", "queId": "880a8e37428c4889b5d2b4703cbe3889", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The pages of a book are numbered 1, 2, 3 $\\cdots$ . In total, it takes 852 digits to number all the pages of the book. What is the number of the last page? ", "answer_option_list": [[{"aoVal": "A", "content": "$$215$$ "}], [{"aoVal": "B", "content": "$$314$$ "}], [{"aoVal": "C", "content": "$$320$$ "}], [{"aoVal": "D", "content": "$$329$$ "}], [{"aoVal": "E", "content": "$$422$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem"], "answer_analysis": ["omitted jmc 2007 \\#24 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9207", "queId": "ac0813321e60496d8537f827af1b9051", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Eddie and Frank can complete a job together in $$15$$ days. Eddie can do it alone in $$20$$ days. Frank can do it alone indays. ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"], "answer_analysis": ["$$\\frac{1}{15}-\\frac{1}{20}=\\frac{1}{60}$$, $$1\\div\\frac{1}{60}=60$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9214", "queId": "d592b49d1e4542c39fcea7e8ab89cf90", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$600$$ pupils in Pip\\textquotesingle s school, with $$30$$ more girls than boys. How many girls are at Pip\\textquotesingle s school? ", "answer_option_list": [[{"aoVal": "A", "content": "$$270$$ "}], [{"aoVal": "B", "content": "$$300$$ "}], [{"aoVal": "C", "content": "$$315$$ "}], [{"aoVal": "D", "content": "$$330$$ "}], [{"aoVal": "E", "content": "$$345$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["Let there be $$g$$ girls in Pip\\textquotesingle s school. Then there are $$(g-30)$$ boys at the school. So $$g+g-30=600$$. Therefore $$2g=630$$, that is $$g=315$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9216", "queId": "67eea995ee504a68a52fff4e078f0adc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A ship was attacked by pirates. One by one the pirates climb a rope to get on the ship. The pirate captain was the $$8$$\\textsuperscript{th}~pirate to climb in line, and there were as many pirates in front of him as behind him. How many pirates climbed the rope? (2015 Math Kangaroo Problem, Level 1 - 2, Question \\#18) $$\\textasciitilde$$ $$\\textasciitilde$$ $$\\textasciitilde$$ $$\\textasciitilde$$ $$\\textasciitilde$$ $$\\textasciitilde$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line"], "answer_analysis": ["The pirate captain was the $$8$$\\textsuperscript{th}~pirate and there were as many pirates in front of him as behind him, which means there were $$7$$ pirates in front of him and there were also $$7$$ pirates behind him. The total number of pirates is~~$$7+7+1=15$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9221", "queId": "ecb8f9ef5d1b4aaa916b9c1ce004c480", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Half a loaf of bread costs $$6$$ pence more than one quarter of a loaf of bread. How many pence does a whole loaf of bread cost? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["One quarter of a loaf of bread is ``$$1$$.'' Half a loaf of bread is ``$$2$$.'' One quarter of a loaf of bread: $$6 \\div (2-1) =6$$. A whole loaf of bread: $$6 \\times 4 =24$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9222", "queId": "880f4cb118f14f90bfc89ece33e6305f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "After Sally takes 20 shots, she has made $40 \\textbackslash\\%$ of her shots. After she takes 5 more shots, she raises her percentage to $52 \\textbackslash\\%$. How many of the last 5 shots did she make? (2004 AMC 8, Question\\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Sally made $0.4 * 20=8$ shots originally. Letting $x$ be the number of shots she made, we have $\\frac{8+x}{25}=0.52$. Solving for $x$ gives us $x=5$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9223", "queId": "55c6a4144e5e44aea914f1e2263db0f6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Seventh grade students from a school line up and form a square array. There are $196$ students in the outermost layer. How many students in total are there in this array? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1960$$ "}], [{"aoVal": "B", "content": "$$2401$$ "}], [{"aoVal": "C", "content": "$$2000$$ "}], [{"aoVal": "D", "content": "$$2601$$ "}], [{"aoVal": "E", "content": "$$2500$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares"], "answer_analysis": ["The number of students on each side of the outermost layer was $$196\\div 4+1=50$$. The total number of students in the array was $$50\\times 50=2500$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9225", "queId": "f603b7e6a99c4d2caef7012f7673bc31", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My first day of vacation is May $$10$$. My last day of vacation is May $$20$$ of the same year. How many days of vacation do I have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$ 10 $$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9229", "queId": "36a6178cc2984c619773488f7dbaf7b5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a jar of red, green, and blue marbles, all but $$6$$ are red marbles, all but $$8$$ are green, and all but $$4$$ are blue. How many marbles are in the jar? ($$2012$$ AMC $$8$$ problem, Question \\#$$19$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems"], "answer_analysis": ["Suppose there are $$x$$ red marbles, $$y$$ green marbles, and $$z$$ blue marbles. Thus, we can get $$\\begin{cases} x+y=4① \\textbackslash\\textbackslash{} y+z=6②\\textbackslash\\x+z=8③\\end{cases}$$, ①$$+$$②$$+$$③: $$2x+2y+2z=18$$, $$x+y+z=9$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9231", "queId": "b0a8da14729546d38e11e4d003e97fca", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "After Anna spends $\\dfrac{1}{3}$~of her money and loses $\\dfrac{1}{2}$~of the remainder, she then has~$\\textbackslash$10$ left. She started with． ", "answer_option_list": [[{"aoVal": "A", "content": "$\\textbackslash$30$ "}], [{"aoVal": "B", "content": "$\\textbackslash$45$ "}], [{"aoVal": "C", "content": "$\\textbackslash$50$ "}], [{"aoVal": "D", "content": "$\\textbackslash$60$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["After Anna spends $\\dfrac{1}{3}$~of her money, she has $\\dfrac{2}{3}$~left. If she loses $\\dfrac{1}{2}$~of this, she has $\\dfrac{1}{3}$~left. Since$\\dfrac{1}{3}=$$\\textbackslash$10$,~$\\dfrac{3}{3}=3\\times$$\\textbackslash$10=$$\\textbackslash$30$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9235", "queId": "43e6c32f5cdd4d81af4f3de94586b61e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given March $$25$$th of a certain year is Monday, what day of the week would May $$1$$st fall on this year? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday "}], [{"aoVal": "B", "content": "Monday "}], [{"aoVal": "C", "content": "Tuesday "}], [{"aoVal": "D", "content": "Wednesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["The cycle includes seven days, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday. There are in total $$7+30+1=38$$ days from March $$25$$ to May $$1$$. Since $$38\\div7=5 \\text{ R }3$$，$$$$May$$$$ $$1$$ is the $$3^{\\rm rd}$$ day in the cycle, it is a Wednesday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9238", "queId": "3263efa465b14b1ba130f0bc30112c1c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In an arts and crafts class, the students cut out some triangles, quadrilaterals and pentagons. All the shapes combined have $$394$$ sides. Among them, there are $$2$$ pentagons and the number of quadrilaterals is $$82$$ more than that of triangles. How many quadrilaterals are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ "}], [{"aoVal": "B", "content": "$$95$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$105$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Let $$x$$ represent the number of quadrilaterals, thus the number of triangles can be represented as $$(x-82)$$. So we have $$2\\times5+4x +3(x-82)=394$$. implying that $$x =90$$. Therefore there are $$90$$ quadrilaterals. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9241", "queId": "3265fed465f44eda9549816f1eeadb1e", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "Sam wants to use two kinds of sugar water with concentrations of $$5\\textbackslash\\%$$ and $$20\\textbackslash\\%$$ to make a sugar water of $$300$$g with a concentration of $$15\\textbackslash\\%$$. He correctly calculated the required ratio of the two solutions, but reversed the two bottles of sugar water when preparing them. The actual concentration of the wrongly mixed sugar water is~\\uline{~~~~~~~~~~}~$$\\textbackslash\\%$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12.5$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9244", "queId": "5ee5a7529d924d24830c90f41fdcde27", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If February contains Friday the $$13^{}\\text{th}$$, what day of the week is February $$1$$st?． ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday　 "}], [{"aoVal": "B", "content": "Monday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Thursday　 "}], [{"aoVal": "E", "content": "Saturday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["We can count backward by days or by weeks. Count a few weeks back to find that February $$6$$ is a Friday. Then count a few days back to find that February $$1$$ is a Sunday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9253", "queId": "3b22152a712a46e3b1f60c74afeca85b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Eddie spends $12$ minutes to climb from the first floor to the third floor at a constant speed. At this speed, how many minutes does Eddie need to climb from the first floor to the sixth floor? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$42$$ "}], [{"aoVal": "E", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$12 \\div (3 - 1) = 6$ $6 \\times (6 - 1) = 30$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9254", "queId": "5a5b821ef2f24238abcfc4879e7f11b6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The number of months in a year minus the number of days in a week equals． ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$19$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["The number of months in a year minus the number of days in a week is $$12-7 = 5$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9257", "queId": "a2da102de4fb4a178058fd96fd618628", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "At the 2018 Tompkins County Fair a vendor is offering a \"fair special\" on hats. If you buy one hat at the regular price of $\\textbackslash$ 30$, you get a second hat at a $40\\textbackslash\\%$ discount, and a third pair at half the regular price. James took advantage of the \"fair special\" to buy three hats. What percentage of the $\\textbackslash$ 90$ regular price did he save? (adapted from 2013 AMC 8, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$25$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["First, the amount of money one will pay for three hats without the discount $=\\textbackslash$ 90$. Then, find the amount of money using the discount: $30+0.6 \\times 30+\\frac{1}{2} \\times 30=\\textbackslash$ 63$. Finding the percentage yields $\\frac{63}{90}=70\\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-70\\textbackslash\\%= 30\\textbackslash\\%$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9258", "queId": "68073846e52148b484031f0a491973a2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Find the average of these numbers: $7,9,5,3,6$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9270", "queId": "b550a910f5b0480a9dac345621313a24", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There were some cupcakes in a bakery. First, Jade ate half of the cupcakes. Then, Neil ate half of the remaining cupcakes. Finally, Terry ate $6$ cupcakes and there were $$2$$ cupcakes left. At beginning, how many cupcakes were there in the bakery? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$6+2=8$$ $$8+8=16$$ $$16+16=32$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9273", "queId": "6ca03b7ad77243b785d6d66961e437fa", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a zoo, there are three monkeys. The monkeys are all younger than $$5$$ years old. None of them has the same age, and all their ages are whole numbers. The product of their ages is $$8$$. What is the sum of their ages? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["The whole numbers smaller than $$5$$ are: $$1, 2, 3, 4$$ (age cannot be $$0$$) The product of three numbers is $$8$$. $$1\\times2\\times4=8$$ Their sum: $$1+2+4=7$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9275", "queId": "e382131f02d0430ab06cb30d744ced61", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "After every $$3$$ steps that Pip takes forward, he takes $$2$$ steps backwards. Each step is $$1 $$$$\\text{m}$$. Pip starts at one end of a $$100$$ $$\\text{m}$$ hall. Pip will first reach the other end after~\\uline{~~~~~~~~~~}~steps. ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ "}], [{"aoVal": "B", "content": "$$488$$ "}], [{"aoVal": "C", "content": "$$490$$ "}], [{"aoVal": "D", "content": "$$500$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"], "answer_analysis": ["3+2=5, 3-2=1 The pattern: Pip move forward 1m in 5 steps $$100-3=97$$ $97\\times5+3=488$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9281", "queId": "48714785331a41c4ba8c40eef02f17b3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Susan is $6$ years old. Her sister is one year younger and her brother is one year older. What is the sum of the ages of the three siblings? ", "answer_option_list": [[{"aoVal": "A", "content": "$10$ "}], [{"aoVal": "B", "content": "$15$ "}], [{"aoVal": "C", "content": "$18$ "}], [{"aoVal": "D", "content": "$21$ "}], [{"aoVal": "E", "content": "$30$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["Susan\\textquotesingle s sister is $6-1=5$ years old and her brother is $6+1=7$ years old. The sum of the ages of the three siblings is $5+6+7=18$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9285", "queId": "7ef85e4c918e415693150305c0b9d315", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Peter has $$20$$ grams of a $$20\\textbackslash\\%$$ salt solution. How many grams of salt should he add to make it a $$25\\textbackslash\\%$$ solution? ", "answer_option_list": [[{"aoVal": "A", "content": "$1$ grams "}], [{"aoVal": "B", "content": "$$\\dfrac{4}{3}$$ grams "}], [{"aoVal": "C", "content": "$4$ grams "}], [{"aoVal": "D", "content": "$5$ grams "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["Method $$1$$: Suppose $$x$$ ounces of salt should be added to the solution: $$\\dfrac{20\\times20\\textbackslash\\%+x}{20+x}=25\\textbackslash\\%$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde x=\\dfrac{4}{3}$$. Method $$2$$: $$20\\times(1-20\\textbackslash\\%)\\div(1-25\\textbackslash\\%)-20=\\dfrac{4}{3}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9293", "queId": "8390112dc36e4b7392c6d60c62a34980", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Bridget bakes $48$ loaves of bread for her bakery. She sells half of them in the morning for ＄$2.50$ each. In the afternoon she sells two thirds of what she has left, and because they are not fresh, she charges only half price. In the late afternoon she sells the remaining loaves at a dollar each. Each loaf costs ＄$0.75$ for her to make. In dollars, what is her profit for the day?($$2014$$ AMC $$10$$A Problem, Question \\#$$3$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$24$ "}], [{"aoVal": "B", "content": "$36$ "}], [{"aoVal": "C", "content": "$44$ "}], [{"aoVal": "D", "content": "$48$ "}], [{"aoVal": "E", "content": "$52$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"], "answer_analysis": ["She first sells one-half of her $48$ loaves, or $$\\frac{48}{2}=24$$ loaves. Each loaf sells for＄$2.50$, so her total earnings in the morning is equal to$24\\times $＄$2.50=$＄$60$. This leaves $24$ loaves left, and Bridget will sell $\\frac{2}{3}\\times24=16$ of them for a price of＄$\\frac{2.50}{2}=$＄$1.25$. Thus, her total earnings for the afternoon is$16\\times~ $＄$1.25=$＄$20$. Finally, Bridget will sell the remaining $24-16=8$ loaves for a dollar each. This is a total of＄$1\\times~ 8=$＄$8$. The total amount of money she makes is equal to $60+20+8=$＄$88$. However, since Bridget spends＄$0.75$ making each loaf of bread, the total cost to make the bread is equal to＄$0.75\\times 48=$＄$36$. Her total profit is the amount of money she spent subtracted from the amount of money she made, which is $88-36=52\\Rightarrow \\left(\\text{E}\\right)52$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9294", "queId": "d10656660c4e405ea503eb7956c53bc4", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "At the \"Think Flea Market\", a vendor is offering a \"fair special\" on sandals. If you buy one pair of sandals at the regular price of $\\textbackslash$ 50$, you get a second pair at a $40 \\textbackslash\\%$ discount, and a third pair at half the regular price. Owen took advantage of the \"fair special\" to buy three pairs of sandals. What percentage of the $\\textbackslash$ 150$ regular price did he save? (adapted from 2013 AMC 8, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$40$$ "}], [{"aoVal": "E", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["First, find the amount of money one will pay for three sandals without the discount. We have $\\textbackslash$ 50 \\times 3$ sandals $=\\textbackslash$ 150$. Then, find the amount of money using the discount: $50+0.6 \\times 50+\\frac{1}{2} \\times 50=\\textbackslash$ 105$. Finding the percentage yields $\\frac{105}{150}=70 \\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-70 \\textbackslash\\%=(\\text{B}) 30$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9301", "queId": "ac2282f76f904dca90a0c7e8c2ccf5da", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Tom, Jim and Peter earned £$620$ together for painting a wall. The ratio of Tom\\textquotesingle s reward to Jim\\textquotesingle s reward is $3:4$. The ratio of Jim\\textquotesingle s reward to Peter\\textquotesingle s reward is $6:5$. How much money did Tom earn? ", "answer_option_list": [[{"aoVal": "A", "content": "£$60$ "}], [{"aoVal": "B", "content": "£$180$ "}], [{"aoVal": "C", "content": "£$80$ "}], [{"aoVal": "D", "content": "£$240$ "}], [{"aoVal": "E", "content": "£$200$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"], "answer_analysis": ["$3:4=9:12$, $6:5=12:10$, their rewards were in the ratio of $9:12:10$. $620\\div(9+12+10)=20$, $20\\times9=180$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9304", "queId": "3faaf71c2f1f43a393c5e1f2d11579d2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My mom\\textquotesingle s birthday is on Sunday, and my dad\\textquotesingle s birthday is $$55$$ days after it. What day of the week will my dad\\textquotesingle s birthday be? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday "}], [{"aoVal": "B", "content": "Monday "}], [{"aoVal": "C", "content": "Tuesday "}], [{"aoVal": "D", "content": "Thursday "}], [{"aoVal": "E", "content": "Saturday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$$55\\div7=7 \\text{R}6$$. It is Saturday. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9306", "queId": "32b210d9db674e38939be320b24f0679", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "John bought some cupcakes, and each of them cost $4$ dollars. He gave the salesperson $20$ dollars and got $4$ dollars as change. How many cupcakes did John buy? (Adapted from 2005 Math Kangaroo Problem, Level 3-4, Question \\#3) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["$(20-4)\\div4=4$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9310", "queId": "63993175d2174396b7242a4febc1367d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are two bookshelves, A and B. Shelf A has $$1100$$ books, and shelf B has books $$300$$. We need to take books from shelf A to shelf B, so that books in shelf B is three times more than self A. ", "answer_option_list": [[{"aoVal": "A", "content": "$$750$$ "}], [{"aoVal": "B", "content": "$$800$$ "}], [{"aoVal": "C", "content": "$$850$$ "}], [{"aoVal": "D", "content": "$$900$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference->Problems Involving Sum and Difference with Two Variables"], "answer_analysis": ["The sum is unchanged, which is $$1400$$，$$1400\\div \\left( 3+1 \\right)=350$$，$$1100-350=750$$． "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9311", "queId": "4424df0ee64643218fea8a7aa5932035", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A mixture of 45 liters of paint is $20 \\textbackslash\\%$ red tint, $30 \\textbackslash\\%$ yellow tint and $50 \\textbackslash\\%$ water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (adapted from 2007 AMC 8, Question \\#17 ) ", "answer_option_list": [[{"aoVal": "A", "content": "$$33$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$37$$ "}], [{"aoVal": "D", "content": "$$39$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Since $30 \\textbackslash\\%$ of the original 45 liters of paint was yellow, and 5 liters of yellow paint were added to make the new mixture, there are $13.5+5=18.5$ liters of yellow tint in the new mixture. Since only 5 liters of paint were added to the original 45 , there are a total of 50 liters of paint in the new mixture. This gives $37 \\textbackslash\\%$ of yellow tint in the new mixture, which is (C) 37 . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9315", "queId": "639b8ea4f783416992f6cfdccd4949aa", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Twice my house number, plus $$4$$, is $$18$$. What\\textquotesingle s my house number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["Twice $$7$$, plus $$4$$ is $$18$$, so $$7$$ is my house number "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9316", "queId": "be96db402a8045fa90c6c392337aeafd", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alex is $8$ years older than her two sisters who are twins. The sum of the ages of all three girls is $32$ years old. How old is Alex? ($2007$ Math Kangaroo Problem, Level $5$-$6$, Question \\#$9$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["The age of each sister is $(32-8) \\div 3 =8$ years old. Thus, Alex is $8 +8 =16$ years old. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9323", "queId": "d5aa1f84df8c4225a656f09d58800967", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Jacob and Zain take pencils from a box of $$21$$ pencils without replacing them. On Monday Jacob takes $$\\frac{2}{3}$$ of the number of pencils that Zain takes. On Tuesday Jacob takes $$\\frac{1}{2}$$ of the number of pencils that Zain takes. On Wednesday morning the box is empty. How many pencils does Jacob take? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Indefinite Equation Word Problems"], "answer_analysis": ["Let the number of pencils Zain takes on Monday and Tuesday be $$x$$ and $$y $$ respectively. Therefore $$x+\\frac{2}{3}x+y+\\frac{1}{2}y=21$$. Hence, when we multiply the equation through by $$6$$ to eliminate the fractions and simplify, we obtain $$10x+9y =126$$. Since $$x$$ and $$y$$ are both positive integers and since the units digit of $$10x$$ is $$0$$, the units digit of $$9y$$ is $$6$$ and hence $$y=4$$. Therefore $$x=9$$ and hence the number of pencils Zain takes is $$9+4=13$$. Therefore the number of pencils Jacob takes is $$21-13= 8$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9325", "queId": "da4ab08a7cc64ec8a99b4777c206a407", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The fruit store sold a total of $$33$$ boxes of apples in the first three days of last week, and an average of $$18$$ boxes of apples per day in the last four days. How many boxes of apples did this fruit store sell on average each day last week? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$$33+18\\times4=105$$ $$105\\div7=15$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9332", "queId": "4436a5189d4245a9836fd4917b4bb007", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The length of Amy\\textquotesingle s string is $$12$$ cm. The length of David\\textquotesingle s string is $$24$$ cm. What is the total length of their strings? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ cm "}], [{"aoVal": "B", "content": "$$26$$ cm "}], [{"aoVal": "C", "content": "$$36$$ cm "}], [{"aoVal": "D", "content": "$$46$$ cm "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["$12+24=36$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9342", "queId": "48a3d7867f584283a9129314bacb8161", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If a construction company can construct a $$1000-$$meter highway in $$5$$ days, how many days does it take to construct a $$2600-$$meter highway at the same rate? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with Two Variables"], "answer_analysis": ["It can construct $$1000\\div5=200$$ meters per day. To construct $$2600$$ meters: $$2600\\div200=13$$ days. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9343", "queId": "68367d59ab1a4d5bbbacd1a5d4bb50e9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A school bought $$12$$ volleyballs and basketballs in total for ＄$$340$$. Each basketball costs ＄$$30$$. Each volleyball costs ＄$$25$$. How many basketballs did the school buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"], "answer_analysis": ["If all were basketballs, $$12\\times $$＄$$30=$$＄$$360$$ the total cost would be ＄$$360$$. ＄$$360-$$＄$$340=$$＄$$20$$ There is a difference of ＄$$20$$. ＄$$30-$$＄$$25=$$＄$$5$$ ＄$$20\\div $$＄$$5=4$$ $$12-4=8$$ The school bought $$8$$ basketballs. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9346", "queId": "b0c894af319c463f86a74ddc5f53f33d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mariam had ＄$$4y$$. After buying some cloth at ＄$$7$$ per metre, she had ＄$$y$$ left. How many metres of cloth did she buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{3y}{7}$$ "}], [{"aoVal": "B", "content": "$$\\frac{5y}{7}$$ "}], [{"aoVal": "C", "content": "$21y$ "}], [{"aoVal": "D", "content": "$$35y$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["Amount of money she spent to buy the cloth $$\\rightarrow$$＄$$4y-$$＄$$y$$ $$=$$＄$$3y$$, Length of cloth she bought $$\\rightarrow$$＄$$3y\\div $$＄$$7/\\text{m}$$ $$= \\frac{3y}{7}\\text{m}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9351", "queId": "e38eca0ea1bc41d7adcf8964194f6ef4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Calculate (1) 6+19= (2) 15-8= ", "answer_option_list": [[{"aoVal": "A", "content": "26, 7 "}], [{"aoVal": "B", "content": "25, 8 "}], [{"aoVal": "C", "content": "26, 8 "}], [{"aoVal": "D", "content": "25, 7 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["Partition 6 into 1 and 5. 19+1=20, 20+5=25 Partition 8 into 5 and 3. 15-5=10, 10-3=7 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9353", "queId": "32e87021545e43359a13988a9a4ff6df", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Nate eats $12$ pizza slices every day. How many pizza slices will nate eat after a week? ", "answer_option_list": [[{"aoVal": "A", "content": "$$81$$ "}], [{"aoVal": "B", "content": "$$82$$ "}], [{"aoVal": "C", "content": "$$83$$ "}], [{"aoVal": "D", "content": "$$84$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$7\\times 12=84$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9364", "queId": "3fe3da3762204b7faf8dcc95a2387167", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There is a tournament at the pool, First, $$13$$ children signed up and then another $$19$$ children signed up, Six teams with an equal number of members each are needed for the tournament, At least how many more children need to sign up so that,the six teams can be formed . (2017 Math Kangaroo Problem, Level 3-4, Question \\#13) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["The total number of children is $$13+19=32$$, To form six teams with the same number of children in each team, we divide $$32$$ by $$6$$, $$32\\div6=5$$$$\\rm R$$$$2$$, The remaining $$2$$ children will need $$4$$ more children to form the sixth team. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9369", "queId": "3b9321d0cd5344f28964bb1bd2ed4d59", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are roughly three million people who live in Wales. Nearly six hundred thousand of them speak Welsh. Approximately what percentage of people living in Wales speak Welsh? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$20\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$30\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$40\\textbackslash\\%$$ "}], [{"aoVal": "E", "content": "$$50\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["The fraction of people living in Wales who speak Welsh is $$\\frac{600000}{3000000}$$. This can be simplified to $$\\frac{1}{5}$$, and so the percentage is $$20\\textbackslash\\%$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9373", "queId": "7a88e2c3a828451b985fa9991af470b7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A slug called Glug eats $$2$$ tomatoes for every $$3$$ strawberries. Yesterday it had eaten $$35$$ tomatoes and strawberries altogether. How many tomatoes did it eat? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["$$35\\times \\frac {2} {2+3} = 14$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9383", "queId": "51b836e5ed254794a5240e03c1eba9ea", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "At dinner, Mom tells Alice to take knifes and forks out of the cupboard and put it on each plate. It is known that there are six plates, four forks, and six knives. How many forks or knives does Alice need to get out of the cupboard ?~ (adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "a fork "}], [{"aoVal": "B", "content": "a knife "}], [{"aoVal": "C", "content": "two forks "}], [{"aoVal": "D", "content": "two knives "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Including and Excluding "], "answer_analysis": ["Each plate needs a knife and a fork. There are six plates here, so $6$$\\times$1$=6$pairs of knives and forks are required, that is, six knives and six forks. But now there are only four forks. $6-4=2$ forks are required. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9384", "queId": "330af63f48784d84b9654320fb470f8d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Linda was born on May $6$\\textsuperscript{th}. Her brother was born $9$ days earlier than her. When her brother was born? (adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$4$$) ", "answer_option_list": [[{"aoVal": "A", "content": "April $27$\\textsuperscript{th} "}], [{"aoVal": "B", "content": "May $15$\\textsuperscript{th} "}], [{"aoVal": "C", "content": "April $28$\\textsuperscript{th} "}], [{"aoVal": "D", "content": "April $26$\\textsuperscript{th} "}], [{"aoVal": "E", "content": "May $16$\\textsuperscript{th} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["Nine days before May $6$\\textsuperscript{th} is April $27$\\textsuperscript{th} "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9387", "queId": "a79efc6360814a91a354cf5f418b371c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$15$$ balls in a box: white balls, red balls and black balls. The number of white balls is $$7$$ times greater than the number of red balls. How many black balls are there in the box? ($$1998$$ Math Kangaroo Problem, Level $$3-4$$, Question \\#$$16$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["The numbers of white balls and red balls in total must be a multiple of $7+1=8$, so from $1$ to $15$, only $8$ itself can match the condition. Thus, there are $15-8=7$ black balls in the box. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9388", "queId": "9e68cd90ef4a44fc8f1f4aa9bd6aa981", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "\\textbf{\\hspace{0pt}If a business owner has a \\textsuperscript{$}100,000 accounting profit and could have made exactly $60,000 in his next best business opportunity, he has earned} ", "answer_option_list": [[{"aoVal": "A", "content": "\\textbf{$160,000 in economic profits.} "}], [{"aoVal": "B", "content": "\\textbf{$100,000 in economic profits.} "}], [{"aoVal": "C", "content": "\\textbf{$40,000 in economic profits.} "}], [{"aoVal": "D", "content": "\\textbf{neither an economic profit or loss.} "}], [{"aoVal": "E", "content": "\\textbf{none of the above.} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["\\textbf{Accounting profit = revenue minus explicit costs. Economic profit = revenue minus both explicit and implicit costs. Accounting profit is always greater than economic profit as there's always an opportunity cost. \\textsuperscript{$}100,000 accounting profit minus the implicit cost of \\textsuperscript{$}60,000 = $40,000 in economic profit.} "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9392", "queId": "a30584fea8314e718e46f33c92bd2181", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "To make coleslaw Cathy uses twice as much carrot (by weight) as cabbage. She then adds half as much yoghurt as cabbage. A pot of Cathy\\textquotesingle s coleslaw weighs $$175\\text{g}$$. How many pots of coleslaw can she make with a $$2 \\text{kg}$$ cabbage? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["The ratio by weight of carrot: cabbage:yoghurt$$=2:1:0.5$$ which we can double to give $$4:2:1$$. We can see that here $$2$$ represents the amount of cabbage and we want $$2 \\text{kg}$$ of cabbage, so there will be $$4+2+1=7\\text{kg}$$ of coleslaw altogether. Therefore the number of pots is $$7000\\div 175 =40$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9395", "queId": "7174833d892340719b5ee5134846175f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Two motor-cyclists John and Kevin were $800 \\text{km}$ apart and travelling towards each other at a constant speed. They started at the same time, meeting after $8$ hours. If Kevin started $1\\dfrac{1}{2}$ hours later than John, they would be $70 \\text{km}$ apart $8$ hours after John started. At what speed was John travelling in $\\text{km/h}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$50$$ "}], [{"aoVal": "B", "content": "$$51 \\frac{2}{3}$$ "}], [{"aoVal": "C", "content": "$$52 \\frac{1}{2}$$ "}], [{"aoVal": "D", "content": "$$53 \\frac{1}{3}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Kevin\\textquotesingle s speed $=\\dfrac{70}{1\\dfrac{1}{2}}=\\dfrac{140}{3} \\text{km/h}$ Let John\\textquotesingle s speed be $x \\text{km/h}$. $$\\left (x+ \\frac{140}{3}\\right ) \\times 8=800 \\Rightarrow x=100- \\frac{140}{3}= \\frac{160}{3}=53 \\frac{1}{3}\\text{km/h}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9396", "queId": "3765c296903248b9a2a598f21391ad5a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "February 8th, 2016 is Monday. What day is March $$30$$th, 2016? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Wednesday "}], [{"aoVal": "D", "content": "Thursday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$29-8+30=51$, $51\\div7=7\\textbackslash{} \\rm R\\textasciitilde2$,~ it\\textquotesingle s Wednesday "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9400", "queId": "83bd76cb4660437d8309b379e16cc0e0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The largest possible sum of $$4$$ unequal even numbers, none greater than $$100$$, is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$380$$ "}], [{"aoVal": "B", "content": "$$388$$ "}], [{"aoVal": "C", "content": "$$390$$ "}], [{"aoVal": "D", "content": "$$394$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["The largest possible sum is $$100 +98+96 + 94 =388$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9401", "queId": "5641a6711ce542b8938bd076880900b8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There were some pieces of candy in a bowl. Sally took half of the pieces of candy. Then Tom took half of the pieces left in the bowl. After that, Clara took half of the remaining pieces. In the end, there were $$6$$ pieces of candy left in the bowl. How many pieces of candy were in the bowl at the beginning? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems->Giving Half of a Whole"], "answer_analysis": ["$6+6=12$ $12+12=24$ $24+24=48$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9402", "queId": "d11e26a15cfa45d39ae9a5033b79cce1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Peter has $$20$$ ounces of a $$20\\textbackslash\\%$$ salt solution. How many ounces of salt should he add to make it a $$25\\textbackslash\\%$$ solution? ", "answer_option_list": [[{"aoVal": "A", "content": "$1$ ounces "}], [{"aoVal": "B", "content": "$$\\dfrac{4}{3}$$ ounces "}], [{"aoVal": "C", "content": "$4$ ounces "}], [{"aoVal": "D", "content": "$5$ ounces "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["Method $$1$$: Suppose $$x$$ ounces of salt should be added to the solution: $$\\dfrac{20\\times20\\textbackslash\\%+x}{20+x}=25\\textbackslash\\%$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde x=\\dfrac{4}{3}$$. Method $$2$$: $$20\\times(1-20\\textbackslash\\%)\\div(1-25\\textbackslash\\%)-20=\\dfrac{4}{3}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9407", "queId": "564444f8cb2d4e8aa46797342ed836f1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There were $$8$$ students in a class. Each student shook hands only once with the other $$7$$ students in the class. How many handshakes were there in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$28$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$49$$ "}], [{"aoVal": "D", "content": "$$56$$ "}]], "knowledge_point_routes": ["Overseas In-curriculum->Knowledge Point->Fun Problems in Math->Reasoning", "Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$7+6+5+4+3+2+1=28$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9409", "queId": "ba0d0fc69ce14a76986a391d0d7acd6e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$1$$ out of $$6$$ lightbulbs is defective and there are $$2016$$ lightbulbs, how many of them are not defective? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$336$$ "}], [{"aoVal": "C", "content": "$$1680$$ "}], [{"aoVal": "D", "content": "$$2016$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["$$5$$ out of $$6$$ of the $$2016$$ lightbulbs are not defective. Thus $$2016 \\times \\frac{5}{6} =1680$$ lightbulbs are not defective. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9413", "queId": "7a9f0435de2c49e9b9cd2e4ab6afba61", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a very popular Chinese restaurant, all seats were filled and there were still $$8$$ customers in line outside the door. After some time, $$11$$ customers finish eating and leave the restaurant, and then $$15$$ more customers join the waiting line. How many people are still in line outside the door? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["The line at the door started with $$8$$ people and $$15$$ more came in, for a total of $$23$$ people. After leaving $$11$$ customers, $$11$$ seats were empty, so the number of people left in line was $$23-11=12$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9416", "queId": "83c440f9d9ac42709734ac3e2b8651ed", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Siti has $$198$$ bookmarks. If she were to give $$6$$ bookmarks to each of her classmates, she would need $$18$$ more bookmarks. How many classmates does Siti have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems"], "answer_analysis": ["$198+18=216$ $216\\div6=36$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9419", "queId": "b57811ed2e0a4b26b9e126946428609f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Debbie bought a loaf of bread for $$$4$$. She paid for the bread with a $$$10$$ note. How much change did Debbie receive? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$$4$$ "}], [{"aoVal": "B", "content": "$$$6$$ "}], [{"aoVal": "C", "content": "$$$14$$ "}], [{"aoVal": "D", "content": "$$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["$$10-4=6$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9420", "queId": "3bcaa3ef644c406ab95c2a21d1a54945", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If I start with $2$ , and begin to count by $3\\textquotesingle s$ , my $50^{th}$ number will be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$149$$ "}], [{"aoVal": "B", "content": "$$150$$ "}], [{"aoVal": "C", "content": "$$151$$ "}], [{"aoVal": "D", "content": "$$152$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression"], "answer_analysis": ["$2+(50-1)\\times3=149$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9421", "queId": "3780a88a18fb41d791f6ac11fecf3dd2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Factory $$A$$ can assemble $$20$$ televisions per hour and Factory $$B$$ can assemble $$30$$ televisions per hour. With these constant rates, if $$A$$ assembles $$300$$ televisions in a period, how many televisions can $$B$$ assemble within the same period? ", "answer_option_list": [[{"aoVal": "A", "content": "$$300$$ "}], [{"aoVal": "B", "content": "$$400$$ "}], [{"aoVal": "C", "content": "$$450$$ "}], [{"aoVal": "D", "content": "$$600$$ "}], [{"aoVal": "E", "content": "$$900$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Simple Work Word Problems"], "answer_analysis": ["Time: $$300\\div20=15$$ hours. So, Factory $$B$$ can assemble $$15\\times30=450$$ televisions. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9422", "queId": "51d69539f09e47c3ae394c70483c6f0e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mike deposited ＄$$10000$$ in the bank. He earned an interest of＄$$2100$$ at the end of the second year. What is the interest rate per year of this bank? ", "answer_option_list": [[{"aoVal": "A", "content": "$21\\textbackslash\\%$ "}], [{"aoVal": "B", "content": "$11\\textbackslash\\%$ "}], [{"aoVal": "C", "content": "$10\\textbackslash\\%$ "}], [{"aoVal": "D", "content": "$9\\textbackslash\\%$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Suppose the interest rate is $$m$$: $$\\begin{eqnarray}10000\\times \\left( 1+m \\right)\\times \\left( 1+m \\right)\\&=\\&10000+2100 \\textbackslash\\textbackslash{} m\\&=\\&0.1 \\end{eqnarray}$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9423", "queId": "402011f692d94d2db9e1004fa7ae8e80", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Given that May $4$ of a given year is a Wednesday, what day is May $30$ of the same year? ", "answer_option_list": [[{"aoVal": "A", "content": "Saturday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Tuesday "}], [{"aoVal": "E", "content": "Monday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems"], "answer_analysis": ["$30-4=26$ days later, it will be May $30$\\textsuperscript{th}. $26\\div7=3R5$, which means May $30$\\textsuperscript{th}~is Monday.~ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9425", "queId": "a30fceda0e3543a3b799604253c82cde", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "There are two factories producing the same kind of car parts. There are $36$ workers in factory $A$, and every worker produces $81$ parts on average. Each worker produces $101$ parts on average in factory $B$. Each worker can produce $89$ parts on average in two factories together. How many workers are there in factory $B$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$38$$ "}], [{"aoVal": "B", "content": "$$34$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$22$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$$36\\times (89-81)\\div (101-89)=24$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9427", "queId": "4d61a97744b0415fb70b60b3bff66ad4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Two motor-cyclists John and Kevin were $800 \\text{km}$ apart and travelling towards each other at a constant speed. They started at the same time, meeting after $8$ hours. If Kevin started $1\\dfrac{1}{2}$ hours later than John, they would be $70 \\text{km}$ apart $8$ hours after John started. At what speed was John travelling in $\\text{km/h}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$50$$ "}], [{"aoVal": "B", "content": "$$51 \\frac{2}{3}$$ "}], [{"aoVal": "C", "content": "$$52 \\frac{1}{2}$$ "}], [{"aoVal": "D", "content": "$$53 \\frac{1}{3}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Kevin\\textquotesingle s speed $=\\dfrac{70}{1\\dfrac{1}{2}}=\\dfrac{140}{3} \\text{km/h}$ Let John\\textquotesingle s speed be $x \\text{km/h}$. $$\\left (x+ \\frac{140}{3}\\right ) \\times 8=800 \\Rightarrow x=100- \\frac{140}{3}= \\frac{160}{3}=53 \\frac{1}{3}\\text{km/h}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9432", "queId": "5f56860399464eeb88bbc7dcfd4b341c", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Alex and Bob love to fold cranes. For a bag of $N$ cranes, Alex will need $2$ hours to complete while Bob will need $3$ hours. One morning, Alex and Bob started to fold cranes at the same time. After $30$ minutes, Alex rested for $10$ minutes before continuing to fold cranes while Bob did not rest at all. When they finished a bag of $N$ cranes together, Alex folded $24$ more cranes than Bob. Find the value of $N$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$120$$ "}], [{"aoVal": "D", "content": "$$150$$ "}], [{"aoVal": "E", "content": "$$180$$ "}], [{"aoVal": "F", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems"], "answer_analysis": ["E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9433", "queId": "8865cb4fc838463e85819689c1175bb6", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Jill is now $$14$$ years old. Jack is now $$6$$ years older than Jill was $$2$$ years ago. How old is Jack now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["Jill is now $$14$$. Two years ago, she was $$12$$. Since Jack is now $$6$$ years older than Jill was $$2$$ years ago, Jack is now $$12 + 6= 18$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9434", "queId": "5acfafb50e9c41a1ab3dab0962101196", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Chole has $64$ crackers and she is distributing the crackers to her $8$ friends. How many crackers will each of them get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$64\\div 8=8$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9440", "queId": "3794b685f0c94fe69155510df6e21e71", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Marko has $$9$$ pieces of candy and Tomo has $$17$$ pieces of candy. How many pieces of candy does Tomo need to give to Marko so that each boy has the same number of pieces of candy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Giving and Receiving"], "answer_analysis": ["Difference: $17-9=8$ Move: Half of $8=4$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9441", "queId": "3bde365a4cfc4b2c875e244600448dd6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a mathematics contest with ten problems, a student gains $$5$$ points for a correct answer and loses $$2$$ points for an incorrect answer. If Olivia answered every problem and her score was $$29$$, how many correct answers did she have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Suppose Olivia has $$x$$ correct answers. $$5x-2(10-x)=29$$, $$x=7$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9442", "queId": "954a5d71488e4d12a664ecf711cbd117", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $10$ trees on one side of a road. Workers plan to set one rubbish bin bwtween every two adjacent trees. How many rubbish bins do they need to prepare? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$10 - 1 = 9$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9444", "queId": "7aa9bb5cffef43f0b8f4da43ad563ea1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mary and Jimmy are eating ice cream of the same size. Jimmy eats ice cream twice as fast as Mary. Mary finishes in four minutes. How many minutes Jimmy need?~(adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["Jimmy\\textquotesingle s speed is twice as fast as Mary\\textquotesingle s, and the ice cream they eat is the same size, so Jimmy\\textquotesingle s time is only half as long as Mary\\textquotesingle s, that is, $4$$\\div$$2= $$2$ minutes. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9447", "queId": "761607a717554c09901566064b91d134", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$60\\text{cm}$$ of snow falls each hour, how much falls in $$100$$ minutes? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90\\text{cm}$$ "}], [{"aoVal": "B", "content": "$$1\\text{m}$$ "}], [{"aoVal": "C", "content": "$$110\\text{cm}$$ "}], [{"aoVal": "D", "content": "$$120\\text{cm}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"], "answer_analysis": ["$$60 \\text{cm}/\\text{hr} =1 \\text{cm}/\\min = 100 \\text{cm}/100 \\text{mins} = 1 \\text{m}/100 \\text{mins}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9451", "queId": "99e1110d7c0544a6b5b802e5b5c00f44", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$9$$ numbers with an average of $$72$$. After eliminating a number, the average of the remaining numbers is $$78$$. What is the eliminated number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$64$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$48$$ "}], [{"aoVal": "E", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$(78-72)\\times8=48$, $72-48=24$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9456", "queId": "beb82440b0c34c1a8810da594fd2322a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "James made a running plan for this week. He ran $4$ km on average for the three days, and ran an average of $6$ km for the next two dyas, and ran $18$ km in total for the remaining two days to complete his plan. How many kilometers are there in James\\textquotesingle{} running plan? ", "answer_option_list": [[{"aoVal": "A", "content": "$$28$$ "}], [{"aoVal": "B", "content": "$$34$$ "}], [{"aoVal": "C", "content": "$$38$$ "}], [{"aoVal": "D", "content": "$$42$$ "}], [{"aoVal": "E", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$4\\times3+6\\times2+18=42$ km. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9457", "queId": "7f3f01a0ea744efc8dde4e4bdd4d58fb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$20$$ years ago Allen was half as old as he is today, how old was he $$10$$ years ago? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->When..., When... Type Age Problems"], "answer_analysis": ["If $$20$$ years ago Allen was half as old as he is today, then today he is $$40$$. Thus, $$10$$ years ago he was $$30$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9459", "queId": "63ec3ea48fbd4c75b97ffa746f26c47d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "THere are 3 families in my neighbourhood with three children each; two of the families have twins. All twins are boys. At most how many girls are in these families? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["There are 3 families with 3 children = 3 x 3=9. If there are 2 twin boys, 2 x 2 = 4, 0-4=5. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9460", "queId": "deff31c98b344779b5d5fa74f12b3163", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Abigail is saving $$50$$p each week. How many weeks will she take to save £$$20$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$35$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["£$$20 \\div 50p=40$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9467", "queId": "9e80d9e01a89420d8120bb710d74a711", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My sister runs $$10\\text{km}$$ per hour, and I run $$2\\text{km}$$ in $$15$$ minutes. If we both run for $$2$$ hours, my sister will run$$\\text{km}$$ farther than I will. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"], "answer_analysis": ["I run $$2\\text{km}$$ in $$15$$ minutes, or $$8\\text{km}$$ in $$1$$ hour. In $$2$$ hours, I will run $$16\\text{km}$$ and my sister will run $$20\\text{km}$$. She will run $$4\\text{km}$$ farther than I will. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9469", "queId": "6d06939582f94b6c808037ef54bdb186", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Tobby attended a Nasional Maths Olympaid (NMO). Tobby answered all $50$ questions. For each correct answer, Tobby will get $4$ marks. However, for each wrong answer, Tobby will deduct $1$ mark. If Tobby scored $110$ marks in total, how many questions did Tobby answer correctly? ", "answer_option_list": [[{"aoVal": "A", "content": "$$42$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems"], "answer_analysis": ["Assume all questions were answered correctly, Total score $=50\\times4=200$ Difference in total score $=200-110=90$ Change in score $=4+1=5$ No. of incorrect answer $=90\\div5=18$ Correct answers $=50-18=32$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9470", "queId": "90bad77418174e2eb47ba413099a043d", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Patrick gets $50 \\textbackslash\\%$ on a 10 -problem test, $30 \\textbackslash\\%$ on a 20 -problem test and $30 \\textbackslash\\%$ on a 30 -problem test. If the three tests are combined into one 60 problem test, which percent is closest to her overall score? (adapted from 2006 AMC 8, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$33$$ "}], [{"aoVal": "B", "content": "$$44$$ "}], [{"aoVal": "C", "content": "$$55$$ "}], [{"aoVal": "D", "content": "$$66$$ "}], [{"aoVal": "E", "content": "$$99$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$50 \\textbackslash\\% \\cdot 10=5$ $30 \\textbackslash\\% \\cdot 20=6$ $30 \\textbackslash\\% \\cdot 30=9$ Adding them up gets $5+6+9=20$. The overall percentage correct would be $\\frac{20}{60}=\\frac{1}{3}=0 . \\overline{3} \\approx(\\mathbf{A}) 33$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9476", "queId": "6d0a5aa02e3d40849e0091c7d87b984c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The state income tax where Kristin lives is levied at the rate of $$p\\textbackslash\\%$$ of the first ＄$$28000$$ of annual income plus $$ \\left( {p+2} \\right) \\textbackslash\\%$$ of any amount above ＄$$28000$$. Kristin noticed that the state income tax she paid amounted to $$ \\left( {p+0.25} \\right) \\textbackslash\\%$$ of her annual income. What was her annual income? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$28000$$ "}], [{"aoVal": "B", "content": "＄$$32000$$ "}], [{"aoVal": "C", "content": "＄$$35000$$ "}], [{"aoVal": "D", "content": "＄$$42000$$ "}], [{"aoVal": "E", "content": "＄$$56000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"], "answer_analysis": ["method $$1$$：$$Let$$ the income amount be denoted by $$A$$. We know that $$\\frac{A\\left( p+.25 \\right)}{100}=\\frac{28000p}{100}+\\frac{\\left( p+2 \\right)\\left( A-28000 \\right)}{100}$$ We can now try to solve for $$A$$: $$\\left( p+.25 \\right)A=28000p+Ap+2A-28000p-56000$$ $$.25A=2A-56000$$ $$A=32000$$ so the answer is $$\\boxed{ \\text {B}}$$. method $$2$$：$$Let$$ $$A$$, $$T$$ be Kristin\\textquotesingle s annual income and the income tax total, respectively. Notice that　 $$T=p\\textbackslash\\%\\cdot 28000+\\left( p+2 \\right)\\textbackslash\\%\\cdot \\left( A-28000 \\right)$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde$$$$=\\left[ p\\textbackslash\\%\\cdot 28000+p\\textbackslash\\%\\cdot \\left( A-28000 \\right) \\right]+2\\textbackslash\\%\\cdot \\left( A-28000 \\right)$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde$$$$=p\\textbackslash\\%\\cdot A+2\\textbackslash\\%\\cdot \\left( A-28000 \\right)$$ We are also given that $$T=\\left( p+0.25 \\right)\\textbackslash\\%\\cdot A=p\\textbackslash\\%\\cdot A+0.25\\textbackslash\\%\\cdot A$$ Thus, $$p\\textbackslash\\%\\cdot A+2\\textbackslash\\%\\cdot \\left( A-28000 \\right)=p\\textbackslash\\%\\cdot A+0.25\\textbackslash\\%\\cdot A$$ $$2\\textbackslash\\%\\cdot \\left( A-28000 \\right)=0.25\\textbackslash\\%\\cdot A$$ Solve for $$A$$ to obtain $$A=32000$$. $$\\boxed{ \\text {B}}$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9481", "queId": "99eafebd63d4426ba4434acd297edb8d", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "A salt solution is made by mixing $$8$$ grams of pure salt and $$32$$ grams of water. Find the percent concentration of the solution. ", "answer_option_list": [[{"aoVal": "A", "content": "$$10\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$15\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$20\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$25\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$8\\div(8+32)=20\\textbackslash\\%$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9485", "queId": "63fe9b708f3a4d7f9d18a7b2052be13b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "There are $$8$$ standing in a straight line. The first student is at the start of the line, and the last student is at the end of the line. The distance between each student is $$2$$ meters. How long is the line? (Ignore the thickness of the trees.) ", "answer_option_list": [[{"aoVal": "A", "content": "$8$ meters "}], [{"aoVal": "B", "content": "$$11$$ meters "}], [{"aoVal": "C", "content": "$$14$$ meters "}], [{"aoVal": "D", "content": "$15$ meters "}], [{"aoVal": "E", "content": "$16$ meters "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["There are $7$ intervals between the first student and the last student. Thus, the line is $7 \\times2 = 14$ meters long. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9488", "queId": "9e87ce49fbae4bc8b2f6069467886260", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "June $$1^{}\\text{st}$$ $$2013$$ falls on a Saturday. On what day of the week will August $$21^{}\\text{st}$$ $$2013$$ fall? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Friday "}], [{"aoVal": "D", "content": "Saturday "}], [{"aoVal": "E", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$$30-1+31+21=81$$, $$81\\div7=11$$R$$4$$. $$4$$ days after a Saturday is a Wednesday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9489", "queId": "37c88c0c80504ab7a8bf8b25caa9090d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2015 P2 Q3 The sum of two numbers is 300. One number is 5 times of the other number. What is the difference between the two numbers? ", "answer_option_list": [[{"aoVal": "A", "content": "$$50$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$180$$ "}], [{"aoVal": "D", "content": "$$200$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems"], "answer_analysis": ["x = 1u y = 5u 6u = 300 1u = 50 So, x=50, y=250 Difference 250-50=200 "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9493", "queId": "44c3033e06794c5fb604ec1f5043387b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Cathy is drawing flowers. The first one is red, the next one blue, the one after it yellow, the fourth one pink, and then again red, blue, yellow, pink, and so on, in the same order. What color will be the $19$\\textsuperscript{th}~flower? (Adapted from 2003 Math Kangaroo Problem, Level 3-4, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$Blue "}], [{"aoVal": "B", "content": "$$$$Pink "}], [{"aoVal": "C", "content": "$$$$Red "}], [{"aoVal": "D", "content": "$$$$Black "}], [{"aoVal": "E", "content": "$$$$Yellow "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"], "answer_analysis": ["$19\\div4=4R3$, so the $19$\\textsuperscript{th} flower is yellow. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9495", "queId": "640439984b8940a5b4123e7571be7d12", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "John drinks $x$ cups of boba everyday on weekdays and $2$ cups of boba everyday on the weekends. Which of the following equations represents how many cups of boba John drinks every week? ", "answer_option_list": [[{"aoVal": "A", "content": "$x+2$ "}], [{"aoVal": "B", "content": "$5x+2$ "}], [{"aoVal": "C", "content": "$5x+4$ "}], [{"aoVal": "D", "content": "$5x-4$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"], "answer_analysis": ["The boba that John drinks during weekdays: $$5x$$ The boba that John drinks during weekends: $$2\\times 2 =4$$ The total boba that John drinks during a week: $$5x+4$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9499", "queId": "ece925b54e5946a7a5ca47b790a8e5a8", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Of $$60$$ flamingos, twice as many stood on $$2$$ legs as stood on $$1$$. All together, on how many legs did all of these flamingos stand? ", "answer_option_list": [[{"aoVal": "A", "content": "$$80$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$110$$ "}], [{"aoVal": "E", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["Of $$60$$ flamingos, $$40$$ stood on $$2$$ legs and $$20$$ stood on $$1$$. All together, these flamingos stood on $$[(40\\times2)+20]$$ legs $$=100$$ legs. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9505", "queId": "ba22cfab830940a2803fdbb3894482f8", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A worm is staying at the bottom of a well with a depth of $$10$$ metres. If it climbs up $$3$$ metres in the daytime and slips down $$2$$ metres at night, which day will it climb up to the ground? ", "answer_option_list": [[{"aoVal": "A", "content": "The $$6$$th day "}], [{"aoVal": "B", "content": "The $$7$$th day "}], [{"aoVal": "C", "content": "The $$8$$th day "}], [{"aoVal": "D", "content": "The $$9$$th day "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9506", "queId": "6d181ba5ace24283aa31d382632d4f86", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Peter has some toy cars, and Paul has $$4$$ more toy cars than Peter. Altogether they have $$28$$ toy cars. How many toy cars does Paul have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference->Sum and Differences Problems with multiple Variables"], "answer_analysis": ["Paul has $$(28 + 4) \\div 2 = 16$$ toy cars. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9509", "queId": "6d1c39511b6046e595339941fd7f6694", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The average age of all the teachers in Gotia School is $34$. There are $3$ male teachers in Gotia School with an average age of $27$. The average age of female teachers is $35$. How many female teachers are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Total age less than the average: $(34-27)\\times3=21$. Thus, there are $21\\div(35-34)=21$ female teachers. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9510", "queId": "406f0a8cb566408a80b07d7c1130d75a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Cagney can frost a cupcake every $$20$$ seconds and Lacey can frost a cupcake every $$30$$ seconds. Working together, how many cupcakes can they frost in $$5$$ minutes? ($$2012$$ AMC $$10\\rm A$$ Problem, Question \\#$$11$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$25$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"], "answer_analysis": ["Method1: Cagney can frost one in $$20$$ seconds, and Lacey can frost one in $$30$$ seconds. Working together, they can frost one in $$\\dfrac{20\\cdot30}{20+30}=\\dfrac{600}{50}=12$$ seconds. In $$300$$ seconds ( $$5$$ minutes), they can frost $$\\boxed{(\\text{D})25}$$ cupcakes. Method2: In $$300$$ seconds ($$5$$ minutes), Cagney will frost $$\\dfrac{300}{20}=15$$ cupcakes, and Lacey will frost $$\\dfrac{300}{30}=10$$ ~cupcakes. Therefore, working together they will frost $$15+10=\\boxed{(\\text{D})25}$$ cupcakes. Method3: Since Cagney frosts $$3$$ cupcakes a minute, and Lacey frosts $$2$$ cupcakes a minute, they together frost $$3+2=5$$ cupcakes a minute. Therefore, in $$5$$ minutes, they frost $$5\\times5=25\\Rightarrow\\boxed{(\\text{D})}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9522", "queId": "407e95181c9940f081c228346190bec2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Bill, Sarah and James each has $4$ candies. Bill gives James some candies and James gives Sarah some candies. How many candies are there in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Giving candies to each other won\\textquotesingle t affect the sum of their candies, so there are $$4+4+4=12$$~in total. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9524", "queId": "4080949176fc456184d584b7e9080f01", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Grandma made some cheese dumplings and some blueberry dumplings. Altogether, she made $$31$$ dumplings. If she had made $$11$$ more cheese dumplings, then there would be the same number of blueberry dumplings as cheese dumplings. How many cheese dumplings did grandma make? (2009 Math Kangaroo Problem, Levels 1-2, Question \\#19) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["$$(31-11)\\div2=10.$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9525", "queId": "99fd17a78eb041abb72bb333d82401a9", "competition_source_list": ["其它"], "difficulty": "4", "qtype": "single_choice", "problem": "If an object is thrown straight upward with an initial speed of 8 m/s and takes 3 seconds to strike the ground, from what height was the object thrown? $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ $\\textasciitilde$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$24.2m$$ "}], [{"aoVal": "B", "content": "$$21m$$ "}], [{"aoVal": "C", "content": "$$23m$$ "}], [{"aoVal": "D", "content": "$$2.3m$$ "}], [{"aoVal": "E", "content": "$$69m$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems->Finding the Height in Snail Climbing out of Wall Problems (completed) "], "answer_analysis": ["Key: object is thrown upward. When it reaches the highest point, the velocity is 0. The whole journey is divided into 2 parts: upward - highest point - downward to hit the ground. 2 parts have different displacement (and different time). "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9528", "queId": "4086c5639b894c18a3a528c6fcf0b1cb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amit, Bede, Cain, Devi, Emily and Frederick sit around a circular table in that order. Amit starts by saying \"$$2015$$\", Bede says \"$$2016$$\", Cain says~\"$$2017$$\" and so on round the table. Who will eventually say\"$$5102$$\"? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$Amit "}], [{"aoVal": "B", "content": "$$$$Bede "}], [{"aoVal": "C", "content": "$$$$Cain "}], [{"aoVal": "D", "content": "$$$$Devi "}], [{"aoVal": "E", "content": "$$$$Emily "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Circular Operations"], "answer_analysis": ["After Amit says \"$$2015$$\", there are $$5102-2015=3087$$ numbers remaining. Thus the counting goes round the table $$3087\\div6= 514$$ times with a remainder of $$3$$, so the last to count is Devi. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9534", "queId": "408fc64c273841a58fdf3c4ea97ff465", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The length of a rectangle is increased by $50\\textbackslash\\%$ and the width is decreased by $20\\textbackslash\\%$. What percent of the old area is the new area? (adapted from 2009 AMC 8, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ "}], [{"aoVal": "B", "content": "$$95$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$110$$ "}], [{"aoVal": "E", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$1.5\\times 0.8= 120\\textbackslash\\%$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9542", "queId": "494f5d85e2a74696823f1a11f9ce794e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$2$$ apples and $$3$$ peaches cost $$$11$$. $$2$$ apples and $$2$$ peaches cost $$$8$$. What is the cost of an apple? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$1$$ "}], [{"aoVal": "B", "content": "$$$2$$ "}], [{"aoVal": "C", "content": "$$$3$$ "}], [{"aoVal": "D", "content": "$$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Equivalent Substitution in Equation Word Problems"], "answer_analysis": ["$$2$$ apples $$+\\textasciitilde3$$ peaches$$\\to $$ ＄$$11$$ $$2$$ apples $$+\\textasciitilde2$$ peaches $$\\to $$ ＄$$8$$ $$1$$ peach $$\\to $$ ＄$$3$$ $$2$$ apples $$+$$ ($$2$$ $$\\times$$ ＄$$3$$) $$\\to $$ ＄$$8$$ $$2$$ apples $$\\to $$ ＄$$8\\textasciitilde-$$ ＄$$6=$$＄$$2$$ $$1$$ apple $$\\to $$ ＄$$2\\div2=$$＄$$1$$ The cost of an apple is ＄$$1$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9550", "queId": "642c501efe3647c98a1998d50006e33a", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "Jenny need to reach her teacher house by $$2.15 \\rm{p.m}$$ for piano class. From her house to teacher\\textquotesingle s house, she need to walk for $$20$$ minutes. She was late for $$10$$ minutes. What time did she leave her house? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2.05 \\rm{a.m.}$$ "}], [{"aoVal": "B", "content": "$$2.05 \\rm{p.m.}$$ "}], [{"aoVal": "C", "content": "$$1.55 \\rm{a.m.}$$ "}], [{"aoVal": "D", "content": "$$1.55 \\rm{p.m.}$$ "}], [{"aoVal": "E", "content": "$$2.25 \\rm{p.m.}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["She reached at $$2.25 \\rm{p.m.}$$, thus, $$20$$ minutes before that is $$2.05 \\rm{p.m.}$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9553", "queId": "a339c18bb7234b0e80add4b2a31bcca8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I am twice the age of each of my sons, Barry and Larry. Our three ages have a total of $$76$$. How old is Barry?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$9\\frac{1}{2}$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$19$$ "}], [{"aoVal": "D", "content": "$$36$$ "}], [{"aoVal": "E", "content": "$$38$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Sums and Multiples in Age Problems"], "answer_analysis": ["The three ages have a total of four times Barry\\textquotesingle s age. So Barry is $$76\\div4 = 19$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9557", "queId": "8c45b197bf7b46b4981024bc06fb180c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mike has $$47$$ ounces of salt solution. Given that there are $$12$$ ounces of pure salt in the solution, how much water is there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ ounces "}], [{"aoVal": "B", "content": "$$35$$ ounces "}], [{"aoVal": "C", "content": "$$45$$ ounces "}], [{"aoVal": "D", "content": "$$59$$ ounces "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$47 -- 12 = 35$$ ounces. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9561", "queId": "6430e68c19724d3e92177cb405b172ea", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Orange peel is a type of orange color mixing red and yellow paint with a ratio of $1:2$. In the shop, red paint is selling at $5$ dollars per ounce and yellow paint is selling at $4$ dollars per ounce. If Richard wants to make $12$ ounces of orange peel, how much money does she need? ", "answer_option_list": [[{"aoVal": "A", "content": "$48$ dollars "}], [{"aoVal": "B", "content": "$52$ dollars "}], [{"aoVal": "C", "content": "$56$ dollars "}], [{"aoVal": "D", "content": "$60$ dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["$12\\div (1+2)=4$ $4\\times (1\\times 5+2\\times 4)=4\\times 13=52$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9563", "queId": "56b4b5e45deb431897b360566bb3d215", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "At the \"Think Flea Market\", a vendor is offering a \"fair special\" on plushies. If you buy one plushie at the regular price of $\\textbackslash$ 50$, you get a second one at a $40 \\textbackslash\\%$ discount, and a third one at half the regular price. Owen takes advantage of the \"fair special\" to buy three plushies. What percentage of the $\\textbackslash$ 150$ regular price will he save? (adapted from 2013 AMC 8, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$40$$ "}], [{"aoVal": "E", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["First, find the amount of money one will pay for three sandals without the discount. We have $\\textbackslash$ 50 \\times 3$ sandals $=\\textbackslash$ 150$. Then, find the amount of money using the discount: $50+0.6 \\times 50+\\frac{1}{2} \\times 50=\\textbackslash$ 105$. Finding the percentage yields $\\frac{105}{150}=70 \\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-70 \\textbackslash\\%=(\\text{B}) 30$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9566", "queId": "3c68ddae9a40404bb32c8a1c4e2d23d9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In London 2012, the USA won the most medals: 46 Gold, 29 Silver and 29 Bronze. China was second with 38 Gold, 27 Silver and 23 Bronze. How many more medals did the USA win compared to China? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$26$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"], "answer_analysis": ["USA won - 104 medals in total\\textquotesingle{} China won 88 medals. Difference = 16. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9567", "queId": "c371e4888cc744ddabb20c3407918d34", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Anna, Bridgit and Carol run in a $$100\\text{m}$$ race. When Anna finishes, Bridgit is $$16\\text{m}$$ behind her and when Bridgit finishes, Carol is $$25\\text{m}$$ behind her. The girls run at constant speeds throughout the race. How far behind was Carol when Anna finished? ", "answer_option_list": [[{"aoVal": "A", "content": "$$37\\text{m}$$ "}], [{"aoVal": "B", "content": "$$41\\text{m}$$ "}], [{"aoVal": "C", "content": "$$50\\text{m}$$ "}], [{"aoVal": "D", "content": "$$55\\text{m}$$ "}], [{"aoVal": "E", "content": "$$60\\text{m}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Carol finishes $$25$$ metres behind Bridgit, so she travels $$75$$ metres while Bridgit runs $$100$$ metres. Therefore she runs $$3$$ metres for every $$4$$ metres Bridgit runs. When Anna finishes, Bridgit has run $$84$$ metres, so that at that time Carol has run $$\\frac{3}{4}\\times 84$$ metres $$=63$$ metres. Hence Carol finishes $$\\left( 100-63 \\right)$$ metres $$= 37$$ metres behind Anna. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9569", "queId": "ba37defb38764d6982883b705696ea00", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Speedy Wiggins cycles to school, a journey that takes $$30$$ minutes at $$12$$mph. How far does he travel to school? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$miles "}], [{"aoVal": "B", "content": "$$4$$miles "}], [{"aoVal": "C", "content": "$$6$$miles "}], [{"aoVal": "D", "content": "$$10$$miles "}], [{"aoVal": "E", "content": "$$20$$miles "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Cycling at $$12$$ mph, Speedy would go $$12$$ miles in an hour. So in $$30$$ minutes he cycles $$12$$ miles $$\\div2 = 6$$ miles. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9570", "queId": "6437e7c89b9b4e20a9c92827a1f5c72b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Geraint always cycles to work, leaving at $$8$$am every morning. When he averages $$15{\\text{km}}/{\\text{h}}\\textbackslash;$$,he arrives $$10$$ minutes late. However, when he averages $$30{\\text{km}}/{\\text{h}}\\textbackslash;$$, he arrives $$10$$ minutes early. What speed should he average to arrive on time? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20{\\text{km}}/{\\text{h}}\\textbackslash;$$ "}], [{"aoVal": "B", "content": "$$21{\\text{km}}/{\\text{h}}\\textbackslash;$$ "}], [{"aoVal": "C", "content": "$$22.5{\\text{km}}/{\\text{h}}\\textbackslash;$$ "}], [{"aoVal": "D", "content": "$$24{\\text{km}}/{\\text{h}}\\textbackslash;$$ "}], [{"aoVal": "E", "content": "$$25{\\text{km}}/{\\text{h}}\\textbackslash;$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Let $$x\\text{km}$$ be the distance Geraint cycles and let $$t $$ hours be the time his journey should take if he is to be on time. Since $$\\frac{\\text{distance}}{\\text{speed}}\\text{=time}$$, the information in the question tells us that $$\\frac{x}{15}=t+\\frac{1}{6}$$ and that $$\\frac{x}{30}=t-\\frac{1}{6}$$. When we subtract the second equation from the first, we obtain $$\\frac{x}{30}=\\frac{2}{6}$$ and so $$x = 10$$. Hence, from the second equation, $$\\frac{10}{30}=t-\\frac{1}{6}$$ and so $$t=\\frac{1}{3}+\\frac{1}{6}=\\frac{1}{2}$$. Therefore, to arrive on time, Geraint needs to travel $$10\\text{km}$$ in~ $$\\frac{1}{2}$$ hour, which is an average speed of $$20{\\text{km}}/{\\text{h}}\\textbackslash;$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9577", "queId": "4514c719b35842dc9d79e45621b76ee0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Susie Starfish and her five sisters went to the cinema with Ollie Octopus and his four brothers. They bought a box of popcorn for every arm they had. How many boxes of popcorn did they buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$57$$ "}], [{"aoVal": "C", "content": "$$62$$ "}], [{"aoVal": "D", "content": "$$65$$ "}], [{"aoVal": "E", "content": "$$70$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["There are $$6$$ starfish and $$5$$ octopuses. So the number of boxes $$=6 \\times5+5\\times8 =70$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9586", "queId": "5fb74c0fec144ef491685e551abd0824", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $$12-$$hour clock loses $$10$$ minutes each day. The clock will first return to the correct time in． ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ days "}], [{"aoVal": "B", "content": "$$72$$ days "}], [{"aoVal": "C", "content": "$$120$$ days "}], [{"aoVal": "D", "content": "$$144$$ days "}], [{"aoVal": "E", "content": "$60$ days "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems"], "answer_analysis": ["Clock shows the correct time after a $$12-$$hr loss. With a $$10-$$min. loss daily, it takes $$6$$ days to lose $$1$$ hr \\& $$72$$ days to lose $$12$$ hr. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9591", "queId": "5b3dd89128d14482b7736fa43031aa5b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "After a discount of $$30\\textbackslash\\%$$, the price of a bed is＄$$210$$. Besides, senior citizens are given a further discount of＄$$15$$. What is the percentage discount given to senior citizens for the bed? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$32\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$35\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$36\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["Original price: $$\\frac{210}{(1-30\\textbackslash\\%)}=300$$. Selling price after discount: $$210-15=195$$. Discount rate: $$1-\\left( {\\frac{195}{300}} \\right)=1-65\\textbackslash\\%=35\\textbackslash\\%$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9598", "queId": "5b44a69771d5483fa2343438ee2dc48a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Alex had some trading cards. After giving $36$ trading cards to Ben, Alex received another $42$ trading cards from David. If Alex has $241$ trading cards now, how many trading cards does he have at first? ", "answer_option_list": [[{"aoVal": "A", "content": "$$235$$ "}], [{"aoVal": "B", "content": "$$230$$ "}], [{"aoVal": "C", "content": "$$225$$ "}], [{"aoVal": "D", "content": "$$220$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["$241-42+36=235$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9606", "queId": "49901f8f792c4a3f9f1fa0d1252a1a87", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "How many digits have to be written in order to write down every number from $$1$$ to $$110$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$110$$ "}], [{"aoVal": "B", "content": "$$109$$ "}], [{"aoVal": "C", "content": "$$221$$ "}], [{"aoVal": "D", "content": "$$222$$ "}], [{"aoVal": "E", "content": "$$330$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem->Correspondence between Numbers and Page Numbers->Applying the Total Number of Numbers"], "answer_analysis": ["From $$1$$ to $$9$$ there are~$1\\times9=9$~digits. From $$10$$ to $$99$$ there are~$2\\times90=180$~digits. From $$100$$ to $$110$$ there are~$3\\times11=33$~digits. In total, there are$9+180+33=222$~digits "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9607", "queId": "bee5b3fe410544feb149680014399d25", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Daniel raises some ducks and dogs. All the ducks and dogs have $18$ legs and $5$ pairs of wings in total. If all the ducks and dogs each lifts one leg off the ground, they lift~\\uline{~~~~~~~~~~}~legs in total. ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems"], "answer_analysis": ["$5$ pairs of wings means there are $5$ ducks, so there are $18-5\\times2=8$ legs for dogs, which is $8\\div4=2$. Thus, there are $2+5=7$ animals and they will lift $7$ legs. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9608", "queId": "71eba6fa8d574e778630b3f6ae41ab5f", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Lewis drives from London to Brighton at an average speed of $$60\\text{mph}$$. On the way back, he gets stuck in traffic and his average speed is only $$40\\text{mph}$$. What is his average speed for the whole journey? ", "answer_option_list": [[{"aoVal": "A", "content": "$$55\\text{mph}$$ "}], [{"aoVal": "B", "content": "$$50\\text{mph}$$ "}], [{"aoVal": "C", "content": "$$48\\text{mph}$$ "}], [{"aoVal": "D", "content": "$$45\\text{mph}$$ "}], [{"aoVal": "E", "content": "Impossible to determine "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Bus Departure Time Word Problems"], "answer_analysis": ["Let the distance from London to Brighton be $$d$$ miles. Since time $$=$$ distance $$\\div$$ speed, the times Lewis spent on the two parts of his journey are $$\\frac{d}{60}$$ hours and $$\\frac{d}{40}$$ hours. Hence the total time in hours that he travelled is$$\\frac{d}{60}+ \\frac{d}{40}= \\frac{2d+3d}{120}= \\frac{5d}{120}= \\frac{d}{24}$$. Therefore his average speed for the whole journey is $$2d \\div \\left( \\frac{d}{24}\\right)\\text{mph}=48 \\text{mph}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9612", "queId": "40ebe1d544954fa0a7a67600a880843a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $$15\\textbackslash\\%$$ sugar solution contains $$18$$ grams of pure sugar. How many ounces of solution are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ grams "}], [{"aoVal": "B", "content": "$$100$$ grams "}], [{"aoVal": "C", "content": "$$120$$ grams "}], [{"aoVal": "D", "content": "$$150$$ grams "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$18\\div15\\textbackslash\\% = 120$$ grams. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9616", "queId": "5fd95fe610f44b40b1a8cf959304cf69", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Judy needed to reach the $10$\\textsuperscript{th} floor of a building. It took her $40$ seconds to walk from the $1$\\textsuperscript{st} floor to the $5$\\textsuperscript{th} floor. How many seconds will it take to go from the $3$\\textsuperscript{rd}~to the $10$\\textsuperscript{th} floor at the same speed? ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$70$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$90$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$40 \\div (5 - 1) = 10$ $(10 - 3) \\times 10 = 70$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9617", "queId": "90fcb230909c44beb9741a17f28dd328", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Bill, Sarah and James each has $4$ cookies at beginning. Bill gives James some cookies and James gives Sarah $2$ cookies. How many cookies do they have in total now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Giving cookies to each other won\\textquotesingle t affect the sum of their cookies, so there are $$4+4+4=12$$~in total. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9620", "queId": "49a31a9abe494b6e853a69f020319dad", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a class of $$18$$ students, $$6$$ are wearing jeans. What is the ratio of students wearing jeans to students \\emph{not} wearing jeans? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1:2$$ "}], [{"aoVal": "B", "content": "$$1:3$$ "}], [{"aoVal": "C", "content": "$$2:3$$ "}], [{"aoVal": "D", "content": "$$2:1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"], "answer_analysis": ["If $$6$$ students are wearing jeans, then $$18-6=12$$ are not. The ratio of students wearing jeans to students \\emph{not} wearing jeans is $$6:12=1:2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9621", "queId": "a7f003d986c043f990962cd6581d9a9f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "On average, each student has $$14$$ balls. Each of the $$15$$ girls has $$24$$ balls on average. There are $$25$$ boys, and their average number of balls is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$$14\\times(15+25)=560$$ $$560-15\\times24=200$$ $$200\\div25=8$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9623", "queId": "b11dfeb06006427fa6255cce3d6cfb3b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "All the animals stand in rows in the magic forest. There is the same number of animals in each row. There are $3$ rows on the left of monkey and $2$ rows on the right of it. In its row, there are $6$ animals in front of it and $2$ animals behind it. How many animals are there in the forest? ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$54$$ "}], [{"aoVal": "E", "content": "$$63$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$(3 + 2 + 1) \\times (6 +2 +1) = 54$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9624", "queId": "ba4b4635915246f482975bf8a3e01e7b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Billy has twice as many basketballs as soccer balls. Milly has four times as many soccer balls as basketballs. They have a total of 18 balls. How many of them are basketballs? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Indefinite Equation Word Problems"], "answer_analysis": ["Let Billy have $$b$$ soccer balls and $$2b$$ basketballs. Let Milly have $$m$$ basketballs and $$4m$$ soccer balls. Therefore, as they have $$17$$ balls in total, $$3b + 5m= 18$$. The only positive integer solution of this equation is $$b= 1$$, $$m= 3$$. So the number of basketballs is $$2b + m = 2 \\times 1 + 3 = 5$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9626", "queId": "76808ce6a12a44cba7141e6fd11c831f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Kate sold some dresses and Tasha sold $30$ more dresses than Kate. If Tasha sold thrice as many dresses as Kate, how many dresses did Kate sell? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$30\\div2=15$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9629", "queId": "d5f0005200f347cdbbf9bc19e46b0c56", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The hands of a circular clock form aangle at $$6:15$$ P.M. ", "answer_option_list": [[{"aoVal": "A", "content": "$$82.5^{}\\circ$$ "}], [{"aoVal": "B", "content": "$$90^{}\\circ$$ "}], [{"aoVal": "C", "content": "$$97.5^{}\\circ$$ "}], [{"aoVal": "D", "content": "$$270^{}\\circ$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems"], "answer_analysis": ["At $$6:15$$, hr. hand has moved $$\\left(1/4\\right)\\times 30^{}\\circ$$ from $$6$$, so $$\\angle =90^{}\\circ+30^{}\\circ/4=97.5^{}\\circ$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9630", "queId": "7b0c281aa954482eb52e53167b4d825f", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "White and White Jr. have $$50$$ apples in total, and White has $$10$$ more appled than junior, so White Jr has~\\uline{~~~~~~~~~~}~apples． ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples"], "answer_analysis": ["$$(50-10)\\div 2=20$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9632", "queId": "49b11d29e56d4be9b986455958cce2a9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which of these months has 31 days? ． ", "answer_option_list": [[{"aoVal": "A", "content": "February "}], [{"aoVal": "B", "content": "April "}], [{"aoVal": "C", "content": "August "}], [{"aoVal": "D", "content": "November "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9635", "queId": "d5f1bd3c843a469ea07f842bd5e999b9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$50$$ students in your class. The ratio of boys to girls is $$2:3$$. How many boys and girls are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ and $$20$$ "}], [{"aoVal": "B", "content": "$$20$$ and $$30$$ "}], [{"aoVal": "C", "content": "$$15$$ and $$20$$ "}], [{"aoVal": "D", "content": "$$20$$ and $$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"], "answer_analysis": ["According to the ratio $$2:3$$, we could know the total is $$5$$. Then the number of boys is $$50\\times\\frac{2}{5}=20$$. The number of girls is $$50\\times\\frac{3}{5}=30$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9637", "queId": "456010b51dde4975bb0d44728b7c8570", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Given that May $2$nd of a given year is a Thursday, what day is May $29$th of the same year? ", "answer_option_list": [[{"aoVal": "A", "content": "Saturday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Tuesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems"], "answer_analysis": ["$29-2=27$ days later, it will be May $29$th. $27\\div7=3R6$, which means May $29$th is Wednesday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9641", "queId": "df2a9aa87ae048b4bf6f574b42c69fc7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Tom has $$20$$ toys in total, and Tim has $$2$$ more toys than Tom. The number of Amanda\\textquotesingle s toys is equal to the sum of that of Tom and Tim. How many toys does Amanda have~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$39$$ "}], [{"aoVal": "B", "content": "$$42$$ "}], [{"aoVal": "C", "content": "$$44$$ "}], [{"aoVal": "D", "content": "$$47$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Word Problems Involving Comparing and Ordering"], "answer_analysis": ["We know that Tim has $$20+2=22$$ toys. The sum of Tom\\textquotesingle s and Tim\\textquotesingle s toys is $$20+22=42$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9642", "queId": "88cac23be17e44e886544fc5401001e0", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The upper shelf of a bookshelf has $$143$$ books. The lower shelf has $$39$$ books. How many books should be taken from the upper shelf to the lower shelf so that both shelves will have the same number of books? ", "answer_option_list": [[{"aoVal": "A", "content": "$$46$$ "}], [{"aoVal": "B", "content": "$$52$$ "}], [{"aoVal": "C", "content": "$$91$$ "}], [{"aoVal": "D", "content": "$$104$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["$$143-39=104$$, $$104$$~$\\div$ $$2$$ = $$52$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9646", "queId": "68f83315aa644531933d40bcb4d37455", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The length of a rectangle is increased by $30\\textbackslash\\%$ and the width is decreased by $25\\textbackslash\\%$. What percent of the old area is the new area? (adapted from 2009 AMC 8, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$90.5$$ "}], [{"aoVal": "B", "content": "$$96.5$$ "}], [{"aoVal": "C", "content": "$$97.5$$ "}], [{"aoVal": "D", "content": "$$98.5$$ "}], [{"aoVal": "E", "content": "$$110.5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$1.3 \\times 0.75 = 97.5\\textbackslash\\%$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9648", "queId": "45730b0f3cc54589bc6286bc8a4546a5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "What is the greatest number of days that can occur after the first of one month and before the first of the next month? ", "answer_option_list": [[{"aoVal": "A", "content": "$$27$$ "}], [{"aoVal": "B", "content": "$$28$$ "}], [{"aoVal": "C", "content": "$$29$$ "}], [{"aoVal": "D", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["A month has at most $$31$$ days, Hence, the greatest number of days in that month, after the first, is $$31 -1=30$$. Then, the next day is another $$1\\text{st}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9653", "queId": "88cfcec172a449bea249a630d62b3d5c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Water from the first faucet fills the swimming pool in $18$ hours. Water from each of the two other faucets fills the same swimming pool $4$ times faster. In how many hours will the swimming pool be filled if all three faucets are opened? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems"], "answer_analysis": ["The efficiency of the first faucet is $\\frac1{18}$ and that of the other two is $\\frac29$. Thus it takes $1\\div (\\frac1{18}+\\frac29\\times2)=2$ hours to fill the pool. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9654", "queId": "570e4403b4c140c78d8cec6593081834", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2015 P2 Q4 Susan prepared a plate of cookies for her friends Ashley, Sam, Max and Olivia. Susan tried the first cookie before serving them to her friends. Ashley took 2 cookies and gave 1 to Sam. Max then took 3 cookies, and gave 1 to Olivia and 1 to Susan. If they each ate the cookies they ended up with, who ate the most cookies? ", "answer_option_list": [[{"aoVal": "A", "content": "Susan "}], [{"aoVal": "B", "content": "Ashley "}], [{"aoVal": "C", "content": "Sam "}], [{"aoVal": "D", "content": "Max "}], [{"aoVal": "E", "content": "Olivia "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Susan: +1+1 Ashley: +1 Sam: +1 Max: +1 Olivia: +1 "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9657", "queId": "49d161441dec4062977f3e3bbc2052c3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The distance between Town A and Town B is $620\\text{km}$. Eric drives from Town A to Town B at a speed of $$75\\text{km/h}$$ while Chien drives from Town B to Town A at a speed of $$80\\text{km/h}$$. How many hours will it take for them to meet each other? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$124$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["As they are driving toward each other, the total speed is $$75+80=155$$ miles per hour. Then the time needed is $$620\\div155=4$$ hours. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9658", "queId": "faf4d91b1b8f44ccbaf8070d53a1ea31", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Elmp vists the Sesame Street Park every Wednesday. If the 1st of January 2017 was Sunday and February has 28 days, what was the last date in March 2017 in which Elmo visited Sesame Street Park? ", "answer_option_list": [[{"aoVal": "A", "content": "28th March "}], [{"aoVal": "B", "content": "29th March "}], [{"aoVal": "C", "content": "30th March "}], [{"aoVal": "D", "content": "31st March "}], [{"aoVal": "E", "content": "None of the above. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems"], "answer_analysis": ["Draw the calendar out. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9660", "queId": "52abc4e0a4364ab99ad6da7edfb30945", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ashley had a basket of apples. Her family took half of the apples after dinner. Next morning, her family took half of the remaining apples. There were $$2$$ apples left in the basket. How many apples were in the basket at first? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems->Giving Half of a Whole"], "answer_analysis": ["$2+2=4$ $4+4=8$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9662", "queId": "faf57d34b55f446191fdcfdae571b0bd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A series of colored lanterns are arranged in the pattern ``red, red, green, yellow, yellow, red, red, green, yellow, yellow$$\\cdots$$'' What color is the $$52^{\\text{th}}$$ lantern? ", "answer_option_list": [[{"aoVal": "A", "content": "red "}], [{"aoVal": "B", "content": "green "}], [{"aoVal": "C", "content": "yellow "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"], "answer_analysis": ["Since $$52\\div(3+2)=10r2$$, the $$52^{\\text{th}}$$ colored lantern is red. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9664", "queId": "5b877b4c6f294dc4a45911e9d85e0ecf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jin loves carrots! Yesterday she ate $$\\frac{1}{2}$$ of her carrots, and today she ate $$\\frac{2}{3}$$ of the remaining carrots. She then discovered that she had $$12$$ carrots left. Yesterday she must have started with carrots. ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$72$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["If $$12$$ carrots are left after Jin eats $$\\frac{2}{3}$$ of today\\textquotesingle s carrots, then $$12$$ carrots are $$\\frac{1}{3}$$ of the carrots she started with today. So Jin began today with $$36$$ carrots. Since Jin ate $$\\frac{1}{2}$$ yesterday, she started with $$2\\times36$$ carrots. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9665", "queId": "45871946ef8244f8a58d197e59f3c60d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "This year, March $$19$$\\textsuperscript{th} falls on a Thursday. What day of the week will it be in $$30$$ days? ", "answer_option_list": [[{"aoVal": "A", "content": "Wednesday "}], [{"aoVal": "B", "content": "Thursday "}], [{"aoVal": "C", "content": "Friday "}], [{"aoVal": "D", "content": "Saturday "}], [{"aoVal": "E", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$$30\\div7=4 \\text{R} 2$$, two days after Thursday, which is Saturday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9667", "queId": "6906e7a13861475397f210d7a6340a16", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $70\\textbackslash\\%$ alcohol solution contains $$120$$ g of water. How many g of solution are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$200$$ g "}], [{"aoVal": "B", "content": "$$300$$ g "}], [{"aoVal": "C", "content": "$$400$$ g "}], [{"aoVal": "D", "content": "$$500$$ g "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"], "answer_analysis": ["$$120\\div(1-70\\textbackslash\\%)=400$$ g. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9668", "queId": "9ed41f37aee047388beb5e8266583b57", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "It\\textquotesingle s summer time! A beverage shop mixes $10$ bottles of apple and $20$ bottles of watermelon juice to make the new blended juice. The costs of a bottle of apple and a bottle of watermelon juice are $8$ and $11$ dollars, respectively. If the size of the bottle does not change, what is the cost of each bottle of the blended juice? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Total cost: $$10\\times 8+11\\times 20=300$$. There are $$10+20=30$$ bottles, so each bottle of the blended juice should be $$300\\div 30=10$$ dollars. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9671", "queId": "52b13edc078f456c8c44ab0eb1e5a3c6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Irene mixes $$100$$ kilograms of dogfood that contains $$50\\textbackslash\\%$$ rice with $$400$$ kilograms of dogfood that contains $$80\\textbackslash\\%$$ rice. Find the percent concentration of the rice in the new mixture. ", "answer_option_list": [[{"aoVal": "A", "content": "$$70\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$72\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$75\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$74\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$\\dfrac{100\\times50\\textbackslash\\%+400\\times80\\textbackslash\\%}{100+400}=74\\textbackslash\\%$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9675", "queId": "49df079d09e041e3a872333615b511bd", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Chris and Debbie want to buy the same book, but they do not take enough money. Chris needs $$2$$ dollars and $$30$$ cents more to buy that book. Debbie needs $$3$$ dollars and $$80$$ cents more to buy that book. The sum of their own money is equal to the price of the book. How much is the book? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ dollars and $$30$$ cents "}], [{"aoVal": "B", "content": "$$4$$ dollars and $$60$$ cents "}], [{"aoVal": "C", "content": "$$7$$ dollars and $$60$$ cents "}], [{"aoVal": "D", "content": "$$3$$ dollars and $$80$$ cents "}], [{"aoVal": "E", "content": "$$6$$ dollars and $$10$$ cents "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"], "answer_analysis": ["$$2$$ dollars and $$30$$ cents + $$3$$ dollars and $$80$$ = $$6$$ dollars and $$10$$ cents "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9676", "queId": "e872082fa33d407788a7481807f372fa", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The average cost of a long-distance call in the USA in 1985 was 56 cents per minute, and the average cost of a long-distance call in the USA in 2018 was 2 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (2007 AMC 8, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ "}], [{"aoVal": "B", "content": "$$95$$ "}], [{"aoVal": "C", "content": "$$96$$ "}], [{"aoVal": "D", "content": "$$97$$ "}], [{"aoVal": "E", "content": "$$98$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $56-2=54$ so the percent decrease is $\\frac{54}{56}$ which is about $ 96 \\textbackslash\\%$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9682", "queId": "df32c5d6e39e43f1bfa7f7e89f65069f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "There are $$2$$ inlets (namely $$\\text{A}$$ and $$\\text{B}$$) in a pool. If only inlet $$\\text{A}$$ is open, it takes $$36$$ minutes to fill up the empty pool. If only inlet $$\\text{B}$$ is open, it takes $$48$$ minutes to fill up the empty pool. Now, inlets $$\\text{A}$$ and $$\\text{B}$$ will be open in turns, according to such an order, open inlet $$\\text{A}$$ for $$1$$ minute, $$\\text{B}$$ for $$2$$ minutes, $$\\text{A}$$ for $$2$$ minutes, $$\\text{B}$$ for $$1$$ minute, $$\\text{A}$$ for $$1$$ minute, $$\\text{B}$$ for $$2$$ minutes $$\\cdots$$ So on and so forth. How long, in the nearest minutes, does it take to fill up the empty pool? ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$39$$ "}], [{"aoVal": "C", "content": "$$41$$ "}], [{"aoVal": "D", "content": "$$44$$ "}], [{"aoVal": "E", "content": "$$48$$ "}], [{"aoVal": "F", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9683", "queId": "f1b3beaa52b6412d87d9a0f46011ffd8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Joe lives on the $3$\\textsuperscript{rd}~floor. He needs to spend $12$ minutes to move from the $4$\\textsuperscript{th} floor to the $5$\\textsuperscript{th} floor. How many minutes does he need to climb from the $1$\\textsuperscript{st} floor to the $3$\\textsuperscript{rd} floor? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$48$$ "}], [{"aoVal": "E", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$12 \\times (3 - 1) = 24$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9687", "queId": "a37058e3a352455b99a8188eb85d422a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Three people $$A$$, $$B$$, and $$C$$ have a total of $$$200$$. Given that the ratio of $${A}'$$ s total to $${B}'$$s total is $$4:3$$, and $$A$$ has $$$20$$ more than $$C$$, how much does $$C$$ have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$72$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"], "answer_analysis": ["Assume that $$C$$ borrows $$$20$$. Therefore, $$A:B:C = 4:3:4$$, for a total sum of $$11$$ increments, or $$$220$$. One increment is $$220\\div 11=20$$ dollars. Therefore, $$C$$ has a total of $$4\\times 20-20=60$$ dollars. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9688", "queId": "4e5378d30db74cd597bd8a1eb3d6563a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$29^{}\\text{th}$$May is Monday, what day of the week is $$1$$\\textsuperscript{st~}May ? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday　 "}], [{"aoVal": "B", "content": "Monday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Tuesday　 "}], [{"aoVal": "E", "content": "Saturday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["There are 29 days between $$29^{}\\text{th}$$May and~ $$1$$\\textsuperscript{st~}May. Apart from $29$\\textsuperscript{th} May itself, there are 28 days = 4 week. Therefore,~~$$1$$\\textsuperscript{st~}March is Monday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9689", "queId": "6d95c5218ecb44c0800ba554304ed5bb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Linda paid $$8$$ dollars for $$4$$ potatoes. How many dollars did Linda pay for the same kind of potatoes if she bought $$6$$ more of them? (adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$13$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["Linda paid ＄$$8$$ for $$4$$ potatoes, $$8\\div4=2$$, so we can know $$1$$ potatoes cost $$2$$ dollars. In total Linda should pay $$2\\times10=20$$ dollars for $$10$$ potatoes. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9694", "queId": "5b9a997201b341e892f56ae1b9dbbbb4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $5$ people in Harry\\textquotesingle s family with an average height of $168$ cm. The heights of Harry, Harry\\textquotesingle s mom, Harry\\textquotesingle s sister, and Harry\\textquotesingle s brother are $170$ cm, $160$ cm, $162$ cm, and $175$ cm, respectively. What is the height of Harry\\textquotesingle s dad? ", "answer_option_list": [[{"aoVal": "A", "content": "$$163$$ "}], [{"aoVal": "B", "content": "$$165$$ "}], [{"aoVal": "C", "content": "$$171$$ "}], [{"aoVal": "D", "content": "$$173$$ "}], [{"aoVal": "E", "content": "$$178$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$(170-168)-(168-160)-(168-162)+(175-168)=-5$. $168+5=173$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9695", "queId": "49f28852c5434e34b444cb408fb0c0e3", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Vera invited $$13$$ guests to her birthday party. She had $$2$$ pizzas, and each of them was cut into $$8$$ slices. Each person at the party ate one slice of pizza. How many slices of pizza were left over? (2015 Math Kangaroo Problem, Level 1-2, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications"], "answer_analysis": ["There were $8\\times2=16$ slices. $13+1=14$ slices of pizza were ate, so there were $16-14=2$ slices left. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9705", "queId": "722f025bcaae4a4fa2cb14d6eb8146f2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If this is March, what month will it be $$1993$$ months from today? ", "answer_option_list": [[{"aoVal": "A", "content": "January　 "}], [{"aoVal": "B", "content": "February　 "}], [{"aoVal": "C", "content": "March　 "}], [{"aoVal": "D", "content": "April　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Since $$12\\times166 +1= 1992 + 1= 1993$$, the month will be April. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9706", "queId": "76b28da6c1f84379a56ebc245f79cf2d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In $$1975$$ it was estimated that there were $$250000$$ lions in Africa. Over $$40$$ years this figure has decreased by $$90\\textbackslash\\%$$. What is the current estimate for the number of lions in Africa ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$25000$$ "}], [{"aoVal": "B", "content": "$$100000$$ "}], [{"aoVal": "C", "content": "$$160000$$ "}], [{"aoVal": "D", "content": "$$225000$$ "}], [{"aoVal": "E", "content": "$$275000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["A $$90\\textbackslash\\%$$ decrease means $$10\\textbackslash\\%$$ of $$250000 = 250000 \\div 10 = 25000$$ of the lions remain. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9709", "queId": "52d505a8f3d44b3492cb7e8d9c3bde52", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Annie usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for $$36$$ hours. If she is using it constantly, the battery will last for only $$10$$ hours. Since the last recharge, her phone has been on $$20$$ hours, and during that time she has used it for $$120$$ minutes. If she only keeps using the phone $3$ hours more and then leaves the phone on, how many more hours will the battery last after she leaves the phone on? (Adapted from $$2004$$ AMC $$8$$ Problem, Question \\#$$12$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Simple Work Word Problems"], "answer_analysis": ["When not being used, the cell phone uses up $$\\dfrac{1}{36}$$ of its battery per hour. When being used, the cell phone uses up $$\\dfrac{1}{10}$$ of its battery per hour. Since Annie\\textquotesingle s phone has been on for $$20$$ hours, of those $$18$$ simply on and $2$ being used, $$18\\times\\left(\\dfrac{1}{36}\\right)+2\\times\\left(\\dfrac{1}{10}\\right)=\\dfrac{7}{10}$$ of its battery has been used up. To drain the remaining $$\\dfrac{3}{10}$$, the phone can last for $$(\\frac{3}{10}-3\\times\\frac1{10})\\div \\frac1{36}=0$$ more hours without being used. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9712", "queId": "4e6efc7dd9234222b405a216a7444318", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "A cow gives $24$ liters of milk each day. If the milkman sells $80$\\% of the milk, how many liters of milk is left with him? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$4.8$$ "}], [{"aoVal": "C", "content": "$$19.2$$ "}], [{"aoVal": "D", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$24 \\times 80$\\%=$19.2$, $24-19.2=4.8$, $4.8$ liters of milk is left with him. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9713", "queId": "6027e8e176db4f13bc404dd0f362ec51", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Patrick got into a lift. He went down six floors, up seven floors and then down eight floors. He was finally on the third floor. Which floor did Patrick get into the lift? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3^{rd}$$ "}], [{"aoVal": "B", "content": "$$4^{th}$$ "}], [{"aoVal": "C", "content": "$$10^{th}$$ "}], [{"aoVal": "D", "content": "$$11^{th}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems->Inverse Operations"], "answer_analysis": ["$3+8-7+6=10$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9718", "queId": "4e7574217a9e4f18a4d06ba660ca5f37", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Together, Bob, Colin and Dave weigh $$195\\text{kg}$$. Bob weighs $$9\\text{kg}$$ more than Colin and $$6\\text{kg}$$ more than Dave. How much does Bob weigh? ", "answer_option_list": [[{"aoVal": "A", "content": "$$60\\text{kg}$$ "}], [{"aoVal": "B", "content": "$$66\\text{kg}$$ "}], [{"aoVal": "C", "content": "$$69\\text{kg}$$ "}], [{"aoVal": "D", "content": "$$70\\text{kg}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference->Sum and Differences Problems with multiple Variables"], "answer_analysis": ["Nil "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9721", "queId": "7fd4bec9942f485db9470667a7f1d3c4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Helen said to Mary, \"If you give me $$4$$ apples, I will have exactly as many apples as you.\" How many more apples does Mary have than Helen? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Difference and Multiple->Differences and Multiples of Two Variables->Differences and Integer Multiples"], "answer_analysis": ["Difference: $4+4=8$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9722", "queId": "574c2289044940d29384c552ef18bfd9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "To make a pudding, you need $$2$$ ounces of flour and $$10$$ ounces of milk. You have $$10$$ ounces of flour and want to make as many puddings as possible. How much milk do you need? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ ounces "}], [{"aoVal": "B", "content": "$$30$$ ounces "}], [{"aoVal": "C", "content": "$$40$$ ounces "}], [{"aoVal": "D", "content": "$$50$$ ounces "}], [{"aoVal": "E", "content": "$$60$$ ounces "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"], "answer_analysis": ["The ratio of flour to milk is $$2:10$$ or $$1:5$$. With $$10$$ ounces of flour, you could make as many as $$5$$ puddings. At the same time, you need $$50$$ more ounces of milk. The ratio of flour to milk is $$10:50$$, or $$1:5$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9724", "queId": "bf0baf867fb04a1890cf2c0d725ae0c2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "NBA playoffs are held annually. The $62$\\textsuperscript{nd~}NBA playoffs were held in $2008$. When Judy was $10$ years old, the $58$\\textsuperscript{th}~NBA playoffs were held. When was Judy born? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1991$$ "}], [{"aoVal": "B", "content": "$$1992$$ "}], [{"aoVal": "C", "content": "$$1994$$ "}], [{"aoVal": "D", "content": "$$1996$$ "}], [{"aoVal": "E", "content": "$$1998$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$62-58=4$ $2008-4-10=1994$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9730", "queId": "76c28a7271da4c22b77302916e516ce8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Frank stands in line and has $$76$$ people behind him, If there are a total of $$110$$ people in line, how many people are there in front of Frank? ", "answer_option_list": [[{"aoVal": "A", "content": "$$33$$ "}], [{"aoVal": "B", "content": "$$34$$ "}], [{"aoVal": "C", "content": "$$35$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line"], "answer_analysis": ["If there are a total of $$110$$ people in line, subtract those behind Frank and Frank himself: $$110-76-1=33$$, the number in front of Frank. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9743", "queId": "daa913b8daeb46db96d7a9c41ea715ba", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A teacher distributes scorecards to students, if everyone gets $3$ cards, there will be a shortage of $12$ cards. If everyone gets $2$ cards, all these cards will just be divided. Then, how many students are there in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems"], "answer_analysis": ["If $2-1=1$ less card is given to students, the situation would transfer from \\textquotesingle a shortage of $12$ cards\\textquotesingle~ to \\textquotesingle all cards are just divided\\textquotesingle{} . Therefore. the shortage of $12$ cards is equal to the number of cards that everyone gets $1$ less card. So, there are in total $12\\div1=12$ students. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9746", "queId": "b5e0bf8c83384ecfb0a3e2a10f750935", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Which date is $$100$$ days after November $$6\\text{th}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "February $$14$$ "}], [{"aoVal": "B", "content": "February $$15$$ "}], [{"aoVal": "C", "content": "February $$16$$ "}], [{"aoVal": "D", "content": "February $$17$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["It\\textquotesingle s $$92$$ days $$\\left( 30+31+31 \\right)$$ from Nov. $$6$$ to Feb. $$6$$;~$$8$$ days later is $$100$$ days. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9748", "queId": "60465f4d2cbc4d7aa78c17d91ec839ee", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Karl Lecter has been collecting $$1\\text{p}$$, $$2\\text{p}$$ and $$5\\text{p}$$ coins in a jar. All but $$10$$ of his coins are $$1\\text{p}$$ coins, all but $$10$$ are $$2\\text{p}$$ coins, and all but $$10$$ are $$5\\text{p}$$ coins. How much money does he have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8\\text{p}$$ "}], [{"aoVal": "B", "content": "$$10\\text{p}$$ "}], [{"aoVal": "C", "content": "$$25\\text{p}$$ "}], [{"aoVal": "D", "content": "$$40\\text{p}$$ "}], [{"aoVal": "E", "content": "$$80\\text{p}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["All but $$10$$ of the coins are $$1\\text{p}$$ coins, which tells us that the number of $$2\\text{p}$$ and $$5\\text{p}$$ coins adds up to $$10$$. Similarly, the total of the $$1\\text{p}$$ and $$5\\text{p}$$ coins is $$10$$ and the total of the $$1\\text{p}$$ and $$2\\text{p}$$ coins is $$10$$. He therefore has $$5$$ of each coin, giving a total of $$(5 \\times1)+ (5 \\times2)+(5\\times5)=40\\text{p}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9749", "queId": "57644ad9f67646e49ad571e3f2ef1386", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When I add together the number of sides of a quadrilateral, a trapezoid, and a parallelogram, I get a total of． ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["Quadrilaterals, trapezoids, and parallelograms each have $$4$$ sides each, so the total number of sides is $$4+4+4=12$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9750", "queId": "ccdb879b2b034301a073c0c16baf50b3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A ship was attacked by pirates. One by one the pirates climb a rope to get on the ship. The pirate captain was the $$8$$\\textsuperscript{th}~pirate to climb in line, and there were as many pirates in front of him as behind him. How many pirates climbed the rope? (2015 Math Kangaroo Problem, Level 1 - 2, Question \\#18) $$\\textasciitilde$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line"], "answer_analysis": ["The pirate captain was the $$8$$\\textsuperscript{th}~pirate and there were as many pirates in front of him as behind him, which means there were $$7$$ pirates in front of him and there were also $$7$$ pirates behind him. The total number of pirates is~~$$7+7+1=15$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9754", "queId": "846e25e2b6454aefa7beb83795f98a63", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$28$$ January $$2000$$ falls on a Friday, which day of the week will $$28$$ January $2001$ fall on? ", "answer_option_list": [[{"aoVal": "A", "content": "Thursday "}], [{"aoVal": "B", "content": "Friday "}], [{"aoVal": "C", "content": "Saturday "}], [{"aoVal": "D", "content": "Sunday "}], [{"aoVal": "E", "content": "Monday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$2000$ is a leap year and the period includes $29$ Feb, so there are $366$ days. $366\\div7=52$ R $2$ Friday $+$ $2$ days $\\rightarrow$ Sunday "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9760", "queId": "b15121ae3dea41d4b9c1a162982af903", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$9$$ benches in the park, which have the same length. They are placed on one side of the road every $$7$$ meters from end to end. Given that the length of the road is $$74$$ meters, how long is the bench? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ m "}], [{"aoVal": "B", "content": "$$2$$ m "}], [{"aoVal": "C", "content": "$$3$$ m "}], [{"aoVal": "D", "content": "$$4$$ m "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Straight Line Type with Objects on Both Sides"], "answer_analysis": ["The $$9-1=8$$ intervals are $$7\\times8=56$$ meters in total. So, the sum of length of all the benches is $$74-56=18$$ meters and each of them is $$18\\div9=2$$ meters. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9765", "queId": "890deee908284801b203f7545682bf20", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Nancy did an experiment. She inserted a paper straw vertically into the bottom of a bottle of black ink. Then, she found that the length of the black part of the paper straw was exactly $12$ cm. She turned the straw upside down and inserted the other end vertically into the bottom of the bottle. She found that the length of the part not colored of the straw was exactly half of that of all the black parts. The paper straw was~\\uline{~~~~~~~~~~}~cm. ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$24$$ "}], [{"aoVal": "C", "content": "$$28$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["The black parts of the straw was $$12+12=24$$ cm, so the part not colored was $$24\\div2=12$$ cm. Thus, the length of the straw was $$24+12=36$$ cm. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9767", "queId": "95d940b6ed914de3991235c3f38a5f33", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "$A$, $B$ and $C$ start from the same place at the same time and chase a cyclist in front of them along the same road. The three cars catch up with him in $6$, $10$ and $12$ minutes respectively. Given that car $A$\\textquotesingle s speed is $24$ kilometers per hour, car $B$\\textquotesingle s speed is $20$ kilometers per hour. Find car $C$\\textquotesingle s speed. ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ "}], [{"aoVal": "B", "content": "$$19$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$16$$ "}], [{"aoVal": "E", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Newton's Problem of Cows and Fields->Basic Newton's Problem of Cows and Fields->Finding the Number of Cows"], "answer_analysis": ["B "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9770", "queId": "5be608c7fee5417a8e48ed7f1db4f1bf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Billy has three times as many llamas as lambs. Milly has twice as many lambs as llamas. They have $$17$$ animals in total. How many of the animals are llamas? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Indefinite Equation Word Problems"], "answer_analysis": ["Let Billy have $$b$$ lambs and $$3b$$ llamas. Let Milly have $$m$$ llamas and $$2m$$ lambs. Therefore, as they have $$17$$ animals in total, $$4b + 3m= 17$$. The only positive integer solution of this equation is $$b= 2$$, $$m= 3$$. So the number of llamas is $$3b + m = 3 \\times 2 + 3 = 6 + 3 = 9$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9776", "queId": "5bea437d97484cd59a0f36c931190e65", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $$25\\textbackslash\\%$$ salt solution contains $$75$$ g of water. How many g of solution are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$100$$ g "}], [{"aoVal": "B", "content": "$$25.5$$ g "}], [{"aoVal": "C", "content": "$$25$$ g "}], [{"aoVal": "D", "content": "$$102$$ g "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$75\\div(1-25\\textbackslash\\%) = 100$$ g. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9780", "queId": "76e4330ed2f44e71abacb80bc32be601", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "At the red light, seven buses of the same length stop in a line. Given that the length of each bus is $$5$$ meters, and the distance between each two adjacent buses is $$2$$ meters, how long is the line? ", "answer_option_list": [[{"aoVal": "A", "content": "$$35$$ m "}], [{"aoVal": "B", "content": "$$49$$ m "}], [{"aoVal": "C", "content": "$$47$$ m "}], [{"aoVal": "D", "content": "$$54$$ m "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Straight Line Type with Objects on Both Sides"], "answer_analysis": ["Among the $$7$$ buses, there are $$7-1=6$$ intervals. So the answer is $$7\\times5+2\\times6=47$$ meters. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9784", "queId": "5bf28e7eac324ec0ab93d306a380b15e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "$$37$$ sakura trees were planted along one side of the road. The trees were planted at $$4m$$ intervals. After drivers complained the road was too pink, pineapple trees were planted on the other side of the road at $$6m$$ intervals. How many pineapple trees were planted, if there were sakura and pineapple trees at both ends of the road? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$144$$ "}], [{"aoVal": "D", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["Number of sakura intervals = $$37-1 = 36$$ Length of road = $$36 \\times 4 = 144m$$ Number of pineapple intervals = $$144m \\div 6m = 24$$ Number of pineapple trees = $$24 + 1 = 25$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9794", "queId": "8cc59965e8964375b9739945e00503d8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Agnijo has half as many apps as Sam who has a third as many apps as Naomi. Altogether, they have $$180$$ apps. How many apps does Sam have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["Let Agnijo have $$n$$ apps. Now Sam has $$2n$$, and Naomi $$6n$$. Therefore $$n+2n+6n = 9n = 180$$, and so $$n = 180\\div9 = 20$$. Hence Sam has $$2\\times20 = 40$$ apps. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9795", "queId": "c8549d345a0c46b6b2caa2ed27aef5c1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the amusement park, Jessie is playing with darts. For each time she hits the bullseye, she can win two toys. At the beginning she has $$3$$ toys and at the end she has $$23$$ toys. How many times did she hit the bullseye? (Adapted from 2006 Math Kangaroo Problem, Level 3-4, Question \\#5) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["$(23-3)\\div2=10$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9801", "queId": "d18678a25e794ad0a46f2566faa2022e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "October 10th, 2021 is Sunday. What day is October $$26$$th of the same year?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday "}], [{"aoVal": "B", "content": "Monday "}], [{"aoVal": "C", "content": "Tuesday "}], [{"aoVal": "D", "content": "Wednesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["$26-10=16$, $16\\div7=2\\textbackslash{} \\rm R\\textasciitilde2$,~ it\\textquotesingle s Tuesday. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9802", "queId": "6df1f19cbcbf4bf59a053da92f7be17f", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "$$380$$ is~\\uline{~~~~~~~~~~}~more than $$254$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$126$$ "}], [{"aoVal": "B", "content": "$$124$$ "}], [{"aoVal": "C", "content": "$$534$$ "}], [{"aoVal": "D", "content": "$$634$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$380-254=126$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9812", "queId": "9f147088efab4199a74f8bf04901274a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$11$$ flags on one side of a road. The distance between neighboring flags is $$5$$ meters. Grace walked from the first flag to the last flag. How many meters did she walk? (Adapted from 2007 Math Kangaroo Problem, Level 3-4, Question \\#5) ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$55$$ "}], [{"aoVal": "D", "content": "$$65$$ "}], [{"aoVal": "E", "content": "$$75$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Straight Line Type with Objects on Both Sides->Planting Trees on Both Sides"], "answer_analysis": ["$(11-1)\\times5=50$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9814", "queId": "8010c1b9f7784c5fb4c0bcc3056c964f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Colin was preparing for the PE test. On the first day, he ran $1$ km. He decided that each day he would be running $100$ m more than the day before. How many meters did he run in total in the first $5$ days? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5600$$ "}], [{"aoVal": "B", "content": "$$5700$$ "}], [{"aoVal": "C", "content": "$$5800$$ "}], [{"aoVal": "D", "content": "$$6000$$ "}], [{"aoVal": "E", "content": "$$6100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression"], "answer_analysis": ["$1000 + 1100 + 1200 + 1300 + 1400 = 6000$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9817", "queId": "ba8f45e790b549b4bca8a52d1a15a513", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a mathematics contest with ten problems, a student gains $$5$$ points for a correct answer and loses $$2$$ points for an incorrect answer. If Olivia answered every problem and her score was $$29$$, how many correct answers did she have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Suppose Olivia has $$x$$ correct answers. $$5x-2(10-x)=29$$, $$x=7$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9819", "queId": "69819cc11a924f929d8c74ad0c150ef1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Wendy had $$30$$ stickers. First, she gave Aiden three stickers. Then, she gave Terry $7$ stickers. Now, each of the three people had the same number of stickers. At the beginning, how many stickers did they have in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$120$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$85$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems"], "answer_analysis": ["Now, Wendy had $30-3-7=20$ stickers. Then, all of them had $20\\times3=60$ stickers, which was equal to the total number of stickers they had at beginning. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9820", "queId": "c3c0f8aa6cbe4dfa9f343ff81acb993e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Bram bought $$60$$ beans for ＄$$3.00$$. At this price, $$100$$ beans cost． ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$3.50$$ "}], [{"aoVal": "B", "content": "＄$$4.00$$ "}], [{"aoVal": "C", "content": "＄$$5.00$$ "}], [{"aoVal": "D", "content": "＄$$5.50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["If $$60$$ beans cost ＄$$3.00$$, then $$1$$ bean costs $$5$$￠and $$100$$ beans cost ＄$$5$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9831", "queId": "7b93b912af3347eca232f73983f51522", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Historians say that William the Conqueror was born in $$1028$$. How many years ago was that? ", "answer_option_list": [[{"aoVal": "A", "content": "$$790$$ "}], [{"aoVal": "B", "content": "$$810$$ "}], [{"aoVal": "C", "content": "$$910$$ "}], [{"aoVal": "D", "content": "$$990$$ "}], [{"aoVal": "E", "content": "$$1010$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["The number of years from William\\textquotesingle s birth is $$2018 - 1028 = 990$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9832", "queId": "8cdc8a9d32fa46a7882ef9654d8fb531", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A 20\\% increase in the price of milk leads to a 10\\% decrease in the quantity of cereal purchased. The cross-price elasticity of demand between milk and cereal is ", "answer_option_list": [[{"aoVal": "A", "content": "-0.5 and the two goods are substitutes. "}], [{"aoVal": "B", "content": "-0.5 and the two goods are complements. "}], [{"aoVal": "C", "content": "0.5 and the two goods are complements. "}], [{"aoVal": "D", "content": "-2 and the two goods are substitutes. "}], [{"aoVal": "E", "content": "2 and the two goods are complements. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["This is an application of the cross-price elasticity equation: \\% change in QDx/\\% change in Py. -0.10/0.2 = -0.5. A negative number means the goods are complements. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9836", "queId": "65153dd72b6e4f3ab19d6bfbe1d41e96", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If one bag of chips costs $$75$$￠, then three of these bags cost ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$$0.25$$ "}], [{"aoVal": "B", "content": "$$$1.50$$ "}], [{"aoVal": "C", "content": "$$$2.25$$ "}], [{"aoVal": "D", "content": "$$$3.00$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["One bag costs $$75$$￠. Three such bags cost $$3\\times $0.75=$2.25$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9838", "queId": "8935325a2f8841329abd457a46dfe8a8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "After Sally takes $20$ shots, she has made $40 \\textbackslash\\%$ of her shots. After she takes $5$ more shots, she raises her percentage to $52 \\textbackslash\\%$. How many of the last $5$ shots did she make? ( adapted from 2004 AMC 8, Question\\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Sally made $0.4 * 20=8$ shots originally. Letting $x$ be the number of shots she made, we have $\\frac{8+x}{25}=0.52$. Solving for $x$ gives us $x=5$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9841", "queId": "d1915cd52aa14043b378c8a248b904d6", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "If $$1$$ August falls on Monday, which day of the week will $$12$$ September fall on? Below is Chris\\textquotesingle~answer. Number of days from 1 Aug to 12 Sept: 31 + 12 = 43 43 $\\div$ 7 = 6 R 1 Hence, 12 September is a Tuesday. Is Chris\\textquotesingle s answer correct? If not, what is the correct answer? ． ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday "}], [{"aoVal": "B", "content": "Monday "}], [{"aoVal": "C", "content": "Tuesday "}], [{"aoVal": "D", "content": "Wednesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Number of days from $$1$$ August to $$12$$ September $$=31+12-1$$ $$=42$$ $$42\\div 7=6$$ weeks Therefore, $$12$$ September will fall on \\textbf{Monday}. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9843", "queId": "bf341e42a94c4fa3a37d73a9ad186470", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The owner of a bicycle store had a sale on bicycles(two-wheelers) and tricycles(three-wheelers). Each cycle had two pedals. When he counted the total number of pedals of the cycles, he got 50 . When he counted the total number of wheels of the cycles, he got 64 . How many tricycles were offered in the sale? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"], "answer_analysis": ["$50\\div 2=25$ let $x$ be the number of bicycles, $y$ be the number of tricycles $2x+3y=64$ $x+y=25$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9849", "queId": "60a49036b33644e6a328cbbc6fb1d903", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Anna, Bridgit and Carol run in a $$100\\text{m}$$ race. When Anna finishes, Bridgit is $$16\\text{m}$$ behind her and when Bridgit finishes, Carol is $$25\\text{m}$$ behind her. The girls run at constant speeds throughout the race. How far behind was Carol when Anna finished? ", "answer_option_list": [[{"aoVal": "A", "content": "$$37\\text{m}$$ "}], [{"aoVal": "B", "content": "$$41\\text{m}$$ "}], [{"aoVal": "C", "content": "$$50\\text{m}$$ "}], [{"aoVal": "D", "content": "$$55\\text{m}$$ "}], [{"aoVal": "E", "content": "$$60\\text{m}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"], "answer_analysis": ["Carol finishes $$25$$ metres behind Bridgit, so she travels $$75$$ metres while Bridgit runs $$100$$ metres. Therefore she runs $$3$$ metres for every $$4$$ metres Bridgit runs. When Anna finishes, Bridgit has run $$84$$ metres, so that at that time Carol has run $$\\frac{3}{4}\\times 84$$ metres $$=63$$ metres. Hence Carol finishes $$\\left( 100-63 \\right)$$ metres $$= 37$$ metres behind Anna. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9851", "queId": "60a687764dd54c1cb27065c9b3e044e2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$6$$ cans of Sweet Stuff Soda all together contain $$96$$ teaspoons of sugar, then there are a total of teaspoons of sugar in $$15$$ cans. ", "answer_option_list": [[{"aoVal": "A", "content": "$$192$$ "}], [{"aoVal": "B", "content": "$$208$$ "}], [{"aoVal": "C", "content": "$$240$$ "}], [{"aoVal": "D", "content": "$$288$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"], "answer_analysis": ["If $$6$$ cans contain $$96$$ teaspoons of sugar, $$1$$ can contains $$96\\div6 = 16$$ teaspoons of sugar. Thus $$15$$ cans contain $$16\\times15 =240$$ teaspoons of sugar. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9853", "queId": "57cd27020a934d9c86ec6c58e07daf7d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that January $$1$$st, $$2018$$ was Monday, on what day did January $$1$$st, $$2019$$ fall? ", "answer_option_list": [[{"aoVal": "A", "content": "Tuesday "}], [{"aoVal": "B", "content": "Monday "}], [{"aoVal": "C", "content": "Sunday "}], [{"aoVal": "D", "content": "Wednesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$2018$ was a common year which had $365$ days. Thus, January $$1$$st, $$2019$$ fell on one day after Monday, which was Tuesday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9857", "queId": "729b7bc7dbfe48a18f4ba5994d47257d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Three zebras take part in a contest. The winner is the zebra with the most number of stripes. QingLe has $$15$$ stripes, ChenXi has $$3$$ more than QingLe. QingLe has $$5$$ fewer stripes than YueYing. How many stripes does the winner have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9859", "queId": "c869bafeca864002b7f9f6b6c2c8e7dd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the yard there is an equal number of pigs, ducks and chickens. Together, they have $$144$$ legs. How many ducks are there in the yard? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$35$$ "}], [{"aoVal": "D", "content": "$$42$$ "}], [{"aoVal": "E", "content": "$$43$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Suppose there are $$x$$ ducks in the yard. Since there is an equal number of pigs, ducks and chickens, $$2x+4x+2x=144$$, $$x=18$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9862", "queId": "5c416d4468a94614aeb7bb1f8cf0578d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Paul was going to buy $$4$$ servings of ice cream, but he was $$80$$ cents short. So, he bought $$3$$ servings and had $$30$$ cents left. What was the price of one serving of ice cream? ", "answer_option_list": [[{"aoVal": "A", "content": "$$70$$ cents "}], [{"aoVal": "B", "content": "$$80$$ cents "}], [{"aoVal": "C", "content": "$$90$$ cents "}], [{"aoVal": "D", "content": "$$1$$ dollar "}], [{"aoVal": "E", "content": "$$1$$ dollar $$10$$ cents "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems"], "answer_analysis": ["$$(80+30)\\div (4-3)=110$$ cents $$=1$$ dollar and $$10$$ cents. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9863", "queId": "72a2131fbcbe4fe08469f2f0c9420ec4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A salt solution is made by mixing $100$ g of salt and $400$ g of water. Find the percent concentration of the mixture. ", "answer_option_list": [[{"aoVal": "A", "content": "$15\\textbackslash\\%$ "}], [{"aoVal": "B", "content": "$20\\textbackslash\\%$ "}], [{"aoVal": "C", "content": "$25\\textbackslash\\%$ "}], [{"aoVal": "D", "content": "$30\\textbackslash\\%$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts->Calculating Price from Cost and Profit"], "answer_analysis": ["$$100\\div \\left( 100+400\\right) \\times 100\\textbackslash\\% =20\\textbackslash\\%$$. ~~ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9868", "queId": "84b5a251e7a7468484238c8415c28f8c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When $$4$$ kilograms of $$30\\textbackslash\\%$$ sugar water is mixed with some $$10\\textbackslash\\%$$ sugar water, it gives a mixture with a sugar concentration of $$26\\textbackslash\\%$$. How much $$10\\textbackslash\\%$$ sugar water is needed?~\\uline{~~~~~~~~~~}~$$\\text{kg}$$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"], "answer_analysis": ["Use the cross method $$\\begin{matrix}30\\textbackslash\\%10\\textbackslash\\% \\textbackslash\\textbackslash{} \\searrow \\swarrow \\textbackslash\\textbackslash{} 26 \\textbackslash\\% \\textbackslash\\textbackslash{} \\swarrow \\searrow \\textbackslash\\textbackslash{} 16 \\textbackslash\\%4\\textbackslash\\% \\textbackslash\\textbackslash\\end{matrix}$$ to see that the ratio of $$30\\textbackslash\\%$$ solution to $$10\\textbackslash\\%$$ solution is $$4:1$$. Therefore, $$1\\text{kg}$$ of $$10\\textbackslash\\%$$ solution is needed. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9872", "queId": "bf3e487cb3b84880b9ffdb70e55f11e0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Cindy has $$50$$ bookmarks. If she were to give $$6$$ bookmarks to each of her classmates, she would need $$10$$ more bookmarks. How many classmates does Cindy have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems"], "answer_analysis": ["$50+10=60$ $60\\div6=10$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9875", "queId": "8cf109382d79418cb58df318e82bb310", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A mixture of 30 liters of paint is $25 \\textbackslash\\%$ red tint, $30 \\textbackslash\\%$ yellow tint and $45 \\textbackslash\\%$ water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (2007 AMC 8, Question \\#17 ) ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$45$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Since $30 \\textbackslash\\%$ of the original 30 liters of paint was yellow, and 5 liters of yellow paint were added to make the new mixture, there are $9+5=14$ liters of yellow tint in the new mixture. Since only 5 liters of paint were added to the original 30 , there are a total of 35 liters of paint in the new mixture. This gives $40 \\textbackslash\\%$ of yellow tint in the new mixture, which is (C) 40 . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9886", "queId": "538bcac7bc50420fba12925c0bf06a47", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Josh lives on the $6$\\textsuperscript{th} floor. He needs to climb $24$ steps to move from the $2$\\textsuperscript{nd~}floor to the $4$\\textsuperscript{th} floor. How many steps does he need to climb from the $1$\\textsuperscript{st} floor to the $6$\\textsuperscript{th} floor? ", "answer_option_list": [[{"aoVal": "A", "content": "$$72$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$36$$ "}], [{"aoVal": "E", "content": "$$32$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$24 \\div 2 \\times (6 - 1) = 60$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9888", "queId": "d6382e90d85940ab8f8d72f37cadd21f", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Find the exact number of minutes after $3.00 \\text{pm}$ when the minute and hour hands are first at $90^{\\circ}$ to each other. ", "answer_option_list": [[{"aoVal": "A", "content": "$$31 \\frac{2}{11}$$ "}], [{"aoVal": "B", "content": "$$31 \\frac{3}{11}$$ "}], [{"aoVal": "C", "content": "$$32 \\frac{8}{11}$$ "}], [{"aoVal": "D", "content": "$$33 \\frac{3}{11}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["The minute hand rotates $6^{\\circ}$ per minute. The hour hand rotates $\\dfrac{1}{60}\\times30^{\\circ}=\\left (\\dfrac{1}{2}\\right )^{\\circ}$ per mimte. Starting at $3$ O\\textquotesingle clock, when the minute and hour hands are next perpendicular: $$(90+90)\\div(6-0.5)=\\frac{360}{11}=32 \\frac{8}{11}$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9889", "queId": "653cee859ff248c8a40c6aac2f74a1e9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The page numbers of a book are from $$1$$ to $$62$$. Tim adds up the $$62$$ page numbers. In his calculation, he misses a page number and the sum of remaining pages is $$1940$$. What is the missing page number~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression"], "answer_analysis": ["$$\\left( 1+62 \\right)\\times 62\\div 2=1953$$ $$1953-1940=13$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9894", "queId": "60cb3a96467a40d08ca28de17fb9d247", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Suppose $50\\textbackslash\\%$ of $x$ equals $30\\textbackslash\\%$ of $y$. What percentage of $y$ is $x$ ? (adapted from 2020 AMC 8, Question 15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$120$ "}], [{"aoVal": "E", "content": "$$200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$50\\textbackslash\\% \\cdot x = 30\\textbackslash\\% \\cdot y$ $ x = 0.6\\cdot y$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9895", "queId": "8cf97d856b064cf3bcbdaf49c7923a9e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Grandma made some cheese dumplings and some blueberry dumplings. Altogether, she made $$31$$ dumplings. If she had made $$11$$ more cheese dumplings, then there would be the same number of blueberry dumplings as cheese dumplings. How many cheese dumplings did grandma make? ($$2009$$ Math Kangaroo Problem, Levels $$1-2$$, Question \\#$$19$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["$$(31-11)\\div2=10.$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9908", "queId": "6e4251001d554e579c1a697e7d609cb8", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "After the game, Owen is thirsty again. This time he gets a mixture of 3 liters of juice, which contain $25 \\textbackslash\\%$ of apple juice, $30 \\textbackslash\\%$ of mango juice, and $45 \\textbackslash\\%$ of water. $0.5$ liters of mango is added to the original mixture. What is the percent of mango in the new mixture? (Adapted from 2007 AMC 8, Question \\#17 ) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2.5$$ "}], [{"aoVal": "B", "content": "$$3.5$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$4.5$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Since $30 \\textbackslash\\%$ of the original 30 liters of paint was yellow, and 5 liters of yellow paint were added to make the new mixture, there are $9+5=14$ liters of yellow tint in the new mixture. Since only 5 liters of paint were added to the original 30 , there are a total of 35 liters of paint in the new mixture. This gives $40 \\textbackslash\\%$ of yellow tint in the new mixture, which is (C) 40 . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9909", "queId": "b61ec9e70032413dad6c919c879b03d6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Grandma made some cheese dumplings and some blueberry dumplings. Altogether, she made $$31$$ dumplings. If she had made $$11$$ more cheese dumplings, then there would be the same number of blueberry dumplings as cheese dumplings. How many cheese dumplings did grandma make? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["$$(31-11)\\div2=10.$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9910", "queId": "53a7e1bc034648468a6aef5180bfcf96", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Find the exact number of minutes after $3.00 \\text{pm}$ when the minute and hour hands are first at $90^{\\circ}$ to each other. ", "answer_option_list": [[{"aoVal": "A", "content": "$$31 \\frac{2}{11}$$ "}], [{"aoVal": "B", "content": "$$31 \\frac{3}{11}$$ "}], [{"aoVal": "C", "content": "$$32 \\frac{8}{11}$$ "}], [{"aoVal": "D", "content": "$$33 \\frac{3}{11}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["The minute hand rotates $6^{\\circ}$ per minute. The hour hand rotates $\\dfrac{1}{60}\\times30^{\\circ}=\\left (\\dfrac{1}{2}\\right )^{\\circ}$ per mimte. Starting at $3$ O\\textquotesingle clock, the minute hand rotates $\\left (6t\\right )^{\\circ}$ and the hour hand rotates ~$$(90+ \\frac{1}{2}t)^{ \\circ }$$. When the minute and hour hands are next perpendicular: $$6t-\\left (90+ \\frac{1}{2}t\\right )=90$$, $$\\frac{11}{2}t=180$$, $$t= \\frac{360}{11}=32 \\frac{8}{11}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9912", "queId": "c879f628ca2e4b6f88ad0188f9ab2cba", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Joann\\textquotesingle s birthday in $$2020$$ was May $$10$$\\textsuperscript{th}, which was Sunday. Elizabeth\\textquotesingle s birthday in $$2020$$ was June $$21$$\\textsuperscript{st}. On what day did Elizabeth\\textquotesingle s birthday fall? ", "answer_option_list": [[{"aoVal": "A", "content": "Thursday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Sunday "}], [{"aoVal": "D", "content": "Tuesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["It passed $$31-10 + 21 = 42$$ days in total. Since $$42 \\div 7 = 6$$, it was Sunday. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9915", "queId": "580db547002f45b2813e55ceb6b9ceea", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Three zebras take part in a contest. The winner is the zebra with the most number of stripes. Runa has $$15$$ stripes, Zara has $$3$$ more than Runa. Runa has $$5$$ fewer stripes than Biba. How many stripes does the winner have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9921", "queId": "72c7c2107ec34471be1bf78da83c6db5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Sara is $$5$$ years old and Mike is $$9$$. How old will Sara be when Mike is $$20$$ years old? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Their difference in age: $$9-5=4$$ When Mike is $$20$$, Sara is $$20-4=16$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9924", "queId": "77496878dc0846308593ea0cfd47adbc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $$15\\textbackslash\\%$$ sugar solution contains $$18$$ grams of pure sugar. How many grams of solution are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ grams "}], [{"aoVal": "B", "content": "$$100$$ grams "}], [{"aoVal": "C", "content": "$$120$$ grams "}], [{"aoVal": "D", "content": "$$150$$ grams "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$18\\div15\\textbackslash\\% = 120$$ ounces. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9925", "queId": "60ecd887e331475d809050b7ff4631c6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The boundary of a lake is $$600\\text{m}$$ long. Trees are planted at regular intervals of $$6\\text{m}$$ round the lake. How many trees are planted round the lake? ", "answer_option_list": [[{"aoVal": "A", "content": "$$99$$ "}], [{"aoVal": "B", "content": "$$100$$ "}], [{"aoVal": "C", "content": "$$101$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Circular Paths"], "answer_analysis": ["In the case of circular tracks, number of intervals $$=$$ number of trees, $$600\\div 6=100$$, $$100$$ trees are planted round the lake. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9931", "queId": "7bd46184d3c44fd1aade750fce65bc51", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that January $$1$$st, $$2018$$ was Monday, on what day did January $$1$$st, $$2019$$ fall? ", "answer_option_list": [[{"aoVal": "A", "content": "Tuesday "}], [{"aoVal": "B", "content": "Monday "}], [{"aoVal": "C", "content": "Sunday "}], [{"aoVal": "D", "content": "Wednesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$2018$ was a common year which had $365$ days. Thus, January $$1$$, $$2019$$ fell on one day after Monday, which was Tuesday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9943", "queId": "7bde4525ce6247b9ad5f2b7c6cb9e982", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A machine started printing posters at $$9.00 \\rm a.m.$$ on Monday at the rate of $$1000$$ posters per hour. After every $$6$$ hours of printing, it was paused for an hour. How many posters were printed by $$\\rm 11.00 a.m$$. the next day? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20000$$ "}], [{"aoVal": "B", "content": "$$22000$$ "}], [{"aoVal": "C", "content": "$$23000$$ "}], [{"aoVal": "D", "content": "$$26000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9953", "queId": "6e6b097009d74ef699bd185958898c54", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A shop purchased a kind of Lego at ＄$$125$$ each. It then sold them at ＄$$168$$ each. How much did the shopkeeper earn for $$5$$ Legos? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$190$$ "}], [{"aoVal": "B", "content": "＄$$200$$ "}], [{"aoVal": "C", "content": "＄$$210$$ "}], [{"aoVal": "D", "content": "＄$$215$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$$(168-125)\\times 5 = 215$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9955", "queId": "897c85839b794050a371f9166f118d3e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Jenny paid $15$ dollars for $3$ books. How many dollars should she pay in total for the same kind of books if she bought $5$ more of them? ", "answer_option_list": [[{"aoVal": "A", "content": "$$34$$ "}], [{"aoVal": "B", "content": "$$37$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$42$$ "}], [{"aoVal": "E", "content": "$$44$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$15=3\\times5$$, so $5$ dollars for each book $$3+5=8$$, $8\\times5=40$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9959", "queId": "897fc78144f249618ede1f5d8bfddb4d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $3600$ baby chickens on a farm. The number of hens on the farm is $\\dfrac{8}{9}$~of the baby chickens, and the number of roosters is $\\dfrac{1}{16}$~of the number of hens. How many roosters are there on the farm? ", "answer_option_list": [[{"aoVal": "A", "content": "$$180$$ "}], [{"aoVal": "B", "content": "$$200$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$225$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["Hens $=$ baby chickens $\\times\\dfrac{8}{9}$, Roosters $=$ hens $\\times\\dfrac{1}{16}$, We can write the formula as:~$3600\\times\\dfrac{8}{9}\\times\\dfrac{1}{16}=3200\\times\\dfrac{1}{16}=200$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9963", "queId": "84f2f84befde404caf11b4aaa0ddabe7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Students in the third grade lined up and formed a square array to perform a dance. Each side of the outermost layer had $37$ students. How many students in total are there on the outermost layer? ", "answer_option_list": [[{"aoVal": "A", "content": "$$148$$ "}], [{"aoVal": "B", "content": "$$152$$ "}], [{"aoVal": "C", "content": "$$144$$ "}], [{"aoVal": "D", "content": "$$140$$ "}], [{"aoVal": "E", "content": "$$156$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares"], "answer_analysis": ["$$36\\times 4=144$$, or $$37\\times 4-4=144$$ students. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9969", "queId": "bf64530309704216896dbed66d9858d9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The mushrooms picked by $2$ white rabbits in $3$ days will be eaten by $3$ gray rabbits in $4$ days. In how many days will $15$ gray rabbits eat up mushrooms picked by $5$ white rabbits in $6$ days? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["The mushrooms picked by $2$ white rabbits in $3$ days will be eaten by $3$ gray rabbits in $4$ days, so the mushrooms picked by $1$ white rabbits in $1$ days will be eaten by $1$ gray rabbits in $2$ days. Thus, the mushrooms picked by $5$ white rabbits in $6$ days will be eaten by $15$ gray rabbits in $4$ days. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9976", "queId": "d655a8343e6f422cbc0220bf9f7d79b6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jimmy\\textquotesingle s father brought Jimmy three pet dogs, and Jimmy could only keep one. How many dogs did Jimmy\\textquotesingle s father want to take away?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$3$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["$3-1=2$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9977", "queId": "9f63be4a5efe46159edd627b01f0d326", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a garage, the ratio of red cars to black cars is $$8:5$$, and the ratio of black cars to white cars is $$3:4$$. The minimum number of cars in the garage is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$59$$ "}], [{"aoVal": "C", "content": "$$74$$ "}], [{"aoVal": "D", "content": "$$91$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"], "answer_analysis": ["The ratio of red cars to black cars is $$8:5=24:15$$; the ratio of black cars to white cars is $$3:4 = 15:20$$. The minimum number of cars is $$24+15+20 =59$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9979", "queId": "9ad6c0f10ebc4e9a84ccb742eabef6a3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the Avengers League, there are $25$ superheroes. Six of the superheroes from the galaxy guard left. How many heroes are left?~(adapted from $$2007$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$6$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$19$$ "}], [{"aoVal": "B", "content": "$$23$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$25$$ "}], [{"aoVal": "E", "content": "$$20$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["There are $25$ superheroes in total. After subtracting $6$, there are $25-6=19$ left. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9980", "queId": "cd24810efd4c4d0189c21eeebebb1e6f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a verbal test, the average score of $$40$$ students is $$25$$. The lowest score is $$5$$. At most how many student(s) can get $$100$$ points? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Total points: $$40\\times 25=1000$$. To have as many $100$ points as possible, we should consider there are only two groups of students: everyone gets $5$ points in a group and everyone gets $100$ in the other group. $$10\\times 100=1000$$, so there must be less than $10$ people getting $100$ points. If there are nine $100$s: $$9\\times 100+31\\times 5=1055\\textgreater1000$$, which is impossible. If there are eight $100$s:$$8\\times 100+32\\times 5=960\\textless{}1000$$. Thus, the answer is $$8$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9981", "queId": "a88ba2f97bdc45a797a44f44f8ea9dc3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If I write all $$26$$ letters of the English alphabet in alphabetical order $$62$$ times in a row, then the $$806$$th letter I write will be． ", "answer_option_list": [[{"aoVal": "A", "content": "$$A$$ "}], [{"aoVal": "B", "content": "$$E$$ "}], [{"aoVal": "C", "content": "$$V$$ "}], [{"aoVal": "D", "content": "$$Z$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"], "answer_analysis": ["Since $$806\\div 26=31$$, the $$806$$th letter Iwrite will be the last letter of the $$31$$st time I write the full alphabet; it will be a $$Z$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9987", "queId": "bf6c2542371a4d119fc19129e06abf81", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy mixes $$10$$ g of a $$20\\textbackslash\\%$$ sugar solution and $$40$$ g of a $$25\\textbackslash\\%$$ sugar solution together. After~\\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of solution is $40\\textbackslash\\%$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ g "}], [{"aoVal": "B", "content": "$$18$$ g "}], [{"aoVal": "C", "content": "$$20$$ g "}], [{"aoVal": "D", "content": "$$25$$ g "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"], "answer_analysis": ["$$10\\times20\\textbackslash\\%+40\\times 25\\textbackslash\\%=12$$ g. $$(10+40)-12\\div40\\textbackslash\\%=20$$ g. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "9999", "queId": "c400d86f14aa4a9c8181428577ff721a", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A snail is climbing up from the bottom of a $15$-meter-deep well. It climbs up $3$ meters during the daytime, and slides down $1$ meter every night. How many days will it take to get out of the well? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"], "answer_analysis": ["It climbs up $$3-1=2$$ meters actually everyday. It takes $$12\\div 2 +1=7$$ days in total, and in the last day, it climbs up $3$ meters. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10003", "queId": "6a1b88528ce448a6a5138ec4155f33dd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Annie had twice as many paper clips as Beth, After Beth had used $$15$$ paper clips, Annie had $$4$$ times as many as Beth. How many paper clips did Annie have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$45$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$75$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Questions Involving Varying Multiples"], "answer_analysis": ["Let the number of Annie\\textquotesingle s and Beth\\textquotesingle s be 2n and n. 2n=4(n-15), so n=30, 2n=30 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10005", "queId": "a89849c4a1c54c18912ad15116faad40", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "It takes $$144$$ workers $$60$$ hours to paint a bridge. Working at the same rate, how many hours would $$108$$ workers require to do the job? ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$65$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$96$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["It takes $$144$$ workers $$60$$ hours to paint a bridge. That\\textquotesingle s $$144\\times60=8640$$ worker-hours. For $$108$$ workers, the job takes $$8640\\div108=80$$ hours. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10009", "queId": "7c0f14c37b3440c2ae86289e840dd6cc", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The speed of high-speed train is approximately $$350$$ kilometers per hour, while the walking speed of a person is approximately $$5$$ meters per second. Approximately, how many times is the speed of a high-speed train faster than the walking speed of a person?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2 $$ "}], [{"aoVal": "B", "content": "$$20 $$ "}], [{"aoVal": "C", "content": "$$70 $$ "}], [{"aoVal": "D", "content": "$$200 $$ "}], [{"aoVal": "E", "content": "$$700$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"], "answer_analysis": ["The speed of high-speed train is approximately $$350$$ kilometers per hour, which is approximately $$100$$ meters per second. So its speed is roughly $$20$$ times faster than $$5$$ meters per second. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10013", "queId": "6a2a68c0f88e412384f6601d339eee68", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A gift store buys some gifts at＄$$125$$ each. It wants to earn＄$$25 $$ for each gift after a discount of $$25 \\textbackslash\\% $$. What is the selling price before the discount for each shirt? ", "answer_option_list": [[{"aoVal": "A", "content": "$$160$$ dollars "}], [{"aoVal": "B", "content": "$$180$$ dollars "}], [{"aoVal": "C", "content": "$$190$$ dollars "}], [{"aoVal": "D", "content": "$$200$$ dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["$$\\left( 125+25 \\right)\\div \\left( 1-25 \\textbackslash\\% \\right)=200$$ dollars. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10015", "queId": "a89f33cfe35c4fcd87680f2fc907aefd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Two motor-cyclists John and Kevin were $800 \\text{km}$ apart and travelling towards each other at a constant speed. They started at the same time, meeting after $8$ hours. If Kevin started $1\\dfrac{1}{2}$ hours later than John, they would be $70 \\text{km}$ apart $8$ hours after John started. At what speed was John travelling in $\\text{km/h}$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$50$$ "}], [{"aoVal": "B", "content": "$$51 \\frac{2}{3}$$ "}], [{"aoVal": "C", "content": "$$52 \\frac{1}{2}$$ "}], [{"aoVal": "D", "content": "$$53 \\frac{1}{3}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["NA "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10018", "queId": "c8a2e0d48226452f957ff7e8057a9e99", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "\\textbf{Daniel is learning that five pennies spread out on his desk are the same number of coins as five pennies in a pile. According to Piaget, how old is Daniel likely to be?} ", "answer_option_list": [[{"aoVal": "A", "content": "1~\\textbf{year} "}], [{"aoVal": "B", "content": "2~\\textbf{years} "}], [{"aoVal": "C", "content": "\\textbf{4 years} "}], [{"aoVal": "D", "content": "\\textbf{8 years} "}], [{"aoVal": "E", "content": "\\textbf{13 years} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["\\textbf{Daniel is learning conservation of number, a skill that Piaget believed children learn in the concrete operational stage} "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10021", "queId": "9f7ed8f805f5458cbfd97d2cc11e1951", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy mixes $$30$$ g of a $$30\\textbackslash\\%$$ salt solution and $$20$$ g of a $$20\\textbackslash\\%$$ salt solution together. How many g of water should she add to the mixture to make it a $$10\\textbackslash\\% $$ solution? ", "answer_option_list": [[{"aoVal": "A", "content": "$$70$$ "}], [{"aoVal": "B", "content": "$$72$$ "}], [{"aoVal": "C", "content": "$$75$$ "}], [{"aoVal": "D", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"], "answer_analysis": ["$$30\\times30\\textbackslash\\%+20\\times 20\\textbackslash\\%=9+4=13$$ g. $$13\\div10\\textbackslash\\%-(30+20)=80$$ g. ~~ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10022", "queId": "8d4d0a0478824030b852ea703dfd2924", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Arrange $$28$$ balls to form a square. One ball is placed at each corner of the square. How many balls are there on each side of the square?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Hallow Squares"], "answer_analysis": ["Put $$1$$ ball in each corner ($$4$$ balls in total). Remaining balls: $$28-4=24$$ $$24\\div4=6$$ So, each side has $$1$$ ball at each corner and $$6$$ balls in the middle, giving a total of $$8$$ balls. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10023", "queId": "c40b07fc65b749179efa63c624a2d9e5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The average pocket money of the whole class is $91$ dollars. Each of the $24$ girls in the class has $92.5$ dollars on average. There are $18$ boys in the class, and their average pocket money is~\\uline{~~~~~~~~~~}~dollars. ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$28$$ "}], [{"aoVal": "C", "content": "$$69$$ "}], [{"aoVal": "D", "content": "$$85$$ "}], [{"aoVal": "E", "content": "$$89$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["More than average: $$(92.5-91)\\times24=36$$. Each boy should have $$36\\div18=2$$ dollars less than the average, so each of them has $91-2=89$ dollars. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10027", "queId": "851eb31f3d104485b20dbc5a10502c5d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\frac{3}{7}$$ of the passengers on the bus were adults and the rest were children. There were $$24$$ children. How many adults were there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$42$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["$$1- \\frac{3}{7}= \\frac{4}{7}$$ $24\\div \\frac47=42$ $42-24=18$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10035", "queId": "89ac077f05174987be450c352e0bd9cb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "When Teddy was $$5$$ years old, his father\\textquotesingle s age was $$7$$ times his age. When his father is $$42$$ years old, how old will Teddy be? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->When..., When... Type Age Problems"], "answer_analysis": ["$$7\\times5=35$$, His father was $$35$$ years old when Teddy was $$5$$ years old. Age difference $=35-5=30$ $42-30=12$ years old $\\textasciitilde$ or $\\textasciitilde$ $$7\\times5=35$$, His father was $$35$$ years old when Teddy was $$5$$ years old. $$42-35=7$$ years later $$5+7=12$$ years old $\\textasciitilde$ Teddy will be $$12$$ years old when his father is $$42$$ years old. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10036", "queId": "e8cf9d14f8394c439980ea0e7bc51cbb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The average height of all the teachers in Grape School is $168$. There are $5$ male teachers in Grape School with an average height of $180$. The average height of female teachers is $162$. How many female teachers are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$18$$ "}], [{"aoVal": "E", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Total height less than the average: $(180-168)\\times5=60$. Thus, there are $60\\div(168-162)=10$ female teachers. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10038", "queId": "6eae84a23c684eb1899dd108e1b92c60", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are only lilies and roses in Bud\\textquotesingle s garden. One third of the flowers are roses. There are 12 roses in total. How many flowers are there in Buds\\textquotesingle s garden? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$12\\div\\frac13=36$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10048", "queId": "f6ad7069dbd04cfa8649fcb5a22d0b61", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A shop purchased some tennis rackets at ＄$$150$$ each. It then sold them at ＄$$175$$ each. How much did the shopkeeper earn for $$10$$ rackets? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$150$$ "}], [{"aoVal": "B", "content": "＄$$200$$ "}], [{"aoVal": "C", "content": "＄$$250$$ "}], [{"aoVal": "D", "content": "＄$$300$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$$(175-150)\\times 10 = 250$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10051", "queId": "852a084f79704329a3e7234f0df71006", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Little Pig is standing in a line. There are $$16$$ animals in the line and her position is the $$4$$\\textsuperscript{th} counting from front to back. How many animals are behind her?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["Ms. Pig is included in the \"$$4$$\" , so there are $$16 - 4 = 12$$ animals behind her. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10053", "queId": "ed6df277297d4a219498823b25d0efcb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $5$ people in Linda\\textquotesingle s family with an average weight of $56$ kg. The weights of Linda, Linda\\textquotesingle s mom, Linda\\textquotesingle s sister, and Linda\\textquotesingle s brother are $45$ kg, $55$ kg, $50$ kg, and $60$ kg, respectively. What is the weight of Harry\\textquotesingle s dad? ", "answer_option_list": [[{"aoVal": "A", "content": "$$65$$ "}], [{"aoVal": "B", "content": "$$66$$ "}], [{"aoVal": "C", "content": "$$68$$ "}], [{"aoVal": "D", "content": "$$70$$ "}], [{"aoVal": "E", "content": "$$75$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$$56\\times5-45-55-50-60=70$$ kg "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10055", "queId": "bae717935691490dbaedd190eb428cd5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Della decides to buy some stationaries for her students. The price of two schoolbags is equal to the price of six notebooks, and the price of six pencilcases is equal to nine notebooks. Given that one schoolbag can be exchanged for four pens, how many pens can be exchanged for one pencilcase? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$2$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["$$1$$ schoolbag$$=3$$ notebooks$$=4$$ pens, and $$6$$ pencilcases$$=9$$ notebooks, Then, $$2$$ pencilcases$$=3$$ notebooks$$=4$$ pens. So, $$1$$ pencilcase$$=2$$ pens. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10059", "queId": "9f8f6bcb5ad141dc80e1c9eff1a82697", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Suppose $20 \\textbackslash\\%$ of $x$ equals $40\\textbackslash\\%$ of $y$. What percentage of $y$ is $x$ ? (adapted from 2020 AMC 8, Question 15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$35$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$75$$ "}], [{"aoVal": "D", "content": "$150$ "}], [{"aoVal": "E", "content": "$$200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$20 \\textbackslash\\% \\cdot x = 40\\textbackslash\\% \\cdot y$ $ x = 2 \\cdot y$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10061", "queId": "6a5292165b2341409836a18a62d96c49", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Iate half an apple pie on Saturday and two thirds of the remainder on Sunday. What fraction of the pie was left for Monday?　 ", "answer_option_list": [[{"aoVal": "A", "content": "None　 "}], [{"aoVal": "B", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "D", "content": "$$\\frac{2}{3}$$ "}], [{"aoVal": "E", "content": "$$\\frac{1}{6}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Understanding the Base"], "answer_analysis": ["After I eat one half, half of the apple pie is left. Eating two thirds of this half leaves one third of one half of the pie, which is one sixth, for Monday. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10062", "queId": "6ec85a1e2fbd4a2c99595d27711fb80d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$1000\\textbackslash\\%$$ of a certain number is $$100$$, the certain number is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$1000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["If $$1000\\textbackslash\\%$$ is $$100$$, then $$\\left(\\frac{1}{10}\\right)\\text{th}$$ of that, $$10$$, is $$100\\textbackslash\\%$$ of the number. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10064", "queId": "91eea44d205446b0a65e7aaac998e481", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Jin loves carrots! Yesterday she ate $$\\frac{7}{9}$$ of her carrots, and today she ate $$\\frac{2}{7}$$ of the number of carrots she ate yesterday. She ate 14 carrots today. Yesterday she had started with carrots. ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$49$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$63$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["$14\\div\\dfrac{2}{7}\\div\\dfrac{7}{9}=63$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10065", "queId": "734262e9f24a4d71922b342d645c8800", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A total of $$20$$ chickens and rabbits are caged together. If there are $$56$$ legs in total, how many chickens are there in the cage? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"], "answer_analysis": ["Suppose the number of chickens is $x$, so the number of rabbits is $(20-x)$. $2x+(20-x)\\times4=56$, $x=12$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10066", "queId": "65ebe75f96b943eaab206cf5336b9351", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ellie and Gloria have to interview a total of $$400$$ people. Ellie can interview $$60$$ people every week. If Gloria and Ellie work together, they can finish all the work in $$4$$ weeks. How many weeks will it take to finish interviewing everyone by Gloria herself? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$16$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"], "answer_analysis": ["Working together: $$400\\div4=100$$ people every week Gloria: $$100-60=40$$ people every week $$400\\div40=10$$ weeks $\\textasciitilde$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10072", "queId": "85401eee5cf84a30b1d10993cbb79b5f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$50$ balloons are distributed to Ariel and seven other children. Each of them can get at least one balloon, and no two of them get the same number of balloons. For Ariel, what is the largest possible number of balloons she can get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$22$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value"], "answer_analysis": ["The largest number of balloons Ariel can get is: $$50 -- (1 + 2 + 3 + 4 + 5+6+7) = 22$$, that is, $$22$$ balloons at most. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10074", "queId": "ad45ededfc2341bf9fd3109431ab96ef", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "$$29$$ students came into the classroom in turn. The number of students that came in before Mike was $$5$$ more than the number of students who came in after him. Which place did Mike come in? (Adapted from 2015 Math Kangaroo Problem, Level 3 - 4, Question \\#13) ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$17$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Order of one Character"], "answer_analysis": ["The sum of the number of students that came in before Tom and the number of students that came in after him is $29 - 1 = 28$. The number of students that came in before Mike was $(28 + 6) \\div 2 = 17$, so Mike was the eighteenth. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10075", "queId": "6a628a3a16d54dd5bdd0196dc359c4f5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $$15\\textbackslash\\%$$ sugar solution contains $$18$$ ounces of pure sugar. How many ounces of solution are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ ounces "}], [{"aoVal": "B", "content": "$$100$$ ounces "}], [{"aoVal": "C", "content": "$$120$$ ounces "}], [{"aoVal": "D", "content": "$$150$$ ounces "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$18\\div15\\textbackslash\\% = 120$$ ounces. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10076", "queId": "9b0d3498866e42d6accf73ee3833b32a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My first day of vacation is May $$10$$. My last day of vacation is May $$20$$ of the same year. How many days of vacation do I have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$ 10 $$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$20-10+1=11$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10079", "queId": "e8dd747172404febbdf716e450fcc095", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of two numbers is $$71$$. The difference of the two numbers is $$9$$. Find the bigger number. ", "answer_option_list": [[{"aoVal": "A", "content": "$$31$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$62$$ "}], [{"aoVal": "D", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["71 + 9 = 80 80 $\\div $ 2 = 40 "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10097", "queId": "9fa8a0cd4c08480391f0e024baaf3cd7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "For a quarter ($$25$$￠), Pat can play a video game for $$5$$ minutes. How many quarters does Pat need to play for an hour? ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["For a quarter ($$25$$￠), Pat can play a video game for $$5$$ minutes. The number of $$5$$-minute intervals in $$1$$ hour is $$60 \\div 5 = 12$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10098", "queId": "d1ebe824fc414485b7edffbd1ba0cd53", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The teacher has $$14$$ sweets. She wants to give eight students the same number of sweets. How many more sweets should she prepare? (adapted from $$2020$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$16$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$14=8+6$$, ~In this equation, $$8$$ means everyone can get $$1$$ sweet. There are $$6$$ sweets left, the teacher also needs $$8-6=2$$ sweets. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10099", "queId": "661500241d7e46cea4ca7d8284f6e719", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that May $$16$$ of a certain year is a Monday, what day of the week will July $$8$$ fall on in the same year? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Wednesday "}], [{"aoVal": "D", "content": "Thursday "}], [{"aoVal": "E", "content": "Friday "}], [{"aoVal": "F", "content": "Saturday "}], [{"aoVal": "G", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["May: $31-16+1=16$ June: $30$ July: $8$ $16+30+8=54$ $54\\div7=7$ R $5$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10101", "queId": "7c5b3d9c23894d118f57006c2f05574b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$\\frac{1}{4}$$ of the beads in a box are blue. $$\\frac{1}{3}$$ of the blue beads are small. lf there are $$700$$ small blue beads, how many beads are there altogether in the box? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1200$$ "}], [{"aoVal": "B", "content": "$$2100$$ "}], [{"aoVal": "C", "content": "$$2450$$ "}], [{"aoVal": "D", "content": "$$4900$$ "}], [{"aoVal": "E", "content": "$$8400$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["$\\frac{1}{4}\\times\\frac{1}{3}=\\frac{1}{12}$ of the total beads are small blue beads. $700\\times12=8400$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10105", "queId": "89e28de887504979bbd887f81e75e37f", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Nick bought $20$ apples from the supermarket. $40$\\% of them were red and $60$\\% of them were green. How many red apples did he buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$12$$ "}], [{"aoVal": "D", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$20 \\times 40$\\%=$8$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10106", "queId": "f6bfde07413443039d5107b3d22eeec8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Famer $$A$$ had $$1233$$ ducks. He had three times as many ducks as Farmer $$B$$. Farmer $$B$$ had $$199$$ more ducks than Farmer $$C$$. How many ducks did Farmer $$C$$ have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$212$$ "}], [{"aoVal": "B", "content": "$$411$$ "}], [{"aoVal": "C", "content": "$$610$$ "}], [{"aoVal": "D", "content": "$$3898$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Word Problems Involving Comparing and Ordering"], "answer_analysis": ["Farmer B\\textquotesingle s duck: $$1233 \\div3 = 411$$ Farmer C\\textquotesingle s duck: $$411-199=212$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10107", "queId": "ed7fecacb49e46d996afa582a543ed7e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that June $$14$$, $$2012$$ was Thursday, what day was June $$14$$, $$2014$$? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Friday "}], [{"aoVal": "D", "content": "Saturday "}], [{"aoVal": "E", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["It would pass $365+365=730$ days, which means June $$14$$, $$2014$$ was two days after Thursday. It was Saturday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10109", "queId": "6a86817df9734b3b8851d9d795a672a9", "competition_source_list": ["其它"], "difficulty": "3", "qtype": "single_choice", "problem": "There are some apples and $8$ pears in a basket, each of them are green or yellow. There are three more apples than the total number of green fruit. There are $6$ yellow pears. How many yellow apples are there in the basket? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10115", "queId": "85626f0234f545929198e86c5d19efdf", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Starting with some gold coins and some empty treasure chests, I tried to put $$9$$ gold coins in each treasure chest, but that left $$2$$ treasure chests empty. So instead I put $$6$$ gold coins in each treasure chest, but then I had $$3$$ gold coins left over. How many gold coins did I have? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$27$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$63$$ "}], [{"aoVal": "E", "content": "$$81$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Suppose $x$ is the number of treasure chests. Thus the number of gold coins can be represented as $$9(x-2)$$ or $$6x + 3$$. So, $$9(x-2)=6x+3$$, $$x=7$$. There are $$9\\times (7-2)=45$$ gold coins. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10116", "queId": "ed8225458c1f4b24b0010c9bec5761e9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There were $$27$$ children in a class. There were twice as many boys as girls. How many boys were there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$21$$ boys "}], [{"aoVal": "B", "content": "$$18$$ boys "}], [{"aoVal": "C", "content": "$$16$$ boys "}], [{"aoVal": "D", "content": "$$14$$ boys "}], [{"aoVal": "E", "content": "$$9$$ boys "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["$$\\dfrac{27}{(2+1)}=9$$, $$9\\times2=18$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10121", "queId": "b6793c50885f45c88b71601d954f0487", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "On a map $4\\text{cm}$ represents $50\\text{km}$. The distance between town A and town B is $14\\text{cm}$. A car leaves town A and travels towards town B at $35$km per hour. How long does it take the car to travel to town B? ", "answer_option_list": [[{"aoVal": "A", "content": "$4\\text{hours}$ "}], [{"aoVal": "B", "content": "$5\\text{hours}$ "}], [{"aoVal": "C", "content": "$10\\text{hours}$ "}], [{"aoVal": "D", "content": "$14\\text{hours}$ "}], [{"aoVal": "E", "content": "$18\\text{hours}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["If $$4\\textasciitilde\\text{cm}$$ represents $$50\\textasciitilde\\text{km}$$, $$2\\textasciitilde\\text{cm}$$ represents $$25\\textasciitilde\\text{km}$$. So, their actual distance apart is $$14\\div2\\times 25=175\\textasciitilde\\text{km}$$. $175\\div35=5$ hours. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10123", "queId": "969ee083a420427f9c66a505aaf596b9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Students guess that Norb\\textquotesingle s age is $$24$$, $$28$$, $$30$$, $$32$$, $$36$$, $$38$$, $$41$$, $$44$$, $$47$$, and $$49$$. Norb says, \"At least half of you guessed too low, two of you are off by one, and my age is a prime number.\" How old is Norb? ($$2011$$ AMC $$8$$ problem, Question \\#$$21$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$29$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$37$$ "}], [{"aoVal": "D", "content": "$$43$$ "}], [{"aoVal": "E", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["If at least half the guesses are too low, then Norb\\textquotesingle s age must be greater than $$36$$. If two of the guesses are off by one, then his age is in between two guesses whose difference is $$2$$. It could be $$31$$, $$37$$, or $$48$$, but because his age is greater than $$36$$, it can only be $$37$$ or $$48$$. Lastly, Norb\\textquotesingle s age is a prime number so the answer must be $$37$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10128", "queId": "80ef214ca0944e1f99b6c093c269d362", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Joan needs $$250$$ pounds of metal with $$27\\textbackslash\\%$$ silver. If Joan combines one metal with $$23\\textbackslash\\%$$ silver, and another with $$43\\textbackslash\\%$$ silver,how much of each metal does Joan need respectively? ", "answer_option_list": [[{"aoVal": "A", "content": "$$200$$;$$50$$ "}], [{"aoVal": "B", "content": "$$150$$;$$100$$ "}], [{"aoVal": "C", "content": "$$100$$;$$150$$ "}], [{"aoVal": "D", "content": "$$50$$;$$200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["$$\\dfrac{43\\textbackslash\\%-27\\textbackslash\\%}{27\\textbackslash\\%-23\\textbackslash\\%}=\\dfrac{16}{4}=\\dfrac{4}{1}$$, $$23\\textbackslash\\%$$ silver:$$250\\times\\dfrac{4}{4+1}=200$$, $$43\\textbackslash\\%$$ silver:$$250\\times\\dfrac{4}{4+1}=50$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10133", "queId": "921e1c9d500f4fb6908ed5ae5bf69f4b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ten years ago, the sum of the ages of my mother and father was $$71$$. What is the sum of their ages today? ", "answer_option_list": [[{"aoVal": "A", "content": "$$51$$ "}], [{"aoVal": "B", "content": "$$61$$ "}], [{"aoVal": "C", "content": "$$81$$ "}], [{"aoVal": "D", "content": "$$91$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["Ten years ago, the sum of the ages of my mother and father was $$71$$. Each has aged $$10$$ years, so the sum of their ages is now $$91$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10135", "queId": "c8ce363c75704746b22d6a22dab82be1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If I start with $2$, and begin to count in $$3$$s, my $50^{}\\text{th}$ number will be~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$148$$ "}], [{"aoVal": "B", "content": "$$149$$ "}], [{"aoVal": "C", "content": "$$150$$ "}], [{"aoVal": "D", "content": "$$151$$ "}], [{"aoVal": "E", "content": "$$152$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression"], "answer_analysis": ["$2+(50-1)\\times3=149$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10142", "queId": "bb0f7f7359024a30b9c03e2c78a9fcf9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the yard there is an equal number of pigs, ducks and chickens. Together, they have $$144$$ legs. How many ducks are there in the yard? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$35$$ "}], [{"aoVal": "D", "content": "$$42$$ "}], [{"aoVal": "E", "content": "$$43$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Suppose there are $$x$$ ducks in the yard. Since there is an equal number of pigs, ducks and chickens, $$2x+4x+2x=144$$, $$x=18$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10145", "queId": "9b376731e4384b4eb5c84d621ed8ae70", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Emma is $9$ years old. Anna is $12$ years old. Peter is older than Emma but younger than Anna. How old is Peter? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["NA "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10146", "queId": "9b377bb4559645a791fbd510ce8e4e95", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Some kangaroos are lining at bakery. Tom is the third kangaroo from the back, and the fifth from the front. How many kangaroos are there lining up in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$3+5-1=7$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10157", "queId": "dfb9468e2d084f5e92efce40a53865cc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Henderson has $$9$$ sweets more than Flora. After teacher Johnny gave each of them $$7$$ more sweets, they have a total of $$43$$ sweets. How many sweets does Flora has at first? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$17$$ "}], [{"aoVal": "E", "content": "$$19$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$43-14-9=20$$ $$20\\div2=10$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10161", "queId": "6ab7c9dc4c474cc1bb6bd67284c2eb66", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If today is a Tuesday, then $$15$$ days ago was a.　 ", "answer_option_list": [[{"aoVal": "A", "content": "Saturday　 "}], [{"aoVal": "B", "content": "Sunday　 "}], [{"aoVal": "C", "content": "Monday　 "}], [{"aoVal": "D", "content": "Wednesday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Today is Tues. $$14$$ days ago was Tues. $$15$$ days ago was Mon. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10167", "queId": "8dae3c7d2b1b4cc7afc61009c5a9b46a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a jar of red, green, and blue marbles, all but $$6$$ are red marbles, all but $$8$$ are green, and all but $$4$$ are blue. How many marbles are in the jar? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems"], "answer_analysis": ["Suppose there are $$x$$ red marbles, $$y$$ green marbles and $$z$$ blue marbles. Thus, we can get $$\\begin{cases} x+y=4① \\textbackslash\\textbackslash{} y+z=6②\\textbackslash\\x+z=8③\\end{cases}$$, ①$$+$$②$$+$$③: $$2x+2y+2z=18$$, $$x+y+z=9$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10173", "queId": "781df94552ff4868aecf85113a21c431", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a jar of red, green, and blue marbles, all but $$16$$ are red marbles, all but $$18$$ are green, and all but $$14$$ are blue. How many marbles are in the jar? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems"], "answer_analysis": ["Suppose there are $$x$$ red marbles, $$y$$ green marbles and $$z$$ blue marbles. Thus, we can get $$\\begin{cases} x+y=14① \\textbackslash\\textbackslash{} y+z=16②\\textbackslash\\x+z=18③\\end{cases}$$, ①$$+$$②$$+$$③: $$2x+2y+2z=48$$, $$x+y+z=24$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10179", "queId": "96c534b4d3dc4f0eb5c95e67274ed430", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sanjay let me finish his box of mints. He had eaten $$\\frac{5}{8}$$ of them. If $$36$$ mints were left for me, how many mints were there in the box at the start? ", "answer_option_list": [[{"aoVal": "A", "content": "$$96$$ "}], [{"aoVal": "B", "content": "$$58$$ "}], [{"aoVal": "C", "content": "$$68$$ "}], [{"aoVal": "D", "content": "$$36$$ "}], [{"aoVal": "E", "content": "$$56$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["$36\\div(1-\\dfrac{5}{8})=96$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10190", "queId": "ad82efc65ea146d6be5abb18ad5c5487", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "On a map of England and Wales the distance between St Ives in Cornwall and St Ives in Cambridgeshire measures $$18\\text{cm}$$. In reality the distance between the two towns is about $$450\\text{km}$$. Which of the options below is the scale of the map? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1:2500000$$ "}], [{"aoVal": "B", "content": "$$1:1000000$$ "}], [{"aoVal": "C", "content": "$$1:750000$$ "}], [{"aoVal": "D", "content": "$$1:500000$$ "}], [{"aoVal": "E", "content": "$$1:250000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["The scale of the map is $$18\\text{cm} : 450\\text{km}$$; converting the actual distance to centimetres, this is equivalent to $$18 : 450 \\times 1000 \\times 100 = 18 : 45 000 000$$. Simplifying gives a scale of $$1 : 2 500 000$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10191", "queId": "ad83a6be67494553a9b4b6808dbf8b25", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Calculate: $\\frac{1}{1\\times 7}+\\frac{1}{7\\times 13}+\\frac{1}{13\\times 19} + \\cdots +\\frac{1}{1207\\times 1213}$ ", "answer_option_list": [[{"aoVal": "A", "content": "$\\frac{1212}{1213}$ "}], [{"aoVal": "B", "content": "$\\frac{303}{1213}$ "}], [{"aoVal": "C", "content": "$\\frac{202}{1213}$ "}], [{"aoVal": "D", "content": "$\\frac{1212}{6065}$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples"], "answer_analysis": ["C "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10194", "queId": "6f543e755cdc4aca9d32c108d1d6b737", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$300$$ students in Think Primary School. Three-tenths of the students are in year $$5$$ and three-fifths of the year $$5$$ students are girls. How many year $$5$$ girls are there in Think Primary School? ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$54$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$90$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages"], "answer_analysis": ["$$300\\times\\frac{3}{10}\\times\\frac{3}{5}=54$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10199", "queId": "d6a3d5d087e74610849ebbfb78ccf315", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The five-digit number $411A2$ is a multiple of $9$. What digit does A represent? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$2$$ "}], [{"aoVal": "D", "content": "$$3$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division"], "answer_analysis": ["From the Divisibility Rule of $9$, the sum of the digit of 411A2 must be divisible by $9$. $4 + 1 + 1+ 4 + 2 = 8 + A$ Hence A = $1$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10200", "queId": "85a50c31d5664a38bac85dcbaf8c7ee1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Iron Man\\textquotesingle s flying speed is $$12,250$$km/h, which is $$25$$ times the speed of a regular airplane. What is the speed of the airplane? ", "answer_option_list": [[{"aoVal": "A", "content": "$$490$$km/h "}], [{"aoVal": "B", "content": "$$500$$km/h "}], [{"aoVal": "C", "content": "$$4900$$km/h "}], [{"aoVal": "D", "content": "$$5000$$km/h "}], [{"aoVal": "E", "content": "$$245$$km/h "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"], "answer_analysis": ["The speed of the airplane is~$12250\\div25=490$km/h. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10204", "queId": "73c802dc558f4bcbab09a12d4d82909f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I am threading blue and purple beads onto a necklace in the ratio $$2 : 5$$. I use $$98$$ beads in total. How many more purple beads than blue do I use? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$42$$ "}], [{"aoVal": "D", "content": "$$14$$ "}], [{"aoVal": "E", "content": "$$49$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"], "answer_analysis": ["The ratio $$2 : 5$$ means that $$2$$ in $$7$$ beads are blue and $$5$$ in $$7$$ purple. Since $$98 \\div 7 = 14$$, there are $$28$$ blue and $$70$$ purple beads, hence $$70 - 28 = 42$$ more purple than blue. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10205", "queId": "813383f185f649208136f6697834391b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "If Pip was 10 years old 5 years ago, how old will he be 7 years from now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$14$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$22$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["$$10+5+7=22$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10206", "queId": "8a2e5395b9eb47f481dc5b4f8b2d0466", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Harry planted some trees around a $20$m by $20$m square garden. If there are trees planted at each of the $4$ corners, and the distance between every $2$ trees is $5$m, at least how many trees did Harry plant? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Circular Paths->Planting Trees (circular path)"], "answer_analysis": ["$20 \\div 5 = 4$ intervals on each side $4+1=5$ trees on each side $4\\times5-4=16$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10207", "queId": "6aebd95af8944cebbc8801aa2e4d8bd2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There is a basket of peaches. Three students take turns to take peaches. Sana takes $2$ less than the half of peaches. Joann takes $2$ more than half of the remaining peaches. Now, there are $5$ peaches in the basket. How many peaches are there in the basket at beginning? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$28$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$5+2=7$$ $7+7=14$ $14-2=12$ $12+12=24$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10209", "queId": "7cb6d56eaf41498887b277546ad90a04", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Mother\\textquotesingle s Day in $$2020$$ was May $$10$$th, which was Sunday. Father\\textquotesingle s Day in $$2020$$ was June $$21$$st. On what day did Father\\textquotesingle s Day fall? ", "answer_option_list": [[{"aoVal": "A", "content": "Thursday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Sunday "}], [{"aoVal": "D", "content": "Tuesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["It passed $$31-10 + 21 = 42$$ days in total. Since $$42 \\div 7 = 6$$, which means the Father\\textquotesingle s Day fell on Sunday as well. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10218", "queId": "9fee5f2c8743488e8e60e6b37f3c2f9c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Andy has $$6$$ candies. Bob has twice as many candies as Andy. Chloe has $$4$$ times as many candies as Andy. How many candies do they have altogether? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$42$$ "}], [{"aoVal": "D", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10220", "queId": "813d58533c104684987e10cc5a3ddd80", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "James wants to make $5$ cakes. Each day he makes one cake. He made the first cake on Tuesday. What day of the week will it be when he makes the last cake? (Adapted from 2011 Math Kangaroo Problem, Level 3-4, Question \\#2) ", "answer_option_list": [[{"aoVal": "A", "content": "Wednesday "}], [{"aoVal": "B", "content": "Thursday "}], [{"aoVal": "C", "content": "Friday "}], [{"aoVal": "D", "content": "Saturday "}], [{"aoVal": "E", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Count day by day directly. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10228", "queId": "e908b28c0b1145519f961769146a5acb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Half a loaf of bread costs $$6$$ pence more than one-fourth of a loaf of bread. How many pence does a whole loaf of bread cost? ($$1998$$ Math Kangaroo Problem, Level $$3-4$$, Question \\#$$14$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["One-fourth of a loaf of bread is \"$$1$$ unit\". Half a loaf of bread is \"$$2$$ units\". One-fourth of a loaf of bread: $$6 \\div (2-1) =6$$. A whole loaf of bread: $$6 \\times 4 =24$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10232", "queId": "b6ac93d6d6744587b2fc2b72a7215a82", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Many years ago, $$1^{\\text{st}}$$ of May was a Friday. Which day of the week was $$23^{\\text{rd}}$$ of May in that year? ", "answer_option_list": [[{"aoVal": "A", "content": "Thursday "}], [{"aoVal": "B", "content": "Friday "}], [{"aoVal": "C", "content": "Saturday "}], [{"aoVal": "D", "content": "Sunday "}], [{"aoVal": "E", "content": "Monday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["First Friday: 　　　$$1^{\\text{st}}$$ of May Second Friday: 　　$$8^{\\text{th}}$$ of May Third Friday: 　　　$$15^{\\text{th}}$$ of May Fourth Friday: 　　$$22^{\\text{nd}}$$ of May $$23^{\\text{rd}}$$ of May was a \\textbf{Saturday} in that year. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10233", "queId": "dfd29d6b2ca9419dbe3a49c5e20ac5c0", "competition_source_list": [], "difficulty": "0", "qtype": "single_choice", "problem": "There are stools and chairs in the room. Each stool has $$3$$ legs, and each chair has $$4$$ legs. Altogether there are $$17$$ legs. How many chairs are there in the room? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"], "answer_analysis": ["If there are five stools, the chairs have $17-3\\times5=2$ legs, which is not applicable. If there are four stools, the chairs have $17-3\\times4=5$~ legs, which is also not applicable. If there are three stools, the chairs have $17-3\\times3=8$ legs, which implies that there are $8\\div4=2$ chairs and is applicable according to the question. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10236", "queId": "a48449112fd6460783b4b789b3befa9d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The cost of my algebra book is $$200\\textbackslash\\%$$ of that of my geometry book. The cost of my geometry book is $$\\frac{4}{3}$$ that of my calculus book. If my calculus book costs ＄$$21$$, how much do all $$3$$ books cost together? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$28$$ "}], [{"aoVal": "B", "content": "＄$$56$$ "}], [{"aoVal": "C", "content": "＄$$84$$ "}], [{"aoVal": "D", "content": "＄$$105$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["The cost of the calculus book is ＄$$21$$. The cost of my geometry book is ＄$$21\\times \\left(\\frac{4}{3}\\right)=$$＄$$28$$. My algebra book costs ＄$$28 \\times2 =$$＄$$56$$. All $$3$$ books cost ＄$$21+$$＄$$28 +$$＄$$56 =$$＄$$105$$ in total. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10239", "queId": "ad9a6562f6074361b85ec39ec692ce41", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$18$$ chocolates in Swee Tuth\\textquotesingle s box, $$2$$ each of $$9$$ flavours. She likes only $$6$$ of the flavours. If she picks a chocolate at random, what is the probability of her getting one she doesn\\textquotesingle t like? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{2}{9}$$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "C", "content": "$$\\frac{4}{9}$$ "}], [{"aoVal": "D", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "E", "content": "$$\\frac{2}{3}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["Out of $$18$$ chocolates there are $$6\\times2=12$$ of the flavours that she likes. So the probability of Swee Tuth getting one she doesn\\textquotesingle t like is $$\\frac{6}{18} =\\frac{1}{3}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10243", "queId": "7cd91dbcecf7462cb5f41be7b7cb341b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Maddie is $$2$$ years older than Lola, and Lola is $$6$$ years younger than Ellie. How much older is Ellie than Maddie? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ years "}], [{"aoVal": "B", "content": "$$3$$ years "}], [{"aoVal": "C", "content": "$$4$$ years "}], [{"aoVal": "D", "content": "$$5$$ years "}], [{"aoVal": "E", "content": "$$6$$ years "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["Ellie is $$6$$ years older than Lola, and Maddie is $$2$$ years older than Lola. Therefore Ellie is $$4$$ years older than Maddie. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10247", "queId": "85ca1cfe946447d49bd78a4fce6c5a9a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Some students are going to an amusement park. If each student carries $9$ bottles of water in his or her backpack, there will be $2$ students carrying nothing; if one of the students carries $2$ bottles of water and the rest students carry $8$ bottles each, all the bottles of water can be carried to the park. There are~\\uline{~~~~~~~~~~}~bottles of water in total that need to be carried. ", "answer_option_list": [[{"aoVal": "A", "content": "$$80$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$92$$ "}], [{"aoVal": "D", "content": "$$102$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Distribution Conversion Problems"], "answer_analysis": ["Solve the problem as a problem of surplus and shortage. If each student carries $9$ bottles, there will be a shortage of $9\\times2=18$ bottles; if each student carries $8$ bottles, there will be a shortage of $8-2=6$ bottles. Therefore, there are $(18-6)\\div(9-8)=12$ students and $12\\times9-18=90$ bottles of water. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10252", "queId": "a004c47a001949c3835adb68300e6dda", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "In a certain calendar year, there are more Mondays than Fridays, and more Sundays than Wednesdays. Which day of the week is $$1^{}\\text{st}$$ March in that year? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday　 "}], [{"aoVal": "B", "content": "Tuesday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Thursday　 "}], [{"aoVal": "E", "content": "Friday　 "}], [{"aoVal": "F", "content": "Saturday　 "}], [{"aoVal": "G", "content": "Sunday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Nil "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10255", "queId": "73f7fbc7b1274949a281c5cb4e6b3934", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A worm is staying at the bottom of a well with a depth of $$13$$ metres. If it climbs up $$4$$ metres in the daytime and slips down $$1$$ metres at night, which day will it climb up to the ground? ", "answer_option_list": [[{"aoVal": "A", "content": "The $$4$$th day "}], [{"aoVal": "B", "content": "The $$5$$th day "}], [{"aoVal": "C", "content": "The $$6$$th day "}], [{"aoVal": "D", "content": "The $$7$$th day "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"], "answer_analysis": ["It climbs up $$4$$ metres in the day time and slips down $$1$$ metre at night, so it climbs up $$3$$ metres in a whole day. For the first $$3$$ days, it climbs $$9$$ metres. During the day time of the forth day, it climbs $$4$$ metres and reaches the ground. Then it needs four days to climb up to the ground. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10262", "queId": "a9228105cf794b369bd1fa87cc69dcae", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A jacket was on sale. The original price was ＄$$180$$, and Peter bought it at ＄$$135$$. What was the discount rate? ", "answer_option_list": [[{"aoVal": "A", "content": "$$135\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$180\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$75\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$25\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["$$1-135\\div180=25\\textbackslash\\%$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10263", "queId": "dfdf9d79237e408ea69cf29acfeca74f", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Justin said to his mom, \"If I had planted three times as many flowers as I planted, I would have planted $48$ more flowers than I have planted now.\" How many flowers did Justin plant? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$23$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["$48\\div(3-1)=24$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10271", "queId": "b237b1c024784dc4bb6d372384aa878b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ella and George are lining up for dinner. Ella is sitting in the fifth from the front of the line, and George is sitting at the sixth from the end of the line. George and Ella are standing together. How many people are there in total?~(adapted from 2001 Math Kangaroo Problem, Level 3-4, Question \\#13) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line"], "answer_analysis": ["$5 + 6 - 1 = 10$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10285", "queId": "b6c73b737eb04e8d8e77d4b402484383", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $20$ children lining up outside a theme park. John is the $14$\\textsuperscript{th}~ person counting from the front of the line and Mary is the $2$\\textsuperscript{th}~person counting from the back of the line. How many children are standing in line between John and Mary? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Mary is the $$20-2+1=19$$\\textsuperscript{th} person in the line, so there are $$19-14-1=4$$ children are between them. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10290", "queId": "85ed71b7a86c4f869899fd18e6142b0d", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A mixture of $80$ liters of paint is $20 \\textbackslash\\%$ red tint, $30 \\textbackslash\\%$ yellow tint and $50 \\textbackslash\\%$ water. $20$ liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (adapted from 2007 AMC 8, Question \\#17 ) ", "answer_option_list": [[{"aoVal": "A", "content": "$$33$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$39$$ "}], [{"aoVal": "D", "content": "$$42$$ "}], [{"aoVal": "E", "content": "$$44$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["The original mixture contains $80 \\times 30\\textbackslash\\% = 24$ liters of yellow tint. $$20$$ liters of yellow tint is added to the mixture, the new mixture now has $24+20=44$ liters of yellow tint. New percent of yellow =$\\frac{44}{80+20} =44\\textbackslash\\% $ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10292", "queId": "92924af626904744a53a4aa24edfbaad", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Calculate: $1^{3}+2^{3}+3^{3}+\\cdots +17^{3}+18^{3}$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$4447881$$ "}], [{"aoVal": "B", "content": "$$23409$$ "}], [{"aoVal": "C", "content": "$$12654$$ "}], [{"aoVal": "D", "content": "$$29241$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples"], "answer_analysis": ["D "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10294", "queId": "edb7ac291f5541629c62d7dd3c0a710f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $30\\textbackslash\\%$ sugar solution contains $12$ g of pure sugar. How many g of solution are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$30$ g "}], [{"aoVal": "B", "content": "$40$ g "}], [{"aoVal": "C", "content": "$50$ g "}], [{"aoVal": "D", "content": "$60$ g "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"], "answer_analysis": ["$$12\\div30\\textbackslash\\%=40$$ g. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10295", "queId": "8a7454b816c54407afc302112d073b2e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Felix and Marmalade are two cats. Together they weigh $$10\\text{kg}$$. Felix weighs $$4\\text{kg}$$ less than Marmalade. How much does Marmalade weigh? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3\\text{kg}$$ "}], [{"aoVal": "B", "content": "$$6\\text{kg}$$ "}], [{"aoVal": "C", "content": "$$7 \\text{kg}$$ "}], [{"aoVal": "D", "content": "$$9\\text{kg}$$ "}], [{"aoVal": "E", "content": "$$14 \\text{kg}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["$$F=M-4$$ $$m-4+M=10$$ $$M=7$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10296", "queId": "9b98aaf8a68f48298d0f2f61414a5981", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "$9$ more than $43$ is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$42$$ "}], [{"aoVal": "B", "content": "$$52$$ "}], [{"aoVal": "C", "content": "$$62$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"], "answer_analysis": ["$$43+9=52$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10297", "queId": "a4ab5599226441c289096e41918bfaf5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My mom\\textquotesingle s birthday is on Sunday, and my dad\\textquotesingle s birthday is $$55$$ days later. On what day of the week will my dad\\textquotesingle s birthday be? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$ $$Sunday$$ $$ "}], [{"aoVal": "B", "content": "$$ $$Monday$$ $$ "}], [{"aoVal": "C", "content": "$$ $$Tuesday$$ $$ "}], [{"aoVal": "D", "content": "$$ $$Thursday$$ $$ "}], [{"aoVal": "E", "content": "$$ $$Saturday$$ $$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["After $$1$$ day, it is Monday; after $$2$$ days, it is Tuesday; after $$3$$ days, it is Wednesday $$\\cdots$$ After $$8$$ days, it is still Monday, and the period is $$7$$ days. $$55\\div 7=7$$(weeks) $$\\rm R$$ $$6$$ (days). The birthday is Saturday. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10301", "queId": "8e18a97bfaa642b9b466b1b99ca05f2b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sammy\\textquotesingle s mom is $$6$$ years older than his dad. Right now, his dad is $$27$$ years old. How old was his mother $$10$$ years ago? ", "answer_option_list": [[{"aoVal": "A", "content": "$$32$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$23$$ "}], [{"aoVal": "E", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages"], "answer_analysis": ["Now, his dad is $27$ years old, his mom is $$6$$ years older than his dad, so his mom is $33$ years old. $10$ years ago, his mom was $33-10=23$ years old. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10302", "queId": "85fc7c11b2ce4b34bd5b08bb03ea86ef", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Find the exact number of minutes after $3.00 \\text{pm}$ when the minute and hour hands are first at $90^{\\circ}$ to each other. ", "answer_option_list": [[{"aoVal": "A", "content": "$$31 \\frac{2}{11}$$ "}], [{"aoVal": "B", "content": "$$31 \\frac{3}{11}$$ "}], [{"aoVal": "C", "content": "$$32 \\frac{8}{11}$$ "}], [{"aoVal": "D", "content": "$$33 \\frac{3}{11}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems"], "answer_analysis": ["The minute hand rotates $6^{\\circ}$ per minute. The hour hand rotates $\\dfrac{1}{60}\\times30^{\\circ}=\\left (\\dfrac{1}{2}\\right )^{\\circ}$ per mimte. Starting at $3$ O\\textquotesingle clock, the minute hand rotates $\\left (6t\\right )^{\\circ}$ and the hour hand rotates ~$$(90+ \\frac{1}{2}t)^{ \\circ }$$. When the minute and hour hands are next perpendicular: $$6t-\\left (90+ \\frac{1}{2}t\\right )=90$$, $$\\frac{11}{2}t=180$$, $$t= \\frac{360}{11}=32 \\frac{8}{11}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10303", "queId": "a0292144be1847b2ae0cee828747fff1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that October $$10$$th, $$2018$$ was Wednesday, on what day will October $$10$$th, $$2022$$ fall? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Wednesday "}], [{"aoVal": "D", "content": "Thursday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["During this period, $$2020$$ is a leap years. Therefore, October $$10$$, $$2022$$ is $$1+2+1+1=5$$ days after Wednesday, which is Monday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10306", "queId": "971c58dc99e649feb3965cee42547cc9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The average cost of a long-distance call in the USA in 1985 was 56 cents per minute, and the average cost of a long-distance call in the USA in 2018 was 2 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (adapted from 2007 AMC 8, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ "}], [{"aoVal": "B", "content": "$$95$$ "}], [{"aoVal": "C", "content": "$$96$$ "}], [{"aoVal": "D", "content": "$$97$$ "}], [{"aoVal": "E", "content": "$$98$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $56-2=54$ so the percent decrease is $\\frac{54}{56}$ which is about $ 96 \\textbackslash\\%$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10308", "queId": "bff860a27e694aeaae9264611d50bd66", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "At which of these times is the angle between the minute hand and the hour hand of a clock equal to $$150^{}\\circ$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9\\text{pm}$$ "}], [{"aoVal": "B", "content": "$$8\\text{pm}$$ "}], [{"aoVal": "C", "content": "$$6\\text{pm}$$ "}], [{"aoVal": "D", "content": "$$5\\text{pm}$$ "}], [{"aoVal": "E", "content": "$$4\\text{pm}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["At all the times given, the minute hand is pointing to $$12$$. When the minute hand is pointing to $$12$$ and the angle between the hands is $$150^{}\\circ$$, the hour hand has turned $$\\frac{150}{360}= \\frac{5}{12}$$ of a complete turn. Therefore the hour hand will point at $$5$$ and the time will be $$5\\text{pm}$$. (There are other times when the angle between the hands is $$150^{}\\circ$$ but, of these, only at $$7\\text{pm}$$ does the minute hand point to $$12$$ and $$7\\text{pm}$$ is not one of the times given.) "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10311", "queId": "7435815422fe4896b89802601c19ee9f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In $$4$$ hours Rob drove $$120 \\text{km}$$. He drove at an average rate of $$\\text{m/min}$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$105$$ "}], [{"aoVal": "C", "content": "$$120$$ "}], [{"aoVal": "D", "content": "$$500$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["NA "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10314", "queId": "bb665ae6d1b546d0af92bbd2e58fae33", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2015 P2 Q10 John is 5 years old this year. His sister is 2 years old. What is the sum of their age after 3 years? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["$$5+3=8$$ $$7+3=10$$ $$10+8=18$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10325", "queId": "972ca3145ba84fb9a281b8dc7e4529b6", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Jack was able to sell $30$\\% of his vegetables before noon. If he had 200 pounds of vegetables in the morning, how many pounds of vegetables was he able to sell by noon? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$140$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$200 \\times 30$\\%=$60$, He was able to sell $60$ pounds of vegetables by noon. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10326", "queId": "8614723849fb462f8a8292cb13335ae9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I am going to travel $$200\\text{km}$$ at a rate of $$60\\text{km}$$ per hour. How many minutes will my trip take? ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$200$$ "}], [{"aoVal": "C", "content": "$$260$$ "}], [{"aoVal": "D", "content": "$$320$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"], "answer_analysis": ["I am going to travel $$200\\text{km}$$ at $$60\\text{km}$$ per hour. Since $$60\\text{km}$$ per hour is the same as $$1\\text{km}$$ per minute, my trip will take $$200$$ minutes. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10329", "queId": "9bb3e04c6e9e4cfea30b76ef236f8eca", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Last year, at the school where Gill teaches Mathematics, $$315$$ out of the $$600$$ pupils were girls. This year, the number of pupils in the school has increased to $$640$$. The proportion of girls is the same as it was last year. How many girls are there at the school this year? ", "answer_option_list": [[{"aoVal": "A", "content": "$$339$$ "}], [{"aoVal": "B", "content": "$$338$$ "}], [{"aoVal": "C", "content": "$$337$$ "}], [{"aoVal": "D", "content": "$$336$$ "}], [{"aoVal": "E", "content": "$$335$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["Last year, the fraction of girls at the school was $$\\frac{{315}}{{600}}=\\frac{{63}}{{120}}=\\frac{{21}}{{40}}$$. This year, there are $$40$$ more pupils at the school, but the proportion of girls has remained the same. So there are $$21$$ more girls at the school this year, making a total of $$315+21=336$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10330", "queId": "92b44d441d4c445b9e410bc21076d1a6", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Chloe is buying candies at a grocery store. She can either spend $8$ dollars on a $15$ ounce bag or $12$ dollars on a $20$ ounce bag. Which is a better buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$15$ ounce bag "}], [{"aoVal": "B", "content": "$20$ ounce bag "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"], "answer_analysis": ["$\\frac{8\\text{dollars}}{15\\text{ounces}}$ $\\frac{12\\text{dollars}}{20\\text{ounces}}$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10331", "queId": "92b46c93d38c45eb96cc67581778d0dd", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Jin loves carrots! Yesterday she ate $$\\frac{1}{4}$$ of her carrots, and today she ate $$\\frac{2}{7}$$ of the number of she ate yesterday. She ate 10 carrots today. Yesterday she have started with carrots. ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$72$$ "}], [{"aoVal": "E", "content": "$$140$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["$10\\div\\dfrac{2}{7}\\div\\dfrac{1}{4}=140$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10333", "queId": "ff8a75f4dedf4cfd864199b80fd8c9de", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Tom scored a basket at the end of the third quarter of a basketball game between the Lakers and the Warriors. At that point, what fraction of the whole game remained to be played? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\frac{1}{4}$$ "}], [{"aoVal": "B", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "D", "content": "$$\\frac{3}{4}$$ "}], [{"aoVal": "E", "content": "$$\\frac{2}{3}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["Basketball games consist of four quarters. Tom\\textquotesingle s scoring at the end of the third quarter implies that there is one quarter left, which is equivalent to 1/4 of the entire game. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10335", "queId": "81b2dbbd3c284454a1b3ad659351ca29", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Five positive integers (not necessarily all different) are written on five cards. Boris calculates the sum of the numbers on every pair of cards. He obtains only three different totals: 57, 70 and 83. What is the largest integer on any card? ", "answer_option_list": [[{"aoVal": "A", "content": "$$35$$ "}], [{"aoVal": "B", "content": "$$42$$ "}], [{"aoVal": "C", "content": "$$48$$ "}], [{"aoVal": "D", "content": "$$53$$ "}], [{"aoVal": "E", "content": "$$82$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Let the five integers be a, b, c, d and e with a ≤ b ≤ c ≤ d ≤ e. The smallest total is 57, which is an odd number so b ≠ a. Similarly, the largest total is 83, which is also an odd number so d ≠ e. Hence we now have a \\textless{} b ≤ c ≤ d \\textless{} e and a + b = 57 and d + e = 83. Only one possible total remains and so b = c = d with c + d = 70. This gives c = d (= b) = 35 and therefore e, the largest integer, is 83 − 35 = 48 (whilst a = 22). "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10339", "queId": "7d4469feaad24219b5be00619ac5bff8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The average cost of a long-distance call in the USA in 1985 was 44 cents per minute, and the average cost of a long-distance call in the USA in 2005 was 11 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (adapted from 2007 AMC 8, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$50$$ "}], [{"aoVal": "C", "content": "$$75$$ "}], [{"aoVal": "D", "content": "$$100$$ "}], [{"aoVal": "E", "content": "$$125$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $44-11=33$ so the percent decrease is $\\frac{33}{44}$ which is about $(\\mathbf{c}) 75 \\textbackslash\\%$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10346", "queId": "d6df55b356eb476284fbc5f21a128585", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "James lives on the second floor, and Paul lives in the same building but has to walk up five times as many stairs as James. There are no stairs to the entrance of the building. On which floor does Paul live? (Adapted from 2000 Math Kangaroo Problem, Level 3-4, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "On the $$2^{\\rm nd}$$ floor "}], [{"aoVal": "B", "content": "On the $$3^{\\rm rd}$$ floor "}], [{"aoVal": "C", "content": "On the $$4^{\\rm th}$$ floor "}], [{"aoVal": "D", "content": "On the $$5^{\\rm th}$$ floor "}], [{"aoVal": "E", "content": "On the $$6^{\\rm th}$$ floor "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Straight Line Type with Objects on Both Sides->Taking the Stairs"], "answer_analysis": ["$5+1=6$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10347", "queId": "e9366a0a02754888b6aba42b509353d3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy mixes $$10$$ grams of a $$20\\textbackslash\\%$$ sugar solution and $$40$$ grams of a $$25\\textbackslash\\%$$ sugar solution together. After~\\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of solution is $40\\textbackslash\\%$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ grams "}], [{"aoVal": "B", "content": "$$18$$ grams "}], [{"aoVal": "C", "content": "$$20$$ grams "}], [{"aoVal": "D", "content": "$$25$$ grams "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"], "answer_analysis": ["$$10\\times20\\textbackslash\\%+40\\times 25\\textbackslash\\%=12$$ grams. $$(10+40)-12\\div40\\textbackslash\\%=20$$ grams. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10353", "queId": "9bccf96246cd42408eb735f1e887d559", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Greta was $$110\\text{cm}$$ tall $$2$$ years ago, when she was $$10\\text{cm}$$ taller than her brother. They both have grown, but now Greta is $$10\\text{cm}$$ shorter than her brother. If her brother grew $$40\\text{cm}$$ in those two years, Greta is now$$\\text{cm}$$ tall. ", "answer_option_list": [[{"aoVal": "A", "content": "$$120$$ "}], [{"aoVal": "B", "content": "$$130$$ "}], [{"aoVal": "C", "content": "$$140$$ "}], [{"aoVal": "D", "content": "$$150$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["Greta was $$110\\text{cm}$$ tall $$2$$ years ago, when she was $$10\\text{cm}$$ taller than her brother. Her brother was $$100\\text{cm}$$ then. Now Greta is $$10\\text{cm}$$ shorter than her brother. If her brother grew $$40\\text{cm}$$, he is now $$140\\text{cm}$$. Greta is now $$130\\text{cm}$$ tall. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10354", "queId": "78eae92279bd483e83ae096cf8a151f2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The average weight of $4$ students in Class $A$ is $37$ kilograms. The average weight of $11$ students in Class $B$ is $41$ kilograms. The total weight of $5$ students in Class $C$ is $161$ kilograms. What is the average weight of the students in the $3$ classes? ", "answer_option_list": [[{"aoVal": "A", "content": "$36$ kilograms "}], [{"aoVal": "B", "content": "$38$ kilograms "}], [{"aoVal": "C", "content": "$40$ kilograms "}], [{"aoVal": "D", "content": "$43$ kilograms "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$4 \\times 37 + 11 \\times 41+ 161 = 760$ kilograms in total. $760 \\div (4 + 11 + 5) = 38$ kg. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10355", "queId": "a969dfbf48ed4e0481eb5e9073bc9760", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Cici and Kiki took the same quiz. They agreed on the following rules: a person got $10$ points for a correct answer and lost $5$ points otherwise (getting a wrong answer or skipping a question). They each answered $10$ questions and together got $95$ points. If Cici got $15$ more points than Kiki, how many questions did Kiki answer correctly? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"], "answer_analysis": ["Kiki got $(95-15)\\div2=40$ points. If she answered all the questions correctly, she would have gotten $100$ points. Hence, she skipped or got $(100-40)\\div(10+5)=4$ wrong answers and she answered $10-4=6$ questions correctly. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10363", "queId": "a0663162452d4fcf870abc0afe742479", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy and Bella bought some cookies in the ratio of $$3:4$$. Bella gave $$9$$ cookies to Amy. Then the ratio of the number of cookies Amy had to that of Bella was $$1:1$$. How many cookies did they have at first? ", "answer_option_list": [[{"aoVal": "A", "content": "$$54$$ "}], [{"aoVal": "B", "content": "$$63$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$126$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with Invariant Sums"], "answer_analysis": ["Total number of cookies both of them had did not change. Make total the same number of units by finding LCM. Before $\\to$ $A:B:Total$ $\\to$ $3:4:7$ $\\to$ $6:8:14$ After $\\to$ $A:B:Total$ $\\to$ $1:1:2$ $\\to$ $7:7:14$ $1u=9$ $14u=14\\times9=126$ cookies at first (and also in the end) in total. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10364", "queId": "fbb4e8b2f7ec45c29bdeca6e8e6bec93", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alex, John and Sam went to buy oranges. Alex paid $\\textbackslash$20$, John paid $\\textbackslash$15$, and Sam only paid $\\textbackslash$5$. They bought $120$ oranges altogether. They divided them in proportion to the amount of money each of them had paid. How many oranges did John get? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division"], "answer_analysis": ["A: J: S 20:15:5 = 40 120/40 = 3 oranges per person 3*15= 45 oranges "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10367", "queId": "c4acf0f4e7b14517b5dfe27326f25955", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$3^{}\\text{th}$$February is Monday, what day of the week is $$27$$\\textsuperscript{th~}February? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday　 "}], [{"aoVal": "B", "content": "Monday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Thursday　 "}], [{"aoVal": "E", "content": "Saturday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["We can count backward by days or by weeks. Count a few weeks back to find that $$22$$\\textsuperscript{nd} February is a Monday. Then count a few days back to find that $$24$$\\textsuperscript{th~}February is a Wednesday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10370", "queId": "a4f110be05004094821c0604421bfa0a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The speed of high-speed train is approximately $$350$$ kilometres per hour, while the walking speed of a person is approximately $$5$$ metres per second. Approximately, how many times is the speed of a high-speed train faster than the walking speed of a person?． ", "answer_option_list": [[{"aoVal": "A", "content": "$$2 $$ "}], [{"aoVal": "B", "content": "$$20 $$ "}], [{"aoVal": "C", "content": "$$70 $$ "}], [{"aoVal": "D", "content": "$$200 $$ "}], [{"aoVal": "E", "content": "$$700$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"], "answer_analysis": ["The speed of high-speed train is approximately $$350$$ kilometres per hour, which is approximately $$100$$ metres per second. So its speed is roughly $$20$$ times faster than $$5$$ metres per second. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10371", "queId": "865cc26bcee2402f8c00658139e33207", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Martha had ＄$$1.50$$. She bought $$12$$ caramels at $$5$$￠ each. How many chocolate mints at $$10$$￠ each can she buy with the money she has left? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$11$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["Martha had ＄$$1.50$$. She bought $$12$$ caramels at $$5$$￠ each, spengding $$60$$￠ and leaving her with $$90$$￠. With $$90$$￠, she can buy $$90 \\div 10 =9$$ mints at $$10$$￠ each. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10383", "queId": "81ff9ff9922c4c8b8e847d921e861c90", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Balloons are sold in packets of $$5$$, $$10$$, and $$25$$. Marius buys exactly $$70$$ balloons. What is the smallest number of packets he can buy? (2017 Math Kangaroo Problem, Level 3 - 4, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications"], "answer_analysis": ["$70 = 25 + 25 + 10 + 10$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10386", "queId": "db8fbe8dac32412b80a8b220b31b59f5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Three hens and four rabbits are in a cage. How many legs do they have?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$4$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$22$$ "}], [{"aoVal": "E", "content": "$$24$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["A hen has two legs and a rabbit has four legs, so three hens have six legs and four chickens have sixteen legs. $6+16=22$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10390", "queId": "c036eb50c7e84ad8bd09f12d6d245f28", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A police spots a burglar from $$480$$ m apart. The burglar immdiately runs away at a speed of $$8$$ m/s and the police starts chasing him at $$12$$ m/s at the same time. At this rate, how long will it take the police to catch the burglar? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ seconds "}], [{"aoVal": "B", "content": "$$40$$ seconds "}], [{"aoVal": "C", "content": "$$1$$ minutes "}], [{"aoVal": "D", "content": "$$2$$ minutes "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"], "answer_analysis": ["The distance between them is $$480$$ m, and the difference between their speeds is $$12-8=4$$ m/s. It takes $$480\\div4=120$$ seconds to catch the burglar, which is $$2$$ minutes "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10392", "queId": "d6fec6acf2974b90945455911c477aa9", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "At the 2013 Winnebago County Fair a vendor is offering a \"fair special\" on sandals. If you buy one pair of sandals at the regular price of $\\textbackslash$ 50$, you get a second pair at a $40 \\textbackslash\\%$ discount, and a third pair at half the regular price. Javier took advantage of the \"fair special\" to buy three pairs of sandals. What percentage of the $\\textbackslash$ 150$ regular price did he save? (2013 AMC 8, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$25$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$40$$ "}], [{"aoVal": "E", "content": "$$45$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["First, find the amount of money one will pay for three sandals without the discount. We have $\\textbackslash$ 50 \\times 3$ sandals $=\\textbackslash$ 150$. Then, find the amount of money using the discount: $50+0.6 \\times 50+\\frac{1}{2} \\times 50=\\textbackslash$ 105$. Finding the percentage yields $\\frac{105}{150}=70 \\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-70 \\textbackslash\\%=(\\text{B}) 30$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10394", "queId": "d701217906454a91b8a534738a6acf95", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There was a $15$-meter long corridor in the school. The teacher asked Jack to put a flowerpot on the corridor every three meters. How many flowerpots did Mike put?~(adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$7$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Planting no Trees on either Side (straight line type)->Cutting the Ropes"], "answer_analysis": ["The corridor is divided into $15\\div3=5$ segments. The number of flowerpots is one more than that of the segments, so $5+1=6$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10397", "queId": "9c088d7837d24ea98075f831157ad76b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The original price of a pair of shoes was $$\\textbackslash$85$$. Then, it was sold at a discount of $$20\\textbackslash\\%$$. What was the price of the pair of shoes after the discount? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$17$$ "}], [{"aoVal": "B", "content": "$$$52$$ "}], [{"aoVal": "C", "content": "$$$68$$ "}], [{"aoVal": "D", "content": "$$$102$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["After discount, price became $100\\textbackslash\\%-20\\textbackslash\\%=80\\textbackslash\\%$ of original price. $\\textbackslash$85\\times80\\textbackslash\\%=\\textbackslash$85\\times0.8=\\textbackslash$68$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10399", "queId": "cde0e43354774440b114a5157dbe3234", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Julia has eaten one-quarter of the pizza. What is the ratio of the number of pizza that remain to the number Julia has eaten? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1:3$$ "}], [{"aoVal": "B", "content": "$$3:1 $$ "}], [{"aoVal": "C", "content": "$$1:4 $$ "}], [{"aoVal": "D", "content": "$$4:1$$ "}], [{"aoVal": "E", "content": "$$4:3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["Julia has eaten one-quarter of the pizza. So three-quarters of the pizza remain. Therefore the required ratio is $$\\frac{3}{4}:\\frac{1}{4}=3:1$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10403", "queId": "8e9e2f64d74747ca880fd85cb9274978", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a certain quiz show there are the following rules: every participant has $$10$$ points at the beginning and has to answer $$10$$ questions. For each correct answer, the participant earns $$1$$ point, and for each incorrect answer, the participant loses $1$ point. Mrs. Smith had $$14$$ points at the end of this quiz show. How many correct answers did she give? ($$2011$$ Math Kangaroo Problem, Level $$3-4$$, Question \\#$$17$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis->Basic Type->Non-typical Types"], "answer_analysis": ["Full score: $10+10\\times1=20$. Smith gets $(20-14)\\div(1+1)=3$ questions wrong, and $10-3=7$ questions correct. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10406", "queId": "edefd62ea9504276a65ab1b548bf88a7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My mom\\textquotesingle s birthday is on Sunday, and my dad\\textquotesingle s birthday is $$55$$ days after it. On what day of the week will my dad\\textquotesingle s birthday be? ($$1999$$ Math Kangaroo Problem, Levels $$3-4$$, Question \\#$$9$$) ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday "}], [{"aoVal": "B", "content": "Monday "}], [{"aoVal": "C", "content": "Tuesday "}], [{"aoVal": "D", "content": "Thursday "}], [{"aoVal": "E", "content": "Saturday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$$55\\div7=7 \\text{R}6$$. It is Saturday. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10411", "queId": "9c16c816a5974dd2be3a013c234de36a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Penelope paid＄$$24.58$$ for pens and pencils. If pens cost $$9$$￠ each and pencils cost $$4$$￠ each, at most how many pens did Penelope purchase? ", "answer_option_list": [[{"aoVal": "A", "content": "$$273$$ "}], [{"aoVal": "B", "content": "$$272$$ "}], [{"aoVal": "C", "content": "$$271$$ "}], [{"aoVal": "D", "content": "$$270$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["Continue subtracting $$4$$￠ from $$2458$$￠ until the difference is a multiple of $$9$$. This happens when the difference is $$2430$$￠ which is $$270 \\times 9$$￠. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10417", "queId": "cdec520781e44101b3c283d4c27a22da", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The selling price of a sofa set is ＄$$5500$$ and the profit percentage is $$10\\textbackslash\\%$$ for each set sold. If the cost of the sofa set is not changed, what is the new profit percentage if raising the profit to ＄$$1800$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$25\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$30\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$36\\textbackslash\\%$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["$$5500\\div(1+10\\textbackslash\\%)=5000$$, $$1800\\div5000=36\\textbackslash\\%$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10420", "queId": "a9af6280af284c15ae306b36b3168743", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A worm is at the bottom of a well with a depth of $$11$$ metres. If it climbs up $$3$$ metres in the day and slips down $$1$$ metre at night, how many days will it take the worm to climb up to the ground? ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"], "answer_analysis": ["It climbs up $$3$$ meters in the day time and slips down $$1$$ meter at night, so it climbs up $$2$$ meters in a whole day. For the first $$4$$ days, it climbs $$8$$ meters. During the day time of the fifth day, it climbs $$3$$ meters and reaches the ground. Then it needs five days to climb up to the ground. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10422", "queId": "bbbfd287b57445c0a7590dfab5553717", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Bowen has $$40$$ ounces of a $$25\\textbackslash\\%$$ sugar solution. After~\\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of the solution is $$40\\textbackslash\\%$$. (Evaporate: the water turns from liquid into vapor and is no longer in the solution anymore.) ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ ounces "}], [{"aoVal": "B", "content": "$$12$$ ounces "}], [{"aoVal": "C", "content": "$$9$$ ounces "}], [{"aoVal": "D", "content": "$$6$$ ounces "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"], "answer_analysis": ["$$40-40\\times25\\textbackslash\\%\\div40\\textbackslash\\%=40-25=15$$ ounces. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10424", "queId": "b737cad19dc64dfbaa85ceaa74e79e5a", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Patrick gets $80 \\textbackslash\\%$ on a 10 -problem test, $60 \\textbackslash\\%$ on a 20 -problem test and $50 \\textbackslash\\%$ on a 30 -problem test. If the three tests are combined into one 60 problem test, which percent is closest to her overall score? (adapted from 2006 AMC 8, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$50$$ "}], [{"aoVal": "B", "content": "$$52$$ "}], [{"aoVal": "C", "content": "$$55$$ "}], [{"aoVal": "D", "content": "$$58$$ "}], [{"aoVal": "E", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$80 \\textbackslash\\% \\cdot 10=8$, $60\\textbackslash\\% \\cdot 20=12$, $50\\textbackslash\\% \\cdot 30=15$ Adding them up gets $8+12+15=35$. The overall percentage correct would be $\\frac{35}{60} \\approx 0.58$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10433", "queId": "97a9ebdec7ab46c893d24eda0e309a27", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Gawel lives on the 2\\textsuperscript{nd} floor, and Pawel lives in the same building but has to walk up twice as many stairs as Gawel. There are no stairs to the entrance of the building. On which floor does Pawel live? ", "answer_option_list": [[{"aoVal": "A", "content": "on the $2$\\textsuperscript{nd} floor "}], [{"aoVal": "B", "content": "on the $3$\\textsuperscript{rd} floor "}], [{"aoVal": "C", "content": "on the $4$\\textsuperscript{th} floor "}], [{"aoVal": "D", "content": "on the $5$\\textsuperscript{th} floor "}], [{"aoVal": "E", "content": "on the $6$\\textsuperscript{th} floor "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["Gawel lives on the second floor, so he only needs to walk up one floor. Pawel has to walk up twice as many stairs as Gawel, so he needs to walk up two floors. So, Pawel lives on the $3$\\textsuperscript{rd} floor. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10438", "queId": "a9b931c0785247b49f4df88545ba82f2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ben stands in line and has $$76$$ people behind him, If there are a total of $$110$$ people in line, how many people are there in front of Ben? ", "answer_option_list": [[{"aoVal": "A", "content": "$$33$$ "}], [{"aoVal": "B", "content": "$$34$$ "}], [{"aoVal": "C", "content": "$$35$$ "}], [{"aoVal": "D", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line"], "answer_analysis": ["If there are a total of $$110$$ people in line, subtract those behind Ben and Ben himself: $$110-76-1=33$$, the number in front of Ben. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10441", "queId": "dbadb592e634467da36311f413432ebd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A jacket was on sale. The original price was ＄$$180$$, and Peter bought it at ＄$$135$$. What was the discount? ", "answer_option_list": [[{"aoVal": "A", "content": "$$135\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$180\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$75\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$25\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["$$1-135\\div180=25\\textbackslash\\%$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10442", "queId": "c05ac13ddb8d4593bc5ed51dd7549cf8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of two numbers is $$800$$. The smaller number is $$356$$. What is the greater number? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1156$$ "}], [{"aoVal": "B", "content": "$$556$$ "}], [{"aoVal": "C", "content": "$$454$$ "}], [{"aoVal": "D", "content": "$$444$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples", "Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Addition and Subtraction of Whole Numbers->Adding and Subtracting within 10000->Subtraction of 3-digit Numbers"], "answer_analysis": ["$$800-356=444$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10447", "queId": "e4d42c8512e64cc6b68b913aeb3e6fb4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$20$$ chickens and rabbits in the case, and the total number of legs is $$48$$. How many rabbits in this case? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"], "answer_analysis": ["If all were rabbits, $20\\times 4= 80$ the total number of legs would be $$$80$$. $80- 48=32$ The difference is $$$32$$. $4-2=2$ $32\\div 2=16$ $20-16=4$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10452", "queId": "8ecc105d859e4a2f8325bb1e2ad92c22", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A sugar solution is made by mixing $$10$$ ounces of sugar and $$15$$ ounces of water. Find the percent concentration of the solution. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$25\\textbackslash\\%$ "}], [{"aoVal": "C", "content": "$30\\textbackslash\\%$ "}], [{"aoVal": "D", "content": "$40\\textbackslash\\%$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["$$10\\div(10+15)=40\\textbackslash\\%$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10455", "queId": "8ecdb8b6938346debe2cfe5c5b9133f5", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mother baked $$40$$ cookies. She gave $$8$$ cookies to her friend and packed the rest equally into bottles. She put $$4$$ cookies in each bottle. How many bottles did she use? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["$$40-8=32$$, $$32\\div4=8$$. Mother used $$8$$ bottles. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10456", "queId": "d720019345ed4aeeb7f91d31778c09c3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Julian started reading a book with $$348$$ pages. He read $$6$$ pages on each day from Monday to Friday and $$11$$ pages on each day on Saturday and Sunday. He started reading on a Thursday. On which day of the week did he finish reading the book? ． ", "answer_option_list": [[{"aoVal": "A", "content": "Friday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Sunday "}], [{"aoVal": "D", "content": "Monday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Thursday to Sunday $$\\rightarrow 6\\times 2+11\\times 2=34$$ pages $$348-34=314$$ $1$ week (Monday to Sunday) $$\\rightarrow 11\\times 2+6\\times 5=52$$ pages $6$ weeks $$\\rightarrow 52\\times6=312$$ pages After reading another $312$ pages in $6$ weeks, Julian has another $(314 -- 312) = 2$ pages left to read. It will now be a Monday and Julian can finish reading the last $2$ pages. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10457", "queId": "c4e4ec253ce148e3bf906a1977b8373e", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "$5$\\% of the students at Hamilton Middle School have red hair. There are $800$ students at Hamilton Middle School. How many students at Hamilton Middle School have red hair? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$400$$ "}], [{"aoVal": "D", "content": "$$760$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$800 \\times 5$\\%=$40$, $40$ students at Hamilton Middle School have red hair. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10459", "queId": "c4e86bb85aef417fb519588e6713531d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My pay is the same every day I work. I worked \\emph{every} day in $$1992$$, even weekends. In March, I earned ＄$$930$$. I earned for all of $$1992$$. ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$11346$$ "}], [{"aoVal": "B", "content": "＄$$11315$$ "}], [{"aoVal": "C", "content": "＄$$10980$$ "}], [{"aoVal": "D", "content": "＄$$10950$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"], "answer_analysis": ["In March, there are $$31$$ days. I earned ＄$$930 \\div 31$$, which is ＄$$30$$ each day. For all of $$1992$$, I earned $$366\\times$$ ＄$$30 =$$＄$$10980$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10465", "queId": "b2d181c5de0b4a0fa4b055bdc3c6e873", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Zosia is drawing kangaroos. The first one is blue, the next one green, the one after it red, the fourth one yellow, and then again blue, green, red, yellow, and so on, in the same order. What color will the seventeenth kangaroo be? (2003 Math Kangaroo Problem, Level 3-4, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$Blue "}], [{"aoVal": "B", "content": "$$$$Green "}], [{"aoVal": "C", "content": "$$$$Red "}], [{"aoVal": "D", "content": "$$$$Black "}], [{"aoVal": "E", "content": "$$$$Yellow "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"], "answer_analysis": ["A group of the blue one, the green one, the red one, and the yellow one is repeating. $17 \\div 4 = 4R1$, so the seventeenth one is blue. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10466", "queId": "c98133a62e8843efbb779f3ec602b5e2", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "William is 15 years old, and his sister is 23 years old. How old will his sister be when William is 23 years old? ", "answer_option_list": [[{"aoVal": "A", "content": "$$23$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$38$$ "}], [{"aoVal": "D", "content": "$$26$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["omitted "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10473", "queId": "b2da42781e6e4b4198e0a4593b7f7ad9", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Luna, Lily, and Lucy are talking about their ages. $6$ years ago, Luna was born, and Lily was $5$ years old. This year, the sum of ages of these $3$ people is $33$. When Luna was born, how old was Lucy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["Six years ago, the sum of ages of Luna, Lily, and Lucy was $33-6\\times3=15$. Lucy was $15-0-5=10$ years old. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10474", "queId": "936325f5ecf5482a889b26091b5af6c9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jack mixed $200$ g of $10\\textbackslash\\%$ salt solution, $200$ g of $15\\textbackslash\\%$ salt solution, and $400$ g of $20\\textbackslash\\%$ salt solution together. What is the percent concentration of salt solution at this time? ", "answer_option_list": [[{"aoVal": "A", "content": "$15\\textbackslash\\%$ "}], [{"aoVal": "B", "content": "$16\\textbackslash\\%$ "}], [{"aoVal": "C", "content": "$16.25\\textbackslash\\%$ "}], [{"aoVal": "D", "content": "$17\\textbackslash\\%$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems->Calculating Solution from Solute and Solvent"], "answer_analysis": ["$$\\frac{200\\times 10\\textbackslash\\%+200\\times 15\\textbackslash\\%+400\\times 20\\textbackslash\\%}{200+200+400}\\times 100\\textbackslash\\%=16.25\\textbackslash\\%$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10475", "queId": "ae596e5d7af44eeab02bc76885169b2d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "After Sally takes 20 shots, she has made $75 \\textbackslash\\%$ of her shots. After she takes 10 more shots, she drops her percentage to $60 \\textbackslash\\%$. How many of the last 5 shots did she make? (adapted from 2004 AMC 8, Question\\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Sally made $0.75 * 20=15$ shots originally. Letting $x$ be the number of shots she made, we have $\\frac{15+x}{30}=0.6$. Solving for $x$ gives us $x=3$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10483", "queId": "a56163296a6f4ac3966d09884be81f4e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Crystal and Angela had a poem recitation game. Each poem in their game earned $$2$$ points. Crystal recited $$7$$ poems and Angela recited $$11$$ poems. How many more points than Crystal did Angela earn?~(adapted from $$2021$$ Math kangaroo, Level $$1-2$$, Question \\#$$14$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Angela recited $$11-7=4$$ poems more than Crystal. There are 4$$\\times$$2$$=8$$ points "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10486", "queId": "8f0021b378ce41c8855c0f791d124e8c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A test is with a full score of $100$ points. Five students in a group wants to reach an average of $92$ points. If everyone scores a different whole number, the lowest score among them could be~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$61$$ "}], [{"aoVal": "C", "content": "$$66$$ "}], [{"aoVal": "D", "content": "$$70$$ "}], [{"aoVal": "E", "content": "$$71$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$92\\times5-(100+99+98+97)=66$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10494", "queId": "d73cf51af8444246b644a1f460042783", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given that April $$15$$, $$2011$$ was Friday, what day was May $$11$$, $$2011$$? ", "answer_option_list": [[{"aoVal": "A", "content": "Thursday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Tuesday "}], [{"aoVal": "D", "content": "Wednesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Counting from April $$15$$, $$2011$$, after $30-15=15$ days it will be April $$30$$, $$2011$$. After $11$ days, it will be May $$11$$, $$2011$$. In total, there are $15+11=26$ days. $26\\div 7 =3R5$, which means May $$11$$, $$2011$$ was Wednesday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10498", "queId": "d73ec4a0eed1465d867908a527a36beb", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The perimeter of a cuboid is $180$. What is the largest volume? ", "answer_option_list": [[{"aoVal": "A", "content": "$$216$$ "}], [{"aoVal": "B", "content": "$$3375$$ "}], [{"aoVal": "C", "content": "$$720$$ "}], [{"aoVal": "D", "content": "$$9600$$ "}], [{"aoVal": "E", "content": "$$1200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value"], "answer_analysis": ["$180\\div12=15$ $15\\times15\\times15=3375$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10500", "queId": "ae757d2fd6004d95b219c4ae422bfbde", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A worm is staying at the bottom of a well with a depth of $$10$$ metres. If it climbs up $$3$$ metres in the daytime and slips down $$2$$ metres at night, which day will it climb up to the ground? ", "answer_option_list": [[{"aoVal": "A", "content": "The $$6$$th day "}], [{"aoVal": "B", "content": "The $$7$$th day "}], [{"aoVal": "C", "content": "The $$8$$th day "}], [{"aoVal": "D", "content": "The $$9$$th day "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"], "answer_analysis": ["omitted "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10501", "queId": "a0f632a738ee4d2e937e89a1f7332f30", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A train travels from Exeter to Cambridge at a~ speed of $$55km/h$$. Given that Cambridge is $$420km$$ away from Exeter, How far is the train away from Cambridge after setting off for 5 hours? ", "answer_option_list": [[{"aoVal": "A", "content": "$$55km$$ "}], [{"aoVal": "B", "content": "$$145km$$ "}], [{"aoVal": "C", "content": "$$275km$$ "}], [{"aoVal": "D", "content": "$$420km$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"], "answer_analysis": ["$420-\\left( 55\\times5\\right)=420-275=145$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10502", "queId": "e05dcc9a48ad4d0a944b7bfcc8c74ac7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the teachers\\textquotesingle{} lounge there are $$6$$ tables with $$4$$ chairs by each one, $$4$$ tables with $$2$$ chairs by each, and $$3$$ tables with $$6$$ chairs by each. How many chairs are there in the lounge? (2003 Math Kangaroo Problem, Level 3-4, Question \\#5) ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$36$$ "}], [{"aoVal": "E", "content": "$$44$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications"], "answer_analysis": ["$6\\times4+4\\times2+3\\times6=50$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10504", "queId": "c99f0bff8f63457c9a5609df53658433", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Helga is climbing stairs in such a way that she goes up $$2$$ steps at a time. She is standing on the third step now. On which step will she be after she moves up $$3$$ times? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$1$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications"], "answer_analysis": ["Moving up $3$ times is $6$ steps. Now she is on the third step, after moving up $6$ steps, she is on the ninth step. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10505", "queId": "f75a7eb69bd0453e9db239af54a7f45d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If today is Tuesday, what day of the week will be 86 days later? ", "answer_option_list": [[{"aoVal": "A", "content": "Wednesday "}], [{"aoVal": "B", "content": "Thursday "}], [{"aoVal": "C", "content": "Friday "}], [{"aoVal": "D", "content": "Saturday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"], "answer_analysis": ["$$86\\div 7=12\\cdots \\cdots 2$$． 2 days later will be Thursday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10514", "queId": "c9a679ccf8b64e3a9347c8fd806e918e", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Last month, the price of a couch increased by $\\textbackslash$600$. During a sale this month, the couch was offered at a $25\\textbackslash\\%$ discount. John bought the couch at $\\textbackslash$2250$ at the sale. What is the percentage decrease in the cost of the couch as compared to the original price of the couch before the discount? ", "answer_option_list": [[{"aoVal": "A", "content": "$6.66\\textbackslash\\%$ "}], [{"aoVal": "B", "content": "$5\\textbackslash\\%$ "}], [{"aoVal": "C", "content": "$6.25\\textbackslash\\%$ "}], [{"aoVal": "D", "content": "None of the above. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages"], "answer_analysis": ["Price before discount $=\\frac{100}{75}\\times\\textbackslash$2250=\\textbackslash$3000$ Original price of the couch before increase $=\\textbackslash$3000-\\textbackslash$600=\\textbackslash$2400$ Price decrease $=\\textbackslash$2400-\\textbackslash$2250=\\textbackslash$150$ Percentage decrease $=\\frac{\\textbackslash$150}{\\textbackslash$2400}\\times100\\textbackslash\\%=6.25\\textbackslash\\%$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10517", "queId": "9c83810199be4080a9f60044fee7500d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Anna is lining up to get some ice-cream. Counting from the front, she is the $$4$$\\textsuperscript{th}~in the line. Counting from the back, she is the $$7$$\\textsuperscript{th}. How many people are there lining up?~\\uline{~~~~~~~~~~}~ ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$4+7-1=10$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10520", "queId": "e9944220da0246b1ad7f10bdfb3b6fc8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jerry starts a savings account with ＄$$7,000$$ at a bank. The interest rate is $$3\\textbackslash\\%$$ per year. How much interest will he earn in his savings account at the end of the second year? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$426$$ "}], [{"aoVal": "B", "content": "＄$$426.3$$ "}], [{"aoVal": "C", "content": "＄$$4,263$$ "}], [{"aoVal": "D", "content": "＄$$4,263.6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Interest Problems"], "answer_analysis": ["$$7000\\times \\left( 1+3\\textbackslash\\% \\right)\\times \\left( 1+3\\textbackslash\\% \\right)-7000=426.3$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10528", "queId": "ae8c396be5174f2f8fcdcba18b3d3a2b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A bookstore purchases some story books at ＄$$22$$ each. If the bookstore wants to earn ＄$$11$$ for each book, what is the selling price of each book? ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$22$$ "}], [{"aoVal": "B", "content": "＄$$33$$ "}], [{"aoVal": "C", "content": "＄$$35$$ "}], [{"aoVal": "D", "content": "＄$$44$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["$$22+11=33$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10530", "queId": "93a6c00328e543d9b88560e67193a71f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are four books on my shelf. The almanac and the dictionary together weigh $$4310\\text{g}$$. The biography and the cookbook together weigh $$2325\\text{g}$$. If the almanac and the biography together weigh $$2795\\text{g}$$, what is the weigh of the cookbook and dictionary together? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2620\\text{g}$$ "}], [{"aoVal": "B", "content": "$$3270\\text{g}$$ "}], [{"aoVal": "C", "content": "$$3840\\text{g}$$ "}], [{"aoVal": "D", "content": "$$4100\\text{g}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Including and Excluding "], "answer_analysis": ["The almanac, the dictionary, the biography, and the cookbook together weigh $$4310\\text{g}+2325\\text{g=6635g}$$. Since the almanac and the biography together weigh $$2795\\text{g}$$, the cookbook and the dictionary together weigh $$6635\\text{g}-2795\\text{g=3840g}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10534", "queId": "dbe6b816ea6641e1a04f845ebb5669a8", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "There are $72$ balloons in the shop. Pip bought $$\\frac49$$ of them. The shop left~\\uline{~~~~~~~~~~}~balloons. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$52$$ "}], [{"aoVal": "E", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["$72\\times(1-\\dfrac{4}{9})=32$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10538", "queId": "b78ecb605cb649dab9a928b15e9b2fdf", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "On Monday morning, a snail fell down a well which is $$10$$ meters deep. During the day, it climbs up $$2$$ meters, and during the night it slides down $$1$$ meter. On what day of the week will the snail get out of the well? ($$1998$$ Math kangaroo Problem, Level $$5-6$$, Question \\#$$18$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$Tuesday "}], [{"aoVal": "B", "content": "$$$$Thursday "}], [{"aoVal": "C", "content": "$$$$Saturday "}], [{"aoVal": "D", "content": "$$$$Sunday "}], [{"aoVal": "E", "content": "$$$$Monday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems->Snail Climbing out of Well (completed)"], "answer_analysis": ["Except the last day, the snail could climb up $2-1=1$ m. Thus, it takes the snail $(10-2)\\div1+1=9$ days to get out of the well. $9$ days from Monday is the next Tuesday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10539", "queId": "b3101b748edd4194976ef37455b0a402", "competition_source_list": [], "difficulty": "3", "qtype": "single_choice", "problem": "When one ounce of water is added to a mixture of acid and water, the new mixture is $$20\\textbackslash\\%$$ acid. When one ounce of acid is added to the new mixture, the result is $$33\\frac{1}{3}\\textbackslash\\%$$ acid. The percentage of acid in the original mixture is ($$1973$$ AHSME Problem, Question \\#$$33$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$22\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$24\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$25\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$30\\textbackslash\\%$$ "}], [{"aoVal": "E", "content": "$$33\\frac{1}{3}\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["Let $$a$$ be the original number of ounces of acid and $$w$$ be the original number of ounces of water. We can write two equations $$\\frac{a}{a+w+1}=\\frac{1}{5}$$ and $$\\frac{a+1}{a+w+2}=\\frac{1}{3}$$. Then cross-multiply to get rid of the fractions. $$5a=a+w+1$$, $$3a+3=a+w+1$$ Solve the system to get $$a=1$$ and $$w=3$$. The percentage of acid in the original mixture is $$\\frac{1}{1+3}=25 \\textbackslash\\% $$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10540", "queId": "ffed284d8b6e472c8a514ab7bf225cf4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Brandon is engaging sprint race on the track. He is in the fifth place now, and there are $8$ players behind him. There are $5$ extra groups signing up for sprint race, and the number of players of each group are idential. How many sprint players are there in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$65$$ "}], [{"aoVal": "B", "content": "$$70$$ "}], [{"aoVal": "C", "content": "$$78$$ "}], [{"aoVal": "D", "content": "$$84$$ "}], [{"aoVal": "E", "content": "$$96$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$(5 + 1 + 8) \\times (5 +1) = 84$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10541", "queId": "a5916a33a7f847baa3019c693e3e1604", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A shop advertises everything is \"half price in today\\textquotesingle s sale.\" In addition, a coupon gives a $25 \\textbackslash\\%$ discount on sale prices. Using the coupon, the price today represents what percentage off the original price? (adapted from 2012 AMC 8, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$40\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$42.5\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$57.5\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$62.5\\textbackslash\\%$$ "}], [{"aoVal": "E", "content": "$$70\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$75 \\textbackslash\\% \\cdot 50\\textbackslash\\% =37.5\\textbackslash\\%$ $1 -37.5\\textbackslash\\% = 62.5\\textbackslash\\%$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10543", "queId": "c525941c815344f69bacc4a3d27a43bb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "James can frost a cookie every $$12$$ seconds and Lacey can frost a cookie every $$15$$ seconds. Working together, how many cookies can they frost in $$10$$ minutes? (Adapted from $$2012$$ AMC $$10\\rm A$$ Problem, Question \\#$$11$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$50$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$90$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"], "answer_analysis": ["In $$600$$ seconds ($$10$$ minutes), James will frost $$\\dfrac{600}{12}=50$$ cookies, and Lacey will frost $$\\dfrac{600}{15}=40$$ cookies. Therefore, working together they will frost $$50+40=\\boxed{(\\text{D})90}$$ cookies. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10547", "queId": "93b59f1f08854802ad730f4ebd312f85", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Judy ran for $$16$$ minutes. If her average speed was $$80$$ meters per minute, then how many meters did Judy run? ", "answer_option_list": [[{"aoVal": "A", "content": "$$800$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$1280$$ "}], [{"aoVal": "D", "content": "$$96$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$80\\times 16 = 1280$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10554", "queId": "ee37582cf77a41cf910c2f3b2968ddcc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The length of a rectangle is increased by $10 \\textbackslash\\%$ and the width is decreased by $10 \\textbackslash\\%$. What percent of the old area is the new area? (2009 AMC 8, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ "}], [{"aoVal": "B", "content": "$$99$$ "}], [{"aoVal": "C", "content": "$$100$$ "}], [{"aoVal": "D", "content": "$$101$$ "}], [{"aoVal": "E", "content": "$$110$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["In a rectangle with dimensions $10 \\times 10$, the new rectangle would have dimensions $11 \\times 9$. The ratio of the new area to the old area is $99 / 100=(\\text{B}) 99$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10555", "queId": "93bd7fea0958495c934623020dc4631d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The price ratio of goods $$A$$ to $$B$$ is $$7:2$$. If their prices were increased by $$\\textbackslash$60$$ respectively, the price ratio would be $$5:2$$. What are the prices of these two goods? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\textbackslash$315$$, $$\\textbackslash$90$$ "}], [{"aoVal": "B", "content": "$$\\textbackslash$320$$, $$\\textbackslash$100$$ "}], [{"aoVal": "C", "content": "$$\\textbackslash$330$$, $$\\textbackslash$120$$ "}], [{"aoVal": "D", "content": "$$\\textbackslash$350$$, $$\\textbackslash$200$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"], "answer_analysis": ["The price difference between the two goods did not change. Before $\\to$ $$A:B:Difference$$ is $$7:2:5$$ After $\\to$ $$A:B:Difference$$ is $$5:2:3$$ $\\textasciitilde$ Make difference the same number of units in both ratios by finding LCM. Before $\\to$ $$A:B:Difference$$ is $$21:6:15$$ After $\\to$ $$A:B:Difference$$ is $$25:10:15$$ $\\textasciitilde$ Therefore, $$4u=\\textbackslash$60$$ $$1u=$$ $$\\textbackslash$60\\div4=\\textbackslash$15$$ $\\textasciitilde$ The original prices of these two goods were $$A=21u=21\\times15=\\textbackslash$315$$ and $$B=6u=6\\times15=\\textbackslash$90$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10556", "queId": "ae9dbe124e1a450d818a809433638948", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ela and Kasia boarded a super-train. Ela took a seat in the seventeenth car counting from the front of the train, and Kasia was seated in the thirty-fourth car counting from the end. The girls were sitting in the same car. How many cars did the super-train have? (2001 Math Kangaroo Problem, Level 3-4, Question \\#13) ", "answer_option_list": [[{"aoVal": "A", "content": "$$48$$ "}], [{"aoVal": "B", "content": "$$49$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$51$$ "}], [{"aoVal": "E", "content": "$$52$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line"], "answer_analysis": ["$17 + 34 - 1 = 50$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10563", "queId": "e07af8769a0f44239de65b126237335b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "James had $$10000$$ dollars, and he deposited ＄$$7000$$ in Bank $$A$$ and ＄$$3000$$ in Bank $$B$$. At the end of the year, James received an interest of＄$$460$$ in total. Given that the sum of the annual interest rates of the two banks is $$10\\textbackslash\\%$$, find the interest rates of the two banks, respectively. ", "answer_option_list": [[{"aoVal": "A", "content": "$$2\\textbackslash\\%$$; $$8\\textbackslash\\%$$. "}], [{"aoVal": "B", "content": "$$3\\textbackslash\\%$$; $$7\\textbackslash\\%$$. "}], [{"aoVal": "C", "content": "$$4\\textbackslash\\%$$; $$6\\textbackslash\\%$$. "}], [{"aoVal": "D", "content": "$$5\\textbackslash\\%$$; $$5\\textbackslash\\%$$. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Interest Problems"], "answer_analysis": ["Let $$x$$ be the interest rate of bank $$A$$: $$7000x+3000(10\\textbackslash\\%-x)=460$$ $$x=4\\textbackslash\\%$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10565", "queId": "a5a47cb9618148d1a9e9b52e8554a746", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Peter has a rope, and he ties some knots, each using $10$-cm rope. He ties $25$ knots in total. After he ties the last knot, the knots divide the rope into pieces~ equally, and the length of each piece is $7$ cm. What is the length of the entire rope? ", "answer_option_list": [[{"aoVal": "A", "content": "$$425$$ cm "}], [{"aoVal": "B", "content": "$$432$$ cm "}], [{"aoVal": "C", "content": "$$456$$ cm "}], [{"aoVal": "D", "content": "$$478$$ cm "}], [{"aoVal": "E", "content": "$$480$$ cm "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$25\\times10+(25+1)\\times7=432$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10575", "queId": "984658792f694f81bf6facccd4a5d188", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The scale of a map is:~$\\dfrac{3}{4}$ of an inch $$=10$$ miles. If the distance on the map between two towns is $$12$$ inches, the actual distance between the towns is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ miles "}], [{"aoVal": "B", "content": "$$120$$ miles "}], [{"aoVal": "C", "content": "$$150$$ miles "}], [{"aoVal": "D", "content": "$$160$$ miles "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with an Invariant Part"], "answer_analysis": ["Since $$12 \\div \\frac{3}{4}=16$$, the actual distance between the towns is $$16\\times10 = 160$$ miles. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10577", "queId": "a139267252094939a90b49c961117584", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Gawel lives on the second floor, and Pawel lives in the same building but has to walk up twice as many stairs as Gawel. There are no stairs to the entrance of the building. On which floor does Pawel live? (2000 Math Kangaroo Problem, Level 3-4, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "on the $2$\\textsuperscript{nd} floor "}], [{"aoVal": "B", "content": "on the $3$\\textsuperscript{rd} floor "}], [{"aoVal": "C", "content": "on the $4$\\textsuperscript{th} floor "}], [{"aoVal": "D", "content": "on the $5$\\textsuperscript{th} floor "}], [{"aoVal": "E", "content": "on the $6$\\textsuperscript{th} floor "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["Gawel lives on the second floor, so he only needs to walk up one floor. Pawel has to walk up twice as many stairs as Gawel, so he needs to walk up two floors. So, Pawel lives on the $3$\\textsuperscript{rd} floor. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10578", "queId": "fffde920e1164d8c8588de40140ad7b6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I ate half an apple pie on Saturday and two thirds of the remainder on Sunday. What fraction of the pie was left for Monday?　 ", "answer_option_list": [[{"aoVal": "A", "content": "None　 "}], [{"aoVal": "B", "content": "$$\\frac{1}{2}$$ "}], [{"aoVal": "C", "content": "$$\\frac{1}{3}$$ "}], [{"aoVal": "D", "content": "$$\\frac{2}{3}$$ "}], [{"aoVal": "E", "content": "$$\\frac{1}{6}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Understanding the Base"], "answer_analysis": ["After I eat one half, half of the apple pie is left. Eating two thirds of this half leaves one third of one half of the pie, which is one sixth, for Monday. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10579", "queId": "c9cc5a0689604a1f9ae1c9d863d52205", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The length of Amy\\textquotesingle s string is $$35\\text{cm}$$. The length of David\\textquotesingle s string is $$29\\text{cm}$$. What is the total length of both strings? ", "answer_option_list": [[{"aoVal": "A", "content": "$$54\\text{cm}$$ "}], [{"aoVal": "B", "content": "$$49\\text{cm}$$ "}], [{"aoVal": "C", "content": "$$64\\text{cm}$$ "}], [{"aoVal": "D", "content": "$$65\\text{cm}$$ "}], [{"aoVal": "E", "content": "$$66\\text{cm}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["$$35+29=64$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10584", "queId": "b7b0ce88aa204c6793e3bde34b8844b7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Cici bought $$12$$ pencils and notebooks in total for $$66$$. Each pencil cost $$2$$. Each notebook costs $8$. How many notebooks did Cici buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$8$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"], "answer_analysis": ["$$12\\times2=24$$ $$8-2=6$$ $$66-24=42$$ $$42\\div6=7$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10585", "queId": "9cc1d229e19d4e469f34a717904897e4", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "There are oranges, apricots and peaches in a big basket. How many fruits are there in the basket if the peaches and the apricots together are 18, the oranges and the apricots together are 28 and 30 fruits are not apricots? ", "answer_option_list": [[{"aoVal": "A", "content": "$$46$$ "}], [{"aoVal": "B", "content": "$$20$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$38$$ "}], [{"aoVal": "E", "content": "$$29$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with Two Variables"], "answer_analysis": ["If we sum up the number of A and P, the result is 18. But if we sum up A and O, result is 28 instead. Hence, there must be 10 more O than P. Note that there are a total of 30 I and P. Therefore, there are (30+10)/2 = 20 Oranges. Total = 20+18=38. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10586", "queId": "e51c571ca64e467c9116b6ab49d529bd", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Suppose $15 \\textbackslash\\%$ of $x$ equals $20 \\textbackslash\\%$ of $y$. What percentage of $x$ is $y$ ? (2020 AMC 8, Question 15) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$75$$ "}], [{"aoVal": "D", "content": "$133\\frac{1}{3}$ "}], [{"aoVal": "E", "content": "$$300$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Since $20 \\textbackslash\\%=\\frac{1}{5}$, multiplying the given condition by 5 shows that $y$ is $15 \\cdot 5=(\\mathbf{C}) 75$ percent of $x$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10590", "queId": "9cc7ab7c016f4b148b1f25f35786da84", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The scale of a map is:~$\\dfrac{3}{4}$ of an inch $$=10$$ miles. If the distance on the map between two towns is $$12$$ inches, the actual distance between the towns is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$90$$ miles "}], [{"aoVal": "B", "content": "$$120$$ miles "}], [{"aoVal": "C", "content": "$$150$$ miles "}], [{"aoVal": "D", "content": "$$160$$ miles "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with an Invariant Part"], "answer_analysis": ["Since $$12 \\div \\frac{3}{4}=16$$, the actual distance between the towns is $$16\\times10 = 160$$ miles. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10591", "queId": "e9b5064a25c24cd2bf0d6c299e8ca03d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Five people took the same test and got an average score of $80$. Four of the people scored $80$, $85$, $82$, and $90$, respectively. What is the score of the remaining person? ", "answer_option_list": [[{"aoVal": "A", "content": "$$80$$ "}], [{"aoVal": "B", "content": "$$76$$ "}], [{"aoVal": "C", "content": "$$73$$ "}], [{"aoVal": "D", "content": "$$63$$ "}], [{"aoVal": "E", "content": "$$56$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["There are $0+5+2+10=17$ points more than the average, so the last score is $80-17=63$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10593", "queId": "b33a52152482460fafe6402546ac5608", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "It is $4:00$ now. How many minutes does it take for the clock\\textquotesingle s hour and minute hands to overlap for the first time? ", "answer_option_list": [[{"aoVal": "A", "content": "$43\\frac 7{11}$ minutes "}], [{"aoVal": "B", "content": "$10\\frac {10}{11}$ minutes "}], [{"aoVal": "C", "content": "$21\\frac 9{11}$ minutes "}], [{"aoVal": "D", "content": "$22\\frac 9{11}$ minutes "}], [{"aoVal": "E", "content": "$42\\frac 7{11}$ minutes "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems"], "answer_analysis": ["$(30\\times 4)\\div (6-0.5)=120\\div 5.5=\\frac {240}{11}=21\\frac 9{11}$ minutes. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10596", "queId": "f7837a9013bf4de0b029c6a76506b96b", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Chloe and Zoe are both students in Ms. Demeanor\\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only $80 \\textbackslash\\%$ of the problems she solved alone, but overall $88 \\textbackslash\\%$ of her answers were correct. Zoe had correct answers to $90 \\textbackslash\\%$ of the problems she solved alone. What was Zoe\\textquotesingle s overall percentage of correct answers? (2017 AMC 8, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$89$$ "}], [{"aoVal": "B", "content": "$$92$$ "}], [{"aoVal": "C", "content": "$$93$$ "}], [{"aoVal": "D", "content": "$$96$$ "}], [{"aoVal": "E", "content": "$$98$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Assume the total amount of problems is 100 per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got 80 problems correct by herself, and got 176 problems correct overall. We also know that Zoe had 90 problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $176-80=96$. Therefore Zoe has $96+90=186$ problems out of 200 problems correct. This is (C) $93$ percent. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10599", "queId": "aa4a715486b7474596d9c7e95e377a90", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Three boxes under my stairs contain apples or pears or both. Each box contains the same number of pieces of fruit. The first box contains all twelve of the apples and one-ninth of the pears. How many pieces of fruit are there in each box? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$16$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["$(1-\\frac19)\\div2=\\frac49$, $\\frac49-\\frac19=\\frac13$, $12\\div\\frac13=36$, $36\\times\\frac49=16$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10603", "queId": "ce616f2455954faaa96cbde1322717a9", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Duckings are walking in a queue when they are following the mother duck. Joey the duckling is the 6th from the front and 8th from the back (including the mother duck). Some of the ducklings at the back moved away from the queue making Joey the middle duckling in the queue. How many ducklings moved away from the queue? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "None of the above. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["total number of duck and ducklings in the queue is 6+(8-1) = 13. if 2 ducklings at the back moved away, it would be 13-2=11 in the queue, and the middle ducking would be 6th from the front, which is Joey\\textquotesingle s position. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10612", "queId": "987373dc98774f7c86d35e1441e74b99", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Every week, Robyn swims while Sam sings. For every $$2$$ of Sam\\textquotesingle s songs, Robyn swims $$9$$ lengths. If Robyn swims $$54$$ lengths, how many songs does Sam sing? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["Sam sings $$2$$ songs in the time that Robyn swims $$9$$ lengths. The time that she takes for $$54$$ lengths is $$54\\div9 =6$$ times longer, so Sam will sing $$2\\times6 =12$$ songs. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10617", "queId": "f79142f6553d444a88d9a79bcc8926be", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If today is a Wednesday, then $$22$$ days ago was a． ", "answer_option_list": [[{"aoVal": "A", "content": "Tuesday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Friday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Today is Wednesday. $$21$$ days ago was Wednesday. $$22$$ days ago was Tuesday. $\\textasciitilde$ or $\\textasciitilde$ $$22\\div7=3$$ weeks $$1$$ day. $$1$$ day before Wednesday was a Tuesday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10626", "queId": "a5e9f61007ce4b08a91e809df6479dae", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "John drinks $x$ cups of boba everyday on weekdays and $1$ cups of boba everyday on the weekends. Which of the following equations represents how many cups of boba John drinks every week? ", "answer_option_list": [[{"aoVal": "A", "content": "$x+2$ "}], [{"aoVal": "B", "content": "$5x+2$ "}], [{"aoVal": "C", "content": "$5x+1$ "}], [{"aoVal": "D", "content": "$5x-1$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"], "answer_analysis": ["The boba that John drinks during weekdays: $$5x$$ The boba that John drinks during weekends: $$2\\times 1 =2$$ The total boba that John drinks during a week: $$5x+2$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10627", "queId": "a5eaf0013626467ea2935363c7092d51", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "This year Gareth is seven times the age of his son Herbie. In six years\\textquotesingle{} time Gareth will be four times as old as Herbie. What is the difference between Gareth\\textquotesingle s and Herbie\\textquotesingle s ages this year? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ years "}], [{"aoVal": "B", "content": "$$20$$ years "}], [{"aoVal": "C", "content": "$$24$$ years "}], [{"aoVal": "D", "content": "$$36$$ years "}], [{"aoVal": "E", "content": "$$42$$ years "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["Let Herbie\\textquotesingle s age this year be $$h$$ years. Then Gareth\\textquotesingle s age this year is $$7h$$ years. In $$6$$ years\\textquotesingle{} time, their ages will be $$h+6$$ years and $$7h+6$$ years respectively. We are told that $$7h+6=$$$$4$$$$\\left(h+6\\right)$$. This gives $$7h+6=4h+24$$ so that $$3h=18$$ and $$h=6$$. So the present ages are $$6$$ and $$7\\times 6=42$$, giving a difference of $$36$$ years. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10630", "queId": "988b12940d1a483b9021106328a6f9af", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A piece of pasture can feed $$17$$ cow for $$30$$ days or $$19$$ cows for $$24$$ days. If the grass grows at the same speed every day, how many cows can it feed for $$6$$ days? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$38$$ "}], [{"aoVal": "B", "content": "$$45$$ "}], [{"aoVal": "C", "content": "$$49$$ "}], [{"aoVal": "D", "content": "$$52$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Newton's Problem of Cows and Fields"], "answer_analysis": ["$17\\times30=510$ $19\\times 24=456$ $510-456=54$ $54\\div(30-24)=9$ $510-30\\times9=240$ $240+6\\times9=294$ $294\\div 6=49$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10632", "queId": "e9cf4bb461884fef889224bee10f4fe4", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The month of February of a given year has five Fridays. What day of the week is January $$31$$ of that year? ", "answer_option_list": [[{"aoVal": "A", "content": "Tuesday "}], [{"aoVal": "B", "content": "Thursday "}], [{"aoVal": "C", "content": "Friday "}], [{"aoVal": "D", "content": "Saturday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["There are seven days in a week; so, in order to have five Fridays, a month has at least $$4\\times7+1=29$$ days. Since February has at most $$29$$ days, the $$1^{\\rm st}$$ and $$29^{\\rm th}$$ days of this February must both be Fridays, which means that January $$31$$ is a Thursday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10636", "queId": "c9f6771fd40b4fc8902b7a92f6c8183c", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Several students are singing in a line. Amy is the fourth one from the left. From the right, Amy is the fourth too. How many students are singing? (adapted from $$2019$$ Math kangaroo Problems, Level $$1-2$$, Question \\#$$5$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$5$ "}], [{"aoVal": "B", "content": "$6$ "}], [{"aoVal": "C", "content": "$7$ "}], [{"aoVal": "D", "content": "$8$ "}], [{"aoVal": "E", "content": "$9$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"], "answer_analysis": ["It comes $4+4=8$ when we count Amy twice. The number of all singing students is $4+4-1=7$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10638", "queId": "e0a799aa552a40b486e80e925ec45e4f", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "In a class of pupils, $80\\textbackslash\\%$ participated in basketball, $85\\textbackslash\\%$ participated in football, $74\\textbackslash\\%$ participated in softball and $68\\textbackslash\\%$ participated in squash. Find the minimum percentage of pupils who participated in all the four sports events. ", "answer_option_list": [[{"aoVal": "A", "content": "$7\\textbackslash\\%$ "}], [{"aoVal": "B", "content": "$10\\textbackslash\\%$ "}], [{"aoVal": "C", "content": "$12\\textbackslash\\%$ "}], [{"aoVal": "D", "content": "$15\\textbackslash\\%$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["Least percentage of pupils who participated in both basketball and football $=80\\textbackslash\\%+ 85\\textbackslash\\%-100\\textbackslash\\% =65\\textbackslash\\%$, Least percentage of pupils who participated in basketball, football and softball $=65\\textbackslash\\%+74\\textbackslash\\%-100\\textbackslash\\% =39\\textbackslash\\%$, Least percentage of pupils who participated in basketball, football, softball and squash $=39\\textbackslash\\%+ 68\\textbackslash\\%-100\\textbackslash\\% = 7\\textbackslash\\%$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10644", "queId": "9d0887064c8b46eba72e3a62483bdde7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If six days ago was a Tuesday, then eight days from today is a． ", "answer_option_list": [[{"aoVal": "A", "content": "Monday　 "}], [{"aoVal": "B", "content": "Tuesday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Thursday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$$6$$ days ago was a Tuesday. Today is Monday. Thus, in $$8$$ days\\textquotesingle{} time, it will be a Tuesday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10648", "queId": "d796f1c92ec148818f18839dab3967ec", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the sequence of letters $$\\text{KANGAROOKANGAROOKANG}\\cdots$$ the word $$\\text{KANGAROO}$$ is repeated indefinitely. What is the $$2017\\text{th}$$ letter in this sequence? ", "answer_option_list": [[{"aoVal": "A", "content": "$$\\text{K}$$ "}], [{"aoVal": "B", "content": "$$\\text{N}$$ "}], [{"aoVal": "C", "content": "$$\\text{G}$$ "}], [{"aoVal": "D", "content": "$$\\text{R}$$ "}], [{"aoVal": "E", "content": "$$\\text{O}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"], "answer_analysis": ["The sequence $$\\text{KANGAROOKANGAROOKANG}\\cdots$$ repeats every $$8$$ letters. Since $$2017=8\\times252+1$$, the $$2017\\text{th}$$ letter in the sequence is the first of the repeating sequence and hence is $$\\text{K}$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10652", "queId": "dc2da65c25c54d129b71d7b3118be4f0", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$30$$ students in your class. The ratio of boys to girls is $$3:2$$. How many boys and girls are there?. ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ and $$20$$ "}], [{"aoVal": "B", "content": "$$20$$ and $$30$$ "}], [{"aoVal": "C", "content": "$$18$$ and $$12$$ "}], [{"aoVal": "D", "content": "$$12$$ and $$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["According to the ratio $$3:2$$, we could know the total is $$5$$. Then the number of boys is $$30\\times \\dfrac{3}{5} =18$$.The number of girls is $$30\\times\\dfrac{2}{5}=12$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10658", "queId": "a60cbbd068f8408d9d68ee9484f46f9e", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A bag contains $$100$$ raffle tickets in red, white and blue. The ratio of red to white tickets is $$5:4$$ and the ratio of white to blue tickets is $$8:7$$. What is the smallest number of tickets that would have to be picked to make sure having selected at least half of \\textbf{one} colour? ", "answer_option_list": [[{"aoVal": "A", "content": "$$48$$ "}], [{"aoVal": "B", "content": "$$49$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$51$$ "}], [{"aoVal": "E", "content": "$$52$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"], "answer_analysis": ["First we must work out the number of tickets of each colour. Let the numbers of red, white and blue tickets be $$r$$, $$w$$ and b respectively; we have $$r : w = 5 : 4$$ and $$w : b = 8 : 7$$. Writing $$r : w$$ as $$10 : 8$$, we can combine the ratios to find $$r : w : b = 10 : 8 : 7$$. Hence for a total of $$100$$ tickets, there must be $$40$$ red, $$32$$ white and $$28$$ blue tickets. Now the largest number of red tickets one can select without having half of them is $$19$$, and likewise $$15$$ and $$13$$ for white and blue tickets. So it would be possible to select $$19 + 15 + 13 = 47$$ tickets and still not have half or more of any particular colour of ticket. However, the very next ticket, the $$48\\text{th}$$, would have to be a red, a white or a blue one, and so one of the colours would now have at least half of its number selected. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10660", "queId": "c58214890d604d8db99bc956ffbe80f7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alice\\textquotesingle s first day in Caterpillar Club was Tuesday. She wants to throw a party on her $40\\rm{th}$ day in the club. If Alice attends the club everyday, on which day of the week will the party be? ", "answer_option_list": [[{"aoVal": "A", "content": "Friday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Sunday "}], [{"aoVal": "D", "content": "Monday "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["40th day = 39th day after first day joining. 39 days/7 = 5 weeks R 4 days. 4 days after Tues is Saturday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10664", "queId": "d7a6e12a2678431da653e1a728b4413f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Jenny is $5$ years old. She has $2$ sisters, Julie and Jas. Julie is $1$ year older than Jas. In two year\\textquotesingle s time, their total age will be $18$ years. How old is Julie now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["NA "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10670", "queId": "bc88d7782d36425bb43adb817ff31970", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Julia has eaten one-quarters of the pizza. What is the ratio of the number of pizza that remain to the number Julia has eaten? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1:3$$ "}], [{"aoVal": "B", "content": "$$3:1 $$ "}], [{"aoVal": "C", "content": "$$1:4 $$ "}], [{"aoVal": "D", "content": "$$4:1$$ "}], [{"aoVal": "E", "content": "$$4:3$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["Julia has eaten one-quarters of the pizza. So three-quarter of the pizza remain. Therefore the required ratio is $$\\frac{3}{4}:\\frac{1}{4}=3:1$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10673", "queId": "ee797a7d0d2f4757b3f9e2597eb9fa8b", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A gardener has a box of bulbs to plant in a garden. The garden has three sections. She plants 1/2~of the bulbs in the first section. She plants 3 /4~of the remaining bulbs in the second section. She has 6 bulbs left, which she plants in the third section. How many bulbs were in the box at the start? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$32$$ "}], [{"aoVal": "E", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["1-1/2-1/2*3/4=1/8，1/8means 6 bulbs，$$so$$ in total there are 6\\div 1/8=48 bulbs. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10675", "queId": "a1a6ebd3fcd142dfafbeece2e0550076", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Will is selling apples at the farmer\\textquotesingle s market. After selling $\\dfrac{2}{5}$ of them, he has $150$ left. How many apples did Will have to start with? ", "answer_option_list": [[{"aoVal": "A", "content": "$$250$$ "}], [{"aoVal": "B", "content": "$$375$$ "}], [{"aoVal": "C", "content": "$$90$$ "}], [{"aoVal": "D", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["He has $\\dfrac{3}{5}$~remaining after selling $\\dfrac{2}{5}$. We can write the equation as:~$150\\div\\dfrac{3}{5}=250$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10677", "queId": "af12f26206f14071a1f9d43ce2ca0f31", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Brandon is engaging sprint race on the track, and he is in the first group. On the track, there are $5$ players in front of him, and there are $8$ players behind him. There are $5$ extra groups signing up for the sprint race, and the number of players of each group are identical. How many sprint players are there in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$65$$ "}], [{"aoVal": "B", "content": "$$70$$ "}], [{"aoVal": "C", "content": "$$78$$ "}], [{"aoVal": "D", "content": "$$84$$ "}], [{"aoVal": "E", "content": "$$96$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["There are $5+8+1=14$ players in each group. There are $14\\times 6=84$ players in total. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10682", "queId": "ee7e218d93e5439eaddeb236c91c3157", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Niko counted a total of $$60$$ birds perching in three trees. Five minutes later, $$6$$ birds had flown away from the first tree, $$8$$ birds had flown away from the second tree and $$4$$ birds had flown away from the third tree. He noticed that there was now the same number of birds in each tree. How many birds were originally perched in the second tree? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Let the number of birds remaining in each tree be $$x$$. Therefore $$x+6+x+8+x+4= 60$$, which has solution $$x=14$$. Hence the number of birds originally perched in the second tree is $$14 + 8 = 22$$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10684", "queId": "b81086188e474252b1190d51efb9ce6a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "A tank filled with $200$ litres of water weighs $350\\rm{kg}$. The same tank filled with $150$ litres of water weighs $315\\rm{kg}$. What is the weight of the empty tank? ", "answer_option_list": [[{"aoVal": "A", "content": "$$120\\rm{kg}$$ "}], [{"aoVal": "B", "content": "$$150\\rm{kg}$$ "}], [{"aoVal": "C", "content": "$$165\\rm{kg}$$ "}], [{"aoVal": "D", "content": "$$210\\rm{kg}$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"], "answer_analysis": ["T + 200L = 350kg $\\cdots $ ① -) T + 150L = 315kg $\\cdots $ ② \\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_ (50L = 35kg) x3 = 150L = 105kg 315kg - 105kg = 210kg "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10685", "queId": "b398ea3e4400435983e03d93bfa758f3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A total of $$42$$ chickens and rabbits are caged together. If there are $$124$$ legs in total, how many chickens and rabbits are in the cage, respectively? ", "answer_option_list": [[{"aoVal": "A", "content": "$20$; $12$ "}], [{"aoVal": "B", "content": "$22$; $20$ "}], [{"aoVal": "C", "content": "$20$; $24$ "}], [{"aoVal": "D", "content": "$19$; $21$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"], "answer_analysis": ["Suppose all the animals in the cage are chickens: there should be $$2\\times 42=84$$ legs. However, $$124-84=40$$ legs are missing because we counted $$40\\div2=20$$ rabbits. Hence, there are $$20$$ rabbits and $$42-20=22$$ chickens. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10687", "queId": "e9f76f1b730c4df2b65ba6c50785a59b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A string $$12$$ meters long is cut into $$6$$ pieces of equal length. What is the sum of the lengths of any $$4$$ of these pieces? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2\\text{m}$$ "}], [{"aoVal": "B", "content": "$$4\\text{m}$$ "}], [{"aoVal": "C", "content": "$$6\\text{m}$$ "}], [{"aoVal": "D", "content": "$$8\\text{m}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"], "answer_analysis": ["The string $$12$$ meters long is cut into $$6$$ pieces of length $$2\\text{m}$$. The sum of the lengths of any $$4$$ of these pieces is $$4\\times2\\text{m}=8\\text{m}$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10689", "queId": "e0d0c37a8432405cadd318e99d0e3f2f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "William plans to take $$16$$ days to drive to New York City from his home. However, since there is heavy traffic, he drives $$20$$ miles less each day and arrives in New York City $$8$$ days later than his plan. What is the distance between William\\textquotesingle s home and New York City? ", "answer_option_list": [[{"aoVal": "A", "content": "$$480$$ miles "}], [{"aoVal": "B", "content": "$$1080$$ miles "}], [{"aoVal": "C", "content": "$$960$$ miles "}], [{"aoVal": "D", "content": "$$720$$ miles "}], [{"aoVal": "E", "content": "$$1200$$ miles "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"], "answer_analysis": ["We set up an equation in terms of $d$ as the distance and $x$ as the speed in miles per day originally. We have $d=16x=24(x-20)$ $16x=24x-480$ $480=8x$ $x=60$ Thus, the distance between William\\textquotesingle s home and New York City is $60\\times16=960$ miles. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10692", "queId": "af28b0c4a6b84bd7b5e76fd7560e8894", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Calculate: $1\\times 10+2\\times 9+3\\times 8+ \\cdots + 9\\times 2+ 10\\times 1$ ", "answer_option_list": [[{"aoVal": "A", "content": "$$200$$ "}], [{"aoVal": "B", "content": "$$140$$ "}], [{"aoVal": "C", "content": "$$210$$ "}], [{"aoVal": "D", "content": "$$180$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples"], "answer_analysis": ["E "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10693", "queId": "dc521414c5e7410e99318378e9567584", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The sum of Ben\\textquotesingle s age and Ben\\textquotesingle s grandma\\textquotesingle s age is $$96$$. Ben\\textquotesingle s grandma\\textquotesingle s age is three times older than Ben\\textquotesingle s age. How old is Ben\\textquotesingle s grandma? ", "answer_option_list": [[{"aoVal": "A", "content": "$$24$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$96$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Sums and Multiples in Age Problems"], "answer_analysis": ["The sum of Ben\\textquotesingle s age and Ben\\textquotesingle s grandma\\textquotesingle s age is $$96$$. Since grandma is three times older than Ben, on the number line, $96$ can be divided into $$4$$ portions, and each portion is $$96\\div(1+3)=24$$. Ben is $$24$$ years old, and grandma is three times older. $$24\\times 3=72$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10696", "queId": "a63e2f1ae6a24e1584f10b7cc05f51eb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Five children divided some cakes equally. What percents of the cakes two of them could get in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$10\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$20\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$40\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"], "answer_analysis": ["Five children divided some cake equally. Two of the children totally got $$\\dfrac{2}{5}$$ of the cake and $$\\dfrac{2}{5}=0.4 = 40\\textbackslash\\%$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10697", "queId": "a1c95d7cb7b64d73b60f3f6155adfbdd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "This year, March $$19$$ falls on a Thursday. What day of the week will it be in $$30$$ days? ", "answer_option_list": [[{"aoVal": "A", "content": "Wednesday　 "}], [{"aoVal": "B", "content": "Thursday　 "}], [{"aoVal": "C", "content": "Friday　 "}], [{"aoVal": "D", "content": "Saturday　 "}], [{"aoVal": "E", "content": "Sunday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$$30\\div4=7 \\text{ R } 2$$, two days after a Thursday is a Saturday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10703", "queId": "dc5c776a10254651bfcf64b5a79c6567", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A group of students go apple-picking. On average, each boy picks $30$ apples and each girl picks $20$ apples. The average number of apples picked by everyone in this groups is $26$. If there are $15$ boys, then how many girls are there in the group? ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$23$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Every boy picks $$30-26=4$$ more than the average, so boys pick $$4\\times 15=60$$ more in total, which is equal to the number that girls picked less than the average in total. Every girl picks $$26-20=6$$ less than the average, so there are $$60\\div 6=10$$ girls. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10704", "queId": "a1d482de2f344a069b532edcb9781703", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$10^{}\\text{th}$$June is Sunday, what day of the week is $$1$$\\textsuperscript{st} June? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday　 "}], [{"aoVal": "B", "content": "Monday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Friday "}], [{"aoVal": "E", "content": "Saturday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["We can count backward by days or by weeks. There are 9 days in between, that means 1 week and 2 days. Then count a few days back to find that $$1$$\\textsuperscript{st} June is a Friday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10705", "queId": "e0e068fe31fb4174add90714c06d682a", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The possible grades on an exam are $$5$$, $$4$$, $$3$$, $$2$$, or $$1$$. In a class of $$200$$ students, $$\\frac{1}{10}$$ of them got $$5$$s, $$\\frac{1}{5}$$ them got $$4$$s, $$25 \\textbackslash\\% $$ of them got $$3$$s, and $$15 \\textbackslash\\%$$ of them got $$2$$s. How many students got $$1$$s ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$60$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$$200\\times \\left( 1-\\frac{1}{10}-\\frac{1}{5}-25 \\textbackslash\\% -15 \\textbackslash\\% ~\\right)=60$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10707", "queId": "ea08f2921d884ebbaa3f60fee63388c5", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The average weight of $4$ students in Class $A$ is $37$ kilograms. The average weight of $11$ students in Class $B$ is $41$ kilograms. The total weight of $5$ students in Class $C$ is $161$ kilograms. What is the average weight of the students in the $3$ classes? ", "answer_option_list": [[{"aoVal": "A", "content": "$36$ kilograms "}], [{"aoVal": "B", "content": "$38$ kilograms "}], [{"aoVal": "C", "content": "$40$ kilograms "}], [{"aoVal": "D", "content": "$43$ kilograms "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$4 \\times 37 + 11 \\times 41+ 161 = 760$ kilograms in total. $760 \\div (4 + 11 + 5) = 38$ kg. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10710", "queId": "dc62d707308842978a8265c0fe0c5873", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "In $$2005$$, both John and Mary have the same amount of pocket money per month. In $$2006$$, John had an increase of $$10\\textbackslash\\%$$ and Mary a decrease of $$10\\textbackslash\\%$$ in their monthly pocket money. In $$2007$$, John had a decrease of $$10\\textbackslash\\%$$ and Mary an increase of $$10\\textbackslash\\%$$ in their monthly pocket money. $\\textasciitilde$ John had a~\\uline{~~~~~~~~~~}~$\\textbackslash\\%$ increase/decrease in his pocket money in $2007$ compared to $2005$. Mary had a~\\uline{~~~~~~~~~~}~$\\textbackslash\\%$ increase/decrease in her pocket money in $2007$ compared to $2005$. $\\textasciitilde$ Which one of the following statements is correct? ", "answer_option_list": [[{"aoVal": "A", "content": "Both have the same amount of pocket money now. "}], [{"aoVal": "B", "content": "John has more pocket money now. "}], [{"aoVal": "C", "content": "Mary has more pocket money now. "}], [{"aoVal": "D", "content": "It is impossible to tell who has more pocket money now. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["Statement $$\\text{A}$$ is correct. In the amount of pocket money that each has be $$x$$. In $$2007$$, John has $$1.1\\times0.9x=0.99x$$ while Mary has $$0.9\\times1.1x=0.99x$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10725", "queId": "ced1ab1899bb4ab0a87e05eebd6f681d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Lena the panda has $$30$$ bamboos. She eats $$3$$ bamboos each day. She ate the $$18th$$ bamboo on Tuesday. On which day did she start eating the bamboos? ", "answer_option_list": [[{"aoVal": "A", "content": "Monday "}], [{"aoVal": "B", "content": "Tuesday "}], [{"aoVal": "C", "content": "Wednesday "}], [{"aoVal": "D", "content": "Thursday "}], [{"aoVal": "E", "content": "Friday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Newton's Problem of Cows and Fields->Basic Newton's Problem of Cows and Fields->Finding the Number of Days"], "answer_analysis": ["NA "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10729", "queId": "eeaa1f787e2d46c58bdf5368396322ca", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A particular cattle is fed $7 \\text{kg}$, $8 \\text{kg}$ and $9 \\text{kg}$ of special food on Day $1$, $2$ and $3$ respectively by a farmer. From Day $4$ onwards, the amount of food fed to the cattle follows the following rule: (i) if the total amount of food fed to the cattle in the past $3$ days is $24 \\text{kg}$ or more, the cattle will be fed $2 \\text{kg}$ less than the day before. (ⅱ) if the total amount of food fed to the cattle in the past $3$ days is less than $24 \\text{kg}$, the cattle will be fed $1 \\text{kg}$ more than the day before. Calculate the minimum number of days for the total amount of food fed to the cattle to exceed $2018 \\text{kg}$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$280$$ "}], [{"aoVal": "B", "content": "$$284$$ "}], [{"aoVal": "C", "content": "$$288$$ "}], [{"aoVal": "D", "content": "$$292$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"], "answer_analysis": ["Amount of food fed to the cattle follows the pattern: $789756$~ ~ $$789756$$~ ~ $789756$~ ~ $789756\\cdots\\cdots$ Total amount of food fed in the first $6$ days$=42 \\text{kg}$. $2018 =48\\times6+1= 289$. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10732", "queId": "ca56d0e864174132a7f950ae6cf78ef1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Emily was $$6$$ years old last year, and her sister was $$6$$ years old six years ago. What is the age difference between Emily and her sister today? (adapted from 2005 Math Kangaroo Problem, Level 1-2, Question \\#17) ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$13$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages"], "answer_analysis": ["Emily was $$6$$ years old last year , which means Emily is $7$ years old this year. Her sister was~ $$6$$ years old six years ago, which tells us her sister is~ $12$ years old this year, so the age difference is $5$ today. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10733", "queId": "ced60cfcbf05434cbc9a5637869db5ba", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Sinnce $$7^{2}=49$$, its ones\\textquotesingle{} digit is a $$9$$. What is the ones\\textquotesingle{} digit of $$2^{50}$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$0$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders "], "answer_analysis": ["The ones\\textquotesingle{} digits repeat in groups of four: $$2$$, $$4$$, $$8$$, $$6$$, $$2$$, $$4$$, $$8$$, $$6$$, $$\\cdots $$. The ones\\textquotesingle{} digits of $$2^{48}$$, $$2^{49}$$, $$2\\%{50}$$ are $$6$$, $$2$$, $$4$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10735", "queId": "e0fbf303526648a985b397d975797356", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If six days ago was a Tuesday, then eight days from today is a． ", "answer_option_list": [[{"aoVal": "A", "content": "Monday　 "}], [{"aoVal": "B", "content": "Tuesday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Thursday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$$6$$ days ago was Tues. Today is Mon. In $$8$$ days it will be Tues. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10739", "queId": "fc7e4e4db79d4aba86fe5d52e60f6af9", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Granny and the triplets Cara, Cate and Chris all have their birthdays today. The ages of all four of them total $$120$$ years. Granny is $$5$$ times as old as each of the triplets. When were the triplets born? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2000$$ "}], [{"aoVal": "B", "content": "$$2002$$ "}], [{"aoVal": "C", "content": "$$2004$$ "}], [{"aoVal": "D", "content": "$$2006$$ "}], [{"aoVal": "E", "content": "$$2008$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Sums and Multiples in Age Problems"], "answer_analysis": ["Given that Granny is $$5$$ times older than each of the three triplets, we know that the age of each triplet is $$120\\div (5+3)= 15$$. So Cara, Cate and Chris were born in $$2004$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10740", "queId": "a67100eadbaf41779a4040f9fa0a7921", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Chloe is buying candies at a grocery store. She can either spend $8$ dollars on a $15\\text{-ounce}$ bag or $12$ dollars on a $20\\text{-ounce}$ bag. Which is a better buy? ", "answer_option_list": [[{"aoVal": "A", "content": "The $15\\text{-ounce}$ bag "}], [{"aoVal": "B", "content": "The $20\\text{-ounce}$ bag "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"], "answer_analysis": ["$\\frac{8\\text{dollars}}{15\\text{ounces}}$ $\\frac{12\\text{dollars}}{20\\text{ounces}}$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10744", "queId": "a673de9dc7924b7ea26020459905e811", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If February is a month that contains Friday the $$13^{}\\text{th}$$, what day of the week is February $$1$$? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday　 "}], [{"aoVal": "B", "content": "Monday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Thursday　 "}], [{"aoVal": "E", "content": "Saturday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["We can count backward by days or by weeks. Count a few weeks back to find that February $$6$$ is a Friday. Then count a few days back to find that February $$1$$ is a Sunday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10746", "queId": "bcdb590870884f1ea2d28c313ce1f4eb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Tower $$A$$ is $$\\rm 64 m$$ high.The total height of Tower $$A$$ and Tower $$B$$ is $$\\rm 112 m$$.What is the difference between the height of the two towers?~\\uline{~~~~~~~~~~}~$$\\rm m$$. ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$17$$ "}], [{"aoVal": "E", "content": "$$18$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["$$112-64=48$$ $$64-48=16$$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10747", "queId": "ca5d6e04cd304ba4a277452b04ecd54a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Clara, Pablo and Miguel share some money in the ratio $$3:1:4$$. Miguel then gave Pablo and Clara each $$25\\textbackslash\\%$$ of his share, leaving Clara with ￡$$6$$ more than Miguel. How much money does Pablo now have? ", "answer_option_list": [[{"aoVal": "A", "content": "￡$$2$$ "}], [{"aoVal": "B", "content": "￡$$3.60$$ "}], [{"aoVal": "C", "content": "￡$$4$$ "}], [{"aoVal": "D", "content": "￡$$6$$ "}], [{"aoVal": "E", "content": "￡$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"], "answer_analysis": ["The initial ratio of the children\\textquotesingle s money is $$3:1:4$$. When Miguel shares half of his portion, the ratio becomee $$3 + 1:1+ 1:4-2=4:2:2=2:1:1$$. Given that Clara now has ￡$$6$$ more than Miguel, Pablo now has ￡$$6$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10749", "queId": "cede5245842e4013a895b48f94735405", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Adam paid £6 for $$15$$ buns. How many dollars did Tom pay for the same kind of buns if he bought $$5$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$2$$ "}], [{"aoVal": "B", "content": "$$3$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"], "answer_analysis": ["There $$3$$ groups of $$5$$ buns in $$15$$ buns: $$15\\div 5=3$$, so $$5$$ buns cost $$6\\div 3=$$£$$2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10761", "queId": "bce9f763f0bd41fca5eacaf5716b6684", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "SASMO 2014 P2 Q7 There are 14 children playing \"The eagle catches the chicks.\" One of them is the \\textquotesingle eagle\\textquotesingle{} while another child is the \\textquotesingle mother hen\\textquotesingle{} whose job is to protect the \\textquotesingle chicks\\textquotesingle. The rest of the children are the \\textquotesingle chicks\\textquotesingle. After a while, the \\textquotesingle eagle\\textquotesingle{} has caught 5 \\textquotesingle chicks\\textquotesingle. How many \\textquotesingle chicks\\textquotesingle{} are still around? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$7$$ "}], [{"aoVal": "C", "content": "$$8$$ "}], [{"aoVal": "D", "content": "$$9$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"], "answer_analysis": ["14 - 1 (eagle) - 1 (mother hen) = 12 (chicks) 12 - 5 7 chicks "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10763", "queId": "b867c9ed64e5436c89831f2be5a62b66", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "For every $$7$$ soccer balls Elena bought for the gym, she bought $$4$$ basketballs. If she bought $$35$$ soccer balls, she bought a total ofballs. ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$45$$ "}], [{"aoVal": "D", "content": "$$55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$$7$$ out of $$11$$ balls that Elena bought are soccer balls. If there are $$7\\times5 =35$$ soccer balls, then there is a total of $$11\\times5=55$$ balls. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10768", "queId": "c5f02cb2e2974724b3e0e17e811a83a3", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Chloe and Zoe are both students in Ms. Demeanor\\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to $90\\textbackslash\\%$ of the problems she solved alone, but overall $60\\textbackslash\\%$ of her answers were correct. Zoe had correct answers to $70\\textbackslash\\%$ of the problems she solved alone. What was Zoe\\textquotesingle s overall percentage of correct answers? (2017 AMC 8, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$45$$ "}], [{"aoVal": "B", "content": "$$48$$ "}], [{"aoVal": "C", "content": "$$50$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$65$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Assume the total amount of problems is 100 per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got 90 problems correct by herself, and got 120 problems correct overall. We also know that Zoe had 70 problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $120-90=30$. Therefore Zoe has $30+70=100$ problems out of $200$ problems correct. Thus $\\frac{100}{200} = 50$ percent. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10769", "queId": "d802fff4b28a4deaa8645d2da8acc555", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "When Cici was born, Linda was $11$ years old. The sum of their ages $4$ years later will be $37$. How old will be Linda $3$ years later? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$22$$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$$26$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["Suppose that Cici will be $x$ years old $4$ years later, Linda will be $$(x+11)$$ years old. $x+(x+11)=37$, so $x=13$. Thus, Linda will be $13+11=24$ years old $3$ years later. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10773", "queId": "d3835445b5ae4475b41da2d97eac9bba", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My mom\\textquotesingle s birthday is on Sunday, and my dad\\textquotesingle s birthday is $$55$$ days later. On what day of the week will my dad\\textquotesingle s birthday be? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$ $$Sunday$$ $$ "}], [{"aoVal": "B", "content": "$$ $$Tuesday$$ $$ "}], [{"aoVal": "C", "content": "$$ $$Thursday$$ $$ "}], [{"aoVal": "D", "content": "$$ $$Saturday$$ $$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["After $$1$$ day, it is Monday; after $$2$$ days, it is Tuesday; after $$3$$ days, it is Wednesday $$\\cdots$$ After $$8$$ days, it is still Monday, and the period is $$7$$ days. $$55\\div 7=7$$(weeks) $$\\rm R$$ $$6$$ (days). The birthday is Saturday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10774", "queId": "dc96297dcf1f4d54a05f153d125a6e62", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My age is $$3$$ years less than $$5$$ times my sister\\textquotesingle s age. If I am $$27$$, the sum of my age and my sister\\textquotesingle s age is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$33$$ "}], [{"aoVal": "B", "content": "$$36$$ "}], [{"aoVal": "C", "content": "$$39$$ "}], [{"aoVal": "D", "content": "$$42$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Differences and Multiples in Age Problems"], "answer_analysis": ["My age, $$27$$, is $$3$$ years less than $$5$$ times my sister\\textquotesingle s age, so $$30$$ is $$5$$ times her age. Thus, my sister is $$6$$. The sum of our ages is $$27+6=33$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10776", "queId": "c5f6f6a35eb249c988537d6d70c8717c", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Valeria has $$65$$ grams of a $$20\\textbackslash\\%$$ sugar solution. How many grams of sugar is in the solution? How many grams of water is in the solution? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$; $$65$$ "}], [{"aoVal": "B", "content": "$$13$$; $$52$$ "}], [{"aoVal": "C", "content": "$$13$$; $$65$$ "}], [{"aoVal": "D", "content": "$$20$$; $$52$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"], "answer_analysis": ["Sugar: $$65\\times 20\\textbackslash\\% = 13$$ ounces; Water: $$65 - 13 = 52$$ ounces. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10777", "queId": "c17aaf695ebd48c3a6930aee72c43d85", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Each watermelon\\textquotesingle s full price is $$4$$ dollars. Currently, the watermelons on a discounted price for $$3$$ dollars each. Ms. Lee ~wants to buy $$3$$ of them. She needs to pay~\\uline{~~~~~~~~~~}~dollars in total. ", "answer_option_list": [[{"aoVal": "A", "content": "$$8$$ "}], [{"aoVal": "B", "content": "$$9$$ "}], [{"aoVal": "C", "content": "$$10$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"], "answer_analysis": ["$$3+3+3=9$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10778", "queId": "d38671853557404db4b6de1b6a487401", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "19 less than 67 is~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$58$$ "}], [{"aoVal": "B", "content": "$$68$$ "}], [{"aoVal": "C", "content": "$$38$$ "}], [{"aoVal": "D", "content": "$$48$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"], "answer_analysis": ["$$67-19=48$$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10780", "queId": "f36020d6e8e04424ace167d65cc67fa8", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Mother\\textquotesingle s Day in $$2020$$ was May $$10$$th, which was Sunday. Father\\textquotesingle s Day in $$2020$$ was June $$21$$st. On what day did Father\\textquotesingle s Day fall? ", "answer_option_list": [[{"aoVal": "A", "content": "Thursday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Sunday "}], [{"aoVal": "D", "content": "Tuesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["It passed $$31-10 + 21 = 42$$ days in total. Since $$42 \\div 7 = 6$$, which means the Father\\textquotesingle s Day fell on Sunday as well. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10781", "queId": "c5f89e1264694a438f2ebb04401ed8ad", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "The ages of Tom\\textquotesingle s father, Tom\\textquotesingle s mother and Tom are $86$ together. Tom\\textquotesingle s mother is $24$ years older than Tom and~~$2$ years younger than Tom\\textquotesingle s father.How old is Tom? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$32$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "$$36$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["Tom\\textquotesingle s mother is $(86+24-2)\\div3=36$ years old. Tom is $36-24=12$ years old. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10786", "queId": "ab1d467c4b2542bfa8437ceb255979f8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many ways are there to make $$$80$$ using some combination of $$$5$$, $$$10$$ and $$$20$$ notes? ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$49$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["Condition on the number of $$$20$$ note you use. $$4$$ gives $$1$$ possibility, $$3$$ gives $$3$$ possibilities, $$2$$ gives $$5$$ possibilities, $$1$$ gives $$7$$ possibilities, $$0$$ gives $$9$$ possibilities. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10797", "queId": "e12692ffb3f54dd0a6b21ca3eaafdf7d", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "Mark and Karl have $$100$$ dollars in total. The money Mark owns is three times the money Karl owns. How many dollars does Mark have? (Adapted from 1999 Math Kangaroo Problem, Level 3 - 4, Question \\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$20$$ "}], [{"aoVal": "B", "content": "$$25$$ "}], [{"aoVal": "C", "content": "$$35$$ "}], [{"aoVal": "D", "content": "$$75$$ "}], [{"aoVal": "E", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple->Sum and Multiple of Two Variables"], "answer_analysis": ["$100 \\div (3 + 1)~ \\times 3= 75$ "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10798", "queId": "ab2637a0065d4ea8a260498872829bba", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If today is Monday, which day of the week will it be $$22$$ days later? ． ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday "}], [{"aoVal": "B", "content": "Monday "}], [{"aoVal": "C", "content": "Tuesday "}], [{"aoVal": "D", "content": "Wednesday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["Since there are 7 days in a week, the day will repeat again after 7 days. Thus, if today is Monday, it will be Monday again a week later. $$22\\div 7=3$$ week R $$1$$. The day after $$22$$ days is the same as the day after $$1$$ day. $$1$$ day after Monday is Tuesday. Therefore, it will be \\textbf{Tuesday} $$22$$ days later. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10804", "queId": "dca86dbec3dc419fb249ac6f1c6910bc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "In a maths test, the average score of $$40$$ students is $$25$$. The lowest score is $$5$$. At most how many student(s) can get $$100$$ points? ", "answer_option_list": [[{"aoVal": "A", "content": "$$11$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Total points: $$40\\times 25=1000$$. To have as many $100$ points as possible, we should consider there are only two groups of students: everyone gets $5$ points in a group and everyone gets $100$ in the other group. $$10\\times 100=1000$$, so there must be less than $10$ people getting $100$ points. If there are nine $100$s: $$9\\times 100+31\\times 5=1055\\textgreater1000$$, which is impossible. If there are eight $100$s:$$8\\times 100+32\\times 5=960\\textless{}1000$$. Thus, the answer is $$8$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10805", "queId": "bd122c1bf5b44fd2a71cbc26ed5460d6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The class organized students to do gymnastics side by side，$$and$$ there are two people in each row. Bob and Tick observed that there were $8$ rows in front of them and $11$ rows in the back. How many people in the class did gymnastics together?~(adapted from 2000 Math Kangaroo Problem, Level 3 - 4, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$36$$ "}], [{"aoVal": "B", "content": "$$38$$ "}], [{"aoVal": "C", "content": "$$40$$ "}], [{"aoVal": "D", "content": "$$42$$ "}], [{"aoVal": "E", "content": "$$44$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares->Basic Solid Square Problems"], "answer_analysis": ["It can be seen from the question that Bob and Tick have $8$ rows in front and $11$ rows in the back. There are $20$ rows in total, and there are two people in each row, so there are $40$ people in total. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10812", "queId": "b896adf0cd8441c1a3ca6261149917b9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Felix and Marmalade are two cats. Together they weigh $$10\\text{kg}$$. Felix weighs $$4\\text{kg}$$ less than Marmalade. How much does Marmalade weigh? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3\\text{kg}$$ "}], [{"aoVal": "B", "content": "$$6\\text{kg}$$ "}], [{"aoVal": "C", "content": "$$7 \\text{kg}$$ "}], [{"aoVal": "D", "content": "$$9\\text{kg}$$ "}], [{"aoVal": "E", "content": "$$14 \\text{kg}$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["It should be a moment\\textquotesingle s work to see that Felix weighs $$3\\text{kg}$$ , and Marmalade $$7\\text{kg}$$ . "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10817", "queId": "eeec830b54b7404197ffc290c20faa8f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $6\\text{cm}$ represents $50\\text{km}$ on a map and the actual distance between two towns is $125\\text{km}$, then their distance apart on the map is ． ", "answer_option_list": [[{"aoVal": "A", "content": "$8\\text{cm}$ "}], [{"aoVal": "B", "content": "$10\\text{cm}$ "}], [{"aoVal": "C", "content": "$15\\text{cm}$ "}], [{"aoVal": "D", "content": "$18\\text{cm}$ "}], [{"aoVal": "E", "content": "$12\\text{cm}$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["If $$6\\textasciitilde\\text{cm}$$ represents $$50\\textasciitilde\\text{km}$$, $$3\\textasciitilde\\text{cm}$$ represents $$25\\textasciitilde\\text{km}$$. So, their distance apart on the map is $$125\\div25\\times 3=15\\textasciitilde\\text{cm}$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10825", "queId": "afb500864735474190e4a69af1f773c9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In the yard there is an equal number of pigs, ducks and chickens. Together, they have $$144$$ legs. How many ducks are there in the yard? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$35$$ "}], [{"aoVal": "D", "content": "$$42$$ "}], [{"aoVal": "E", "content": "$$43$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"], "answer_analysis": ["Suppose there are $$x$$ ducks in the yard. Since there is an equal number of pigs, ducks and chickens, $$2x+4x+2x=144$$, $$x=18$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10828", "queId": "e148f89fac4c42348a20c0599453583e", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "How many days are there in exactly $$52$$ weeks? ", "answer_option_list": [[{"aoVal": "A", "content": "$$364$$ "}], [{"aoVal": "B", "content": "$$365$$ "}], [{"aoVal": "C", "content": "$$366$$ "}], [{"aoVal": "D", "content": "$$367$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["Each week has $$7$$ days, so $$52$$ weeks has $$52 \\times 7 = 364$$ days. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10829", "queId": "d83dc23a6ead4ab59f29daf001ead1bb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A \"combo\"~ticket to enter the fair and ride unlimited rides is ＄$$30$$. A``per ride\" ticket costs ＄$$12.50$$ to enter and ＄$$5$$ per ride. For a\"combo''ticket to cost less than a \"per ride\" ticket, a person must go on at least rides. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["A fair sells a``combo\" ticket for ＄$$30$$ entry and a ``per ride\" ticket for ＄$$12.50$$ to enter plus ＄$$5$$ per ride. A``per ride\" ticket costs ＄$$12.50+$$ ＄$$15 =$$＄$$27.50$$ for $$3$$ rides and ＄$$12.50 +$$ ＄$$20 = $$＄$$32.50$$ for $$4$$ rides. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10831", "queId": "cf337ba3004f414396571fba844d02cb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for $$24$$ hours. If she is using it constantly, the battery will last for only $$3$$ hours. Since the last recharge, her phone has been on $$9$$ hours, and during that time she has used it for $$60$$ minutes. If she doesn\\textquotesingle t use it any more but leaves the phone on, how many more hours will the battery last? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Simple Work Word Problems"], "answer_analysis": ["When not being used, the cell phone uses up $$\\dfrac{1}{24}$$ of its battery per hour. When being used, the cell phone uses up $$\\dfrac{1}{3}$$ of its battery per hour. Since Niki\\textquotesingle s phone has been on for $$9$$ hours, of those $$8$$ simply on and~~being used to talk, $$8\\left(\\dfrac{1}{24}\\right)+1\\left(\\dfrac{1}{3}\\right)=\\dfrac{2}{3}$$ of its battery has been used up. To drain the remaining $$\\dfrac{1}{3}$$ the phone can last for $$\\dfrac{\\dfrac{1}{3}}{\\dfrac{1}{24}}=\\boxed{(\\text{B})8}$$ more hours without being used. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10839", "queId": "fcdbfea5b37b44e2bd41668bf6b89bf0", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A worm is staying at the bottom of a well with a depth of $$11$$ meters. If it climbs up $$3$$ meters in the day time and slips down $$1$$ meter at night, which day will it climb up to the ground? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"], "answer_analysis": ["It climbs up $$3$$ meters in the day time and slips down $$1$$ meter at night, so it climbs up $$2$$ meters in a whole day. For the first $$4$$ days, it climbs $$8$$ meters. During the day time of the fifth day, it climbs $$3$$ meters and reaches the ground. Then it needs five days to climb up to the ground. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10841", "queId": "d8516c9a20bb4c3da9ed8ba840c6f48b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The sum of the ages of Anita and Peter is $$20$$ years. What is the sum of their ages three years ago? ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$17$$ "}], [{"aoVal": "C", "content": "$$14$$ "}], [{"aoVal": "D", "content": "$$11$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Basic Sum and Differences Problems in Age Problems"], "answer_analysis": ["$20-3\\times2=14$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10842", "queId": "cac7c619987d42a29c06c3caebda43ed", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "James makes a long noodle. He takes some bites of the noodle, each time eating $5$ cm of the noodle from the middle of only one piece. At last, he has $12$ pieces of the noodle with the total length of $24$ cm. How long was the entire noodle in cm at the beginning? (Adapted from 2022 AMC 8 Problem, Question \\#11) ", "answer_option_list": [[{"aoVal": "A", "content": "$$94$$ "}], [{"aoVal": "B", "content": "$$89$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$79$$ "}], [{"aoVal": "E", "content": "$$75$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["There are $12$ pieces of noodle left, so he takes $12-1=11$ bites of the noodle. Thus, the length of the noodle he ate is $11\\times5=55$ cm. The total length of the entire noodle was $55+24=79$ cm. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10844", "queId": "dce2d446acf74baab5a3ef6428497dcb", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "A mixture of $25$ liters of paint is $16 \\textbackslash\\%$ red tint, $24\\textbackslash\\%$ yellow tint and $60\\textbackslash\\%$ water. $15$ liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (adapted from 2007 AMC 8, Question \\#17 ) ", "answer_option_list": [[{"aoVal": "A", "content": "$$52.5$$ "}], [{"aoVal": "B", "content": "$$55$$ "}], [{"aoVal": "C", "content": "$$57.5$$ "}], [{"aoVal": "D", "content": "$$60$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["The original mixture contains $25\\times 24\\textbackslash\\% = 6$ liters of yellow tint. $$15$$ liters of yellow tint is added to the mixture, the new mixture now has $6+15=21$ liters of yellow tint. New percent of yellow =$\\frac{21}{25+15} =52.5\\textbackslash\\% $ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10845", "queId": "fce2f9c0b015465787ca31eeba5c79bc", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Edwin has three flowers, one red, one blue and one yellow. They have $50$ petals in total. The blue flower has $4$ petals less than the red one and $5$ petals more than the yellow one. How many petals does the red flower have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$13$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$21$$ "}], [{"aoVal": "E", "content": "$$22$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Word Problems Involving Comparing and Ordering"], "answer_analysis": ["Blue: $(50 + 5 - 4) \\div 3 = 17$ Red: $17 + 4 = 21$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10846", "queId": "ea8ae7e5ea5d4903af610ef23198ec6f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mike has a bookcase with three layers, and the proportion of books placed on the upper, middle and lower layers is $$5:6:4$$. Given that there are $$240$$ books on the middle level, books should be removed from middle level and added to the lower level so that the number of books on each level can be exactly the same. ", "answer_option_list": [[{"aoVal": "A", "content": "$$48$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$60$$ "}], [{"aoVal": "D", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with an Invariant Part"], "answer_analysis": ["Lower level: $$240\\div6\\times4=160$$, The number of books to be added to the lower level: $$(240-160)\\div2=40$$. So, the answer is $$\\text{B}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10855", "queId": "bd5608e79fb641ee82c5bd4efc82c96f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Barb likes to help her father with housework. She dusts every $3$ days, sweeps every $4$ days, and cooks dinner every $5$ days. If she does all $3$ chores on one Sunday, she next does all $3$ on the same day on a ． ", "answer_option_list": [[{"aoVal": "A", "content": "Wednesday "}], [{"aoVal": "B", "content": "Thursday "}], [{"aoVal": "C", "content": "Friday "}], [{"aoVal": "D", "content": "Saturday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["The least common multiple of $3$, $4$ and $5$ is $60$. We know that $60\\div7=8\\ldots\\ldots4$, then the remainder tells us that it will be on Thursday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10861", "queId": "f859175dd7e743ecb21e03a74af1bff1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "This year, October $$28$$ falls on a Sunday. What day of the week will it be after $$38$$ days? (adapted from 2015 Math Kangaroo Problem, Level 3-4, Question \\#8) ", "answer_option_list": [[{"aoVal": "A", "content": "Wednesday "}], [{"aoVal": "B", "content": "Thursday "}], [{"aoVal": "C", "content": "Tuesday "}], [{"aoVal": "D", "content": "Friday "}], [{"aoVal": "E", "content": "Sunday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$$38\\div7=5 \\text{R} 3$$, three days after Sunday, which is Wednesday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10862", "queId": "bd5b7c4ea0c04ba2b4219b56e674c081", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A family made a $$100\\text{km}$$ trip. For half the distance, they drove at $$50\\text{km}$$~ per hour; for the other half, they drove at $$25\\text{km}$$~ per hour How many hours did this trip take? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["For the first $$50\\text{km}$$, they drove at $$50\\text{km/hr}$$-that took $$1\\text{hr}$$. For the other second $$50\\text{km}$$, they drove at $$25\\text{km/hr}$$-that took $$2\\text{hrs}$$ . The trip took $$3\\text{hrs}$$ . "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10863", "queId": "c656052f1ecc4f1e988bc8aba1c123ea", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "James has $600$ g of a $$8\\textbackslash\\%$$ salt solution, and then $120$ g of water evaporates. Find the percent concentration of salt solution at this time. ", "answer_option_list": [[{"aoVal": "A", "content": "$10\\textbackslash\\%$ "}], [{"aoVal": "B", "content": "$12\\textbackslash\\%$ "}], [{"aoVal": "C", "content": "$15\\textbackslash\\%$ "}], [{"aoVal": "D", "content": "$18\\textbackslash\\%$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"], "answer_analysis": ["$$600\\times 8\\textbackslash\\%=48$$ g, $$600-120=480$$ g, $$48\\div 480\\times 100\\textbackslash\\%=10\\textbackslash\\%$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10866", "queId": "c1dfd36b8b8a464a877aa32fb1daf406", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Alex is $8$ years older than her two sisters who are twins. The sum of the ages of all three girls is $32$ years old. How old is Alex? ($2007$ Math Kangaroo Problem, Level $5$-$6$, Question \\#$9$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$12$$ "}], [{"aoVal": "B", "content": "$$18$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["The age of each twin is $(32-8) \\div 3 =8$ years old. Thus, Alex is $8 +8 =16$ years old. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10868", "queId": "f86310003b5e4716bbb570b3e2a5319d", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The rabbit Cici picks mushrooms in the forest. She finds one mushroom every $5$ meters, and she finds $8$ mushrooms in total. How long does Cici walk from where she finds the first mushroom to where she finds the last one? ", "answer_option_list": [[{"aoVal": "A", "content": "$$13$$ "}], [{"aoVal": "B", "content": "$$35$$ "}], [{"aoVal": "C", "content": "$$36$$ "}], [{"aoVal": "D", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["There are $8-1=7$ spaces. $7\\times 5=35$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10875", "queId": "dd09551c3d2040c98f687424453295c8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Given March $$25$$ of a certain year is Monday, what day of the week would May $$1$$ fall on that year? ． ", "answer_option_list": [[{"aoVal": "A", "content": "Tuesday "}], [{"aoVal": "B", "content": "Wednesday "}], [{"aoVal": "C", "content": "Thursday "}], [{"aoVal": "D", "content": "Friday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$$1$$ May is $$6+30+1=37$$ days after March $$25$$. Since $$37\\div7=5 \\text{ R }2$$, $$5$$ weeks after is still Monday and $$2$$ days after that is a Wednesday. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10877", "queId": "f872d69250cb44339f248088ab3d7346", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jane released a homing pigeon at $$5:30\\rm$$ a.m.. The pigeon arrived at its destination at $$11:30\\rm$$ a.m.. How many miles did the pigeon travel if it flies $$120$$ miles in $$2$$ hours? (adapted from 2007 Math Kangaroo Problem, Level 5-6, Question \\#18) ", "answer_option_list": [[{"aoVal": "A", "content": "$$120$$ "}], [{"aoVal": "B", "content": "$$720$$ "}], [{"aoVal": "C", "content": "$$360$$ "}], [{"aoVal": "D", "content": "$$300$$ "}], [{"aoVal": "E", "content": "$$420$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["The flying speed is $$120\\div2=60$$ miles/hr, and the flying time is $$11:30-5:30=6$$ hours. So, the total distance is $$60\\times 6=360$$ miles. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10878", "queId": "d880a796509f493ca64dbfc21040d942", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A bag of toffee is $8$ dollars, a bag of cotton candy is $6$ dollars, and a bag of orange candy is $13$ dollars. Now, the candy shop decides to mix $30$ bags of toffee, $50$ bags of cotton candy, and $20$ bags of orange candy for $100$ bags of assorted candy. What should be the price of the assorted candy in dollars to keep the total revenue unchanged? ", "answer_option_list": [[{"aoVal": "A", "content": "$$7.5$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9.5$$ "}], [{"aoVal": "D", "content": "$$10$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["Total revenue: $30\\times 8+50\\times 6+20\\times 13=800$ dollars A bag of assorted candy: $$800\\div 100=8$$ dollars "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10879", "queId": "eab4c059f20b4c68bd1acf3c7b8aa509", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "There are some ducks and sheep in a farm. The number of sheep is $10$ more than ducks. The number of ducks is half the number of sheep. In total, how many ducks and sheep are there in the farm? ~ ", "answer_option_list": [[{"aoVal": "A", "content": "$26$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$33$$ "}], [{"aoVal": "D", "content": "$$39$$ "}], [{"aoVal": "E", "content": "$$40$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$10+10+10=30$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10881", "queId": "eab5d8df6c8e4746b94a05c0950f393a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Pat paints twice as fast as Lee. If it took Lee $6$ hours to paint a room, how long would it have taken if both had painted the room together? ", "answer_option_list": [[{"aoVal": "A", "content": "$2$ hours "}], [{"aoVal": "B", "content": "$3$ hours "}], [{"aoVal": "C", "content": "$9$ hours "}], [{"aoVal": "D", "content": "$18$ hours "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"], "answer_analysis": ["Lee paints the room once in $6$ hours. Pat paints the room twice in $6$ hours. Together, they paint the room $3$ times in $6$ hours. So, it takes them $2$ hours to paint it once together. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10883", "queId": "eab84d29c50f4431ae3a5bdf454ce089", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Ben and Ken have some books. After Ben sends $4$ books to Ken, he has $1$ fewer book than Ken. Which of the following is true? ", "answer_option_list": [[{"aoVal": "A", "content": "Originally, Ben had $3$ more books than Ken. "}], [{"aoVal": "B", "content": "Originally, Ben had $4$ more books than Ken. "}], [{"aoVal": "C", "content": "Originally, Ben had $1$ fewer book than Ken. "}], [{"aoVal": "D", "content": "Originally, Ben had $9$ more books than Ken. "}], [{"aoVal": "E", "content": "Originally, Ben had $7$ more books than Ken. "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$4+4-1=7$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10886", "queId": "b8f7de5669c54c3f8bddf07da035b750", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "John bought $10$ pencils and notebooks in total for £$44$. Each pencil cost £$$2$$. Each notebook costs £$$8$$. How many notebooks did John buy? ", "answer_option_list": [[{"aoVal": "A", "content": "$$4$$ "}], [{"aoVal": "B", "content": "$$5$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$7$$ "}], [{"aoVal": "E", "content": "$$8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"], "answer_analysis": ["If all were pencils, $10\\times 2= 20$ the total cost would be £$$20$$. $44- 20=24$ The difference is £$$24$$. $8-2=6$ $24\\div 6=4$ John bought $4$ notebooks. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10888", "queId": "c67b7463cfcb46ae9a200fb4b12db722", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Lily\\textquotesingle s age plus Judy\\textquotesingle s age was equal to $$17$$ two years ago. What is the sum of their ages this year? (adapted from 2016 Math Kangaroo Problem, Level 1-2, Question \\#16) ", "answer_option_list": [[{"aoVal": "A", "content": "$$16$$ "}], [{"aoVal": "B", "content": "$$17$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$19$$ "}], [{"aoVal": "E", "content": "$$21$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Sum of Ages"], "answer_analysis": ["$17 + 2 \\times 2 = 21$ "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10889", "queId": "cb04b9ba8ef54e68aa7742dd6a8105e6", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If I start with $2$, and begin to count by $$3\\textquotesingle$$s, my $50^{}\\text{th}$ number will be~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$148$$ "}], [{"aoVal": "B", "content": "$$149$$ "}], [{"aoVal": "C", "content": "$$150$$ "}], [{"aoVal": "D", "content": "$$151$$ "}], [{"aoVal": "E", "content": "$$152$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression"], "answer_analysis": ["$2+(50-1)\\times3=149$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10893", "queId": "f88d93c0be73464f8dd106863d5e53b7", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Jucy and Nicole are celebrating their birthdays together. Seven years ago, when Jucy turned $6$ years old, she received a newborn cat as a birthday present. Today the sum of the ages of the two people and the cat is $34$ years. Jucy is~\\uline{~~~~~~~~~~}~years younger than Nicole. ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"], "answer_analysis": ["Seven years ago: Jucy : $7$ cat: $$0$$ This year: Jucy : $7+6=13$ cat: $0+7=7$ Nicole : $34-13-7=14$$ $$14-13=1$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10894", "queId": "e63bc810b05a44a6af4b5315a7cec303", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Bowen has $$40$$ grams of a $$25\\textbackslash\\%$$ sugar solution. After~\\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of the solution is $$40\\textbackslash\\%$$. (Evaporate: the water turns from liquid into vapor and is no longer in the solution anymore.) ", "answer_option_list": [[{"aoVal": "A", "content": "$$15$$ grams "}], [{"aoVal": "B", "content": "$$12$$ grams "}], [{"aoVal": "C", "content": "$$9$$ grams "}], [{"aoVal": "D", "content": "$$6$$ grams "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"], "answer_analysis": ["$$40-40\\times25\\textbackslash\\%\\div40\\textbackslash\\%=40-25=15$$ grams. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10903", "queId": "d41ec1beecf04ed99fd65db4265077b1", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Tom goes to the supermarket to buy egg tarts. There are two kinds of egg tarts. One has $$6$$ tarts in the box and the other has $$10$$ tarts in the box. The unit price of the egg tarts is the same. If Tom wants $$76$$ egg tarts, how many boxes does he need at least?~(adapted from 2011 Math Kangaroo Problem, Level 3 - 4, Question \\#10) ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$8$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$11$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["$$76=10+10+10+10+10+10+10+6$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10908", "queId": "f8a5f577bf8a445881a0be7fe49a9a40", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A gift store buys some gifts at＄$$125$$ each. It wants to earn＄$$25 $$ for each gift after a discount of $$25 \\textbackslash\\% $$. What is the selling price before the discount for each gift? ", "answer_option_list": [[{"aoVal": "A", "content": "$$160$$ dollars "}], [{"aoVal": "B", "content": "$$180$$ dollars "}], [{"aoVal": "C", "content": "$$190$$ dollars "}], [{"aoVal": "D", "content": "$$200$$ dollars "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["$$\\left( 125+25 \\right)\\div \\left( 1-25 \\textbackslash\\% \\right)=200$$ dollars. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10911", "queId": "c6a359a5e6b7450d926ddb79b0e044bf", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The average weight of $4$ students in Class $A$ is $37$ kilograms. The average weight of $11$ students in Class $B$ is $41$ kilograms. The total weight of $5$ students in Class $C$ is $161$ kilograms. What is the average weight of the students in the $3$ classes? ", "answer_option_list": [[{"aoVal": "A", "content": "$36$ kilograms "}], [{"aoVal": "B", "content": "$38$ kilograms "}], [{"aoVal": "C", "content": "$40$ kilograms "}], [{"aoVal": "D", "content": "$43$ kilograms "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$4 \\times 37 + 11 \\times 41+ 161 = 760$ kilograms in total. $760 \\div (4 + 11 + 5) = 38$ kg. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10913", "queId": "d8bfbee5febb463482a9e7bbd019fc32", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "It takes Mary $$30$$ minutes to walk uphill $$300 $$ m from her home to school, but it takes her only $$10$$ minutes to walk from school to home along the same route. What is her average speed, in m/min, for the round trip? (adapted from 2003 AMC 10 Problem, Question \\#4) ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$30$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"], "answer_analysis": ["Mary walks a total of $$300+300=600\\rm$$ meters in $$40$$ minutes. Average speed: $600\\div40=15$ m/min "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10915", "queId": "cfb3dee404c84707a8ee3b7e9e48b1a2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$6$$ cans of Sweet Stuff Soda all together contain $$96$$ teaspoons of sugar, then there are a total of teaspoons of sugar in $$15$$ cans. ", "answer_option_list": [[{"aoVal": "A", "content": "$$192$$ "}], [{"aoVal": "B", "content": "$$208$$ "}], [{"aoVal": "C", "content": "$$240$$ "}], [{"aoVal": "D", "content": "$$270$$ "}], [{"aoVal": "E", "content": "$$288$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"], "answer_analysis": ["If $$6$$ cans contain $$96$$ teaspoons of sugar, $$1$$ can contains $$96\\div6 = 16$$ teaspoons of sugar. Thus $$15$$ cans contain $$16\\times15 =240$$ teaspoons of sugar. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10916", "queId": "c2359d75d5a4409a84ea23dcbda94f8f", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Twenty-eight students from the fourth grade competed in a math competition. Each student earned a different number of points. The number of students who received more points than Tomek is two times smaller than the number of students who had fewer points than Tomek. In which position did Tomek finish that competition?~ ($2002$~Math Kangaroo Problem, Level $3-4$, Question \\#$23$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$\\textsuperscript{th} "}], [{"aoVal": "B", "content": "$10$\\textsuperscript{th} "}], [{"aoVal": "C", "content": "$8$\\textsuperscript{th} "}], [{"aoVal": "D", "content": "$9$\\textsuperscript{th} "}], [{"aoVal": "E", "content": "$7$\\textsuperscript{th} "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"], "answer_analysis": ["Except for Tomek, there are~$28-1=27$~students. The number of students who received more points than Tomek is~$27\\div(2+1)=9$, so Tomek is in the~$9+1=10^{th}$~place. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10917", "queId": "f417000eb34242e7a177b524a29aaebb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "January $$1$$, $$1989$$ was a Sunday. January $$1$$, $$1988$$ (a leap year) was a． ", "answer_option_list": [[{"aoVal": "A", "content": "Friday "}], [{"aoVal": "B", "content": "Saturday "}], [{"aoVal": "C", "content": "Sunday "}], [{"aoVal": "D", "content": "Monday "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["$$366$$ days $$=52$$ weeks $$2$$ days. Jan $$1$$ $$1988$$ is $$52$$ weeks $$2$$ days before Jan $$1$$ $$1989$$. This date in $$1988$$ is $$2$$ days before Sunday so it is on a Friday. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10921", "queId": "e66ed2c2c7b34bcc8a9f9f15e69f0eda", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Algebra books cost $$$12.50$$ each, and geometry books cost $$$14$$ each. How much do $$6$$ algebra books and $$5$$ geometry books cost in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$145.00$$ "}], [{"aoVal": "B", "content": "$$$146.50$$ "}], [{"aoVal": "C", "content": "$$$150.00$$ "}], [{"aoVal": "D", "content": "$$$151.50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["Six algebra books cost $$$12.50 \\times 6 = $75$$. Five geometry books cost $$$14\\times5 = $70$$. All together, they cost a total of $$$145$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10925", "queId": "eb04e626e45c407e8a9c9c8c47fa12d8", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In $$1975$$ it was estimated that there were $$250000$$ lions in Africa. Over $$40$$ years this figure has decreased by $$90\\textbackslash\\%$$. What is the current estimate for the number of lions in Africa ? ", "answer_option_list": [[{"aoVal": "A", "content": "$$25000$$ "}], [{"aoVal": "B", "content": "$$100000$$ "}], [{"aoVal": "C", "content": "$$160000$$ "}], [{"aoVal": "D", "content": "$$225000$$ "}], [{"aoVal": "E", "content": "$$275000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["A $$90\\textbackslash\\%$$ decrease means $$10\\textbackslash\\%$$ of $$250000 = 250000 \\div 10 = 25000$$ of the lions remain. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10927", "queId": "cfc8a365056048e3bdebc44c41a51a1d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A test is with a full score of $100$ points. Five students in a group wants to reach an average of $91$ points. If everyone scores a different whole number, the lowest score among them could be~\\uline{~~~~~~~~~~}~. ", "answer_option_list": [[{"aoVal": "A", "content": "$$60$$ "}], [{"aoVal": "B", "content": "$$61$$ "}], [{"aoVal": "C", "content": "$$67$$ "}], [{"aoVal": "D", "content": "$$70$$ "}], [{"aoVal": "E", "content": "$$71$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "], "answer_analysis": ["$91\\times5-(100+99+98+97)=61$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10931", "queId": "c24f96a3cb04418d919e14ab2e028fb9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jack\\textquotesingle s sister is $$22$$ years old, which is $$2$$ less than $$4$$ times Jack\\textquotesingle s age. Assume Jack is $$x$$ years old, then． ", "answer_option_list": [[{"aoVal": "A", "content": "$$x=4$$ "}], [{"aoVal": "B", "content": "$$x=5$$ "}], [{"aoVal": "C", "content": "$$x=6$$ "}], [{"aoVal": "D", "content": "$$x=8$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"], "answer_analysis": ["The equation can represents this situation is $$4x-2=22$$, so, $$4x=24$$, $$x=6$$. So, the answer is $$6$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10935", "queId": "c6d52006a4af459d8edb41c932accb55", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Jason and Ross are in line to check tickets. There are $36$ people in front of Jason and $16$ people behind. Ross happens to be in the middle of the entire line. How many people are there between Ross and Jason?~(adapted from 2000 Math Kangaroo Problem, Level 3 - 4, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$18$$ "}], [{"aoVal": "B", "content": "$$17$$ "}], [{"aoVal": "C", "content": "$$16$$ "}], [{"aoVal": "D", "content": "$$15$$ "}], [{"aoVal": "E", "content": "$$14$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares->Basic Solid Square Problems"], "answer_analysis": ["The total: $36+16+1=53$ , Jack\\textquotesingle s location: $$(53-1)\\div2=21$$, so there are $15$ people between Jack and Rose. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10939", "queId": "efadc5a5662d49d7b3e2cab50238d6d7", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Amy mixes $$30$$ grams of a $$30\\textbackslash\\%$$ salt solution and $$20$$ grams of a $$20\\textbackslash\\%$$ salt solution together. How many grams of water should she add to the mixture to make it a $$10\\textbackslash\\% $$ solution? ", "answer_option_list": [[{"aoVal": "A", "content": "$$70$$ "}], [{"aoVal": "B", "content": "$$72$$ "}], [{"aoVal": "C", "content": "$$75$$ "}], [{"aoVal": "D", "content": "$$80$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"], "answer_analysis": ["$$30\\times30\\textbackslash\\%+20\\times 20\\textbackslash\\%=9+4=13$$ ounces. $$13\\div10\\textbackslash\\%-(30+20)=80$$ ounces. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10942", "queId": "eb2afccdc85f485683aa23fe19a16d70", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "$$12$$ dogs are cqually divided into $$3$$ groups, how many dogs are there in each group. ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$6$$ "}], [{"aoVal": "D", "content": "$$2$$ "}], [{"aoVal": "E", "content": "$$12$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$12\\div3=4$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10944", "queId": "f44dcc3392324978bbab9b65020652ab", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My pet frog jumps $$3\\text{m}$$ per jump. If it wants to jump from one end of a $$100\\text{m}$$ field to another, the least number of jumps it will take is． ", "answer_option_list": [[{"aoVal": "A", "content": "$$33$$ "}], [{"aoVal": "B", "content": "$$34$$ "}], [{"aoVal": "C", "content": "$$70$$ "}], [{"aoVal": "D", "content": "$$97$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"], "answer_analysis": ["Since $$100\\div 3=33$$ with remainder $$1$$, it takes my frog $$33$$ jumps to jump $$99\\text{m}$$. It needs $$1$$ more jump, for $$34$$ jumps in all, to go at least $$100\\text{m}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10952", "queId": "c70a24e2530544d88f92317979862f7a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In $$2010$$, the Math Kangaroo competition is taking place in some schools for the $19$\\textsuperscript{th}~time. Alice took part in the $10$\\textsuperscript{th}~Math Kangaroo when she was $$9$$ years old. In what year was Alice born? (Adapted from 2008 Math kangaroo Problem, Level 3-4, Question \\#9) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1996$$ "}], [{"aoVal": "B", "content": "$$1994$$ "}], [{"aoVal": "C", "content": "$$1992$$ "}], [{"aoVal": "D", "content": "$$1990$$ "}], [{"aoVal": "E", "content": "$$1988$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Time"], "answer_analysis": ["The $10$\\textsuperscript{th}~Math Kangaroo was taking place in $2001$, which means that Alice was $9$ years old in $2001$, so she was born in $1992$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10954", "queId": "e6be2d2a80c643ef85a9aa3f83c3217a", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Half a loaf of bread costs $$6$$ pence more than one-fourth of a loaf of bread. How many pence does a whole loaf of bread cost? ", "answer_option_list": [[{"aoVal": "A", "content": "$$6$$ "}], [{"aoVal": "B", "content": "$$12$$ "}], [{"aoVal": "C", "content": "$$18$$ "}], [{"aoVal": "D", "content": "$$24$$ "}], [{"aoVal": "E", "content": "$$30$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"], "answer_analysis": ["One-fourth of a loaf of bread is ``$$1$$.'' Half a loaf of bread is ``$$2$$.'' One-fourth of a loaf of bread: $$6 \\div (2-1) =6$$. A whole loaf of bread: $$6 \\times 4 =24$$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10959", "queId": "ddb2e175ea3d44748618401e363b1485", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Ben has $$9$$ pairs of shoes, of which $$4$$ shoes are red, $$2$$ shoes are bule, and the rest are green. How many pairs of shoes are green? ", "answer_option_list": [[{"aoVal": "A", "content": "$$3$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$4$$ "}], [{"aoVal": "D", "content": "$$5$$ "}], [{"aoVal": "E", "content": "$$7$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"], "answer_analysis": ["$$9-2-1=6$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10962", "queId": "f91f556c65a748248c7168a2fb259d85", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Antonette gets $70 \\textbackslash\\%$ on a 10 -problem test, $80 \\textbackslash\\%$ on a 20 -problem test and $90 \\textbackslash\\%$ on a 30 -problem test. If the three tests are combined into one 60 problem test, which percent is closest to her overall score? (2006 AMC 8, Question \\#12) ", "answer_option_list": [[{"aoVal": "A", "content": "$$40$$ "}], [{"aoVal": "B", "content": "$$77$$ "}], [{"aoVal": "C", "content": "$$80$$ "}], [{"aoVal": "D", "content": "$$83$$ "}], [{"aoVal": "E", "content": "$$87$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$70 \\textbackslash\\% \\cdot 10=7$ $80 \\textbackslash\\% \\cdot 20=16$ $90 \\textbackslash\\% \\cdot 30=27$ Adding them up gets $7+16+27=50$. The overall percentage correct would be $\\frac{50}{60}=\\frac{5}{6}=5 \\cdot 16 . \\overline{6}=83 . \\overline{3} \\approx(\\mathbf{D}) 83$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10966", "queId": "e24822c2e3224c60bb569e44d1e04098", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Rick and Roy each stands at different ends of a straight road that is $$2021$$m long. They run toward each other. Rick\\textquotesingle s speed is $$21\\text{m/s}$$ and Roy\\textquotesingle s speed is $$22\\text{m/s}$$. They will meet in~\\uline{~~~~~~~~~~}~seconds. ", "answer_option_list": [[{"aoVal": "A", "content": "$$35$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$47$$ "}], [{"aoVal": "D", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$$2021\\div (21+22)=47$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10969", "queId": "e6dfee64ce534a96b65e50bca1e747e2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "You have $12$ green cards and the ratio of your red cards to green cards is $3:2$. How many cards do you have? ", "answer_option_list": [[{"aoVal": "A", "content": "$18$ "}], [{"aoVal": "B", "content": "$20$ "}], [{"aoVal": "C", "content": "$$24$$ "}], [{"aoVal": "D", "content": "$30$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"], "answer_analysis": ["$12$ is the product of $6$ and $2$.Then multiple $3$ by $6$ is the number of red cards. The total number of cards is $30$. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10970", "queId": "eb73455750894407b59cb7ce7c9dbbdc", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Chloe and Zoe are both students in Ms. Demeanor\\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to $80\\textbackslash\\%$ of the problems she solved alone, but overall $90\\textbackslash\\%$ of her answers were correct. Zoe had correct answers to $75\\textbackslash\\%$ of the problems she solved alone. What was Zoe\\textquotesingle s overall percentage of correct answers? (2017 AMC 8, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$87.5$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$92.5$$ "}], [{"aoVal": "D", "content": "$$95.5$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Assume the total amount of problems is 100 per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got 80 problems correct by herself, and got 180 problems correct overall. We also know that Zoe had 75 problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $180-80=100$. Therefore Zoe has $100+75=175$ problems out of $200$ problems correct. Thus $\\frac{175}{200} = 87.5$ percent. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10973", "queId": "d4be355c5b884316955a09e6f19880b9", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Mr. $$A$$ owns a home worth ＄$$10000$$. He sells it to Mr. $$B$$ at a $$10\\textbackslash\\%$$ profit based on the worth of the house. Mr. $$B$$ sells the house back to Mr. $$A$$ at a $$10\\textbackslash\\%$$ loss. Then: ($$1951$$ AHSME Problem, Question \\#$$5$$) ", "answer_option_list": [[{"aoVal": "A", "content": "$$A$$ comes out even "}], [{"aoVal": "B", "content": "$$A$$ makes ＄$$1100$$ on the deal "}], [{"aoVal": "C", "content": "$$A$$ makes ＄$$1000$$ on the deal "}], [{"aoVal": "D", "content": "$$A$$ loses ＄$$900$$ on the deal "}], [{"aoVal": "E", "content": "$$A$$ loses ＄$$1000$$ on the deal "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["Mr. $$ A$$ sells his home for $$(1 + 10\\textbackslash\\%)\\times 10000$$ dollars$$= 1.1\\times 10000$$ dollars$$ = 11000$$ dollars to Mr. $$ B$$. Then, Mr. $$ B$$ sells it at a price of $$(1- 10\\textbackslash\\%)\\times 11000$$ dollars $$= 0.9\\times 11000$$ dollars $$= 9900$$ dollars, thus $$11000- 9900=\\boxed{ (\\rm B) \\textasciitilde A\\textasciitilde makes\\textasciitilde1100\\textasciitilde on\\textasciitilde the\\textasciitilde deal}$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10974", "queId": "f93a88544cf444eeb54911c7d24fe08b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A $60\\textbackslash\\%$ alcohol solution contains $120$ grams of water. How many grams of solution are there? ", "answer_option_list": [[{"aoVal": "A", "content": "$$200$$ "}], [{"aoVal": "B", "content": "$$250$$ "}], [{"aoVal": "C", "content": "$$300$$ "}], [{"aoVal": "D", "content": "$$400$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"], "answer_analysis": ["$120\\div(1-60\\textbackslash\\%)=300$ ounces. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10975", "queId": "f005c813b48d4889866c96fc9515388b", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "A, B, C, D and E sit around a circular table in that order. A starts by saying \"$$100$$\", B says \"$$101$$\", C says~\"$$102$$\" and so on round the table. Who will eventually say\"$$2023$$\"? ", "answer_option_list": [[{"aoVal": "A", "content": "$$$$A "}], [{"aoVal": "B", "content": "$$$$B "}], [{"aoVal": "C", "content": "$$$$Cain "}], [{"aoVal": "D", "content": "$$$$Devi "}], [{"aoVal": "E", "content": "$$$$Emily "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Circular Operations"], "answer_analysis": ["After Amit says \"$$2015$$\", there are $$5102-2015=3087$$ numbers remaining. Thus the counting goes round the table $$3087\\div6= 514$$ times with a remainder of $$3$$, so the last to count is Devi. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10976", "queId": "eb7b6431d7864b0da46a806ccc5f9888", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Brown wants to put some board between his books. He has $10$ books in total. If he wants to put one board between every two adjacent books, how many boards does he need to prepare? ", "answer_option_list": [[{"aoVal": "A", "content": "$$9$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$11$$ "}], [{"aoVal": "D", "content": "$$12$$ "}], [{"aoVal": "E", "content": "$$13$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"], "answer_analysis": ["$10 - 1 = 9$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10977", "queId": "f0066ee74aea417f880ec1c14d83ad55", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a class of $$18$$ students, $$6$$ are wearing jeans. What is the ratio of students wearing jeans to students not wearing jeans? ", "answer_option_list": [[{"aoVal": "A", "content": "$$1:2$$ "}], [{"aoVal": "B", "content": "$$1:3$$ "}], [{"aoVal": "C", "content": "$$2:3$$ "}], [{"aoVal": "D", "content": "$$2:1$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"], "answer_analysis": ["If $$6$$ students are wearing jeans, then $$18-6=12$$ are not. The ratio of students wearing jeans to students not wearing jeans is $$6:12=1:2$$. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10981", "queId": "f00cf6290ccd41a7a563bade34da8939", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "How many two-digit numbers are divisible by $3$ but not by $6$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$14$$ "}], [{"aoVal": "B", "content": "$$15$$ "}], [{"aoVal": "C", "content": "$$17$$ "}], [{"aoVal": "D", "content": "$$30$$ "}], [{"aoVal": "E", "content": "None of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division"], "answer_analysis": ["There are $99$ $4-3 = 33$-multiples of $3$ less than $100$. $3$ of them are one-digit numbers: $3$, $6$ and $9$. Hence there are $30$ $2$-digit multiples of $3$. Similarly, there are $96 + 6 -1 = 16 -1 = 15$ $2$-digit multiples of $6$. Hence, the answer is 30 - 15 = \\textbf{15.} Answer： \\textbf{(B)} "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10982", "queId": "d4c9f344a62348df844a9a674d0e9737", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Water from the first faucet fills the swimming pool in $70$ minutes. Water from each of the two other faucets fills the same swimming pool $3$ times faster. In how many minutes will the swimming pool be filled if all three faucets are opened? ", "answer_option_list": [[{"aoVal": "A", "content": "$$210$$ "}], [{"aoVal": "B", "content": "$$40$$ "}], [{"aoVal": "C", "content": "$$30$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$10$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems"], "answer_analysis": ["The efficiency of the first faucet is $\\frac1{70}$ and that of the other two is $\\frac3{70}$. Thus, it takes $1\\div (\\frac1{70}+\\frac3{70}\\times2)=10$ minutes to fill the pool. "], "answer_value": "E"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10983", "queId": "d4caf0a4f7e049b3ad2b5d92aba1bbee", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Chloe and Zoe are both students in Ms. Demeanor\\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to $80\\textbackslash\\%$ of the problems she solved alone, but overall $90\\textbackslash\\%$ of her answers were correct. Zoe had correct answers to $75\\textbackslash\\%$ of the problems she solved alone. What was Zoe\\textquotesingle s overall percentage of correct answers? (adapted from 2017 AMC 8, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$87.5$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$92.5$$ "}], [{"aoVal": "D", "content": "$$95.5$$ "}], [{"aoVal": "E", "content": "$$100$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Assume the total amount of problems is 100 per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got 80 problems correct by herself, and got 180 problems correct overall. We also know that Zoe had 75 problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $180-80=100$. Therefore Zoe has $100+75=175$ problems out of $200$ problems correct. Thus $\\frac{175}{200} = 87.5$ percent. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10984", "queId": "eb856f9de2cc4a59a6402401de56b7ed", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There is an empty tank which needs $29$ bottles of water to fill with. The workers pour $5$ bottles of water during the day, but uses $1$ bottle of water during the night. In how many days can the tank be filled with water? ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$6$$ "}], [{"aoVal": "C", "content": "$$7$$ "}], [{"aoVal": "D", "content": "$$8$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["Every day: $5-1=4$ bottles. $29\\div4=7R1$ But for the last day, the tank can be filled with water without using during the night. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "10986", "queId": "e6f6b3835f9d49b0911843affde2934f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The selling price of a sofa set is＄$$6500$$ and the profit percentage is $$30\\textbackslash\\%$$ for each set sold. If the cost of the sofa set is not changed, what is the profit percentage if the profit is ＄$$1200$$? ", "answer_option_list": [[{"aoVal": "A", "content": "$$20\\textbackslash\\%$$ "}], [{"aoVal": "B", "content": "$$24\\textbackslash\\%$$ "}], [{"aoVal": "C", "content": "$$25\\textbackslash\\%$$ "}], [{"aoVal": "D", "content": "$$30\\textbackslash\\%$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"], "answer_analysis": ["$$6500\\div(1+30\\textbackslash\\%)=5000$$, $$1200\\div5000=24\\textbackslash\\%$$. "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11001", "queId": "f4cfdd12e1104c6196a8e57cbb3b65d4", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Owen sees an archery right after he entered the carnival. After Owen takes 20 shots, he has made $55 \\textbackslash\\%$ of his shots. After he takes 5 more shots, he raises his percentage to $56 \\textbackslash\\%$. How many of the last 5 shots did she make?~ (adapted from 2004 AMC 8, Question\\#6) ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$2$$ "}], [{"aoVal": "C", "content": "$$3$$ "}], [{"aoVal": "D", "content": "$$4$$ "}], [{"aoVal": "E", "content": "$$5$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Owen made $0.55 * 20=11$ shots originally. Letting $x$ be the number of shots she made, we have $\\frac{11+x}{25}=0.56$. Solving for $x$ gives us $x=$ (C) 3 "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11014", "queId": "e736c16ff8314588a37ac98176e10375", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "I read $1$ page of a book on Nov $1$, $2$ pages on Nov $2$, $3$ pages on Nov $3$, and so on. I followed this pattern for the whole month. Altogether, how many pages did I read in November? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$31$$ "}], [{"aoVal": "C", "content": "$$465$$ "}], [{"aoVal": "D", "content": "$$496$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem"], "answer_analysis": ["There are in total $30$ days in Nov. $1+2+3+4+\\cdots+30=(1+30)\\times30\\div2=465$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11018", "queId": "fe2f48a2876c4e2182ab55fcfb778a97", "competition_source_list": ["其它"], "difficulty": "2", "qtype": "single_choice", "problem": "Chloe and Zoe are both students in Ms. Demeanor\\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to $90 \\textbackslash\\%$ of the problems she solved alone, but overall $84 \\textbackslash\\%$ of her answers were correct. Zoe had correct answers to $80 \\textbackslash\\%$ of the problems she solved alone. What was Zoe\\textquotesingle s overall percentage of correct answers? (adapted from 2017 AMC 8, Question \\#14) ", "answer_option_list": [[{"aoVal": "A", "content": "$$79$$ "}], [{"aoVal": "B", "content": "$$82$$ "}], [{"aoVal": "C", "content": "$$84$$ "}], [{"aoVal": "D", "content": "$$86$$ "}], [{"aoVal": "E", "content": "$$88$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["Assume the total amount of problems is $100$ per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got $90$ problems correct by herself, and got $168$ problems correct overall. We also know that Zoe had $80$ problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $168-90=78$. Therefore Zoe has $80+78=158$ problems out of $200$ problems correct. This is (C) $79$ percent. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11021", "queId": "f066ad13f1af4cfe932463194bd43981", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "If $$15^{}\\text{th}$$April is Friday, what day of the week is $$1$$\\textsuperscript{st~}April ? ", "answer_option_list": [[{"aoVal": "A", "content": "Sunday　 "}], [{"aoVal": "B", "content": "Monday　 "}], [{"aoVal": "C", "content": "Wednesday　 "}], [{"aoVal": "D", "content": "Friday　 "}], [{"aoVal": "E", "content": "Saturday　 "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"], "answer_analysis": ["There are 14 days between $$1$$\\textsuperscript{st~}April and $$15^{}\\text{th}$$April. 14 days = 2 week Therefore, $$1$$\\textsuperscript{st~}April is Friday. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11025", "queId": "f50915c336e745ba9c6804acc93cc4e3", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Grandma made some cheese dumplings and some blueberry dumplings. Altogether, she made $$31$$ dumplings. If she had made $$11$$ more cheese dumplings, then there would be the same number of blueberry dumplings as cheese dumplings. How many cheese dumplings did grandma make?（$$2009$$ Math Kangaroo Problem, Levels $$1-2$$, Question \\#$$19$$） ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["$$(31-11)\\div2=10.$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11031", "queId": "f07e432e562344738c8da68471e83f39", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "A worm is staying at the bottom of a well with a depth of $$13$$ metres. If it climbs up $$4$$ metres in the day time and slips down $$1$$ metre at night, which day will it climb up to the ground? ", "answer_option_list": [[{"aoVal": "A", "content": "The $$4$$th day "}], [{"aoVal": "B", "content": "The $$5$$th day "}], [{"aoVal": "C", "content": "The $$6$$th day "}], [{"aoVal": "D", "content": "The $$7$$th day "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"], "answer_analysis": ["It climbs up $$4$$ metres in the day time and slips down $$1$$ metre at night, so it climbs up $$3$$ metres in a whole day. For the first $$3$$ days, it climbs $$9$$ metres. During the day time of the forth day, it climbs $$4$$ metres and reaches the ground. Then it needs four days to climb up to the ground. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11033", "queId": "f517c72c4420404fb04b325c6c44a936", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "The volume of a cuboid is $216$. What is the least sum of the length of all its edges? ", "answer_option_list": [[{"aoVal": "A", "content": "$$216$$ "}], [{"aoVal": "B", "content": "$$32$$ "}], [{"aoVal": "C", "content": "$$72$$ "}], [{"aoVal": "D", "content": "$$96$$ "}], [{"aoVal": "E", "content": "$$120$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value"], "answer_analysis": ["Given the product of three numbers, the smaller the difference, the smaller the sum. $6\\times6\\times6=216$, so the answer is $6\\times 12=72.$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11034", "queId": "f519edb62aed40618a7c3447ccaa855f", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "The state income tax where Kristin lives is levied at the rate of $$p\\textbackslash\\%$$ of the first ＄$$28000$$ of annual income plus $$ \\left( {p+2} \\right) \\textbackslash\\%$$ of any amount above ＄$$28000$$. Kristin noticed that the state income tax she paid amounted to $$ \\left( {p+0.25} \\right) \\textbackslash\\%$$ of her annual income. What was her annual income? ($$2001$$ AMC $$12$$ Problem, Question \\#$$3$$) ", "answer_option_list": [[{"aoVal": "A", "content": "＄$$28000$$ "}], [{"aoVal": "B", "content": "＄$$32000$$ "}], [{"aoVal": "C", "content": "＄$$35000$$ "}], [{"aoVal": "D", "content": "＄$$42000$$ "}], [{"aoVal": "E", "content": "＄$$56000$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"], "answer_analysis": ["Method $$1$$：$$Let$$ the income amount be denoted by $$A$$. We know that $$\\frac{A\\left( p+.25 \\right)}{100}=\\frac{28000p}{100}+\\frac{\\left( p+2 \\right)\\left( A-28000 \\right)}{100}$$ We can now try to solve for $$A$$: $$\\left( p+.25 \\right)A=28000p+Ap+2A-28000p-56000$$ $$0.25A=2A-56000$$ $$A=32000$$ so the answer is $$\\boxed{ \\text {B}}$$. Method $$2$$: Let $$A$$, $$T$$ be Kristin\\textquotesingle s annual income and the income tax total, respectively. Notice that　 $$T=p\\textbackslash\\%\\cdot 28000+\\left( p+2 \\right)\\textbackslash\\%\\cdot \\left( A-28000 \\right)$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde$$$$=\\left[ p\\textbackslash\\%\\cdot 28000+p\\textbackslash\\%\\cdot \\left( A-28000 \\right) \\right]+2\\textbackslash\\%\\cdot \\left( A-28000 \\right)$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde$$$$=p\\textbackslash\\%\\cdot A+2\\textbackslash\\%\\cdot \\left( A-28000 \\right)$$ We are also given that $$T=\\left( p+0.25 \\right)\\textbackslash\\%\\cdot A=p\\textbackslash\\%\\cdot A+0.25\\textbackslash\\%\\cdot A$$ Thus, $$p\\textbackslash\\%\\cdot A+2\\textbackslash\\%\\cdot \\left( A-28000 \\right)=p\\textbackslash\\%\\cdot A+0.25\\textbackslash\\%\\cdot A$$ $$2\\textbackslash\\%\\cdot \\left( A-28000 \\right)=0.25\\textbackslash\\%\\cdot A$$ Solve for $$A$$ to obtain $$A=32000$$. $$\\boxed{ \\text {B}}$$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11038", "queId": "ebffdcfbaa844800a19d5142aac799cd", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Kate sold $$10$$ dresses and Tasha sold thrice as many dresses as Kate. How many dresses did Tasha sell? ", "answer_option_list": [[{"aoVal": "A", "content": "$$30$$ "}], [{"aoVal": "B", "content": "$$26$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$42$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$3$~$\\times$~$10$ = $30$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11046", "queId": "f9e949c676674428a6c6883e7582c92d", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "My cat snoozes for $$50$$ minutes in each hour. For how many hours a day does my cat snooze?　 ", "answer_option_list": [[{"aoVal": "A", "content": "$$5$$ "}], [{"aoVal": "B", "content": "$$10$$ "}], [{"aoVal": "C", "content": "$$15$$ "}], [{"aoVal": "D", "content": "$$20$$ "}], [{"aoVal": "E", "content": "$$50$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"], "answer_analysis": ["Sleeping for $$50$$ minutes every hour through the day is $$\\frac{5}{6}$$ of every hour and thus $$\\frac{5}{6}$$ of the day. Of $$24$$ hours, $$\\frac{5}{6}$$ is $$20$$ hours. "], "answer_value": "D"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11047", "queId": "fe86a8a236f84e06897b4344fa670b02", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "In a candy shop, the shopkeeper allows the exchange of $$3$$ sweet wrappers for $$1$$ new sweet. Peter has $$81$$ sweets at first. What is the largest possible number of sweets that Peter could have eaten? ", "answer_option_list": [[{"aoVal": "A", "content": "$$119$$ "}], [{"aoVal": "B", "content": "$$120$$ "}], [{"aoVal": "C", "content": "$$121$$ "}], [{"aoVal": "D", "content": "$$122$$ "}], [{"aoVal": "E", "content": "Non of the above "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"], "answer_analysis": ["With $$81$$ sweets wrappers. Peter can exchange for $$\\frac{81}{3}=27$$ more sweets With the additional $$27$$ sweets wrappers, Peter can exchange for $$\\frac{27}{3}=9$$ more sweets. with the~~additional $$9$$ sweets wrappes. Peter can exchange for $$\\frac{9}{3}=3$$ more sweets. with the additional $$3$$ sweets wrappers. Peter can exchange for $$\\frac{3}{3}=1$$ more sweet. Therefore, the largest possible number of sweets Peter could have eaten is $$81+27+9+3+1=121$$. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11052", "queId": "fa005a1c2f574aff9ce7345d92925efb", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "There are $$15$$ roses in a garden, and the number of daisies is $$5$$ more than $6$ times that of roses. How many flowers are there in the garden altogether? ", "answer_option_list": [[{"aoVal": "A", "content": "$$95$$ "}], [{"aoVal": "B", "content": "$$110$$ "}], [{"aoVal": "C", "content": "$$120$$ "}], [{"aoVal": "D", "content": "$$135$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"], "answer_analysis": ["$15\\times6=90$ $90+5=95$ $95+15=110$ "], "answer_value": "B"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11055", "queId": "f0d3b78f3d8242cf833da1bf1d819922", "competition_source_list": [], "difficulty": "2", "qtype": "single_choice", "problem": "The sum of the ages of four children Anil, Benu, Chas and Dave is $$20$$. Dave is $$5$$ years older than Chas, and $$3$$ years older than Benu. Anil is $$3$$ years younger than Chas. How old is Anil? ． ", "answer_option_list": [[{"aoVal": "A", "content": "$$1$$ "}], [{"aoVal": "B", "content": "$$4$$ "}], [{"aoVal": "C", "content": "$$5$$ "}], [{"aoVal": "D", "content": "$$6$$ "}], [{"aoVal": "E", "content": "$$9$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"], "answer_analysis": ["Two of the pieces of information relate to Chas, so we can try to relate the ages of the others to his age. Given Dave is $$5$$ years older than Chas, but $$3$$ years older than Benu, we can tell that Benu is $$2$$ years older than Chas. Given also that Anilis $$3$$ years younger than Chas, we can say that the sum of the ages of the four children is $$\\left( -3+2+5=4 \\right) $$ more than four times Chas' age. So four times Chas' age plus four is twenty, and so Chas must be four. So Anil is just $$ 1$$ year old. "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11057", "queId": "fea80af2e2ee471b8aad5215ffee39bc", "competition_source_list": ["其它"], "difficulty": "0", "qtype": "single_choice", "problem": "Allen has a collection of $240$ fossils. Of these, $35$\\% are fossilized snail shells. How many fossilized snail shells does Allen have? ", "answer_option_list": [[{"aoVal": "A", "content": "$$205$$ "}], [{"aoVal": "B", "content": "$$156$$ "}], [{"aoVal": "C", "content": "$$84$$ "}], [{"aoVal": "D", "content": "$$35$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"], "answer_analysis": ["$240 \\times 35$\\%=$84$, Allen has $84$ fossilized snail shells. "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11058", "queId": "fa116f9b3deb4cf09dcc965b60ec2640", "competition_source_list": ["其它"], "difficulty": "1", "qtype": "single_choice", "problem": "Daniel had $51$ Lego pieces, he used $42$ pieces to make a mini statue. How many pieces of Lego does Daniel have now? ", "answer_option_list": [[{"aoVal": "A", "content": "$$42$$ "}], [{"aoVal": "B", "content": "$$19$$ "}], [{"aoVal": "C", "content": "$$9$$ "}], [{"aoVal": "D", "content": "$$0$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules"], "answer_analysis": ["$51-42=9$ "], "answer_value": "C"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11059", "queId": "fa139029459b4899854fdbeedaed6ff2", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Grandma made some cheese dumplings and some blueberry dumplings. Altogether, she made $$31$$ dumplings. If she had made $$11$$ more cheese dumplings, then there would be the same number of blueberry dumplings as cheese dumplings. How many cheese dumplings did grandma make?（2009 Math Kangaroo Problem, Question \\#19） ", "answer_option_list": [[{"aoVal": "A", "content": "$$10$$ "}], [{"aoVal": "B", "content": "$$21$$ "}], [{"aoVal": "C", "content": "$$20$$ "}], [{"aoVal": "D", "content": "$$15$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"], "answer_analysis": ["$$(31-11)\\div2=10.$$ "], "answer_value": "A"} +{"dataset_name": "prime_math_competition_en_single_choice_8K_dev", "dataset_version": "2023-07-07", "qid": "11061", "queId": "feb9dbe07adc4cb0bce2c48c143904ef", "competition_source_list": [], "difficulty": "1", "qtype": "single_choice", "problem": "Wendy had $$30$$ stickers. First, she gave Aiden $3$ stickers. Then, she gave Terry $7$ stickers. Now, each of the three people has the same number of stickers. At the beginning, how many stickers did they have in total? ", "answer_option_list": [[{"aoVal": "A", "content": "$$120$$ "}], [{"aoVal": "B", "content": "$$90$$ "}], [{"aoVal": "C", "content": "$$85$$ "}], [{"aoVal": "D", "content": "$$60$$ "}], [{"aoVal": "E", "content": "$$55$$ "}]], "knowledge_point_routes": ["Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems"], "answer_analysis": ["Now, Wendy has $30-3-7=20$ stickers. Thus, all of them have $20\\times3=60$ stickers, which is equal to the total number of stickers they had at the beginning. "], "answer_value": "D"}