math-eval/TAL-SCQ5K huggingface dataset:
Problem: In the four-digit number $192N$, what value of $N$ will allow the four digit number to be divisible by $6$? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$8$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Source: 其它
Problem: For a positive integer~~the factorial notation $n!$ represents the product of the integers from $n$ to $1$ (For example,~$6!=6\cdot5\cdot4\cdot3\cdot2\cdot1$) What value of $N$ satisfies the following equation? $5!\cdot9!=12\cdot N!$ 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$11$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$13$$ 
aoVal: E
content: $$14$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples
Source: 其它
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->Prime Factorization
Source: 其它
Problem: How many factors do $8, 12$ and $20$ have in common? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
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 Multiple Numbers
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 remainder when $$n$$ is divided by $$77$$? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$6$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->Questions Involving Remainders
Problem: $GCF(24,36)=$ 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$12$$ 
aoVal: C
content: $$24$$ 
aoVal: D
content: $$36$$ 
Answer: B
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
Source: 其它
Problem: What is the length of a pendulum whose period, at the equator, is 1 s? 
Options:
aoVal: A
content: $$0.15m$$ 
aoVal: B
content: $$0.25m$$ 
aoVal: C
content: $$0.30m$$ 
aoVal: D
content: $$0.45m$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: What is the sum of the first four odd numbers? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$16$$ 
aoVal: D
content: $$20$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers
Problem: There are~\uline{~~~~~~~~~~}~common multiples of $$6$$ and $$8$$ that are smaller than $$50$$. 
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: On the number line, any number on the right side of the origin is ． 
Options:
aoVal: A
content: positive number 
aoVal: B
content: negative Number 
aoVal: C
content: non-postive number 
aoVal: D
content: opposite Number 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Problem: Tintin is taller than Tiantian, Amy is shorter than Tiantian. Do you know which child is the tallest? 
Options:
aoVal: A
content: Amy 
aoVal: B
content: Tintin 
aoVal: C
content: Tiantian 
aoVal: D
content: They have the same height 
aoVal: E
content: None of them above 
Answer: B
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Use the graph to find the profit the monopoly makes with the socially efficient price regulation. Is it positive, negative, or zero? 
Options:
aoVal: A
content: Positive 
aoVal: B
content: Negative 
aoVal: C
content: Zero 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases
Source: 其它
Problem: I have two equations: one multiplication and one division.  Is it possible for both these equations to contain the exact same numbers, but in different places, and have different final answers? 
Options:
aoVal: A
content: Yes 
aoVal: B
content: No 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits
Source: 其它
Problem: What is the remainder of $$235\div3$$? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$0$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$4$$ 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders
Problem: The sum of 2 SAME digits is ODD or EVEN? 
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: A two-digit number can be divided by both $$3$$ and $$5$$. It is also an even numebr. How many such numbers are there? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$30$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$43$$ 
aoVal: E
content: None of the above 
Answer: A
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
Source: 其它
Problem: Which of these numbers is exactly divisible by $$2$$ and $$3$$? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$28$$ 
aoVal: C
content: $$33$$ 
aoVal: D
content: $$42$$ 
aoVal: E
content: $$51$$ 
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: Find the smallest prime number that is greater than $90$. 
Options:
aoVal: A
content: $$93$$ 
aoVal: B
content: $$96$$ 
aoVal: C
content: $$97$$ 
aoVal: D
content: $$99$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers
Source: 其它
Problem: How many expressions following have two-digits quotients?  $$750\div 7$$~ ~ ~$$75\div 7$$~ ~ ~ $$750\div 8$$~ ~ ~$$705\div 7$$ 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$1$$ 
aoVal: D
content: $$4$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Short Division
Problem: After the first blow, the balloon becomes two times as~big as the original. And after the second blow, the size of the balloon becomes four times the original size. Each time the balloon is blown, the size of the balloon becomes twice as large as the last time. How many times does the balloon become the original after the sixth blowing? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$32$$ 
aoVal: D
content: $$24$$ 
aoVal: E
content: $$64$$ 
Answer: E
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: What is the average power used to pitch a 0.142 kg baseball at 42 m/s, if it takes 0.3 s to accelerate it from rest? 
Options:
aoVal: A
content: $$251W$$ 
aoVal: B
content: $$417W$$ 
aoVal: C
content: $$501W$$ 
aoVal: D
content: $$835W$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: ? 
Options:
aoVal: A
content: A 
aoVal: B
content: B 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: After the first blow, the balloon becomes two times as~big as the original. And after the second blow, the size of the balloon becomes four times the original size. Each time the balloon is blown, the size of the balloon becomes twice as large as the last time. How many times the does balloon become the original after the sixth blowing? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$32$$ 
aoVal: D
content: $$24$$ 
aoVal: E
content: $$64$$ 
Answer: E
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Find the difference between the values of the digit $$5$$ in $$5034$$ and $$3054$$. 
Options:
aoVal: A
content: $$1980$$ 
aoVal: B
content: $$4950$$ 
aoVal: C
content: $$5050$$ 
aoVal: D
content: $$8088$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers
Problem: On the number line, any number on the left side of the origin is ． 
Options:
aoVal: A
content: Positive number 
aoVal: B
content: Negative number 
aoVal: C
content: Non-positive number 
aoVal: D
content: Opposite number 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Problem: How many numbers are there from $34$ to $82$? (including both $34$ and $82$) 
Options:
aoVal: A
content: $$48$$ 
aoVal: B
content: $$49$$ 
aoVal: C
content: $$50$$ 
aoVal: D
content: $$51$$ 
aoVal: E
content: $$52$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers
Source: 其它
Problem: Use the octal system (base-$8$ numeral system) to calculate $\left (773\right )\_8 + \left (6\right )\_8$. The answer should be~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $\left (1001\right )\_8$ 
aoVal: B
content: $\left (779\right )\_8$ 
aoVal: C
content: $\left (111\right )\_8$ 
aoVal: D
content: $\left (781\right )\_8$ 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Properties and Applications of Number Bases
Problem: The remainder of dividing $$3^{20}\times 5^{30}-2$$ by $$15$$ equals． 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$13$$ 
Answer: E
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->Questions Involving Remainders
Problem: The North lighthouse flashes every $$20$$ seconds.  The South lighthouse flashes every $$25$$ seconds.  The two lighthouses have just flashed at the same time.  How many seconds will it be before they next flash at the same time? 
Options:
aoVal: A
content: $$500$$ 
aoVal: B
content: $$300$$ 
aoVal: C
content: $$200$$ 
aoVal: D
content: $$100$$ 
aoVal: E
content: $$50$$ 
Answer: D
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 one of the following numbers is a factor of $$24$$? 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$16$$ 
aoVal: D
content: $$48$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples
Problem: At a restaurant, every $$2$$\textsuperscript{nd} customer is given a free drink, every $$5$$\textsuperscript{th}~customer is given a free sweet and every $$9$$\textsuperscript{th} customer is given a free chocolate bar. Lynn was given all three gifts on her first visit. Given that she was among the first $$100$$ customers, what was Lynn\textquotesingle s queue number? 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$45$$ 
aoVal: C
content: $$55$$ 
aoVal: D
content: $$90$$ 
Answer: D
Analysis: \hspace{0pt}N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
Problem: Person $A$ has six times as many storybooks as $B$. If each of them buys two more, $A$ has four times as many books as $B$. How many storybooks does $A$? 
Options:
aoVal: A
content: $$18$$ 
aoVal: B
content: $$16$$ 
aoVal: C
content: $$15$$ 
aoVal: D
content: $$14$$ 
aoVal: E
content: $$13$$ 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Tom bought $$$100$$ worth of groceries and paid $$10$$\% GST (Goods and Services Tax) for them. How much did he pay in total? 
Options:
aoVal: A
content: $$$101$$ 
aoVal: B
content: $$$102$$ 
aoVal: C
content: $$$110$$ 
aoVal: D
content: $$$120$$ 
aoVal: E
content: $$$130$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: The perimeter of a rectangle is $$18cm$$. Assuming that the side lengths are integers, how many different cases are there for the area of this rectangle? 
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->Number Theory Modules
Source: 其它
Problem: In order to take the OC exam, John spent five weeks practising the OC exercises. In the first week, he practised one set of OC exercises. Since then, he had practised twice as many times each week as the previous before. How many sets of exercises did John practise in total while preparing for the OC exam? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$63$$ 
aoVal: C
content: $$31$$ 
aoVal: D
content: $$30$$ 
aoVal: E
content: $$21$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: A department store manager wants to know if a greater proportion of customers on the store\textquotesingle s mailing list would redeem a coupon for $\textbackslash$$5 off the price of an item than would redeem a coupon for 10 percent off the price of anitem. The manager mails a $\textbackslash$$5 off coupon to a random sample of 500 customers and mails a 10 percent off coupon to an independent random sample of 500 customers. The number of coupons of each type that were redeemed was recorded. Assuming that the conditions for inference are met, what test procedure should be usedto answer the manager\textquotesingle s question? 
Options:
aoVal: A
content: A one-sample t-test for a mean 
aoVal: B
content: A one-sample z-test for a proportion 
aoVal: C
content: A t-test for the slope of a regression line 
aoVal: D
content: A matched-pairs t-test for a mean difference 
aoVal: E
content: A two-sample z-test for a difference between two proportions 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: $\textasciitilde$  The digit $$3$$ in $$7.934$$ stands for $$3$$． 
Options:
aoVal: A
content: ones 
aoVal: B
content: tens 
aoVal: C
content: tenths 
aoVal: D
content: hundredths 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Overseas In-curriculum->Knowledge Point->Knowing Numbers->Decimals->Meaning for Decimals ->Decimal Place Value
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: $$9$$ 
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  $1000\div8$ =． 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$25$$ 
aoVal: C
content: $$125$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Source: 其它
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: ? 
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: The answer of the following equation:  $$(203+204+\ldots \ldots +288)-(49+50+51+\ldots \ldots +131)$$ is an~\uline{~~~~~~~~~~}~number. 
Options:
aoVal: A
content: odd 
aoVal: B
content: even 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers
Problem: A two-sample t-test of the hypotheses H\textsubscript{0} :~$\mu\_{1}-\mu\_{2}$~= 0 versus H\textsubscript{a}~:~$\mu\_{1}-\mu\_{2}$ \textgreater{} 0 produces a p-value of 0.03. Which of the following must be true?  $\textasciitilde$ I. A 90 percent confidence interval for the difference in means will contain the value 0.  $\textasciitilde$ Il. A 95 percent confidence interval for the difference in means will contain the value 0.  $\textasciitilde$ II. A 99 percent confidence interval for the difference in means will contain the value 0. 
Options:
aoVal: A
content: I only 
aoVal: B
content: III only 
aoVal: C
content: I and II only 
aoVal: D
content: Il and III only 
aoVal: E
content: I, Il, and I 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: When a number is divided by $$9$$, it gives a quotient of $$23$$ and a remainder of $$5$$. What is the number? 
Options:
aoVal: A
content: $$115$$ 
aoVal: B
content: $$124$$ 
aoVal: C
content: $$207$$ 
aoVal: D
content: $$212$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders
Problem: ? 
Options:
aoVal: A
content: a 
aoVal: B
content: b 
aoVal: C
content: c 
aoVal: D
content: d 
aoVal: E
content: e 
aoVal: F
content: f 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Source: 其它
Problem: How many factors are there? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$9$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization
Source: 其它
Problem: Without calculating, determine if the answer is an odd or even number.  $$33 \times 7 \times 11$$ is an~\uline{~~~~~~~~~~}~number, $$28 \times 9 \times 4$$ is an~\uline{~~~~~~~~~~}~number. 
Options:
aoVal: A
content: odd, even 
aoVal: B
content: even, even 
aoVal: C
content: even, odd 
aoVal: D
content: odd, odd 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Multiplication Rules of Odd and Even Numbers
Problem: The least whole number whose digits add up to $$82$$ hasdigits. 
Options:
aoVal: A
content: $$11$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$8$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
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: How many zeroes does the number $$2^{29}\times5^{10}$$ end with? 
Options:
aoVal: A
content: $$39$$ 
aoVal: B
content: $$29$$ 
aoVal: C
content: $$19$$ 
aoVal: D
content: $$10$$ 
Answer: D
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: Which of these numbers is a factor of $12$? 
Options:
aoVal: A
content: $$24$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$4$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples
Problem: In the $$3$$-digit number $$2M4$$ is divisible by $$6$$, what is the smallest value of the digit $$M$$? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: None of the above 
Answer: A
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Source: 其它
Problem: When my number is divided by $$3$$, I have a quotient of $$15$$ and a remainder of $$2$$.  What number am I? 
Options:
aoVal: A
content: $$7$$ 
aoVal: B
content: $$33$$ 
aoVal: C
content: $$43$$ 
aoVal: D
content: $$47$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders
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: $\left (3639\right )\_7$ 
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: The correct prime factorization of number $84$ is ． 
Options:
aoVal: A
content: $$1\times 2\times 2\times 2\times 7$$ 
aoVal: B
content: $$14\times 6$$ 
aoVal: C
content: $$7\times 12$$ 
aoVal: D
content: $$2\times 2\times 3\times 7$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization
Problem: Which of the following is a factor of $21$? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$4$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers
Source: 其它
Problem: A number when divided by $$5$$ has a quotient of $$62$$ and a remainder of $$3$$.  What is the number? 
Options:
aoVal: A
content: $$186$$ 
aoVal: B
content: $$191$$ 
aoVal: C
content: $$310$$ 
aoVal: D
content: $$313$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders
Problem: What is the square root of the number whose square is $$16$$? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$\sqrt{{8}}$$ 
aoVal: D
content: $$16$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers
Problem: Which of the following numbers is divisible by $$4$$? 
Options:
aoVal: A
content: $$5783954$$ 
aoVal: B
content: $$1090196$$ 
aoVal: C
content: $$742826$$ 
aoVal: D
content: $$9928962$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Source: 其它
Problem: The smallest positive integer greater than 1 that leaves a remainder of 1 when divided by 4, 5, and 6 lies between which of the following pairs of numbers? 
Options:
aoVal: A
content: 2 and 19 
aoVal: B
content: 20 and 39 
aoVal: C
content: 40 and 59 
aoVal: D
content: 60 and 79 
aoVal: E
content: 80 and 124 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Source: 其它