math-eval/TAL-SCQ5K huggingface dataset:
Problem: Compute the average angular acceleration and the angular displacement during the 2 seconds a rotating object speeds up from 0.5 rad/s to 0.7 rad/s. 
Options:
aoVal: A
content: a = 0.1 rad/s\textsuperscript{2}~$\Delta\theta$~= 0.3 radians 
aoVal: B
content: a = 0.2 rad/s\textsuperscript{2~}$\Delta\theta$~= 0.5 radians 
aoVal: C
content: a = 0.1 rad/s\textsuperscript{2~}$\Delta\theta$~= 1.2 radians 
aoVal: D
content: a = 0.2 rad/s\textsuperscript{2~}$\Delta\theta$~= 1.2 radians 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: A 35 kg child ziplines from rest on a platform 12 m high to the ground with negligible friction. In the last 8 m of the zipline, which is approximately horizontal, a braking mechanism applies a constant force opposing the motion to slow the child down so that she\textquotesingle s traveling at 2.5 m/s when she finally lands on the safety padding at the end. The padding compresses for1.5 s when the child lands on it and stops.  $\textasciitilde$  What is the magnitude of the force applied by the braking mechanism? 
Options:
aoVal: A
content: $$350N$$ 
aoVal: B
content: $$511N$$ 
aoVal: C
content: $$525N$$ 
aoVal: D
content: $$4090N$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: The $$7$$-digit number $$\overline{123P688}$$ is divisible by $$8$$. How many possible values are there for $$P$$? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: $$10$$ 
Answer: E
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Source: 其它
Problem: What is the value of the digit $7$ in the number $32.679$? 
Options:
aoVal: A
content: seven hundred 
aoVal: B
content: \emph{seventy} 
aoVal: C
content: seven tenths 
aoVal: D
content: seven hundredths 
aoVal: E
content: seven thousandths 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits
Problem: George buys boxes of mangoes for $$$16$$ each and sells them for $$$23$$ per box. How many boxes of mangoes would he have to sell to make $$$56$$? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: $$7$$ 
Answer: B
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Find a whole number between $$0$$ and $$100$$ that has the following properties.  When the number is divided by $$5$$ the remainder is $$4$$.  When the number is divided by $$6$$ the remainder is $$0$$.  When the number is divided by $$7$$ the remainder is $$0$$.  What is the number? 
Options:
aoVal: A
content: $$42$$ 
aoVal: B
content: $$84$$ 
aoVal: C
content: $$46$$ 
aoVal: D
content: $$90$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->Questions Involving Remainders
Problem: l am a four$$-$$digit number. The digit in the ones place is $$9$$. The digit in the thousands place has a value of $$1000$$. The digit in the tens place is twice the digit in the hundreds place. What number am I? 
Options:
aoVal: A
content: $$1009$$ 
aoVal: B
content: $$1209$$ 
aoVal: C
content: $$1249$$ 
aoVal: D
content: $$1429$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers
Problem: Without calculating, determine if the following sums are odd or even.  $$25\times 3$$ is an~\uline{~~~~~~~~~~}~number，$$45\times 2$$ is an~\uline{~~~~~~~~~~}~number，$$33\times 5\times 7\times 9\times 8\times 11\times 13$$ is an~\uline{~~~~~~~~~~}~number． ~\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt} 
Options:
aoVal: A
content: odd, odd, even 
aoVal: B
content: odd, even, odd 
aoVal: C
content: odd, even, even 
aoVal: D
content: even, odd, even 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers
Problem: $$1$$ 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Source: 其它
Problem: $LCM[5,15]=$ 
Options:
aoVal: A
content: $$75$$ 
aoVal: B
content: $$45$$ 
aoVal: C
content: $$30$$ 
aoVal: D
content: $$15$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Multiples and Least Common Multiples->Least Common Multiple of Two Numbers
Source: 其它
Problem: Putting these lines~$\left\textbar{} \right\textbar$ round a number or calculation makes sure the answer is positive; for example both $\left\textbar{} 8\right\textbar$~and $\left\textbar{} -8\right\textbar$~ would give the answer $8$.What is the answer to:$10-\left\textbar{} 4-20\right\textbar$ 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$26$$ 
aoVal: C
content: $$-6$$ 
aoVal: D
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: Adil says "I have chosen a prime number less than $$20$$. It is one more than a multiple of $$4$$."  How many possible numbers could Adil have chosen? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$1$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$3$$ 
aoVal: E
content: $$4$$ 
Answer: D
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: With how many zeroes does the product of the first $$2006$$ consecutive prime numbers end? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$1$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: $$26$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization->The Number of Zeros at the end of a Product
Problem: Calculate quickly  $100\div5\div5$~=． 
Options:
aoVal: A
content: $100\div（5\times5）$ 
aoVal: B
content: $100\div（5-5）$ 
aoVal: C
content: $100\div（5\div5）$ 
aoVal: D
content: $100\div（5+5）$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Source: 其它
Problem: The $$4$$-digit number $$6H74$$ is divisible by $$11$$. What is $$H$$? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$7$$ 
aoVal: E
content: $$9$$ 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Problem: If  $$-$$ means $$\times$$  $$+$$ means $$\div$$  $$\times$$ means $$+$$  $$\div$$ means $$-$$  Then: $$20+(4\div 2)-2\times 5=$$？ 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$25$$ 
aoVal: D
content: $$22$$ 
aoVal: E
content: $$35$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Adam wrote out all the numbers from $$1$$ to $$60$$ inclusive. How many times did he use the digit $$5$$? ($$2008$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$15$$) 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$16$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$7$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Questions Involving Applying Place Value Principle
Problem: Is $$1234$$ divisible by $$11$$ ? 
Options:
aoVal: A
content: Yes 
aoVal: B
content: No 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Problem: \textbf{Sums of squares}  Exactly one of these statements is correct. Which one?  Circle the correct answer:． 
Options:
aoVal: A
content: $$44^{2}+77^{2}=4477$$ 
aoVal: B
content: $$55^{2}+66^{2}=5566$$ 
aoVal: C
content: $$66^{2}+55^{2}=6655$$ 
aoVal: D
content: $$88^{2}+33^{2}=8833$$ 
aoVal: E
content: $$99^{2}+22^{2}=9922$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Questions involving Square Numbers
Problem: What is the size of a rectangle if the original $$15 cm$$ length is reduced by $40\textbackslash\%$~and the $$12 cm$$ width is reduced by $50\textbackslash\%$? 
Options:
aoVal: A
content: $$6cm\times 3cm$$ 
aoVal: B
content: $$7cm\times 3cm$$ 
aoVal: C
content: $$4cm\times 3cm$$ 
aoVal: D
content: $$9cm\times 6cm$$ 
aoVal: E
content: $$9cm\times 7cm$$ 
Answer: D
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: How many of the following statements are true?  ($$A$$) If a number $$A$$ is a multiple of $$4$$, then any multiple of $$A$$ is a multiple of $$4$$.  ($$B$$) If $$4$$ is a factor of $$A$$, then any multiple of $$4$$ is also a multiple of $$A$$  ($$C$$) If both number $$A$$ and number $$B$$ are multiple of $$4$$, Then $$A+B$$ is a multiple of $$4$$.  ($$D$$) If a number $$B$$ is a multiple of $$20$$, then $$B$$ is a multiple of $$4$$. 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$1$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$3$$ 
aoVal: E
content: $$4$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples
Source: 其它
Problem: A seven-digit number $$\overline{579A379}$$ is divisible by $$11$$. Which number does $$A$$ represent? ． 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Problem: I multiply a whole number by $$3$$.  Which of the following could be my answer? 
Options:
aoVal: A
content: $$325$$ 
aoVal: B
content: $$326$$ 
aoVal: C
content: $$327$$ 
aoVal: D
content: $$328$$ 
aoVal: E
content: $$329$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Problem: If $1a2a3a4a5a$ is divisible by $11$, what is the value of $a$? 
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->Division without Remainders->Divisibility Rules
Problem: There are~\uline{~~~~~~~~~~}~common multiples of $$3$$ and $$4$$ that are smaller than $$30$$. 
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->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
Problem: Find the difference in the values of digit $$4$$ in $$4100$$ and $$8340$$. 
Options:
aoVal: A
content: $$3006$$ 
aoVal: B
content: $$3060$$ 
aoVal: C
content: $$3600$$ 
aoVal: D
content: $$3960$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers
Problem: Which of the following prime factorizations below is correct? 
Options:
aoVal: A
content: $97=1\times97$ 
aoVal: B
content: $85=5\times17$ 
aoVal: C
content: $64=2\times32$ 
aoVal: D
content: $52=1\times2\times2\times13$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization
Source: 其它
Problem: What is the total value of all the odd numbers between $$34$$ and $$42$$? 
Options:
aoVal: A
content: $$35$$ 
aoVal: B
content: $$72$$ 
aoVal: C
content: $$111$$ 
aoVal: D
content: $$152$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers
Problem: In a restaurant, there are $$7$$ tables with $$2$$ chairs each; $$5$$ tables with $$4$$ chairs each; $$4$$ tables with $$6$$ chairs each and one table with 8 chairs. If each chair is used by $$5$$ customers who spend $$$20$$ per day, what is the total daily revenue of all the chairs? 
Options:
aoVal: A
content: $$1500$$ 
aoVal: B
content: $$100$$ 
aoVal: C
content: $$6600$$ 
aoVal: D
content: $$330$$ 
aoVal: E
content: $$1320$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: How many perfect cubes lie between 2\textsuperscript{8}~+1 and 2\textsuperscript{18}+1, inclusive? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$57$$ 
aoVal: E
content: $$58$$ 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers
Source: 其它
Problem: In $$47186$$, the digit $$7$$ stands for． 
Options:
aoVal: A
content: $$7$$ ten thousands 
aoVal: B
content: $$7$$ thousands 
aoVal: C
content: $$7$$ hundreds 
aoVal: D
content: $$7$$ tens 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers
Problem: Is the answer of 1+2+3+4+5+6+\ldots+23 an odd number or even number? 
Options:
aoVal: A
content: Odd 
aoVal: B
content: Even 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers
Source: 其它
Problem: Which \textbf{ONE~}of the following numbers is \textbf{NOT} divisible by $$3$$? 
Options:
aoVal: A
content: $$18171$$ 
aoVal: B
content: $$44481$$ 
aoVal: C
content: $$38501$$ 
aoVal: D
content: $$57060$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Simple Questions of Division without Remainders
Problem: A large cuboid box measures~$$9 cm \times 15 cm \times 12 cm$$. How many cubes with an~edge length of $$3 cm$$ can fit in this large box? 
Options:
aoVal: A
content: $$76$$ 
aoVal: B
content: $$56$$ 
aoVal: C
content: $$60$$ 
aoVal: D
content: $$192$$ 
aoVal: E
content: $$58$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: The five-digit number $24x8y$ is divisible by $$4$$, $$5$$, and $$9$$. The sum of the digits $$x$$ and $$y$$ is equal to ． 
Options:
aoVal: A
content: $$13$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$5$$ 
aoVal: E
content: $$4$$ 
Answer: E
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Simple Questions of Division without Remainders
Problem: The diameter of an iron atom is $0.000000014$ inches, what is the diameter of an iron atom written in scientific notation? 
Options:
aoVal: A
content: $1.4\times 10^{8}$ inches 
aoVal: B
content: $1.4\times 10^{-8}$ inches 
aoVal: C
content: $0.14\times 10^{9}$ inches 
aoVal: D
content: $0.14\times 10^{-9}$ inches 
Answer: B
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: Several different positive integers are written on the board. Exactly two of them are divisible by $$2$$ and exactly $$13$$ of them are divisible by $$13$$. Let $$M$$ be the greatest of these numbers. What is the smallest possible value of $$M$$? 
Options:
aoVal: A
content: $$169$$ 
aoVal: B
content: $$260$$ 
aoVal: C
content: $$273$$ 
aoVal: D
content: $$299$$ 
aoVal: E
content: $$325$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Questions Involving Properties of Dividing without Remainders
Source: 其它
Problem: Adam wrote out all the numbers from $$1$$ to $$60$$ inclusive. How many times did he use the digit $$5$$? 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$16$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$7$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Questions Involving Applying Place Value Principle
Problem: What is the sum of all the prime numbers are between $$10$$ and $$20$$? 
Options:
aoVal: A
content: $$55$$ 
aoVal: B
content: $$58$$ 
aoVal: C
content: $$60$$ 
aoVal: D
content: $$64$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers
Problem: How many digit 1 can you see below?  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases
Source: 其它
Problem: Which of these numbers is exactly divisible by $$3$$ and $$9$$? 
Options:
aoVal: A
content: $$66$$ 
aoVal: B
content: $$24$$ 
aoVal: C
content: $$33$$ 
aoVal: D
content: $$126$$ 
aoVal: E
content: $$89$$ 
Answer: D
Analysis: N/A.  Revise from (GL Assessment book$$1$$《Paper $$2$$》 $$6$$ years Question \#$$23$$) 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules->Simple Questions of Division without Remainders
Problem: Barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. The sums of the two numbers on each of the three cards are equal. The three numbers on the hidden sides are prime numbers. What is the average of the hidden prime numbers? 
Options:
aoVal: A
content: $$13$$ 
aoVal: B
content: $$14$$ 
aoVal: C
content: $$15$$ 
aoVal: D
content: $$16$$ 
aoVal: E
content: $$17$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers
Source: 其它
Problem: There~are eighteen squares, when placed next to each other in two rows, that fit exactly into a rectangle. If the perimeter of a square is $$4 cm$$, what is the perimeter of the rectangle? 
Options:
aoVal: A
content: $$24cm$$ 
aoVal: B
content: $$22cm$$ 
aoVal: C
content: $$16cm$$ 
aoVal: D
content: $$18cm$$ 
aoVal: E
content: $$64cm$$ 
Answer: B
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: What is the missing number?  $$4673$$, $$4973$$,~\uline{~~~~~~~~~~}~, $$5873$$, $$6473$$ 
Options:
aoVal: A
content: $$5173$$ 
aoVal: B
content: $$5273$$ 
aoVal: C
content: $$5373$$ 
aoVal: D
content: $$5473$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Overseas In-curriculum->Knowledge Point->Algebra->Numbers and Figures->Patterns in Number Sequences
Problem: A number is greater than $$15$$ but smaller than $$20$$. It is divisible by $$2$$ and $$3$$. What is this number?~\uline{~~~~~~~~~~}~ 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$18$$ 
aoVal: C
content: $$23$$ 
aoVal: D
content: $$25$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders
Problem: A number when divided by $$5$$ gives a quotient of $$170$$ and a remainder of $$4$$.What is the number? 
Options:
aoVal: A
content: $$680$$ 
aoVal: B
content: $$846$$ 
aoVal: C
content: $$850$$ 
aoVal: D
content: $$854$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder
Problem: What is the difference between the largest $$5$$-digit number and the smallest $$6$$-digit number?~\uline{~~~~~~~~~~}~ 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value
Problem: Which one of the following is an odd number? 
Options:
aoVal: A
content: $$352$$ 
aoVal: B
content: $$134$$ 
aoVal: C
content: $$96$$ 
aoVal: D
content: $$647$$ 
aoVal: E
content: $$770$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers
Source: 其它
Problem: There~are 18 squares, when placed next to each other in 2 rows, that fit exactly into a rectangle. If the perimeter of a square is $$4 cm$$, what is the perimeter of the rectangle? 
Options:
aoVal: A
content: $$24cm$$ 
aoVal: B
content: $$22cm$$ 
aoVal: C
content: $$16cm$$ 
aoVal: D
content: $$18cm$$ 
aoVal: E
content: $$64cm$$ 
Answer: B
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: One day Randy was bored and he wrotre all the whole numbers from 49 to 97 on his paper. How many times did he write the digit \textquotesingle\textquotesingle8\textquotesingle\textquotesingle{} on his paper? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$11$$ 
aoVal: D
content: $$13$$ 
aoVal: E
content: None of the above 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits
Source: 其它
Problem: Grandmother baked cookies for her grandchildren, some of whom were going to visit her that day. She wanted each of her grandchildren to have the same number of cookies, but she forgot if three, five, or six grandchildren were coming. So, she baked enough cookies so that there would be an equal number for every grandchild regardless of how many visited. Which of these could be the number of cookies Grandmother baked? 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$15$$ 
aoVal: C
content: $$18$$ 
aoVal: D
content: $$24$$ 
aoVal: E
content: $$30$$ 
Answer: E
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: Which of the following is a set of prime numbers? 
Options:
aoVal: A
content: $$1$$, $$5$$, $$37$$, $$41$$ 
aoVal: B
content: $$2$$, $$77$$, $$86$$, $$13$$ 
aoVal: C
content: $$3$$, $$11$$, $$29$$, $$41$$ 
aoVal: D
content: $$9$$, $$13$$, $$56$$, $$79$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers
Problem: Calculate quickly  $100\div5\div5$~=． 
Options:
aoVal: A
content: $100\div（5\times5）$ 
aoVal: B
content: $100\div（5-5）$ 
aoVal: C
content: $100\div（5\div5）$ 
aoVal: D
content: $100\div（5+5）$ 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
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