math-eval/TAL-SCQ5K huggingface dataset:
Problem: How many times does the number $$2$$ appear when counting from $$1$$ to $$43$$? 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$16$$ 
aoVal: C
content: $$17$$ 
aoVal: D
content: $$18$$ 
aoVal: E
content: $$19$$ 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Change a digit of the number $12315$ to make the new five-digit number be divisible by $25$. What is the new five-digit number? 
Options:
aoVal: A
content: $$12325$$ 
aoVal: B
content: $$12335$$ 
aoVal: C
content: $$12345$$ 
aoVal: D
content: $$12355$$ 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Source: 其它
Problem: Which answer is \textbf{NOT} a square number? 
Options:
aoVal: A
content: $$72$$ 
aoVal: B
content: $$49$$ 
aoVal: C
content: $$81$$ 
aoVal: D
content: $$64$$ 
aoVal: E
content: $$169$$ 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers
Problem: Ravi divides a large number by a smaller number.  The remainder is $$5$$.  Which of these numbers could he have divided by? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$5$$ 
aoVal: E
content: $$6$$ 
Answer: E
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders->Feature of Remainder
Problem: $(3+4)^{2}-2\times 3^{2}$ 
Options:
aoVal: A
content: $$29$$ 
aoVal: B
content: $$30$$ 
aoVal: C
content: $$31$$ 
aoVal: D
content: $$32$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->The Relationship between Exponents and the Number of Factors
Source: 其它
Problem: An ice cream stand was selling ice cream in five different flavors. A group of children came to the stand and each child bought two scoops of ice cream with two different flavors. If none of the children chose the same combination of flavors and every such combination of favors was chosen, how many children were there? 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$20$$ 
aoVal: D
content: $$25$$ 
aoVal: E
content: $$30$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Word Problems Involving Factors and Multiples->Multiples Word Problems
Problem: One class is on PE class. If each row is $12$ people, the last row is $8$ people. If each row is $15$ people, the last row is $11$ people. Two student of the class were sick and absent from the PE class. How many students are there in the class? 
Options:
aoVal: A
content: $$48$$ 
aoVal: B
content: $$58$ 
aoVal: C
content: $$45$$ 
aoVal: D
content: $$36$$ 
aoVal: E
content: $$64$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: 11 + 24 + 36 = 
Options:
aoVal: A
content: Odd 
aoVal: B
content: Even 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers
Source: 其它
Problem: The characteristic of numbers that are divisible by $$9$$ is． 
Options:
aoVal: A
content: Last digit is divisible by $$9$$. 
aoVal: B
content: Last two digits are divisible by $$9$$. 
aoVal: C
content: The sum of digits is divisible by $$3$$. 
aoVal: D
content: The sum of digits is divisible by $$9$$. 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Problem: George buys boxes of mangoes for $$$18$$ each and sells them for $$$25$$ per box. How many boxes of mangoes would he have to sell to make $$$63$$? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: $$7$$ 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: The teacher writes a two-digit number on the whiteboard, then writes the smallest one-digit number to its right, and at last, adds $$11$$ to the number. The teacher gets a sum of $$111$$. ~Which two-digit number did the teacher write at first on the whiteboard? 
Options:
aoVal: A
content: $$13$$ 
aoVal: B
content: $$12$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$11$$ 
aoVal: E
content: $$10$$ 
Answer: E
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: What is thirty million, fourty-five thousand, five hundred and three in figures? 
Options:
aoVal: A
content: 3 450 503 
aoVal: B
content: 3 045 503 
aoVal: C
content: 30 045 053 
aoVal: D
content: 30 450 503 
aoVal: E
content: 30 045 503 
Answer: E
Analysis: N/A.　 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits
Problem: How many divisors does the number $$ 2\times 3\times5\times7\times11$$ have? 
Options:
aoVal: A
content: $$2310$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$2004$$ 
aoVal: E
content: $$32$$ 
Answer: E
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Theorem of the Number of Factors of a Number->Applying Theorem of the Number of Factors of a Number Directly->The Total Number of Factors
Problem: The children go outing together, the number of the first team is more than the second team, the number of first team is less than the third team. The number of fourth team is more than the second team. Which group has the most people? 
Options:
aoVal: A
content: team $3$ 
aoVal: B
content: team $1$ 
aoVal: C
content: team $2$ 
aoVal: D
content: team $4$ 
aoVal: E
content: None of them above 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: A number gives a remainder of $$1$$ when divided by $$5$$, a remainder of $$2$$ when divided by $$6$$, and a remainder of $$9$$ when divided by $$11$$. What is the smallest number? 
Options:
aoVal: A
content: $$26$$ 
aoVal: B
content: $$30$$ 
aoVal: C
content: $$56$$ 
aoVal: D
content: $$86$$ 
aoVal: E
content: $$116$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems
Source: 其它
Problem: 109 divided by a 2-digit number has a remainder of 4. How many such 2-digit numbe are there? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems
Source: 其它
Problem: Which of the following is not a multiple of $$8$$? 
Options:
aoVal: A
content: $$32$$ 
aoVal: B
content: $$56$$ 
aoVal: C
content: $$68$$ 
aoVal: D
content: $$96$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples
Problem: Complete the number pattern.  2946, 2926, 2906,~\uline{~~~~~~~~~~}~, 2866 . 
Options:
aoVal: A
content: $$2706$$ 
aoVal: B
content: $$2886$$ 
aoVal: C
content: $$2926$$ 
aoVal: D
content: $$2986$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: The 5-digit number~\uline{2018U}~is divisible by 9. What is the remainder when this number is divided by 8? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$7$$ 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems
Source: 其它
Problem: ? 
Options:
aoVal: A
content: a 
aoVal: B
content: B 
aoVal: C
content: c 
aoVal: D
content: d 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization
Source: 其它
Problem: What is the theoretical probability of getting an "$A$" from "THINK ACADEMY"? 
Options:
aoVal: A
content: $1$ 
aoVal: B
content: $0$ 
aoVal: C
content: $\frac{1}{12}$ 
aoVal: D
content: $\frac{1}{6}$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: A large clinical trial was designed to determine whether a certain vitamin improves the general health of adults.The investigators first identified 85 variables that measure various aspects of the general health of adults. Because each adult in the clinical trial was to serve as his or her own control, the 85 variables were measured for each adult, both before taking the vitamin and after taking the vitamin for three months. The investigators then performed 85 matched-pair t-tests, one for each variable. They found statistically significant results at the 0.05evel in 2 of the variables, both in the direction of improved general health. Which of the following should the investigators conclude? 
Options:
aoVal: A
content: There is evidence that the vitamin improves the health of adults because 2 of the 85 tests were statistically significant. 
aoVal: B
content: There is evidence that the vitamin improves the health of adults because in clinical trials investigators typically underestimate the proportion of the population that is helped by a vitamin. 
aoVal: C
content: There is insufficient evidence that the vitamin improves the health of adults because at the 0.05 significance level, one could easily get statistically significant results in 2 out of 85 tests just due to chance variability. 
aoVal: D
content: There is insufficient evidence that the vitamin improves the health of adults because the sample size of 85 is not large enough to draw a conclusion. 
aoVal: E
content: No conclusion can be drawn because an even number of variables is needed for a matched-pairs design. 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Take a piece of string of length $8$, fold it in half $3$ times, cut it down the middle with scissors, and get some short string. So how many ropes are there of length $1$? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$7$$ 
aoVal: E
content: $$8$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: When a number is divided by $$8$$, the quotient and the remainder are the same. which of the following is the number? 
Options:
aoVal: A
content: $$62$$ 
aoVal: B
content: $$63$$ 
aoVal: C
content: $$64$$ 
aoVal: D
content: $$65$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders
Problem: A wall measures $$\rm 8m$$ by $$\rm 20m$$.  Pip wants to wallpaper this wall with square pictures.  What is the length of the largest picture he can use so that all of the wall will be covered? 
Options:
aoVal: A
content: $$\rm 2m$$ 
aoVal: B
content: $$\rm 3m$$ 
aoVal: C
content: $$\rm 4m$$ 
aoVal: D
content: $$\rm 5m$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Factors and the Greatest Common Factors->The Greatest Common Factor of Two Numbers
Problem: Which one of these numbers has exactly two different prime factors?  $$42\textasciitilde\textasciitilde\textasciitilde11\textasciitilde\textasciitilde\textasciitilde26\textasciitilde\textasciitilde\textasciitilde49\textasciitilde\textasciitilde\textasciitilde30$$ 
Options:
aoVal: A
content: $$42$$ 
aoVal: B
content: $$11$$ 
aoVal: C
content: $$26$$ 
aoVal: D
content: $$49$$ 
aoVal: E
content: $$30$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers->Knowing Prime and Composite Numbers
Problem: There are $$100$$ cars and motorcycles parked in a parking lot. If there are $$360$$ wheels in total, how many motorcycles are parked there? 
Options:
aoVal: A
content: $$20$$ 
aoVal: B
content: $$12$$ 
aoVal: C
content: $$80$$ 
aoVal: D
content: $$15$$ 
aoVal: E
content: $$100$$ 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Which of the following is the correct expression of the base $7$ numeral system? 
Options:
aoVal: A
content: $\left (3423\right )\_5$ 
aoVal: B
content: $\left (5143\right )\_6$ 
aoVal: C
content: $\left (3256\right )\_7$ 
aoVal: D
content: $\left (3634\right )\_5$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Properties and Applications of Number Bases
Problem: 989 pieces of candy are packed into packages, each of which contains 4 pieces of candy. In order to complete the last package, how many more pieces of candy are needed? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$5$$ 
aoVal: E
content: None of the above 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Source: 其它
Problem: What number between 37 and 47 is exactly divisble by both 2 and 3? 
Options:
aoVal: A
content: $$38$$ 
aoVal: B
content: $$39$$ 
aoVal: C
content: $$42$$ 
aoVal: D
content: $$44$$ 
aoVal: E
content: $$45$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
Source: 其它
Problem: Which of the following is a prime number? ． 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$15$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$16$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers
Problem: ? 
Options:
aoVal: A
content: a 
aoVal: B
content: b 
aoVal: C
content: c 
aoVal: D
content: d 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization
Source: 其它
Problem: Which of the following statements is incorrect? 
Options:
aoVal: A
content: $$3$$ is a multiple of $$39$$ 
aoVal: B
content: $$2$$ is a common factor of $$26$$ and $$54$$ 
aoVal: C
content: $$52$$ is a multiple of $$13$$ 
aoVal: D
content: $$6$$ is a common factor of $$18$$ and $$72$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
Problem: There is a three-digit number. The hundreds digit of the number is $$6$$ more than the smallest even number. The tens digit is the smallest odd number and this number is a multiple of both $$2 $$ and $$5$$ . What is this number? ． 
Options:
aoVal: A
content: $$210$$ 
aoVal: B
content: $$205$$ 
aoVal: C
content: $$800$$ 
aoVal: D
content: $$810$$ 
aoVal: E
content: $$815$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Problem: The first four numbers of a sequence are $$12$$, $$15$$, $$18$$, and $$21$$. What is the difference between the sixth and tenth numbers of this sequence? 
Options:
aoVal: A
content: $$14$$ 
aoVal: B
content: $$13$$ 
aoVal: C
content: $$11$$ 
aoVal: D
content: $$12$$ 
aoVal: E
content: $$22$$ 
Answer: D
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Which of the numbers below is odd regardless of the value of the natural number $$n$$? 
Options:
aoVal: A
content: $$2003n$$ 
aoVal: B
content: $$n^{2}+2003$$ 
aoVal: C
content: $$n^{3}$$ 
aoVal: D
content: $$2n^{2}+2003$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Mixed Calculations of Odd and Even Numbers
Problem: Which of these numbers is not a prime number? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$9$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Prime Factorization (Equations)
Problem: ? 
Options:
aoVal: A
content: a 
aoVal: B
content: b 
aoVal: C
content: c 
aoVal: D
content: d 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers
Source: 其它
Problem: Today, the restaurant sold $$5$$ sandwiches, and $$3$$ less than hamburgers. How many sandwiches and hamburgers did the restaurant sell today? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$13$$ 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Problem: The numbers $1$, $2$, $3$, $5$, $6$, $7$ and $8$ are divided into groups of one or more numbers. The sum of the numbers in each group is the same. Which of the following can be the sum of the numbers in each group? 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$18$$ 
aoVal: D
content: $$16$$ 
aoVal: E
content: $$8$$ or $$16$$ 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Which of the following numbers is not an integer? ($$2015$$ Math Kangaroo Problem, Level $$7-8$$, Question \#$$6$$) 
Options:
aoVal: A
content: $$\frac{2011}{1}$$ 
aoVal: B
content: $$\frac{2012}{2}$$ 
aoVal: C
content: $$\frac{2013}{3}$$ 
aoVal: D
content: $$\frac{2014}{4}$$ 
aoVal: E
content: $$\frac{2015}{5}$$ 
Answer: D
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers
Source: 其它
Problem: How many three-digit numbers are there such that the sum of their digits equals $$4$$? (2001 Math Kangaroo Problem, Level 3-4, Question \#20) 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$7$$ 
aoVal: E
content: $$6$$ 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits
Problem: Determine if the results of the following are odd or even numbers. 
Options:
aoVal: A
content: Odd 
aoVal: B
content: Even 
Answer: B
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers
Source: 其它
Problem: Chris bought $$$89.90$$ worth of groceries and paid $$10$$\% GST (Goods and Services Tax) for them. How much did he pay in total? 
Options:
aoVal: A
content: $$$97.89$$ 
aoVal: B
content: $$$97.69$$ 
aoVal: C
content: $$$98.79$$ 
aoVal: D
content: $$$97.79$$ 
aoVal: E
content: $$$98.89$$ 
Answer: E
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Which of the following numbers is a multiple of $$25$$? 
Options:
aoVal: A
content: $$902345$$ 
aoVal: B
content: $$103970$$ 
aoVal: C
content: $$2349200$$ 
aoVal: D
content: $$1398052$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Source: 其它
Problem: Alice and Sara made a total of $26$ cookies. Sara\textquotesingle s number of cookies is three times that of Alice, and there are two more. How many cookies did Sara make? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$18$$ 
aoVal: C
content: $$19$$ 
aoVal: D
content: $$20$$ 
aoVal: E
content: $$22$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: The sum of $$1+12+123+1234$$ is an~\uline{~~~~~~~~~~}~number. 
Options:
aoVal: A
content: odd 
aoVal: B
content: even 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers
Problem: Which number is divisible by both $$3$$ and $$4$$? 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$16$$ 
aoVal: C
content: $$20$$ 
aoVal: D
content: $$48$$ 
aoVal: E
content: $$56$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Simple Questions of Division without Remainders
Problem: George has $$46$$ stamps; Gina has $$28$$ stamps and John has $$22$$ stamps. If all the stamps were mixed together and redistributed to these three children, how many stamps would each person get? 
Options:
aoVal: A
content: $$14$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$32$$ 
aoVal: E
content: $$24$$ 
Answer: D
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: When three identical rectangles are placed next to each other, they form a square. If the area of a rectangle is $$48$$ square centimetres, what is the length of the rectangle? 
Options:
aoVal: A
content: $$6cm$$ 
aoVal: B
content: $$16cm$$ 
aoVal: C
content: $$4cm$$ 
aoVal: D
content: $$12cm$$ 
aoVal: E
content: $$16cm$$ 
Answer: D
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: A person pushes a 60 kg grocery cart, initially at rest, across a parking lot. He exerts a pushing force directed 20$^{\circ}$~below the horizontal. If the person pushes the cart with a force of 300 N for 5 m across horizontal ground and then releases the cart, the cart has a speed of 3 m/s. What is the work done by friction during this motion? 
Options:
aoVal: A
content: $$-1230J$$ 
aoVal: B
content: $$-1140J$$ 
aoVal: C
content: $$1140J$$ 
aoVal: D
content: $$1230J$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: If $n$ is an even positive integer, the double factorial notation $n!!$ represents the product of all the even integers from $2$ to $n$. For example, $8!!=2\cdot4\cdot6\cdot8$. What is the units digit of the following sum?  $2!!+4!!+6!!+\cdot\cdot\cdot+2018!!+2020!!+2022!!$ 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$8$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples
Source: 其它
Problem: Lily cut a disc~with a radius of $$10 cm$$ from the middle. What is the circumference of each half disc after cutting?($\pi=3$) 
Options:
aoVal: A
content: $$20 cm$$ 
aoVal: B
content: $$30 cm$$ 
aoVal: C
content: $$40 cm$$ 
aoVal: D
content: $$50 cm$$ 
aoVal: E
content: $$60 cm$$ 
Answer: D
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: When you divide a natural number $$n$$ by $$7$$, you get a remainder of $$4$$. When you divide the number $$n$$ by $$11$$ you also get a remainder of $$4$$. What is the smallest value of $$n$$? 
Options:
aoVal: A
content: $$31$$ 
aoVal: B
content: $$28$$ 
aoVal: C
content: $$81$$ 
aoVal: D
content: $$77$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->Questions Involving Remainders
Problem: There are $$19$$ girls and $$12$$ boys in the school yard. At least how many students need to join them so that six groups with the same number of students can be formed? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: E
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples