math-eval/TAL-SCQ5K huggingface dataset:
Problem: During a party four friends are going to give each other gifts in such a way that everybody gives one gift and receives one gift (of course, no one should receive a gift from himself or herself). In how many ways can this be accomplished? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$16$$ 
aoVal: E
content: $$24$$ 
Answer: A
Analysis: N/A.　 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication->Matching Objects (with specific requirements)
Problem: Adam can travel from City $$A$$ to City $$B$$ by a bus, a train or a plane. To get from City $$B$$ to Town $$C$$, he can hire a taxi, rent a car, a motorcycle or a bicycle. There is no direct transportation from City $$A$$ to Town $$C$$. How many ways can Adam travel from City $$A$$ to Town $$C$$? 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: None of the above 
Answer: C
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration
Source: 其它
Problem: Noa is deciding what to wear. He has $$5$$ T-shirt and $$6$$ jeans to choose. He hasdifferent ways of dressing. 
Options:
aoVal: A
content: $$11$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$30$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication
Problem: Barbie purchased $\textbackslash$52$ worth of mangoes. The mangoes were priced at $\textbackslash$25$ per$\textasciitilde kg$. Determine the mass of mangoes purchased. 
Options:
aoVal: A
content: $2.8\textasciitilde kg$ 
aoVal: B
content: $2\textasciitilde kg$ $8\textasciitilde g$ 
aoVal: C
content: $28\textasciitilde kg$ 
aoVal: D
content: $2\textasciitilde kg$ $80\textasciitilde g$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: Determine the height of the triangle. 
Options:
aoVal: A
content: $13\textasciitilde cm$ 
aoVal: B
content: $23\textasciitilde cm$ 
aoVal: C
content: $48\textasciitilde cm$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: If today is Sunday, tomorrow will be Monday. 
Options:
aoVal: A
content: Certain 
aoVal: B
content: Impossible 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Simple Questions Involving Probability->Possibility
Source: 其它
Problem: $72$ people play a one-on-one knockout tournament. How many games will be played to determine the winner? 
Options:
aoVal: A
content: $$24$$ games 
aoVal: B
content: $$36$$ games 
aoVal: C
content: $$71$$ games 
aoVal: D
content: $$72$$ games 
aoVal: E
content: $$144$$ games 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition
Problem: The desks in a Primary $$3$$ classroom are arranged in straight rows. Each row has the same number of desks. Greggory sits at the desk that is in the fourth row from the front and back. He sits at the centre of his row and there are $$5$$ desks to his left. How many desks are in the classroom? 
Options:
aoVal: A
content: $$63$$ 
aoVal: B
content: $$99$$ 
aoVal: C
content: $$77$$ 
aoVal: D
content: $$81$$ 
aoVal: E
content: None of the above 
Answer: C
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems
Source: 其它
Problem: Any of the signs $$+$$, $$-$$, $$\times$$, $$\div$$ and brackets can be filled in the gaps below to make the equality true. Which of the following choices is true?  $$8\textasciitilde\textasciitilde\textasciitilde8\textasciitilde\textasciitilde\textasciitilde8\textasciitilde\textasciitilde\textasciitilde8\textasciitilde\textasciitilde\textasciitilde=8$$ 
Options:
aoVal: A
content: $8\times8\div8+8=8$ 
aoVal: B
content: $8-8\times8+8=8$ 
aoVal: C
content: $8\times8\div8+8=8$ 
aoVal: D
content: $\left( 8-8\right)\times8+8=8$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Zachary left a birthday party at $$2.05$$ p.m.  He was at the party for $$3$$ h $$15$$ min.  At what time did he arrive at the party? 
Options:
aoVal: A
content: $$5.20$$ a.m. 
aoVal: B
content: $$10.50$$ a.m. 
aoVal: C
content: $$5.20$$ p.m. 
aoVal: D
content: $$10.50$$ p.m. 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation
Problem: How many different real numbers $x$ satisfy the equation $(\sqrt{x}-4)^{2}=16$? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: The year $$2022$$ is an $$interesting$$ year because it contains only digit $$2$$ and $$0$$. How many years later will be the next interesting year? 
Options:
aoVal: A
content: $$178$$ 
aoVal: B
content: $$180$$ 
aoVal: C
content: $$198$$ 
aoVal: D
content: $$200$$ 
aoVal: E
content: None of the above 
Answer: A
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration
Source: 其它
Problem: Water is dripping from a tap into a pail, at a rate of $$4\rm ml$$ every second.  At this rate, how much water will be in the pail after $$2$$ minutes? 
Options:
aoVal: A
content: $$120\rm ml$$ 
aoVal: B
content: $$240\rm ml$$ 
aoVal: C
content: $$480\rm ml$$ 
aoVal: D
content: $$800\rm ml$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Multiplication of Whole Numbers->Multiplication of Multi-Digit Numbers and 1-Digit Numbers->Multiplication of 3-digit Numbers(with 0 in the tens or ones place) and 1-digit Numbers 
Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Problem: Which one of the following is not a common factor of $$12$$ and $$18$$? 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas In-curriculum->Knowledge Point->Knowing Numbers->Characteristics of Numbers ->Factors and Multiples->The Common Factors of Two Given Numbers
Overseas Competition->Knowledge Point->Counting Modules
Problem: Which of the following statements is false about MAD? 
Options:
aoVal: A
content: For every given finite data set, we can find its MAD. 
aoVal: B
content: In order to find the MAD of a data set, we have to first find its mean. 
aoVal: C
content: MAD is a measure of center. 
aoVal: D
content: MAD is a measure of spread. 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Basic Concepts of Statistics
Source: 其它
Problem: For the number sentence below, what is the answer?  15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 
Options:
aoVal: A
content: $$210$$ 
aoVal: B
content: $$215$$ 
aoVal: C
content: $$220$$ 
aoVal: D
content: $$225$$ 
aoVal: E
content: None of the above 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication
Source: 其它
Problem: How many of the numbers between $1$ and $50$ are divisible by both $2$ and $5$? 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$25$$ 
aoVal: D
content: $$30$$ 
aoVal: E
content: $$35$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: SASMO 2014 P2 Q4  Jane wrote the word STUDENTS thrice. How many times did she write the letter S? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$10$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Source: 其它
Problem: In a class of $50$, every student had to take an extra module. Some students took extra mathematics modules while some students took extra science modules. A total of $38$ students took the extra mathematics modules while $24$ students took extra mathematics and science modules. How many students took extra science modules? 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$24$$ 
aoVal: C
content: $$26$$ 
aoVal: D
content: $$36$$ 
aoVal: E
content: $$39$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: If a fair dice is rolled $30$ times, how many times would you expect to get a ``$2$''? 
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: Mark has some one-dollar coins and some two-dollar coins, and there are $$48$$ coins in total.  The total value of them is the same.  Given that the one-dollar coin weighs $8$ grams and the two-dollar coin weighs $9$ grams.  What is the total weight of all the coins? 
Options:
aoVal: A
content: $$400$$g 
aoVal: B
content: $$404$$g 
aoVal: C
content: $$408$$g 
aoVal: D
content: $$412$$g 
aoVal: E
content: $$416$$g 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Typical Probability Problems->Tossing Coins
Source: 其它
Problem: Every day John leaves home at $$8:45$$. It takes him $$15$$ minutes to get to school.  What time does he get to school? 
Options:
aoVal: A
content: 8:30 
aoVal: B
content: 9:00 
aoVal: C
content: 9:30 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation
Problem: Boston left his home at $$\text{11.58 a}\text{.m}.$$ to meet his friend for lunch at the mall. He took $$\text{1h 12min}$$ to reach the mall. What time did Boston arrange to meet his friend? 
Options:
aoVal: A
content: $$10\text{.46 a}\text{.m}.$$ 
aoVal: B
content: $$10\text{.46 p}\text{.m}.$$ 
aoVal: C
content: $$1\text{.10 a}\text{.m}.$$ 
aoVal: D
content: $$1\text{.10 p}\text{.m}.$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Which of the following is the same as $40010\textasciitilde g$? 
Options:
aoVal: A
content: $4.01\textasciitilde kg$ 
aoVal: B
content: $40\textasciitilde kg$ $10\textasciitilde g$ 
aoVal: C
content: $40.1\textasciitilde kg$ 
aoVal: D
content: $40\textasciitilde kg$ $100\textasciitilde g$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: Mrs Lim completed a puzzle at $$5.45$$ p.m.  She took $$\rm 3h15min$$ to complete it.  At what time did she start working on the puzzle? 
Options:
aoVal: A
content: $$2.30$$ p.m. 
aoVal: B
content: $$3.00$$ p.m. 
aoVal: C
content: $$3.30$$ p.m. 
aoVal: D
content: $$9.00$$ p.m. 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Length of tunnel $=$~\uline{~~~~~~~~~~}~$\textasciitilde m$ 
Options:
aoVal: A
content: $800-120=680$ 
aoVal: B
content: $800+120=920$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: If a fair dice is rolled $30$ times, how many times would you expect to get a ``$2$''? 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$2$$ 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Typical Probability Problems->Rolling Dice
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: $\frac {1}{15}$ 
aoVal: E
content: $\frac {1}{10}$ 
Answer: B
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Source: 其它
Problem: $$45\div 5=3\square 3$$  Choose a suitable sign to be put in the box for the above number sentence. 
Options:
aoVal: A
content: $$+$$ 
aoVal: B
content: $$-$$ 
aoVal: C
content: $$\times $$ 
aoVal: D
content: $$\div $$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Nellie went for a movie. The movie ended at $$23$$ $$50$$.  If the movie lasted for $$2\text{h}$$ $$5$$$$\min $$, at what time did the movie start? 
Options:
aoVal: A
content: $$1.55$$ a.m. 
aoVal: B
content: $$1.55$$ p.m. 
aoVal: C
content: $$9.45$$ a.m. 
aoVal: D
content: $$9.45$$ p.m. 
Answer: D
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation
Problem: What is the sum of the $$2^{\text{nd}}$$ multiple and the $$4^{\text{th}}$$ multiple of $$8$$? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$32$$ 
aoVal: C
content: $$48$$ 
aoVal: D
content: $$64$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules
Overseas In-curriculum->Knowledge Point->Knowing Numbers->Characteristics of Numbers ->Factors and Multiples->Finding Multiples of a Given Number
Problem: Which of the following numbers, when rounded to the nearest thousand, hundred, and ten, equals $$3000$$, $$3500$$, and $$3460$$ respectively? 
Options:
aoVal: A
content: $$3210$$ 
aoVal: B
content: $$3333$$ 
aoVal: C
content: $$3456$$ 
aoVal: D
content: $$3517$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules
Source: 其它
Problem: A drawer contains ten identical yellow socks, eight identical blue socks and four identical pink socks. Amrita picks socks from the drawer without looking. What is the smallest number of socks she must pick to be sure that she has at least three pairs of matching socks? 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$11$$ 
aoVal: E
content: $$13$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems
Problem: Fourteen cats took part in a cat play. Some of them played moms and some of them played their kids. Every mom in this play had at least two kids. What is the greatest possible number of cat-moms in the play? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$7$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations->Questions Involving Combinations
Problem: A bag contains $$20$$ red discs, $$10$$ green discs and $$30$$ blue discs. A disc is chosen at random. Which of these events is the \textbf{most} likely? 
Options:
aoVal: A
content: The chosen disc is red. 
aoVal: B
content: The chosen disc is blue 
aoVal: C
content: The chosen disc is not red. 
aoVal: D
content: The chosen disc is green or blue. 
aoVal: E
content: The chosen disc is not green. 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability
Problem: After giving $$8$$ stickers each to $$38$$ pupils in school, Mrs Ho had $$12$$ stickers left.  How many stickers did Mrs Ho have at first? 
Options:
aoVal: A
content: $$292$$ 
aoVal: B
content: $$304$$ 
aoVal: C
content: $$316$$ 
aoVal: D
content: $$480$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Mixed Operations->Mixed Operations of Multiplication and Addition of Whole Numbers
Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication
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: The students had a race. Can you tell who runs the fastest?  \textbf{Pip came in third.}  \textbf{Bud was in front of Eddie.}  \textbf{Avril lost to Pip in the race.} 
Options:
aoVal: A
content: Bud 
aoVal: B
content: Avril 
aoVal: C
content: Eddie 
aoVal: D
content: Pip 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions
Problem: How many minutes are there in three and a half hours? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$60$$ 
aoVal: C
content: $$210$$ 
aoVal: D
content: $$180$$ 
aoVal: E
content: $$3600$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: Suppose you estimate the flu vaccine has an external benefit of ¥10/shot. The government recognizes this positive externality and votes to give people who get vaccinated a ¥15/shot subsidy. What happens as a result 
Options:
aoVal: A
content: there is no longer a market failure 
aoVal: B
content: too many people get vaccinated but there is no DWL 
aoVal: C
content: too few people get vaccinated so there is DWL 
aoVal: D
content: too many people get vaccinated so there is DWL 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Source: 其它
Problem: How many different ways are there of paying exactly £$$1$$ using $$5$$p and/or $$10$$p pieces? 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$21$$ 
aoVal: D
content: $$11$$ 
aoVal: E
content: $$100$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: What is the second smallest positive integer greater than $1$ that leaves a remainder of $3$ when divided by $8$, $9$, and $10$? 
Options:
aoVal: A
content: $$363$$ 
aoVal: B
content: $$366$$ 
aoVal: C
content: $$543$$ 
aoVal: D
content: $$723$$ 
aoVal: E
content: $$726$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: $$55+505+5005+50005+\ldots +5\underbrace{00\ldots 0}\_{50"0"s}5=$$ 
Options:
aoVal: A
content: $$\underbrace{55\ldots\ldots 5}\_{50 "5"s}805$$ 
aoVal: B
content: $$\underbrace{55\ldots\ldots 5}\_{49 "5"s}705$$ 
aoVal: C
content: $$\underbrace{55\ldots\ldots 5}\_{49 "5"s}805$$ 
aoVal: D
content: $$\underbrace{55\ldots\ldots 5}\_{49 "5"s}750$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Problem: Marcus took half an hour to complete his homework. He started doing his homework at $$11.50 \rm a.m$$. What time did Marcus complete his homework? 
Options:
aoVal: A
content: $$11.20 \rm a.m$$. 
aoVal: B
content: $$11.20 \rm p.m$$. 
aoVal: C
content: $$12.20 \rm a.m$$. 
aoVal: D
content: $$12.20 \rm p.m$$. 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: What is the missing sign in the box?  $8\square2=16$ 
Options:
aoVal: A
content: $$+$$ 
aoVal: B
content: $$-$$ 
aoVal: C
content: $$\times$$ 
aoVal: D
content: $$\div$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: There were $$10$$ students in a class. Each student shook hands only once with the other $$9$$ students in the class. How many handshakes were there in total? 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$45$$ 
aoVal: C
content: $$55$$ 
aoVal: D
content: $$90$$ 
Answer: B
Analysis: N/A.　 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition->Number of Handshake Problem
Overseas In-curriculum->Knowledge Point->Fun Problems in Math->Reasoning
Problem: Toss a fair coin three times. What is the probability of getting one head and two tails? 
Options:
aoVal: A
content: $$\frac{1}{2}$$ 
aoVal: B
content: $$\frac{1}{4}$$ 
aoVal: C
content: $$\frac{1}{8}$$ 
aoVal: D
content: $$\frac{3}{8}$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability
Problem: How many whole numbers from $$1$$ to $$201$$ consist of only even digits? 
Options:
aoVal: A
content: $$201$$ 
aoVal: B
content: $$40$$ 
aoVal: C
content: $$25$$ 
aoVal: D
content: $$20$$ 
aoVal: E
content: None of the above 
Answer: C
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration
Source: 其它
Problem: Granny went out to the yard and called all the hens and her cat. All 20 legs ran to her. How many hens does granny have? 
Options:
aoVal: A
content: $$11$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$4$$ 
Answer: C
Analysis: $$N.A.$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules
Source: 其它
Problem: For the number sentence below, what is the answer?  $15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15 + 15$ 
Options:
aoVal: A
content: $$210$$ 
aoVal: B
content: $$215$$ 
aoVal: C
content: $$220$$ 
aoVal: D
content: $$225$$ 
aoVal: E
content: None of the above 
Answer: D
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication
Source: 其它
Problem: Mary\textquotesingle s violin class started at $$11.15\textbackslash{} \text{a .m.}$$ It lasted for $$90$$ minutes.  What time did her violin class end? 
Options:
aoVal: A
content: $$12.05\textbackslash{} \text{a. m.}$$ 
aoVal: B
content: $$12.05\textbackslash{} \text{p. m.}$$ 
aoVal: C
content: $$12.45\textbackslash{} \text{a. m.}$$ 
aoVal: D
content: $$12.45\text{ p. m.}$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations
Problem: How would determine $\angle DKI$ from $\angle KIJ$ and $\angle KJI$? 
Options:
aoVal: A
content: Vertically opposite angles 
aoVal: B
content: Exterior angles 
aoVal: C
content: Alternate angles 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle
Source: 其它
Problem: What is 2014 + 2 x 0 x 1 x 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
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication
Source: 其它
Problem: Which of the following expressions is easier to calculate if we do it in order? 
Options:
aoVal: A
content: $$15+7-5$$ 
aoVal: B
content: $$15-5+7$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules
Source: 其它