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timestamp[s] | qid
stringlengths 1
5
| queId
stringlengths 32
32
| competition_source_list
sequence | difficulty
stringclasses 5
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stringlengths 6
1.51k
| answer_option_list
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sequence | answer_analysis
sequence | answer_value
stringclasses 7
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---|---|---|---|---|---|---|---|---|---|---|---|
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10739 | fc7e4e4db79d4aba86fe5d52e60f6af9 | [] | 2 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$2000$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2002$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2004$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2006$$ "
}
],
[
{
"aoVal": "E",
"content": "$$2008$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Sums and Multiples in Age Problems"
] | [
"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 $$2004$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10740 | a67100eadbaf41779a4040f9fa0a7921 | [
"其它"
] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "The $15\\text{-ounce}$ bag "
}
],
[
{
"aoVal": "B",
"content": "The $20\\text{-ounce}$ bag "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"
] | [
"$\\frac{8\\text{dollars}}{15\\text{ounces}}$ $\\frac{12\\text{dollars}}{20\\text{ounces}}$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10744 | a673de9dc7924b7ea26020459905e811 | [] | 1 | single_choice | If February is a month that contains Friday the $$13^{}\text{th}$$, what day of the week is February $$1$$? | [
[
{
"aoVal": "A",
"content": "Sunday "
}
],
[
{
"aoVal": "B",
"content": "Monday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Thursday "
}
],
[
{
"aoVal": "E",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"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. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10746 | bcdb590870884f1ea2d28c313ce1f4eb | [] | 1 | single_choice | 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{~~~~~~~~~~}~$$\rm m$$. | [
[
{
"aoVal": "A",
"content": "$$14$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ "
}
],
[
{
"aoVal": "D",
"content": "$$17$$ "
}
],
[
{
"aoVal": "E",
"content": "$$18$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"$$112-64=48$$ $$64-48=16$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10747 | ca5d6e04cd304ba4a277452b04ecd54a | [] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "￡$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "￡$$3.60$$ "
}
],
[
{
"aoVal": "C",
"content": "￡$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "￡$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "￡$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"
] | [
"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 ￡$$6$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10749 | cede5245842e4013a895b48f94735405 | [] | 1 | single_choice | Adam paid £6 for $$15$$ buns. How many dollars did Tom pay for the same kind of buns if he bought $$5$$? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"There $$3$$ groups of $$5$$ buns in $$15$$ buns: $$15\\div 5=3$$, so $$5$$ buns cost $$6\\div 3=$$£$$2$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10761 | bce9f763f0bd41fca5eacaf5716b6684 | [
"其它"
] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"
] | [
"14 - 1 (eagle) - 1 (mother hen) = 12 (chicks) 12 - 5 7 chicks "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10763 | b867c9ed64e5436c89831f2be5a62b66 | [] | 1 | single_choice | 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. | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$35$$ "
}
],
[
{
"aoVal": "C",
"content": "$$45$$ "
}
],
[
{
"aoVal": "D",
"content": "$$55$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"$$7$$ 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. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10768 | c5f02cb2e2974724b3e0e17e811a83a3 | [
"其它"
] | 2 | single_choice | 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) | [
[
{
"aoVal": "A",
"content": "$$45$$ "
}
],
[
{
"aoVal": "B",
"content": "$$48$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
],
[
{
"aoVal": "E",
"content": "$$65$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"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. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10769 | d802fff4b28a4deaa8645d2da8acc555 | [
"其它"
] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$22$$ "
}
],
[
{
"aoVal": "C",
"content": "$$24$$ "
}
],
[
{
"aoVal": "D",
"content": "$$26$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"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. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10773 | d3835445b5ae4475b41da2d97eac9bba | [] | 1 | single_choice | 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? ． | [
[
{
"aoVal": "A",
"content": "$$ $$Sunday$$ $$ "
}
],
[
{
"aoVal": "B",
"content": "$$ $$Tuesday$$ $$ "
}
],
[
{
"aoVal": "C",
"content": "$$ $$Thursday$$ $$ "
}
],
[
{
"aoVal": "D",
"content": "$$ $$Saturday$$ $$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"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. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10774 | dc96297dcf1f4d54a05f153d125a6e62 | [] | 1 | single_choice | 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． | [
[
{
"aoVal": "A",
"content": "$$33$$ "
}
],
[
{
"aoVal": "B",
"content": "$$36$$ "
}
],
[
{
"aoVal": "C",
"content": "$$39$$ "
}
],
[
{
"aoVal": "D",
"content": "$$42$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Differences and Multiples in Age Problems"
] | [
"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 $$27+6=33$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10776 | c5f6f6a35eb249c988537d6d70c8717c | [] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$20$$; $$65$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13$$; $$52$$ "
}
],
[
{
"aoVal": "C",
"content": "$$13$$; $$65$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$; $$52$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"
] | [
"Sugar: $$65\\times 20\\textbackslash\\% = 13$$ ounces; Water: $$65 - 13 = 52$$ ounces. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10777 | c17aaf695ebd48c3a6930aee72c43d85 | [] | 1 | single_choice | 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. | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$9$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"
] | [
"$$3+3+3=9$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10778 | d38671853557404db4b6de1b6a487401 | [
"其它"
] | 1 | single_choice | 19 less than 67 is~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "$$58$$ "
}
],
[
{
"aoVal": "B",
"content": "$$68$$ "
}
],
[
{
"aoVal": "C",
"content": "$$38$$ "
}
],
[
{
"aoVal": "D",
"content": "$$48$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"
] | [
"$$67-19=48$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10780 | f36020d6e8e04424ace167d65cc67fa8 | [] | 2 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "Thursday "
}
],
[
{
"aoVal": "B",
"content": "Saturday "
}
],
[
{
"aoVal": "C",
"content": "Sunday "
}
],
[
{
"aoVal": "D",
"content": "Tuesday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"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. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10781 | c5f89e1264694a438f2ebb04401ed8ad | [
"其它"
] | 2 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ "
}
],
[
{
"aoVal": "C",
"content": "$$32$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30$$ "
}
],
[
{
"aoVal": "E",
"content": "$$36$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"
] | [
"Tom\\textquotesingle s mother is $(86+24-2)\\div3=36$ years old. Tom is $36-24=12$ years old. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10786 | ab1d467c4b2542bfa8437ceb255979f8 | [] | 1 | single_choice | How many ways are there to make $$$80$$ using some combination of $$$5$$, $$$10$$ and $$$20$$ notes? | [
[
{
"aoVal": "A",
"content": "$$16$$ "
}
],
[
{
"aoVal": "B",
"content": "$$25$$ "
}
],
[
{
"aoVal": "C",
"content": "$$36$$ "
}
],
[
{
"aoVal": "D",
"content": "$$49$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"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. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10797 | e12692ffb3f54dd0a6b21ca3eaafdf7d | [] | 2 | single_choice | 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) | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$25$$ "
}
],
[
{
"aoVal": "C",
"content": "$$35$$ "
}
],
[
{
"aoVal": "D",
"content": "$$75$$ "
}
],
[
{
"aoVal": "E",
"content": "$$80$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple->Sum and Multiple of Two Variables"
] | [
"$100 \\div (3 + 1)~ \\times 3= 75$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10798 | ab2637a0065d4ea8a260498872829bba | [] | 1 | single_choice | If today is Monday, which day of the week will it be $$22$$ days later? ． | [
[
{
"aoVal": "A",
"content": "Sunday "
}
],
[
{
"aoVal": "B",
"content": "Monday "
}
],
[
{
"aoVal": "C",
"content": "Tuesday "
}
],
[
{
"aoVal": "D",
"content": "Wednesday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"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. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10804 | dca86dbec3dc419fb249ac6f1c6910bc | [
"其它"
] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$11$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
],
[
{
"aoVal": "E",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"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 $$8$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10805 | bd122c1bf5b44fd2a71cbc26ed5460d6 | [] | 1 | single_choice | 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) | [
[
{
"aoVal": "A",
"content": "$$36$$ "
}
],
[
{
"aoVal": "B",
"content": "$$38$$ "
}
],
[
{
"aoVal": "C",
"content": "$$40$$ "
}
],
[
{
"aoVal": "D",
"content": "$$42$$ "
}
],
[
{
"aoVal": "E",
"content": "$$44$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares->Basic Solid Square Problems"
] | [
"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. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10812 | b896adf0cd8441c1a3ca6261149917b9 | [] | 1 | single_choice | 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? | [
[
{
"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": "$$14 \\text{kg}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"
] | [
"It should be a moment\\textquotesingle s work to see that Felix weighs $$3\\text{kg}$$ , and Marmalade $$7\\text{kg}$$ . "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10817 | eeec830b54b7404197ffc290c20faa8f | [] | 1 | single_choice | 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 ． | [
[
{
"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": "$12\\text{cm}$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"
] | [
"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 $$125\\div25\\times 3=15\\textasciitilde\\text{cm}$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10825 | afb500864735474190e4a69af1f773c9 | [] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$21$$ "
}
],
[
{
"aoVal": "C",
"content": "$$35$$ "
}
],
[
{
"aoVal": "D",
"content": "$$42$$ "
}
],
[
{
"aoVal": "E",
"content": "$$43$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"
] | [
"Suppose there are $$x$$ ducks in the yard. Since there is an equal number of pigs, ducks and chickens, $$2x+4x+2x=144$$, $$x=18$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10828 | e148f89fac4c42348a20c0599453583e | [] | 1 | single_choice | How many days are there in exactly $$52$$ weeks? | [
[
{
"aoVal": "A",
"content": "$$364$$ "
}
],
[
{
"aoVal": "B",
"content": "$$365$$ "
}
],
[
{
"aoVal": "C",
"content": "$$366$$ "
}
],
[
{
"aoVal": "D",
"content": "$$367$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"Each week has $$7$$ days, so $$52$$ weeks has $$52 \\times 7 = 364$$ days. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10829 | d83dc23a6ead4ab59f29daf001ead1bb | [] | 1 | single_choice | 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. | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"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. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10831 | cf337ba3004f414396571fba844d02cb | [] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Simple Work Word Problems"
] | [
"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. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10839 | fcdbfea5b37b44e2bd41668bf6b89bf0 | [] | 2 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"
] | [
"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. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10841 | d8516c9a20bb4c3da9ed8ba840c6f48b | [] | 1 | single_choice | The sum of the ages of Anita and Peter is $$20$$ years. What is the sum of their ages three years ago? | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$17$$ "
}
],
[
{
"aoVal": "C",
"content": "$$14$$ "
}
],
[
{
"aoVal": "D",
"content": "$$11$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Basic Sum and Differences Problems in Age Problems"
] | [
"$20-3\\times2=14$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10842 | cac7c619987d42a29c06c3caebda43ed | [
"其它"
] | 1 | single_choice | 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) | [
[
{
"aoVal": "A",
"content": "$$94$$ "
}
],
[
{
"aoVal": "B",
"content": "$$89$$ "
}
],
[
{
"aoVal": "C",
"content": "$$80$$ "
}
],
[
{
"aoVal": "D",
"content": "$$79$$ "
}
],
[
{
"aoVal": "E",
"content": "$$75$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"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. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10844 | dce2d446acf74baab5a3ef6428497dcb | [
"其它"
] | 2 | single_choice | 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 ) | [
[
{
"aoVal": "A",
"content": "$$52.5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$55$$ "
}
],
[
{
"aoVal": "C",
"content": "$$57.5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"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\\% $ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10845 | fce2f9c0b015465787ca31eeba5c79bc | [
"其它"
] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13$$ "
}
],
[
{
"aoVal": "C",
"content": "$$17$$ "
}
],
[
{
"aoVal": "D",
"content": "$$21$$ "
}
],
[
{
"aoVal": "E",
"content": "$$22$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Word Problems Involving Comparing and Ordering"
] | [
"Blue: $(50 + 5 - 4) \\div 3 = 17$ Red: $17 + 4 = 21$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10846 | ea8ae7e5ea5d4903af610ef23198ec6f | [] | 1 | single_choice | 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. | [
[
{
"aoVal": "A",
"content": "$$48$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$60$$ "
}
],
[
{
"aoVal": "D",
"content": "$$80$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with an Invariant Part"
] | [
"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 $$\\text{B}$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10855 | bd5608e79fb641ee82c5bd4efc82c96f | [] | 1 | single_choice | 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 ． | [
[
{
"aoVal": "A",
"content": "Wednesday "
}
],
[
{
"aoVal": "B",
"content": "Thursday "
}
],
[
{
"aoVal": "C",
"content": "Friday "
}
],
[
{
"aoVal": "D",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"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. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10861 | f859175dd7e743ecb21e03a74af1bff1 | [] | 1 | single_choice | 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) | [
[
{
"aoVal": "A",
"content": "Wednesday "
}
],
[
{
"aoVal": "B",
"content": "Thursday "
}
],
[
{
"aoVal": "C",
"content": "Tuesday "
}
],
[
{
"aoVal": "D",
"content": "Friday "
}
],
[
{
"aoVal": "E",
"content": "Sunday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"$$38\\div7=5 \\text{R} 3$$, three days after Sunday, which is Wednesday. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10862 | bd5b7c4ea0c04ba2b4219b56e674c081 | [] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"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 $$3\\text{hrs}$$ . "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10863 | c656052f1ecc4f1e988bc8aba1c123ea | [] | 1 | single_choice | 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. | [
[
{
"aoVal": "A",
"content": "$10\\textbackslash\\%$ "
}
],
[
{
"aoVal": "B",
"content": "$12\\textbackslash\\%$ "
}
],
[
{
"aoVal": "C",
"content": "$15\\textbackslash\\%$ "
}
],
[
{
"aoVal": "D",
"content": "$18\\textbackslash\\%$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"
] | [
"$$600\\times 8\\textbackslash\\%=48$$ g, $$600-120=480$$ g, $$48\\div 480\\times 100\\textbackslash\\%=10\\textbackslash\\%$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10866 | c1dfd36b8b8a464a877aa32fb1daf406 | [
"其它"
] | 1 | single_choice | 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 \#$9$) | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"The age of each twin is $(32-8) \\div 3 =8$ years old. Thus, Alex is $8 +8 =16$ years old. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10868 | f86310003b5e4716bbb570b3e2a5319d | [
"其它"
] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$13$$ "
}
],
[
{
"aoVal": "B",
"content": "$$35$$ "
}
],
[
{
"aoVal": "C",
"content": "$$36$$ "
}
],
[
{
"aoVal": "D",
"content": "$$40$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"There are $8-1=7$ spaces. $7\\times 5=35$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10875 | dd09551c3d2040c98f687424453295c8 | [] | 1 | single_choice | Given March $$25$$ of a certain year is Monday, what day of the week would May $$1$$ fall on that year? ． | [
[
{
"aoVal": "A",
"content": "Tuesday "
}
],
[
{
"aoVal": "B",
"content": "Wednesday "
}
],
[
{
"aoVal": "C",
"content": "Thursday "
}
],
[
{
"aoVal": "D",
"content": "Friday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"$$1$$ 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. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10877 | f872d69250cb44339f248088ab3d7346 | [] | 1 | single_choice | 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) | [
[
{
"aoVal": "A",
"content": "$$120$$ "
}
],
[
{
"aoVal": "B",
"content": "$$720$$ "
}
],
[
{
"aoVal": "C",
"content": "$$360$$ "
}
],
[
{
"aoVal": "D",
"content": "$$300$$ "
}
],
[
{
"aoVal": "E",
"content": "$$420$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"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. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10878 | d880a796509f493ca64dbfc21040d942 | [] | 2 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$7.5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9.5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
],
[
{
"aoVal": "E",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"Total revenue: $30\\times 8+50\\times 6+20\\times 13=800$ dollars A bag of assorted candy: $$800\\div 100=8$$ dollars "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10879 | eab4c059f20b4c68bd1acf3c7b8aa509 | [
"其它"
] | 2 | single_choice | 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? ~ | [
[
{
"aoVal": "A",
"content": "$26$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$33$$ "
}
],
[
{
"aoVal": "D",
"content": "$$39$$ "
}
],
[
{
"aoVal": "E",
"content": "$$40$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$10+10+10=30$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10881 | eab5d8df6c8e4746b94a05c0950f393a | [] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$2$ hours "
}
],
[
{
"aoVal": "B",
"content": "$3$ hours "
}
],
[
{
"aoVal": "C",
"content": "$9$ hours "
}
],
[
{
"aoVal": "D",
"content": "$18$ hours "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"
] | [
"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. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10883 | eab84d29c50f4431ae3a5bdf454ce089 | [
"其它"
] | 2 | single_choice | 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? | [
[
{
"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. "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"$4+4-1=7$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10886 | b8f7de5669c54c3f8bddf07da035b750 | [] | 1 | single_choice | John bought $10$ pencils and notebooks in total for £$44$. Each pencil cost £$$2$$. Each notebook costs £$$8$$. How many notebooks did John buy? | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
],
[
{
"aoVal": "E",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"
] | [
"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. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10888 | c67b7463cfcb46ae9a200fb4b12db722 | [
"其它"
] | 1 | single_choice | 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) | [
[
{
"aoVal": "A",
"content": "$$16$$ "
}
],
[
{
"aoVal": "B",
"content": "$$17$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$19$$ "
}
],
[
{
"aoVal": "E",
"content": "$$21$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Sum of Ages"
] | [
"$17 + 2 \\times 2 = 21$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10889 | cb04b9ba8ef54e68aa7742dd6a8105e6 | [] | 1 | single_choice | If I start with $2$, and begin to count by $$3\textquotesingle$$s, my $50^{}\text{th}$ number will be~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "$$148$$ "
}
],
[
{
"aoVal": "B",
"content": "$$149$$ "
}
],
[
{
"aoVal": "C",
"content": "$$150$$ "
}
],
[
{
"aoVal": "D",
"content": "$$151$$ "
}
],
[
{
"aoVal": "E",
"content": "$$152$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression"
] | [
"$2+(50-1)\\times3=149$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10893 | f88d93c0be73464f8dd106863d5e53b7 | [
"其它"
] | 1 | single_choice | 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. | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"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$$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10894 | e63bc810b05a44a6af4b5315a7cec303 | [] | 1 | single_choice | Bowen has $$40$$ grams of a $$25\textbackslash\%$$ sugar solution. After~\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of the solution is $$40\textbackslash\%$$. (Evaporate: the water turns from liquid into vapor and is no longer in the solution anymore.) | [
[
{
"aoVal": "A",
"content": "$$15$$ grams "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ grams "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ grams "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ grams "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"
] | [
"$$40-40\\times25\\textbackslash\\%\\div40\\textbackslash\\%=40-25=15$$ grams. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10903 | d41ec1beecf04ed99fd65db4265077b1 | [] | 1 | single_choice | Tom goes to the supermarket to buy egg tarts. There are two kinds of egg tarts. One has $$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$$ egg tarts, how many boxes does he need at least?~(adapted from 2011 Math Kangaroo Problem, Level 3 - 4, Question \#10) | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$11$$ "
}
],
[
{
"aoVal": "E",
"content": "$$13$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"
] | [
"$$76=10+10+10+10+10+10+10+6$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10908 | f8a5f577bf8a445881a0be7fe49a9a40 | [] | 1 | single_choice | A gift store buys some gifts at＄$$125$$ each. It wants to earn＄$$25 $$ for each gift after a discount of $$25 \textbackslash\% $$. What is the selling price before the discount for each gift? | [
[
{
"aoVal": "A",
"content": "$$160$$ dollars "
}
],
[
{
"aoVal": "B",
"content": "$$180$$ dollars "
}
],
[
{
"aoVal": "C",
"content": "$$190$$ dollars "
}
],
[
{
"aoVal": "D",
"content": "$$200$$ dollars "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"$$\\left( 125+25 \\right)\\div \\left( 1-25 \\textbackslash\\% \\right)=200$$ dollars. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10911 | c6a359a5e6b7450d926ddb79b0e044bf | [
"其它"
] | 1 | single_choice | The average weight of $4$ students in Class $A$ is $37$ kilograms. The average weight of $11$ students in Class $B$ is $41$ kilograms. The total weight of $5$ students in Class $C$ is $161$ kilograms. What is the average weight of the students in the $3$ classes? | [
[
{
"aoVal": "A",
"content": "$36$ kilograms "
}
],
[
{
"aoVal": "B",
"content": "$38$ kilograms "
}
],
[
{
"aoVal": "C",
"content": "$40$ kilograms "
}
],
[
{
"aoVal": "D",
"content": "$43$ kilograms "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"$4 \\times 37 + 11 \\times 41+ 161 = 760$ kilograms in total. $760 \\div (4 + 11 + 5) = 38$ kg. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10913 | d8bfbee5febb463482a9e7bbd019fc32 | [] | 1 | single_choice | It takes Mary $$30$$ minutes to walk uphill $$300 $$ m from her home to school, but it takes her only $$10$$ minutes to walk from school to home along the same route. What is her average speed, in m/min, for the round trip? (adapted from 2003 AMC 10 Problem, Question \#4) | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
],
[
{
"aoVal": "E",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"
] | [
"Mary walks a total of $$300+300=600\\rm$$ meters in $$40$$ minutes. Average speed: $600\\div40=15$ m/min "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10915 | cfb3dee404c84707a8ee3b7e9e48b1a2 | [] | 1 | single_choice | If $$6$$ cans of Sweet Stuff Soda all together contain $$96$$ teaspoons of sugar, then there are a total of teaspoons of sugar in $$15$$ cans. | [
[
{
"aoVal": "A",
"content": "$$192$$ "
}
],
[
{
"aoVal": "B",
"content": "$$208$$ "
}
],
[
{
"aoVal": "C",
"content": "$$240$$ "
}
],
[
{
"aoVal": "D",
"content": "$$270$$ "
}
],
[
{
"aoVal": "E",
"content": "$$288$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"
] | [
"If $$6$$ cans contain $$96$$ teaspoons of sugar, $$1$$ can contains $$96\\div6 = 16$$ teaspoons of sugar. Thus $$15$$ cans contain $$16\\times15 =240$$ teaspoons of sugar. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10916 | c2359d75d5a4409a84ea23dcbda94f8f | [
"其它"
] | 2 | single_choice | Twenty-eight students from the fourth grade competed in a math competition. Each student earned a different number of points. The number of students who received more points than Tomek is two times smaller than the number of students who had fewer points than Tomek. In which position did Tomek finish that competition?~ ($2002$~Math Kangaroo Problem, Level $3-4$, Question \#$23$) | [
[
{
"aoVal": "A",
"content": "$$6$$\\textsuperscript{th} "
}
],
[
{
"aoVal": "B",
"content": "$10$\\textsuperscript{th} "
}
],
[
{
"aoVal": "C",
"content": "$8$\\textsuperscript{th} "
}
],
[
{
"aoVal": "D",
"content": "$9$\\textsuperscript{th} "
}
],
[
{
"aoVal": "E",
"content": "$7$\\textsuperscript{th} "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"
] | [
"Except for Tomek, there are~$28-1=27$~students. The number of students who received more points than Tomek is~$27\\div(2+1)=9$, so Tomek is in the~$9+1=10^{th}$~place. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10917 | f417000eb34242e7a177b524a29aaebb | [] | 1 | single_choice | January $$1$$, $$1989$$ was a Sunday. January $$1$$, $$1988$$ (a leap year) was a． | [
[
{
"aoVal": "A",
"content": "Friday "
}
],
[
{
"aoVal": "B",
"content": "Saturday "
}
],
[
{
"aoVal": "C",
"content": "Sunday "
}
],
[
{
"aoVal": "D",
"content": "Monday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"$$366$$ days $$=52$$ weeks $$2$$ days. Jan $$1$$ $$1988$$ is $$52$$ weeks $$2$$ days before Jan $$1$$ $$1989$$. This date in $$1988$$ is $$2$$ days before Sunday so it is on a Friday. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10921 | e66ed2c2c7b34bcc8a9f9f15e69f0eda | [] | 1 | single_choice | Algebra books cost $$$12.50$$ each, and geometry books cost $$$14$$ each. How much do $$6$$ algebra books and $$5$$ geometry books cost in total? | [
[
{
"aoVal": "A",
"content": "$$$145.00$$ "
}
],
[
{
"aoVal": "B",
"content": "$$$146.50$$ "
}
],
[
{
"aoVal": "C",
"content": "$$$150.00$$ "
}
],
[
{
"aoVal": "D",
"content": "$$$151.50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"Six algebra books cost $$$12.50 \\times 6 = $75$$. Five geometry books cost $$$14\\times5 = $70$$. All together, they cost a total of $$$145$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10925 | eb04e626e45c407e8a9c9c8c47fa12d8 | [] | 1 | single_choice | In $$1975$$ it was estimated that there were $$250000$$ lions in Africa. Over $$40$$ years this figure has decreased by $$90\textbackslash\%$$. What is the current estimate for the number of lions in Africa ? | [
[
{
"aoVal": "A",
"content": "$$25000$$ "
}
],
[
{
"aoVal": "B",
"content": "$$100000$$ "
}
],
[
{
"aoVal": "C",
"content": "$$160000$$ "
}
],
[
{
"aoVal": "D",
"content": "$$225000$$ "
}
],
[
{
"aoVal": "E",
"content": "$$275000$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"A $$90\\textbackslash\\%$$ decrease means $$10\\textbackslash\\%$$ of $$250000 = 250000 \\div 10 = 25000$$ of the lions remain. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10927 | cfc8a365056048e3bdebc44c41a51a1d | [] | 1 | single_choice | A test is with a full score of $100$ points. Five students in a group wants to reach an average of $91$ points. If everyone scores a different whole number, the lowest score among them could be~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "$$60$$ "
}
],
[
{
"aoVal": "B",
"content": "$$61$$ "
}
],
[
{
"aoVal": "C",
"content": "$$67$$ "
}
],
[
{
"aoVal": "D",
"content": "$$70$$ "
}
],
[
{
"aoVal": "E",
"content": "$$71$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"$91\\times5-(100+99+98+97)=61$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10931 | c24f96a3cb04418d919e14ab2e028fb9 | [] | 1 | single_choice | Jack\textquotesingle s sister is $$22$$ years old, which is $$2$$ less than $$4$$ times Jack\textquotesingle s age. Assume Jack is $$x$$ years old, then． | [
[
{
"aoVal": "A",
"content": "$$x=4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$x=5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$x=6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$x=8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"
] | [
"The equation can represents this situation is $$4x-2=22$$, so, $$4x=24$$, $$x=6$$. So, the answer is $$6$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10935 | c6d52006a4af459d8edb41c932accb55 | [] | 1 | single_choice | Jason and Ross are in line to check tickets. There are $36$ people in front of Jason and $16$ people behind. Ross happens to be in the middle of the entire line. How many people are there between Ross and Jason?~(adapted from 2000 Math Kangaroo Problem, Level 3 - 4, Question \#12) | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$17$$ "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares->Basic Solid Square Problems"
] | [
"The total: $36+16+1=53$ , Jack\\textquotesingle s location: $$(53-1)\\div2=21$$, so there are $15$ people between Jack and Rose. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10939 | efadc5a5662d49d7b3e2cab50238d6d7 | [] | 1 | single_choice | Amy mixes $$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\% $$ solution? | [
[
{
"aoVal": "A",
"content": "$$70$$ "
}
],
[
{
"aoVal": "B",
"content": "$$72$$ "
}
],
[
{
"aoVal": "C",
"content": "$$75$$ "
}
],
[
{
"aoVal": "D",
"content": "$$80$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"
] | [
"$$30\\times30\\textbackslash\\%+20\\times 20\\textbackslash\\%=9+4=13$$ ounces. $$13\\div10\\textbackslash\\%-(30+20)=80$$ ounces. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10942 | eb2afccdc85f485683aa23fe19a16d70 | [] | 1 | single_choice | $$12$$ dogs are cqually divided into $$3$$ groups, how many dogs are there in each group. | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2$$ "
}
],
[
{
"aoVal": "E",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$12\\div3=4$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10944 | f44dcc3392324978bbab9b65020652ab | [] | 1 | single_choice | My pet frog jumps $$3\text{m}$$ per jump. If it wants to jump from one end of a $$100\text{m}$$ field to another, the least number of jumps it will take is． | [
[
{
"aoVal": "A",
"content": "$$33$$ "
}
],
[
{
"aoVal": "B",
"content": "$$34$$ "
}
],
[
{
"aoVal": "C",
"content": "$$70$$ "
}
],
[
{
"aoVal": "D",
"content": "$$97$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"
] | [
"Since $$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}$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10952 | c70a24e2530544d88f92317979862f7a | [] | 1 | single_choice | In $$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$$ years old. In what year was Alice born? (Adapted from 2008 Math kangaroo Problem, Level 3-4, Question \#9) | [
[
{
"aoVal": "A",
"content": "$$1996$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1994$$ "
}
],
[
{
"aoVal": "C",
"content": "$$1992$$ "
}
],
[
{
"aoVal": "D",
"content": "$$1990$$ "
}
],
[
{
"aoVal": "E",
"content": "$$1988$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Time"
] | [
"The $10$\\textsuperscript{th}~Math Kangaroo was taking place in $2001$, which means that Alice was $9$ years old in $2001$, so she was born in $1992$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10954 | e6be2d2a80c643ef85a9aa3f83c3217a | [] | 1 | single_choice | Half a loaf of bread costs $$6$$ pence more than one-fourth of a loaf of bread. How many pence does a whole loaf of bread cost? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$24$$ "
}
],
[
{
"aoVal": "E",
"content": "$$30$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"One-fourth of a loaf of bread is ``$$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$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10959 | ddb2e175ea3d44748618401e363b1485 | [] | 1 | single_choice | Ben has $$9$$ pairs of shoes, of which $$4$$ shoes are red, $$2$$ shoes are bule, and the rest are green. How many pairs of shoes are green? | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"$$9-2-1=6$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10962 | f91f556c65a748248c7168a2fb259d85 | [
"其它"
] | 2 | single_choice | Antonette gets $70 \textbackslash\%$ on a 10 -problem test, $80 \textbackslash\%$ on a 20 -problem test and $90 \textbackslash\%$ on a 30 -problem test. If the three tests are combined into one 60 problem test, which percent is closest to her overall score? (2006 AMC 8, Question \#12) | [
[
{
"aoVal": "A",
"content": "$$40$$ "
}
],
[
{
"aoVal": "B",
"content": "$$77$$ "
}
],
[
{
"aoVal": "C",
"content": "$$80$$ "
}
],
[
{
"aoVal": "D",
"content": "$$83$$ "
}
],
[
{
"aoVal": "E",
"content": "$$87$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$70 \\textbackslash\\% \\cdot 10=7$ $80 \\textbackslash\\% \\cdot 20=16$ $90 \\textbackslash\\% \\cdot 30=27$ Adding them up gets $7+16+27=50$. The overall percentage correct would be $\\frac{50}{60}=\\frac{5}{6}=5 \\cdot 16 . \\overline{6}=83 . \\overline{3} \\approx(\\mathbf{D}) 83$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10966 | e24822c2e3224c60bb569e44d1e04098 | [] | 1 | single_choice | Rick and Roy each stands at different ends of a straight road that is $$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}$$. They will meet in~\uline{~~~~~~~~~~}~seconds. | [
[
{
"aoVal": "A",
"content": "$$35$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$47$$ "
}
],
[
{
"aoVal": "D",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$2021\\div (21+22)=47$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10969 | e6dfee64ce534a96b65e50bca1e747e2 | [] | 1 | single_choice | You have $12$ green cards and the ratio of your red cards to green cards is $3:2$. How many cards do you have? | [
[
{
"aoVal": "A",
"content": "$18$ "
}
],
[
{
"aoVal": "B",
"content": "$20$ "
}
],
[
{
"aoVal": "C",
"content": "$$24$$ "
}
],
[
{
"aoVal": "D",
"content": "$30$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"
] | [
"$12$ is the product of $6$ and $2$.Then multiple $3$ by $6$ is the number of red cards. The total number of cards is $30$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10970 | eb73455750894407b59cb7ce7c9dbbdc | [
"其它"
] | 2 | single_choice | Chloe and Zoe are both students in Ms. Demeanor\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to $80\textbackslash\%$ of the problems she solved alone, but overall $90\textbackslash\%$ of her answers were correct. Zoe had correct answers to $75\textbackslash\%$ of the problems she solved alone. What was Zoe\textquotesingle s overall percentage of correct answers? (2017 AMC 8, Question \#14) | [
[
{
"aoVal": "A",
"content": "$$87.5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$90$$ "
}
],
[
{
"aoVal": "C",
"content": "$$92.5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$95.5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$100$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"Assume the total amount of problems is 100 per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got 80 problems correct by herself, and got 180 problems correct overall. We also know that Zoe had 75 problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $180-80=100$. Therefore Zoe has $100+75=175$ problems out of $200$ problems correct. Thus $\\frac{175}{200} = 87.5$ percent. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10973 | d4be355c5b884316955a09e6f19880b9 | [] | 1 | single_choice | Mr. $$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$$) | [
[
{
"aoVal": "A",
"content": "$$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$$ on the deal "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"Mr. $$ 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}$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10974 | f93a88544cf444eeb54911c7d24fe08b | [] | 1 | single_choice | A $60\textbackslash\%$ alcohol solution contains $120$ grams of water. How many grams of solution are there? | [
[
{
"aoVal": "A",
"content": "$$200$$ "
}
],
[
{
"aoVal": "B",
"content": "$$250$$ "
}
],
[
{
"aoVal": "C",
"content": "$$300$$ "
}
],
[
{
"aoVal": "D",
"content": "$$400$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"
] | [
"$120\\div(1-60\\textbackslash\\%)=300$ ounces. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10975 | f005c813b48d4889866c96fc9515388b | [] | 1 | single_choice | A, B, C, D and E sit around a circular table in that order. A starts by saying "$$100$$", B says "$$101$$", C says~"$$102$$" and so on round the table. Who will eventually say"$$2023$$"? | [
[
{
"aoVal": "A",
"content": "$$$$A "
}
],
[
{
"aoVal": "B",
"content": "$$$$B "
}
],
[
{
"aoVal": "C",
"content": "$$$$Cain "
}
],
[
{
"aoVal": "D",
"content": "$$$$Devi "
}
],
[
{
"aoVal": "E",
"content": "$$$$Emily "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Circular Operations"
] | [
"After Amit says \"$$2015$$\", there are $$5102-2015=3087$$ numbers remaining. Thus the counting goes round the table $$3087\\div6= 514$$ times with a remainder of $$3$$, so the last to count is Devi. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10976 | eb7b6431d7864b0da46a806ccc5f9888 | [
"其它"
] | 1 | single_choice | Brown wants to put some board between his books. He has $10$ books in total. If he wants to put one board between every two adjacent books, how many boards does he need to prepare? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
],
[
{
"aoVal": "E",
"content": "$$13$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"$10 - 1 = 9$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10977 | f0066ee74aea417f880ec1c14d83ad55 | [] | 1 | single_choice | In a class of $$18$$ students, $$6$$ are wearing jeans. What is the ratio of students wearing jeans to students not wearing jeans? | [
[
{
"aoVal": "A",
"content": "$$1:2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1:3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2:3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2:1$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"
] | [
"If $$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$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10981 | f00cf6290ccd41a7a563bade34da8939 | [
"其它"
] | 1 | single_choice | How many two-digit numbers are divisible by $3$ but not by $6$? | [
[
{
"aoVal": "A",
"content": "$$14$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ "
}
],
[
{
"aoVal": "C",
"content": "$$17$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division"
] | [
"There are $99$ $4-3 = 33$-multiples of $3$ less than $100$. $3$ of them are one-digit numbers: $3$, $6$ and $9$. Hence there are $30$ $2$-digit multiples of $3$. Similarly, there are $96 + 6 -1 = 16 -1 = 15$ $2$-digit multiples of $6$. Hence, the answer is 30 - 15 = \\textbf{15.} Answer： \\textbf{(B)} "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10982 | d4c9f344a62348df844a9a674d0e9737 | [
"其它"
] | 1 | single_choice | Water from the first faucet fills the swimming pool in $70$ minutes. Water from each of the two other faucets fills the same swimming pool $3$ times faster. In how many minutes will the swimming pool be filled if all three faucets are opened? | [
[
{
"aoVal": "A",
"content": "$$210$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$30$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems"
] | [
"The efficiency of the first faucet is $\\frac1{70}$ and that of the other two is $\\frac3{70}$. Thus, it takes $1\\div (\\frac1{70}+\\frac3{70}\\times2)=10$ minutes to fill the pool. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10983 | d4caf0a4f7e049b3ad2b5d92aba1bbee | [
"其它"
] | 2 | single_choice | Chloe and Zoe are both students in Ms. Demeanor\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to $80\textbackslash\%$ of the problems she solved alone, but overall $90\textbackslash\%$ of her answers were correct. Zoe had correct answers to $75\textbackslash\%$ of the problems she solved alone. What was Zoe\textquotesingle s overall percentage of correct answers? (adapted from 2017 AMC 8, Question \#14) | [
[
{
"aoVal": "A",
"content": "$$87.5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$90$$ "
}
],
[
{
"aoVal": "C",
"content": "$$92.5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$95.5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$100$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"Assume the total amount of problems is 100 per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got 80 problems correct by herself, and got 180 problems correct overall. We also know that Zoe had 75 problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $180-80=100$. Therefore Zoe has $100+75=175$ problems out of $200$ problems correct. Thus $\\frac{175}{200} = 87.5$ percent. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10984 | eb856f9de2cc4a59a6402401de56b7ed | [] | 1 | single_choice | There is an empty tank which needs $29$ bottles of water to fill with. The workers pour $5$ bottles of water during the day, but uses $1$ bottle of water during the night. In how many days can the tank be filled with water? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
],
[
{
"aoVal": "E",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"Every day: $5-1=4$ bottles. $29\\div4=7R1$ But for the last day, the tank can be filled with water without using during the night. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10986 | e6f6b3835f9d49b0911843affde2934f | [] | 1 | single_choice | The selling price of a sofa set is＄$$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$$? | [
[
{
"aoVal": "A",
"content": "$$20\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$24\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$25\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"$$6500\\div(1+30\\textbackslash\\%)=5000$$, $$1200\\div5000=24\\textbackslash\\%$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11001 | f4cfdd12e1104c6196a8e57cbb3b65d4 | [
"其它"
] | 1 | single_choice | Owen sees an archery right after he entered the carnival. After Owen takes 20 shots, he has made $55 \textbackslash\%$ of his shots. After he takes 5 more shots, he raises his percentage to $56 \textbackslash\%$. How many of the last 5 shots did she make?~ (adapted from 2004 AMC 8, Question\#6) | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
],
[
{
"aoVal": "E",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"Owen made $0.55 * 20=11$ shots originally. Letting $x$ be the number of shots she made, we have $\\frac{11+x}{25}=0.56$. Solving for $x$ gives us $x=$ (C) 3 "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11014 | e736c16ff8314588a37ac98176e10375 | [] | 1 | single_choice | I read $1$ page of a book on Nov $1$, $2$ pages on Nov $2$, $3$ pages on Nov $3$, and so on. I followed this pattern for the whole month. Altogether, how many pages did I read in November? | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$31$$ "
}
],
[
{
"aoVal": "C",
"content": "$$465$$ "
}
],
[
{
"aoVal": "D",
"content": "$$496$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem"
] | [
"There are in total $30$ days in Nov. $1+2+3+4+\\cdots+30=(1+30)\\times30\\div2=465$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11018 | fe2f48a2876c4e2182ab55fcfb778a97 | [
"其它"
] | 2 | single_choice | Chloe and Zoe are both students in Ms. Demeanor\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to $90 \textbackslash\%$ of the problems she solved alone, but overall $84 \textbackslash\%$ of her answers were correct. Zoe had correct answers to $80 \textbackslash\%$ of the problems she solved alone. What was Zoe\textquotesingle s overall percentage of correct answers? (adapted from 2017 AMC 8, Question \#14) | [
[
{
"aoVal": "A",
"content": "$$79$$ "
}
],
[
{
"aoVal": "B",
"content": "$$82$$ "
}
],
[
{
"aoVal": "C",
"content": "$$84$$ "
}
],
[
{
"aoVal": "D",
"content": "$$86$$ "
}
],
[
{
"aoVal": "E",
"content": "$$88$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"Assume the total amount of problems is $100$ per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got $90$ problems correct by herself, and got $168$ problems correct overall. We also know that Zoe had $80$ problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $168-90=78$. Therefore Zoe has $80+78=158$ problems out of $200$ problems correct. This is (C) $79$ percent. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11021 | f066ad13f1af4cfe932463194bd43981 | [] | 1 | single_choice | If $$15^{}\text{th}$$April is Friday, what day of the week is $$1$$\textsuperscript{st~}April ? | [
[
{
"aoVal": "A",
"content": "Sunday "
}
],
[
{
"aoVal": "B",
"content": "Monday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Friday "
}
],
[
{
"aoVal": "E",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"There are 14 days between $$1$$\\textsuperscript{st~}April and $$15^{}\\text{th}$$April. 14 days = 2 week Therefore, $$1$$\\textsuperscript{st~}April is Friday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11025 | f50915c336e745ba9c6804acc93cc4e3 | [] | 1 | single_choice | Grandma made some cheese dumplings and some blueberry dumplings. Altogether, she made $$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$$） | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$21$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"
] | [
"$$(31-11)\\div2=10.$$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11031 | f07e432e562344738c8da68471e83f39 | [] | 2 | single_choice | A worm is staying at the bottom of a well with a depth of $$13$$ metres. If it climbs up $$4$$ metres in the day time and slips down $$1$$ metre at night, which day will it climb up to the ground? | [
[
{
"aoVal": "A",
"content": "The $$4$$th day "
}
],
[
{
"aoVal": "B",
"content": "The $$5$$th day "
}
],
[
{
"aoVal": "C",
"content": "The $$6$$th day "
}
],
[
{
"aoVal": "D",
"content": "The $$7$$th day "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"
] | [
"It climbs up $$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$$ metres and reaches the ground. Then it needs four days to climb up to the ground. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11033 | f517c72c4420404fb04b325c6c44a936 | [
"其它"
] | 1 | single_choice | The volume of a cuboid is $216$. What is the least sum of the length of all its edges? | [
[
{
"aoVal": "A",
"content": "$$216$$ "
}
],
[
{
"aoVal": "B",
"content": "$$32$$ "
}
],
[
{
"aoVal": "C",
"content": "$$72$$ "
}
],
[
{
"aoVal": "D",
"content": "$$96$$ "
}
],
[
{
"aoVal": "E",
"content": "$$120$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value"
] | [
"Given the product of three numbers, the smaller the difference, the smaller the sum. $6\\times6\\times6=216$, so the answer is $6\\times 12=72.$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11034 | f519edb62aed40618a7c3447ccaa855f | [] | 1 | single_choice | The state income tax where Kristin lives is levied at the rate of $$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$$) | [
[
{
"aoVal": "A",
"content": "＄$$28000$$ "
}
],
[
{
"aoVal": "B",
"content": "＄$$32000$$ "
}
],
[
{
"aoVal": "C",
"content": "＄$$35000$$ "
}
],
[
{
"aoVal": "D",
"content": "＄$$42000$$ "
}
],
[
{
"aoVal": "E",
"content": "＄$$56000$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"
] | [
"Method $$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 $$A=32000$$. $$\\boxed{ \\text {B}}$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11038 | ebffdcfbaa844800a19d5142aac799cd | [] | 1 | single_choice | Kate sold $$10$$ dresses and Tasha sold thrice as many dresses as Kate. How many dresses did Tasha sell? | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$26$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$42$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$3$~$\\times$~$10$ = $30$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11046 | f9e949c676674428a6c6883e7582c92d | [] | 1 | single_choice | My cat snoozes for $$50$$ minutes in each hour. For how many hours a day does my cat snooze? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$15$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"
] | [
"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. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11047 | fe86a8a236f84e06897b4344fa670b02 | [] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$119$$ "
}
],
[
{
"aoVal": "B",
"content": "$$120$$ "
}
],
[
{
"aoVal": "C",
"content": "$$121$$ "
}
],
[
{
"aoVal": "D",
"content": "$$122$$ "
}
],
[
{
"aoVal": "E",
"content": "Non of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"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 $$81+27+9+3+1=121$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11052 | fa005a1c2f574aff9ce7345d92925efb | [] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$95$$ "
}
],
[
{
"aoVal": "B",
"content": "$$110$$ "
}
],
[
{
"aoVal": "C",
"content": "$$120$$ "
}
],
[
{
"aoVal": "D",
"content": "$$135$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"
] | [
"$15\\times6=90$ $90+5=95$ $95+15=110$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11055 | f0d3b78f3d8242cf833da1bf1d819922 | [] | 2 | single_choice | 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? ． | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"
] | [
"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. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11057 | fea80af2e2ee471b8aad5215ffee39bc | [
"其它"
] | 0 | single_choice | Allen has a collection of $240$ fossils. Of these, $35$\% are fossilized snail shells. How many fossilized snail shells does Allen have? | [
[
{
"aoVal": "A",
"content": "$$205$$ "
}
],
[
{
"aoVal": "B",
"content": "$$156$$ "
}
],
[
{
"aoVal": "C",
"content": "$$84$$ "
}
],
[
{
"aoVal": "D",
"content": "$$35$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$240 \\times 35$\\%=$84$, Allen has $84$ fossilized snail shells. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11058 | fa116f9b3deb4cf09dcc965b60ec2640 | [
"其它"
] | 1 | single_choice | Daniel had $51$ Lego pieces, he used $42$ pieces to make a mini statue. How many pieces of Lego does Daniel have now? | [
[
{
"aoVal": "A",
"content": "$$42$$ "
}
],
[
{
"aoVal": "B",
"content": "$$19$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$0$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$51-42=9$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11059 | fa139029459b4899854fdbeedaed6ff2 | [] | 1 | single_choice | 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） | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$21$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"
] | [
"$$(31-11)\\div2=10.$$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 11061 | feb9dbe07adc4cb0bce2c48c143904ef | [] | 1 | single_choice | 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? | [
[
{
"aoVal": "A",
"content": "$$120$$ "
}
],
[
{
"aoVal": "B",
"content": "$$90$$ "
}
],
[
{
"aoVal": "C",
"content": "$$85$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
],
[
{
"aoVal": "E",
"content": "$$55$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems"
] | [
"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. "
] | D |