math-eval/TAL-SCQ5K huggingface dataset:
Problem: A large cuboid box measures~$$28 cm \times 16 cm \times 8 cm$$. How many cubes with an~edge length of $$4 cm$$ can fit in this large box? 
Options:
aoVal: A
content: $$76$$ 
aoVal: B
content: $$56$$ 
aoVal: C
content: $$48$$ 
aoVal: D
content: $$192$$ 
aoVal: E
content: $$58$$ 
Answer: B
Analysis: N/A 
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
Source: 其它
Problem: In $$432768$$, the digit $$3$$ is in the~\uline{~~~~~~~~~~}~place. 
Options:
aoVal: A
content: hundreds 
aoVal: B
content: thousands 
aoVal: C
content: ten thousands 
aoVal: D
content: hundred thousands 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers
Problem: There are four different natural numbers, the sum of any two of them is a multiple of $$2$$, and the product of any three numbers is a multiple of $$3$$. In order to make the sum of these four numbers as small as possible, these four numbers are ． 
Options:
aoVal: A
content: $$1$$，$$3$$，$$5$$，$$9$$ 
aoVal: B
content: $$3$$，$$9$$，$$15$$，$$21$$ 
aoVal: C
content: $$1$$，$$3$$，$$7$$，$$9$$ 
aoVal: D
content: $$3$$，$$6$$，$$9$$，$$12$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples
Problem: Which one of the following statements is true? 
Options:
aoVal: A
content: If you add two odd numbers you always get an odd number. 
aoVal: B
content: If you multiply two odd numbers you always get an even number. 
aoVal: C
content: If you add an odd and an even number you always get an even number. 
aoVal: D
content: If you multiply an odd and an even number you always get an even number. 
aoVal: E
content: If you multiply two even numbers you always get an odd number. 
Answer: D
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Odd and Even Numbers
Problem: What is the missing number in this sequence?  ~ $$1$$，$$3$$，$$5$$，$$7$$，$$9$$，$$11$$，$$?$$，$$15$$，$$17$$，$$19$$ 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$13$$ 
aoVal: D
content: $$11$$ 
aoVal: E
content: $$10$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Ming, Liang and Gang went fishing. They counted the number of fish they caught and found that Ming caught $4$ times as many fish as Liang caught, Liang caught $5$ fewer fish than Xiao Gang caught, Gang caught $7$ fewer fish than Ming caught. How many fish did Ming catch？ 
Options:
aoVal: A
content: $$64$$ 
aoVal: B
content: $$32$$ 
aoVal: C
content: $$16$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: $$34$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: There is a $$4$$-digit number.  The first digit and the last digit of the number are even.  The difference between the first digit and the last digit of the number is $$2$$.  The digit in the hundreds place is the sum of the digit in the thousands place and tens place.  What is the number? 
Options:
aoVal: A
content: $$4532$$ 
aoVal: B
content: $$4732$$ 
aoVal: C
content: $$6734$$ 
aoVal: D
content: $$6932$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas In-curriculum->Knowledge Point->Fun Problems in Math->Reasoning
Overseas Competition->Knowledge Point->Number Theory Modules
Problem: The radius of a circle is $$\frac{1}{2}$$~the length of the side of the square. How many times the perimeter of a square is the diameter of a circle? 
Options:
aoVal: A
content: $$\frac{1}{4}$$ 
aoVal: B
content: $$\frac{1}{2}$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$8$$ 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: The store sold $25$ red balloons and blue balloons. The number of red balloons sold is four times that of blue balloons. How many red balloons and blue balloons are sold respectively? 
Options:
aoVal: A
content: $$5$$ and $$20$$ 
aoVal: B
content: $$18$$ and $$7$$ 
aoVal: C
content: $$15$$ and $$10$$ 
aoVal: D
content: $$20$$ and $$5$$ 
aoVal: E
content: $$21$$ and $$4$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: In the number $$3602$$, the digit \textquotesingle$$6$$\textquotesingle{} is in the． 
Options:
aoVal: A
content: tens place. 
aoVal: B
content: hundreds place. 
aoVal: C
content: thousands place. 
aoVal: D
content: ones place. 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases
Problem: How many prime numbers are between $$10$$ and $$20$$. 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$5$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers
Problem: $14532$ can be written as $10000 + 4000 + 500 + 30 + 2$  What is the value of the 6 in the number $3796423$? 
Options:
aoVal: A
content: $$600$$ 
aoVal: B
content: $$6000$$ 
aoVal: C
content: $$60000$$ 
aoVal: D
content: $$60$$ 
aoVal: E
content: $$600000$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Applying the Principle of Place Value->Expression of Place Value Principle
Problem: John, George and Oscar ran around the circular track in the same direction at the same time. John took $$6$$ seconds, George took $$20$$ seconds, and Oscar took $$30$$ seconds. If they continue to chase each other, when will they meet again at the starting point? 
Options:
aoVal: A
content: $$6$$ hours 
aoVal: B
content: $$1$$ day 
aoVal: C
content: $$4$$ minutes 
aoVal: D
content: $$124$$ minutes 
aoVal: E
content: $$9$$ hours 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Which one of these numbers has exactly two different prime factors?  $$78\textasciitilde\textasciitilde\textasciitilde105\textasciitilde\textasciitilde\textasciitilde121\textasciitilde\textasciitilde\textasciitilde97\textasciitilde\textasciitilde\textasciitilde183$$ 
Options:
aoVal: A
content: $$78$$ 
aoVal: B
content: $$105$$ 
aoVal: C
content: $$121$$ 
aoVal: D
content: $$97$$ 
aoVal: E
content: $$183$$ 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers->Knowing Prime and Composite Numbers
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: Ellie travels 65km each month starting from March. Ryan travels 80km each month starting in June.  In which month will Ellie and Ryan have an equal total distance travelled? 
Options:
aoVal: A
content: July 
aoVal: B
content: August 
aoVal: C
content: September 
aoVal: D
content: October 
aoVal: E
content: November 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Cut four identical squares~at~the corner out~of a $$15 cm \times 6 cm$$ rectangle. The perimeter of the 4 squares is 4 cm each. What is the perimeter of the rest~of~the shape? 
Options:
aoVal: A
content: $$40cm$$ 
aoVal: B
content: $$42cm$$ 
aoVal: C
content: $$90cm$$ 
aoVal: D
content: $$58cm$$ 
aoVal: E
content: $$50cm$$ 
Answer: B
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Choose the number that can be divided exactly by both $$2$$ and $$5$$.　 
Options:
aoVal: A
content: $$44$$ 
aoVal: B
content: $$15$$ 
aoVal: C
content: $$52$$ 
aoVal: D
content: $$90$$ 
aoVal: E
content: $$25$$ 
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: $GCF(16,21)=$ 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$21$$ 
aoVal: C
content: none 
aoVal: D
content: $$1$$ 
Answer: D
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: With how many zeros does the product of the first $$10$$ consecutive prime numbers end? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$1$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$3$$ 
aoVal: E
content: $$4$$ 
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: I am a $2$ digit number.  When $2$ is subtracted from me and the answer is doubled,  I am the same $2$ digit number with my digits reversed.  What number am I? 
Options:
aoVal: A
content: $$33$$ 
aoVal: B
content: $$24$$ 
aoVal: C
content: $$49$$ 
aoVal: D
content: $$34$$ 
aoVal: E
content: $$28$$ 
Answer: C
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: Which one of the following numbers has the digit `$$3$$' in the ten thousands place? 
Options:
aoVal: A
content: $$895321$$ 
aoVal: B
content: $$859231$$ 
aoVal: C
content: $$853921$$ 
aoVal: D
content: $$835921$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers
Problem: A pie is $3$ dollars more expensive than $2$ donuts and a biscuit. A donut, a biscuit and a pie are $22$ dollars in total. A pie is $10$ dollars more expensive than a donut. How much are $2$ donuts, a biscuit and a pie in total? 
Options:
aoVal: A
content: $$15$$ dollars 
aoVal: B
content: $$20$$ dollars 
aoVal: C
content: $$22$$ dollars 
aoVal: D
content: $$25$$ dollars 
aoVal: E
content: $$27$$ dollars 
Answer: E
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Find the smallest prime number that is greater than $$70$$. 
Options:
aoVal: A
content: $$71$$ 
aoVal: B
content: $$76$$ 
aoVal: C
content: $$73$$ 
aoVal: D
content: $$74$$ 
Answer: A
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers
Problem: Calculate quickly:  $92\div4$~=． 
Options:
aoVal: A
content: $100\div4-8\div4$ 
aoVal: B
content: $100\div4+8\div4$ 
aoVal: C
content: $92\div4+8\div4$ 
Answer: A
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Source: 其它
Problem: The month of December of a certain calendar year has exactly $$5$$ Saturdays and $$4$$ Sundays. On which day of the week does the first day of December fall? 
Options:
aoVal: A
content: Monday 
aoVal: B
content: Tuesday 
aoVal: C
content: Wednesday 
aoVal: D
content: Thursday 
aoVal: E
content: None of the above 
Answer: D
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems
Source: 其它
Problem: Which one of the following is not a common factor of $$24$$ and $$32$$? 
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
Problem: Which of the following statement is correct? 
Options:
aoVal: A
content: $$7$$ is a factor of $$28$$ 
aoVal: B
content: $$12$$ is a multiple of $$8$$ 
aoVal: C
content: $$3$$ is a common factor of $$18$$ and $$32$$ 
aoVal: D
content: $$24$$ is a common multiple of $$6$$ and $$14$$ 
Answer: A
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
Problem: There is a row of chairs with $27$ seats, in order to make the person to go to sit at any position are adjacent to the original person. How many people should sit first at least? 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$12$$ 
aoVal: E
content: $$14$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Last year, Gina saved $$$4$$ in January, $$$8$$ in February, $$$12$$ in March, $$$16$$ in April, and so on. She saved $$$48$$ in December. How much money did Gina save in total over the last year? 
Options:
aoVal: A
content: $$316$$ 
aoVal: B
content: $$315$$ 
aoVal: C
content: $$312$$ 
aoVal: D
content: $$306$$ 
aoVal: E
content: $$314$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: How many squares of 4cm side can fit in a square of $$16cm$$ 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: What is the quotient of $$600\div 9$$? 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$66$$ 
aoVal: D
content: $$72$$ 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Questions involving Divisions with Remainders
Problem: The sum of the digits of the $$10$$-digit number is $$9$$. What is the product of the digits of this number? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$1$$ 
aoVal: C
content: $$45$$ 
aoVal: D
content: $$9\times 8\times 7\times \cdots \times 2\times 1$$ 
aoVal: E
content: $$10$$ 
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->Questions Involving Applying Place Value Principle
Problem: $$40509$$  What is this number in words? 
Options:
aoVal: A
content: Four thousand five hundred and nine 
aoVal: B
content: Four thousand and fifty-nine 
aoVal: C
content: Fourty thousand fifty hundred and nine 
aoVal: D
content: Fourty thousand and fifty-nine 
aoVal: E
content: Fourty thousand five hundred and nine 
Answer: E
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits
Problem: $11\times12\times13\times15$~= 
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: There are three whole number $A$, $B$, $C$. $A\times B=91$, $B\times C=112$, $$B\neq1$$. $A+B+C=$~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$33$$ 
aoVal: B
content: $$34$$ 
aoVal: C
content: $$35$$ 
aoVal: D
content: $$36$$ 
aoVal: E
content: $$37$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization
Source: 其它
Problem: There are only apple trees and pear trees in the orchard. The number of apple trees is three times that of pear trees. Pear trees are 12 less than apple trees. How many fruit trees are there in the orchard？ 
Options:
aoVal: A
content: $$18$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$22$$ 
aoVal: D
content: $$24$$ 
aoVal: E
content: $$26$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: What is the remainder when dividing the sum: $$2001+2002+2003+2004+2005$$ by $$2004$$? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$1999$$ 
aoVal: C
content: $$2002$$ 
aoVal: D
content: $$2003$$ 
Answer: B
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Characteristics of Remainder ->The additive property of the remainder
Problem: Which of the following prime factorization is correct? 
Options:
aoVal: A
content: $$97=1\times97$$ 
aoVal: B
content: $$85=5\times 17$$ 
aoVal: C
content: $$64=8\times 8$$ 
aoVal: D
content: $$52=1\times 2\times 2\times 13$$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization
Problem: There is a balance and four weights $$1$$g, $$2$$g, $$5$$g and $$10$$g. If Sara wants to weigh an object weighing $$8$$g, how many weights should she use at least? 
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->Number Theory Modules
Problem: There are boys and girls swimming in the swimming pool. The number of boys is four times that of girls. There are $6$ girls less than boys. How many children are swimming in the swimming pool in total? 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$11$$ 
aoVal: E
content: $$12$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: $$157255$$ is divisible by ． 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$9$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Source: 其它
Problem: Which of the following numbers are divisible by $3$? 
Options:
aoVal: A
content: $$1234567$$ 
aoVal: B
content: $$2345678$$ 
aoVal: C
content: $$3456789$$ 
aoVal: D
content: $$4567890$$ 
Answer: C
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: In $$7108$$, the digit $$1$$ is in the  place. 
Options:
aoVal: A
content: ones 
aoVal: B
content: tens 
aoVal: C
content: hundreds 
aoVal: D
content: thousands 
Answer: C
Analysis: N/A. 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers
Problem: ? 
Options:
aoVal: A
content: a 
aoVal: B
content: b 
aoVal: C
content: c 
aoVal: D
content: d 
aoVal: E
content: e 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization
Source: 其它
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
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples
Problem: Ali surveyed 200 students at a school and recorded the eye color and the gender of each student. Of the 80 male students who were surveyed, 60 had brown eyes. If eye color and gender are independent, how many female students surveyed would be expected to have brown eyes? 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$30$$ 
aoVal: D
content: $$90$$ 
aoVal: E
content: $$100$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Five-digit number $$63\square 25$$ can be divisible by $$45$$. What digit should be filled in the $$\square $$? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: B
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Divisibility Rules
Problem: Suppose N is a whole number.  If N satisfies that $\dfrac{N}{10}+\dfrac{N}{15}$~is also an integer, how many such N\textquotesingle s are there within 100? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$16$$ 
aoVal: E
content: $$20$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: Which answer is \textbf{NOT} a square number? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$49$$ 
aoVal: E
content: $$100$$ 
Answer: C
Analysis: N/A.  Revise from (GL Assessment book$$2$$《Paper $$4$$》 $$6$$ years Question \#$$9$$) 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers
Problem: If two different natural numbers have the same digits but in reverse order, each number is called the palimage of the other.  For example, 12 and 21 are palimages of~each other.  What is the maximum difference between two-digit palimages？ 
Options:
aoVal: A
content: $$18$$ 
aoVal: B
content: $$36$$ 
aoVal: C
content: $$54$$ 
aoVal: D
content: $$72$$ 
aoVal: E
content: $$90$$ 
Answer: D
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: The five-digit number $$25M48$$ is a multiple of $$9$$. What digit does $$M$$ represent? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: None of the above 
Answer: B
Analysis: $$N.A$$ 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders
Source: 其它
Problem: All natural numbers from $$1$$ to $$1000$$ were written down. How many times was the digit $$4$$ used? 
Options:
aoVal: A
content: $$110$$ 
aoVal: B
content: $$300$$ 
aoVal: C
content: $$121$$ 
aoVal: D
content: $$200$$ 
aoVal: E
content: $$100$$ 
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: A rocket of mass m is launched with kinetic energy K\textsubscript{0~}from the surface of the Earth. How much less kinetic energy does the rocket have at an altitude of two Earth radii in terms of the gravitational constant, G; the mass of the Earth, m\textsubscript{E}; the radius of the Earth, R\textsubscript{E}; and the mass of the rocket? 
Options:
aoVal: A
content: $\dfrac{GM\_{E}m}{2R\_{E}}$ 
aoVal: B
content: $\dfrac{2GM\_{E}m}{3R\_{E}}$ 
aoVal: C
content: $\dfrac{3GM\_{E}m}{4R\_{E}}$ 
aoVal: D
content: $\dfrac{8GM\_{E}m}{9R\_{E}}$ 
Answer: B
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: If  $$○$$ means $$+$$  $$△$$ means $$-$$  Then: $$160○17△61○9△10=$$ 
Options:
aoVal: A
content: $$120$$ 
aoVal: B
content: $$200$$ 
aoVal: C
content: $$115$$ 
aoVal: D
content: $$125$$ 
aoVal: E
content: $$135$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它
Problem: During Easter, tickets are $$$4$$ for a single person and $$$12$$ for a family ($$2$$ adults and $$2$$ children). What is the difference in price between $$4$$ single tickets and a family ticket? 
Options:
aoVal: A
content: $$$13$$ 
aoVal: B
content: $$$2$$ 
aoVal: C
content: $$$4$$ 
aoVal: D
content: $$$7$$ 
aoVal: E
content: $$$12$$ 
Answer: C
Analysis: N/A 
Knowledge points: Overseas Competition->Knowledge Point->Number Theory Modules
Source: 其它