math-eval/TAL-SCQ5K huggingface dataset:
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
Problem: The muzzle velocity of a 0.003-kg paintball pellet is 90 m/s. If it takes 0.002 s for the pellet to be shot from the paintball gun, what is the average force of the recoilon the paintball gun? 
Options:
aoVal: A
content: $$24N$$ 
aoVal: B
content: $$60N$$ 
aoVal: C
content: $$68N$$ 
aoVal: D
content: $$135N$$ 
Answer: D
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: In $$39$$, the value of the digit in the tens place is． 
Options:
aoVal: A
content: $$3$$ ones 
aoVal: B
content: $$30$$ ones 
aoVal: C
content: $$30$$ tens 
aoVal: D
content: $$30$$ hundreds 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers
Problem: Which of the following is not a multiple of $6$? 
Options:
aoVal: A
content: $$(49+35)\times 6$$ 
aoVal: B
content: $$(49-35)\times 42$$ 
aoVal: C
content: $$24\times 12-1$$ 
aoVal: D
content: $$35\times 6+48$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers
Source: 其它
Problem: The value of the side of a square is a prime number and which of the following statements is true? 
Options:
aoVal: A
content: The value of its area is a prime number 
aoVal: B
content: The value of its area is a composite number 
aoVal: C
content: It can not be determined whether the value of its area is a prime number or not. 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers
Source: 其它
Problem: Which of the following numbers is not divisible by $$2$$? 
Options:
aoVal: A
content: $$578397490$$ 
aoVal: B
content: $$57893084$$ 
aoVal: C
content: $$5791592$$ 
aoVal: D
content: $$24618221$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Source: 其它
Problem: Prime factorization: $$598=$$． 
Options:
aoVal: A
content: $$2\times13\times23$$ 
aoVal: B
content: $$5\times15\times25$$ 
aoVal: C
content: $$2\times23\times10$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization
Problem: How many zeroes does the number $$12^{2}\times15^{3}$$ end with? 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$12$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$3$$ 
aoVal: E
content: $$1$$ 
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: Elmo is packing $$107$$ cookies. He wants to put $$5$$ cookies exactly in each plastic bag. How many cookies will not be packed into plastic bags? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$1$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$3$$ 
aoVal: E
content: $$4$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Source: 其它
Problem: Determine if the result of~$$1+2+3+4+5+6\cdots\cdots+99+100$$~is an odd or even~number. 
Options:
aoVal: A
content: Odd 
aoVal: B
content: Even 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers
Problem: There are $$17$$ children participating in a competition. The competition requires them to divide into $$4$$ teams on the average. How many more children are needed for this competition? 
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->Division without Remainders->Applying the Properties of Dividing without Remainders->Guessing Dividends
Source: 其它
Problem: George has $$120$$ stamps; Gina has $$220$$ stamps and John has $$320$$ stamps. If all the stamps were mixed together and redistributed to these three children, how many stamps would each person get? 
Options:
aoVal: A
content: $$140$$ 
aoVal: B
content: $$180$$ 
aoVal: C
content: $$240$$ 
aoVal: D
content: $$220$$ 
aoVal: E
content: $$320$$ 
Answer: D
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn\textquotesingle t know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true."  (1) It is prime.  (2) It is even.  (3) It is divisible by $7$.  (4) One of its digits is $9$.  This information allows Malcolm to determine Isabella\textquotesingle s house number. What is its units digit? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$9$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: In a cricket match, George scores double~the runs in each round compared to the one before. If George scored $$1$$ run in the first round, in which round did he score $$32$$ runs? 
Options:
aoVal: A
content: $$4^{th}$$ 
aoVal: B
content: $$7^{th}$$ 
aoVal: C
content: $$6^{th}$$ 
aoVal: D
content: $$8^{th}$$ 
aoVal: E
content: $$5^{th}$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Which of the following statements is correct? 
Options:
aoVal: A
content: $$4$$ is a factor of $$38$$. 
aoVal: B
content: $$6$$ is a factor of $$72$$. 
aoVal: C
content: $$8$$ is a common factor of $$72$$ and $$84$$. 
aoVal: D
content: $$9$$ is a common factor of $$38$$ and $$72$$. 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
Problem: Adrian has two ribbons of length $$12 \rm{cm}$$ and $$30 \rm{cm}$$. He cuts each ribbon into shorter pieces of equal length. Every shorter piece from both ribbons is of the same length. What is the greatest length of each shorter piece? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$12$$ 
aoVal: E
content: None of the above 
Answer: E
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Source: 其它
Problem: Without calculating, determine if the sum of $$1+2+3+\cdots +1993$$ is an odd or even 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: What is the remainder when dividing the sum: $$2001+2002+2003+2004+2005$$ by $$2004$$? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2001$$ 
aoVal: C
content: $$2002$$ 
aoVal: D
content: $$2003$$ 
aoVal: E
content: $$1999$$ 
Answer: E
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->The additive property of the remainder
Problem: A ball is thrown from the top of a building, and each time the ball bounces to half of its previous height. If the height of the building is $$1024m$$, what is the height it bounces to on the fifth bounce? 
Options:
aoVal: A
content: $$32m$$ 
aoVal: B
content: $$16m$$ 
aoVal: C
content: $$128m$$ 
aoVal: D
content: $$256m$$ 
aoVal: E
content: $$4m$$ 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: How many factors of 2020 have more than 3 factors? (As an example, 12 has 6 factors, namely 1,2,3,4,6 and 12) 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: $$10$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples
Source: 其它
Problem: After adding a two-digit number $$N$$ and a two-digit number that has the same digits as $$N$$ but written in reverse order, we got a square of a natural number as result. How many such numbers $$N$$ are there? 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$2$$ 
aoVal: E
content: other answer 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers
Problem: Divide $$74$$ by $$6$$. The remainder is ． 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$14$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders->Relationship between Dividend, Divisor, Quotient and Remainder in Division
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
Problem: Pressed 12 times, on or off 
Options:
aoVal: A
content: on 
aoVal: B
content: off 
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 $$25$$? 
Options:
aoVal: A
content: $$7950$$ 
aoVal: B
content: $$6925$$ 
aoVal: C
content: $$7500$$ 
aoVal: D
content: $$25255$$ 
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: A number is called flippy if its digits alternate between two distinct digits. For example, 2020 and 37373 are flippy, but 3883 and 123123 are not. How many five-digit flippy numbers are divisible by 15? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$8$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Source: 其它
Problem: How many squares of 5cm side can fit in a square of $$20cm$$ side? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$12$$ 
aoVal: C
content: $$16$$ 
aoVal: D
content: $$20$$ 
aoVal: E
content: $$10$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: How many hundreds are there in eight million?　 
Options:
aoVal: A
content: $$80$$ 
aoVal: B
content: $$800$$ 
aoVal: C
content: $$8000$$ 
aoVal: D
content: $$80000$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value
Problem: Jack and Linda participated in the school activity, got a total of $90$ dollars of charity money. Linda got $10$ dollars more than Jack, how many dollars of charity money did Jack get? 
Options:
aoVal: A
content: $$40$$ 
aoVal: B
content: $$50$$ 
aoVal: C
content: $$30$$ 
aoVal: D
content: $$60$$ 
aoVal: E
content: $$20$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: How many multiples of $5$ are there from $1$ to $50$? 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$15$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples
Problem: What is the remainder when dividing the sum: $$2001+2002+2003+2004+2005$$ by $$2004$$? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2001$$ 
aoVal: C
content: $$2002$$ 
aoVal: D
content: $$2003$$ 
aoVal: E
content: $$1999$$ 
Answer: E
Analysis: N/A.  (US $$2004$$ Math kangaroo Problems, Level $$7-8$$, Question \#$$3$$)$$ 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->The additive property of the remainder
Problem: What is the next square number after $$49$$?  Choose the answer. 
Options:
aoVal: A
content: $$50$$ 
aoVal: B
content: $$55$$ 
aoVal: C
content: $$64$$ 
aoVal: D
content: $$76$$ 
aoVal: E
content: $$98$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers
Problem: There are $15$ floors in a building, and every two floors have the same number of stairs. They tell us that person $A$ goes up the stairs twice as fast as person $B$, so they both start on floor $1$, and when person $B$ gets to floor $6$, which floor is Person $A$ on? 
Options:
aoVal: A
content: on the $11$th floor 
aoVal: B
content: on the $12$th floor 
aoVal: C
content: on the $8$th floor 
aoVal: D
content: on the $6$th floor 
aoVal: E
content: on the $7$th floor 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: When t = 4, which answer is the odd one out? 
Options:
aoVal: A
content: $$2t$$ 
aoVal: B
content: $t + 2$ 
aoVal: C
content: $32 \div t$ 
aoVal: D
content: $t + 4$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers->Understanding Odd and Even Numbers
Problem: All~\uline{~~~~~~~~~~}~numbers are divisible by $2$. 
Options:
aoVal: A
content: even 
aoVal: B
content: odd 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Source: 其它
Problem: Fill in the blanks.  $$(432)\_5=4\times $$~\uline{~~~~~~~~~~}~$$+3\times $$~\uline{~~~~~~~~~~}~$$+2\times $$~\uline{~~~~~~~~~~}~$$=($$~\uline{~~~~~~~~~~}~$$)\_{10}$$ 
Options:
aoVal: A
content: $$10^{2}$$;~$$10^{1}$$;~$$10^{0}$$; $$111$$ 
aoVal: B
content: $$5^{2}$$;~$$5^{1}$$;~$$5^{0}$$; $$117$$ 
aoVal: C
content: $$5^{2}$$;~$$5^{1}$$;~$$5^{0}$$; $$31$$ 
aoVal: D
content: $$10^{2}$$;~$$10^{1}$$;~$$10^{0}$$; $$432$$ 
Answer: B
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Properties and Applications of Number Bases
Problem: $$6$$ hundreds $$+ 48$$ thousands $$=\square $$  What is the missing number in the box?　 
Options:
aoVal: A
content: $$48600$$ 
aoVal: B
content: $$54000$$ 
aoVal: C
content: $$486000$$ 
aoVal: D
content: $$648000$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value
Problem: A bicycle wheel with a diameter of 62.2 cm and a rotational inertia of 0.40 kg·m\textsuperscript{2} is rotating at a rate of 8 rad/s when the brakes are applied. The brakes apply a normal force of 85 N on the brake pad at the edge of the wheel.The coefficient of kinetic friction between the brake pad and the wheel is 0.32. How long does it take for the bicycle to stop? 
Options:
aoVal: A
content: $$0.19s$$ 
aoVal: B
content: $$0.29s$$ 
aoVal: C
content: $$0.38s$$ 
aoVal: D
content: $$2.6s$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Let $N$ be the greatest five-digit number whose digits have a product of $120$. What is the sum of the digits of $N$? 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$16$$ 
aoVal: C
content: $$17$$ 
aoVal: D
content: $$18$$ 
aoVal: E
content: $$20$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples
Source: 其它
Problem: How many positive factors does $$23,232$$ have? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$12$$ 
aoVal: C
content: $$28$$ 
aoVal: D
content: $$36$$ 
aoVal: E
content: $$42$$ 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization
Source: 其它
Problem: What is the missing number in this sequence?  ~ $$1$$，$$3$$，$$5$$，$$7$$，？，$$11$$，$$13$$，$$15$$，$$17$$，$$19$$ 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$15$$ 
aoVal: D
content: $$11$$ 
aoVal: E
content: $$10$$ 
Answer: B
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: A number is opposite to $$-\frac{1}{3}$$ and the aboslute value of that number is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$-3$$ 
aoVal: C
content: $$\frac{1}{3}$$ 
aoVal: D
content: $$-\frac{1}{3}$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Problem: A ball is thrown from the top of a building and each time the ball bounces to half of its previous height. If the height of the building is $$512$$ meters, which time does it bounce when it bounces to a height of $$16$$ meters? 
Options:
aoVal: A
content: $$4^{th}$$ 
aoVal: B
content: $$7^{th}$$ 
aoVal: C
content: $$6^{th}$$ 
aoVal: D
content: $$8^{th}$$ 
aoVal: E
content: $$5^{th}$$ 
Answer: E
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: What is seventy thousand and fourty-one in figures? 
Options:
aoVal: A
content: $$7041$$ 
aoVal: B
content: $$70401$$ 
aoVal: C
content: $$70410$$ 
aoVal: D
content: $$70041$$ 
aoVal: E
content: $$700041$$ 
Answer: D
Analysis: N/A.　 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits
Problem: What is the probability of getting an letter grade that is lower than $B$ from "THINK ACADEMY"? 
Options:
aoVal: A
content: $\frac{5}{12}$ 
aoVal: B
content: $\frac{1}{4}$ 
aoVal: C
content: $\frac{1}{12}$ 
aoVal: D
content: $\frac{1}{6}$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Find the difference between $56$ hundreds and $19$ tens and $5$ ones. 
Options:
aoVal: A
content: $$365$$ 
aoVal: B
content: $$536$$ 
aoVal: C
content: $$5405$$ 
aoVal: D
content: $$5576$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases
Source: 其它
Problem: In the apartment building where Linda lives, $13$ floors above the ground are residential buildings, and $2$ underground floors are parking lots. When Linda takes the elevator from the 2nd underground floor to the $26$th floor. How many floors does the elevator go up? 
Options:
aoVal: A
content: $$25$$ 
aoVal: B
content: $$26$$ 
aoVal: C
content: $$27$$ 
aoVal: D
content: $$28$$ 
aoVal: E
content: $$29$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: ? 
Options:
aoVal: A
content: a 
aoVal: B
content: B 
aoVal: C
content: C 
aoVal: D
content: d 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization
Source: 其它
Problem: Malcolm wants to visit Isabella after school today and knows the street where she lives but doesn\textquotesingle t know her house number. She tells him, "My house number has two digits, and exactly three of the following four statements about it are true."  (1) It is prime.  (2) It is even.  (3) It is divisible by 7.  (4) One of its digits is 9.  This information allows Malcolm to determine Isabella\textquotesingle s house number. What is its units digit? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$9$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Seven million, three hundred and eight thousand and twenty-eight in numerals is． 
Options:
aoVal: A
content: $$7008328$$ 
aoVal: B
content: $$7030828$$ 
aoVal: C
content: $$738028$$ 
aoVal: D
content: $$7380028$$ 
aoVal: E
content: $$7308028$$ 
Answer: E
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers
Problem: I\textquotesingle m thinking of a number.  When I divide the number by $$5$$, its quotient is $$43$$ and its remainder is $$3$$.  What is the number? 
Options:
aoVal: A
content: $$230$$ 
aoVal: B
content: $$218$$ 
aoVal: C
content: $$215$$ 
aoVal: D
content: $$212$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders
Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Division of Whole Numbers->Division with Remainder->Meaning of Division with Remainders
Problem: Which one of the following numbers has $$4$$ as a factor? 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$30$$ 
aoVal: C
content: $$42$$ 
aoVal: D
content: $$64$$ 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples
Problem: The numbers $1$, $2$, $3$, $7$, $8$, $10$, $14$ and $15$ are divided into groups of one or more numbers. The sum of the numbers in each group is the same. Which of the following can be the sum of the numbers in each group? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$15$$ 
aoVal: C
content: $$14$$ 
aoVal: D
content: $$13$$ 
aoVal: E
content: $$12$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: How many factors of $2020$ have more than $3$ factors? (As an example, $12$ has $6$ factors, namely $1$,$2$,$3$,$4$,$6$ and $12$) 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: $$10$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples
Source: 其它
Problem: Bud is setting a problem for \textquotesingle Find the Number!\textquotesingle{}  She wants the number to be $$75$$.  Her first two clues are:  Clue $$1$$: The number is a factor of $$150$$.  Clue $$2$$: The number is a multiple of $$3$$.  What should her third clue be to completely identify the number? 
Options:
aoVal: A
content: The number is divisible by $15$. 
aoVal: B
content: The number is divisible by $25$. 
aoVal: C
content: The number is a two-digit number. 
aoVal: D
content: The number is an odd number. 
aoVal: E
content: The number is a prime number. 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples
Problem: Two numbers have infinite amount of~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: multiples 
aoVal: B
content: least common multiples 
aoVal: C
content: factors 
aoVal: D
content: greatest common factors 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Multiples and Least Common Multiples