math-eval/TAL-SCQ5K huggingface dataset:
Problem: The ratio of boys to girls in a school was $4:3$. The ratio of girls to teachers was $9:1$. If there were $144$ boys, how many people were there in the school in total? 
Options:
aoVal: A
content: $$108$$ 
aoVal: B
content: $$240$$ 
aoVal: C
content: $$264$$ 
aoVal: D
content: $$12$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: There are 50 stories in a book.~ Pip read 24 stories, Bud read 16 stories, Mary read 12 stories.~~What is the largest possible number of children who read only one kind of these stories? 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$40$$ 
aoVal: C
content: $$52$$ 
aoVal: D
content: $$49$$ 
aoVal: E
content: $$50$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: How many shortest paths are there from point A to point B? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
Answer: B
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Finding the Shortest Path by Number Notation->Finding the Shortest Path by Number Notation (simple)->Finding the Shortest Routes
Source: 其它
Problem: In Jane\textquotesingle s school, there are $30$ students born in April, and each of them was born in a different day. What is the probability of choosing one student who was exactly born in the first ten days of April? 
Options:
aoVal: A
content: $\frac {1}{30}$ 
aoVal: B
content: $\frac {1}{3}$ 
aoVal: C
content: $\frac {1}{4}$ 
aoVal: D
content: $\frac {1}{15}$ 
Answer: B
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Source: 其它
Problem: What time is $$300$$ minutes after $$10$$ A.M.? ． 
Options:
aoVal: A
content: $$3:00$$ A.M. 
aoVal: B
content: $$15:00$$ A.M. 
aoVal: C
content: $$5:00$$ P.M. 
aoVal: D
content: $$ 3:00$$ P.M. 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Hansen took a flight to Perth from Singapore and arrived at $$05:30$$. If the journey took him $$5\text{h}$$ $$40$$$$\min$$, at what time did the plane take off from Changi Airport in Singapore? 
Options:
aoVal: A
content: $$11:50$$ 
aoVal: B
content: $$11:10$$ 
aoVal: C
content: $$23:50$$ 
aoVal: D
content: $$23:10$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: How many numbers that the digit in tens place is $5$ less than the digit in ones place? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$5$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration
Source: 其它
Problem: Aaron finished watching a concert at $$2.45$$ p.m. The concert lasted $$\text{1h}$$$$\text{20min}$$.  What time did the concert start? 
Options:
aoVal: A
content: $$1.25$$ p.m. 
aoVal: B
content: $$1.45$$ p.m. 
aoVal: C
content: $$3.05$$ p.m. 
aoVal: D
content: $$3.35$$ p.m. 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: How many squares are there in equal part? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures
Source: 其它
Problem: A stationery shop is selling several items at different prices:  Highlighters: $\textbackslash$3$, $\textbackslash$6$  Scissors: $\textbackslash$6$, $\textbackslash$9$, $\textbackslash$11$, $\textbackslash$14$  If you want to buy one highlighter and one pair of scissors, then there are~\uline{~~~~~~~~~~}~combinations with different total prices. 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$8$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration
Source: 其它
Problem: Susan prepared a plate of cookies for her friends Ashley, Sam, Max and Olivia, Susan tried the first cookie before serving them to her friends. Ashley took $2$ cookies and gave $1$ to Sam. Max then took $3$ cookies, and gave $1$ to Olviia and $1$ to Susan. If they each ate the cookies they ended up with, who ate the most cookies? 
Options:
aoVal: A
content: Susan 
aoVal: B
content: Ashley 
aoVal: C
content: Sam 
aoVal: D
content: Max 
aoVal: E
content: Olivia 
Answer: A
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition
Source: 其它
Problem: What is the missing digit represented by $$B$$? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (vertical forms)
Problem: Johnathan has $176$ stickers. If he wants to paste $8$ stickers on each page of his sticker album, he will need $16$ more stickers. How many pages are there in the sticker album? 
Options:
aoVal: A
content: $$20$$ 
aoVal: B
content: $$22$$ 
aoVal: C
content: $$24$$ 
aoVal: D
content: $$25$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication
Source: 其它
Problem: Ali took a bus from Singapore to Malacca at $$10:45$$. The bus ride took $$4\text{h}40$$$$\min $$. What time did he reach Malacca? 
Options:
aoVal: A
content: $$02:25$$ 
aoVal: B
content: $$03:25$$ 
aoVal: C
content: $$14:25$$ 
aoVal: D
content: $$15:25$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation
Problem: Here is a figure with 12 matchsticks.  How many squares are there in the figure?  There are~\uline{~~~~~~~~~~}~squares. 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$6$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures->Classifying and Enumerating->Counting Regular Figures
Source: 其它
Problem: David takes 30 seconds to climb from the first floor to the third floor. How many seconds will it take him to climb from the third floor to the sixth floor? 
Options:
aoVal: A
content: $$30\rm{ seconds}$$ 
aoVal: B
content: $$35\rm{ seconds}$$ 
aoVal: C
content: $$40\rm{ seconds}$$ 
aoVal: D
content: $$45\rm{seconds}$$ 
aoVal: E
content: $$50\rm{seconds}$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication
Source: 其它
Problem: Seven out of forty pupils said they watch the news on television. What angle would this be on a pie chart? 
Options:
aoVal: A
content: $9^{\^{\circ}}$ 
aoVal: B
content: $36^{\circ}$ 
aoVal: C
content: $63^{\circ}$ 
aoVal: D
content: $70^{\circ}$ 
aoVal: E
content: $90^{\circ}$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Statistical Graphs->Pie Charts
Problem: The "Think Imaginary Academy" is trying to collect opinions to improve the school lunch program, which of the following information should not be collected via samples? 
Options:
aoVal: A
content: students\textquotesingle{} allergy situation 
aoVal: B
content: students\textquotesingle{} food preference 
aoVal: C
content: students\textquotesingle{} health demand 
aoVal: D
content: students\textquotesingle{} cultural background 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Source: 其它
Problem: The correct information we can get from the statement~"the chance of raining tomorrow in Boston is $$20\textbackslash\%$$"~is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: It will rain in $$20\textbackslash\%$$ of the regions of Boston tomorrow. 
aoVal: B
content: It will rain $$20\textbackslash\%$$ of the time tomorrow in Boston. 
aoVal: C
content: The probability of raining in Boston tomorrow is low. 
aoVal: D
content: It won\textquotesingle t rain in Boston tomorrow. 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Problem: Casey placed the cake batter in the oven at $$10:35$$ and she took the cake out at $$11:20$$. How long did it take for the cake to bake? 
Options:
aoVal: A
content: $$20$$ minutes 
aoVal: B
content: $$25$$ minutes 
aoVal: C
content: $$45$$ minutes 
aoVal: D
content: $$85$$ minutes 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation
Problem: There are $$4$$ children in a queue.  Ravi is in front of Janice.  Huiling is behind Siti.  Siti is $$2^{{nd}}$$ from the back in the queue.  Which of the following shows the correct order of the children in the queue counting from the front? 
Options:
aoVal: A
content: Huiling, Janice, Ravi, Siti 
aoVal: B
content: Ravi, Siti, Janice, Huiling 
aoVal: C
content: Ravi, Janice, Siti, Huiling 
aoVal: D
content: Siti, Huling, Ravi, Janice 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: What sign is missing from this number sentence?  Choose the answer.  $$720\textasciitilde?\textasciitilde16 = 45$$ 
Options:
aoVal: A
content: $$+$$ 
aoVal: B
content: $$-$$ 
aoVal: C
content: $$\times $$ 
aoVal: D
content: $$\div $$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)
Problem: Three children are queueing up.  Cindy is third in the queue.  Ali is standing between Cindy and Danny.  Who is second in the queue? 
Options:
aoVal: A
content: Ali 
aoVal: B
content: Cindy 
aoVal: C
content: Danny 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems
Problem: Some children are queuing up to buy books in the bookshop.  Ali is first in the queue.  Edward is standing between Ali and Geetha.  Geetha is queuing in front of Xueli.  Who is second in the queue? 
Options:
aoVal: A
content: Ali$$\textasciitilde$$ 
aoVal: B
content: Edward $$\textasciitilde$$ 
aoVal: C
content: Geetha$$\textasciitilde$$ 
aoVal: D
content: Xueli$$\textasciitilde$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Find the digits represented by $$A$$ and $$B$$. 
Options:
aoVal: A
content: $$A=8$$,$$B=4$$ 
aoVal: B
content: $$A=8$$,$$B=5$$ 
aoVal: C
content: $$A=9$$,$$B=4$$ 
aoVal: D
content: $$A=9$$,$$B=5$$ 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (vertical forms)
Problem: Sandra has a bag of $12$ counters.  $3$ of the counters are red.  $2$ of the counters are blue.  The rest of the counters are yellow.  Sandra takes at random a counter from the bag.  What is the probability that the counter is yellow? 
Options:
aoVal: A
content: $\dfrac{5}{7}$ 
aoVal: B
content: $\dfrac{7}{12}$ 
aoVal: C
content: $\dfrac{3}{12}$ 
aoVal: D
content: $\dfrac{2}{12}$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Simple Questions Involving Probability->Possibility
Problem: How many 2-digit numbers contain at least one sixs? 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$18$$ 
aoVal: D
content: $$20$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers->Complex Forming Numbers (with special requirements)
Problem: How many positive factors does $9072$ have? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$32$$ 
aoVal: C
content: $$50$$ 
aoVal: D
content: $$72$$ 
aoVal: E
content: $$100$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: Find the missing digit in the box. What is the missing digit?  $$\begin{matrix}\& \&~9~\&~\boxed{?}~\& 4 \textbackslash\textbackslash\& \times\& \& \&~6 \textbackslash\textbackslash{} \hline~\&5~\&~6~\& 0~\& 4\end{matrix}$$ 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (vertical forms)
Problem: What is $$2014 + 2 \times 0 \times 1 \times 4$$ equal to? 
Options:
aoVal: A
content: $$2014$$ 
aoVal: B
content: $$2016$$ 
aoVal: C
content: $$2021$$ 
aoVal: D
content: $$2022$$ 
aoVal: E
content: None of the above 
Answer: A
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication
Source: 其它
Problem: Elizabeth watched a movie that lasted $$1$$ $$\text{h}$$ $$50$$ $$\rm min$$.  The movie ended at $$1.40$$ p.m.  What time did the movie start? 
Options:
aoVal: A
content: $$11.50$$ a.m. 
aoVal: B
content: $$11.50$$ p.m. 
aoVal: C
content: $$12.10$$ a.m. 
aoVal: D
content: $$12.10$$ p.m. 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation
Problem: In a family, each boy has 3 sisters and each girl has 3 brothers. How many children are there in the family? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: None of the above 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Source: 其它
Problem: How many sqaures in each part? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures
Source: 其它
Problem: Each of $$100$$ participants of a mathematical competition received four problems to solve. The first question was solved by $$90$$ of the participants, the second by $$85$$, the third by $$80$$, and the fourth by $$70$$. From this information we can deduce that the number of participants who solved all four questions is at least:． 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$15$$ 
aoVal: C
content: $$20$$ 
aoVal: D
content: $$25$$ 
aoVal: E
content: $$70$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Extreme Value in Inclusion-Exclusion for Multi-sets
Problem: Eight people play a one-on-one knockout tournament. How many games will be played to determine the winner? 
Options:
aoVal: A
content: $$8$$ games 
aoVal: B
content: $$7$$ games 
aoVal: C
content: $$6$$ games 
aoVal: D
content: $$4$$ games 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition
Problem: A movie ended at $$3.35$$ p.m. It lasted $$\rm 1$$ $$\text{h}$$ $$\rm 50$$ $$\min $$. What time did the movie start? 
Options:
aoVal: A
content: $$1.45$$ p.m. 
aoVal: B
content: $$2.15$$ p.m. 
aoVal: C
content: $$2.45$$ p.m. 
aoVal: D
content: $$5.25$$ p.m. 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Every day Tom leaves home at $$8:30$$. It takes him $$30$$ minutes to get to the company.  What time will he get to the company? 
Options:
aoVal: A
content: 8:00 
aoVal: B
content: 9:00 
aoVal: C
content: 9:30 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: How many different five digit numbers can be made using the digits $6$~~ $3$~~ $2$~~ $6$~~ $1$? 
Options:
aoVal: A
content: $$20$$ 
aoVal: B
content: $$30$$ 
aoVal: C
content: $$40$$ 
aoVal: D
content: $$60$$ 
aoVal: E
content: $$120$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Questions Involving Permutations and Combinations
Problem: The correct information we can get from the statement~"the chance of raining tomorrow in Boston is $$20\textbackslash\%$$"~is~\uline{~~~~~~~~~~}~． 
Options:
aoVal: A
content: It will rain in $$20\textbackslash\%$$ of the regions of Boston tomorrow. 
aoVal: B
content: It will rain $$20\textbackslash\%$$ of the time tomorrow in Boston. 
aoVal: C
content: The probability of raining in Boston tomorrow is low. 
aoVal: D
content: It won\textquotesingle t rain in Boston tomorrow. 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Problem: We call a number palindromic if it doesn\textquotesingle t change after its digits are written in reverse order. Some examples of such numbers are $$1331$$ and $$24642$$. A certain car\textquotesingle s odometer shows $$15951$$ kilometers. After how many more kilometers will a palindromic number show up on the odometer again? (2007 Math Kangaroo Problem, Level 3-4, Question \#18) 
Options:
aoVal: A
content: after $$100$$ km 
aoVal: B
content: after $$110$$ km 
aoVal: C
content: after $$710$$ km 
aoVal: D
content: after $$900$$ km 
aoVal: E
content: after $$1010$$ km 
Answer: B
Analysis: N/A.　 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Dictionary Ordering->Forming Multi-Digit Numbers->Symmetric Numbers
Problem: Ben lives on the floor just below Chris.  Denise lives on the floor just above Alvin.  Denise lives on a higher floor than Chris.  Who lives on the lowest floor? 
Options:
aoVal: A
content: $$\textasciitilde$$Alvin 
aoVal: B
content: $$\textasciitilde$$Ben 
aoVal: C
content: $$\textasciitilde$$Chris 
aoVal: D
content: $$\textasciitilde$$Denise 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions
Problem: The number of purple cupcakes is $\frac{32}{56}$ the number of pink cupcakes. There were $49$ pink cupcakes. What is the ratio of the number of pink cupcakes to purple cupcakes? 
Options:
aoVal: A
content: $4:7$ 
aoVal: B
content: $7:4$ 
aoVal: C
content: $4:11$ 
aoVal: D
content: $7:11$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: Femi takes $$2$$ hours and $$53$$ minutes to cycle from London to Reading. If he arrived at~ $$15:21$$, at what time must he have set off? 
Options:
aoVal: A
content: $$12:24$$pm 
aoVal: B
content: $$1:24$$pm 
aoVal: C
content: $$12:28$$pm 
aoVal: D
content: $$12:18$$pm 
aoVal: E
content: $$1:28$$pm 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: $3$ plumbers were needed to fix $4$ identical pipes in $2$ days. How many plumbers are needed to fix $6$ identical pipes in a day? 
Options:
aoVal: A
content: $1$ 
aoVal: B
content: $4$ 
aoVal: C
content: $6$ 
aoVal: D
content: $9$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: Amy tosses two dice.  Before she saw the results, she asked her three friends to guess what the sum of the two dice she threw was.  Jimmy gave the answer of 6, Daisy gave the answer of 7, and Kitty gave the answer of 8.  Who had the best chance of winning? 
Options:
aoVal: A
content: Jimmy 
aoVal: B
content: Daisy 
aoVal: C
content: Kitty 
aoVal: D
content: Jimmy and Daisy 
aoVal: E
content: Daisy and Kitty 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Typical Probability Problems->Tossing Coins
Source: 其它
Problem: Elizabeth watched a movie that lasted $$1$$ $$\text{h}$$ $$50$$ $$\rm min$$. The movie ended at $$1.40$$ p.m. What time did the movie start? 
Options:
aoVal: A
content: $$11.50$$ a.m. 
aoVal: B
content: $$11.50$$ p.m. 
aoVal: C
content: $$12.10$$ a.m. 
aoVal: D
content: $$12.10$$ p.m. 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation
Problem: There are $$25$$ players in a chess tournament. If each game is played by $$2$$ players, and each player plays every other player exactly once, what is the total number of games played in the tournament? 
Options:
aoVal: A
content: $$300$$ 
aoVal: B
content: $$600$$ 
aoVal: C
content: $$625$$ 
aoVal: D
content: $$150$$ 
aoVal: E
content: $$50$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition
Problem: There are $$9$$ players in a chess tournament. If each game is played by $$2$$ players and each player plays every other player exactly once, what is the total number of games played in the tournament? 
Options:
aoVal: A
content: $$90$$ 
aoVal: B
content: $$18$$ 
aoVal: C
content: $$36$$ 
aoVal: D
content: $$72$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition
Problem: Which of the following is the correct order of the fractions $1\frac{3}{5}$, $\frac{20}{14}$, $\frac{14}{11}$ from least to greatest? 
Options:
aoVal: A
content: $1\frac{3}{5}$\textless$\frac{20}{14}$\textless$\frac{14}{11}$ 
aoVal: B
content: $\frac{14}{11}$\textless$\frac{20}{14}$\textless$1\frac{3}{5}$ 
aoVal: C
content: $1\frac{3}{5}$\textless$\frac{14}{11}$\textless$\frac{20}{14}$ 
aoVal: D
content: $\frac{14}{11}$\textless$1\frac{3}{5}$\textless$\frac{20}{14}$ 
aoVal: E
content: $\frac{20}{14}$\textless$\frac{14}{11}$\textless$1\frac{3}{5}$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: If a fair die is rolled $30$ times, how many times would you expect to get a \textquotesingle$2$\textquotesingle? 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$2$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Typical Probability Problems->Rolling Dice
Problem: Express $9k-4-5k+6+2k$ in the simplest form. 
Options:
aoVal: A
content: $6k+2$ 
aoVal: B
content: $6k-2$ 
aoVal: C
content: $2k+2$ 
aoVal: D
content: $2k-2$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: James has $12$ strawberries that he wants to split into $3$ groups so that each group is not empty and has a different number of strawberries. How many different ways can he do that? 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$11$$ 
aoVal: E
content: $$13$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Splitting Whole Numbers
Source: 其它
Problem: What operations ($$+$$, $$-$$, $$\times$$, $$\div$$) can be put in the blanks to make the equality true?  $$16$$~\uline{~~~~~~~~~~}~$$8$$~\uline{~~~~~~~~~~}~$$4=32$$. 
Options:
aoVal: A
content: $16+8+4=32$ 
aoVal: B
content: $16-8\times4=32$ 
aoVal: C
content: $16+8\times4=32$ 
aoVal: D
content: $16\times8\div4=32$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)