math-eval/TAL-SCQ5K huggingface dataset:
Problem: Bob sees that the license plate number of the car consists of $5$ digits: $1$, $2$, $6$, $7$, $9$. If these $5$ digits are filled in the square~$$\huge\square+\square =\square +\square $$, which number is not used?~(adapted from $$2017$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$8$$) 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$7$$ 
aoVal: E
content: $$9$$ 
Answer: E
Analysis: $1+7=2+6$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form
Source: 其它
Problem: Tiantian drank $$6\frac{3}{8}$$ litres of water. Matthew drank $$4\frac{5}{6}$$ litres of water. How many litres of water did the both of them drink altogether? Give your answer as a mixed number in the simplest form. 
Options:
aoVal: A
content: $$10\frac{4}{7}\ell$$ 
aoVal: B
content: $$10\frac{5}{8}\ell$$ 
aoVal: C
content: $$10\frac{15}{24}\ell$$ 
aoVal: D
content: $$11\frac{5}{24}\ell$$ 
Answer: D
Analysis: $$6\frac{3}{8}+4\frac{5}{6}=6\frac{9}{24}+4\frac{20}{24}=11\frac{5}{24}\ell$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions
Problem: $$3\times2016 + 0\times2016 + 3\times2016=$$? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$2016$$ 
aoVal: C
content: $$6048$$ 
aoVal: D
content: $$12096$$ 
aoVal: E
content: None of the above 
Answer: D
Analysis: $$(3+0+3)\times2016=6\times2016=12096$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: In the diagram below, a circle centered at $O$ has radius $4 \text{cm}$. It is divided into $4$ regions by two chords that are perpendicular to each other at point $N$. It is known that $OM=1 \text{cm}$, $MN=2\text{cm}$. Find the value of: Area of $(I + III) -$ Area of $(II+IV)$ 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$8$$ 
Answer: D
Analysis: D 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Area
Source: 其它
Problem: Greta Grasshopper sits on a long line of lily pads in a pond. From any lily pad, Greta can jump $5$ pads to the right or $3$ pads to the left. What is the fewest number of jumps Greta must make to reach the lily pad located $2023$ pads to the right of her starting position? 
Options:
aoVal: A
content: $$405$$ 
aoVal: B
content: $$407$$ 
aoVal: C
content: $$409$$ 
aoVal: D
content: $$411$$ 
aoVal: E
content: $$413$$ 
Answer: A
Analysis: D 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: $$3^{336}\times 9^{336}\times 27^{336}=$$． 
Options:
aoVal: A
content: $$3^{1008}$$ 
aoVal: B
content: $$3^{1344}$$ 
aoVal: C
content: $$3^{1680}$$ 
aoVal: D
content: $$3^{2016}$$ 
Answer: D
Analysis: $$3^{336}\times 9^{336}\times 27^{336}=3^{336}\times 3^{672}\times 3^{1008}=3^{336+672+1008}=3^{2016}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers
Problem: What is the value of $$1+3+5+\cdots +2017+2019-2-4-6-\cdots -2016-2018$$? 
Options:
aoVal: A
content: $$1010$$ 
aoVal: B
content: $$1009$$ 
aoVal: C
content: $$1008$$ 
aoVal: D
content: $$-1009$$ 
aoVal: E
content: $$-1010$$ 
Answer: A
Analysis: Solution 1  Rearranging the terms, we get $$(1-2)+(3-4)+(5-6)+\cdots (2017-2018)+2019$$, and our answer is $$-1009+2019=1010$$.  Solution 2  We can rewrite the given expression as  $$1+(3-2)+(5-4)+\cdots +(2017-2016)+(2019-2018)=1+1+1+\cdots +1$$. The number of $$1$$s is the same as the number of terms in $$1$$, $$3$$, $$5$$, $$7\cdots $$, $$2017$$, $$2019$$. Thus the answer is $$1010$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Grouping in Fast Addition and Subtraction of Whole Numbers
Problem: $$2\times \left( 3+1 \right)\times \left( {{3}^{2}}+1 \right)\times \left( {{3}^{4}}+1 \right)\times \left( {{3}^{8}}+1 \right)\times \left( {{3}^{16}}+1 \right)\times \left( {{3}^{32}}+1 \right)=$$． 
Options:
aoVal: A
content: $${{3}^{64}}+1$$． 
aoVal: B
content: $${{3}^{128}}-1$$． 
aoVal: C
content: $${{3}^{32}}-1$$． 
aoVal: D
content: $${{3}^{64}}-1$$． 
Answer: D
Analysis: $$=\left( 3-1 \right)\times \left( 3+1 \right)\times \left( {{3}^{2}}+1 \right)\times \left( {{3}^{4}}+1 \right)\times \left( {{3}^{8}}+1 \right)\times \left( {{3}^{16}}+1 \right)\times \left( {{3}^{32}}+1 \right)$$  $$=\left( {{3}^{2}}-1 \right)\times \left( {{3}^{2}}+1 \right)\times \left( {{3}^{4}}+1 \right)\times \left( {{3}^{8}}+1 \right)\times \left( {{3}^{16}}+1 \right)\times \left( {{3}^{32}}+1 \right)$$  $$=\left( {{3}^{4}}-1 \right)\times \left( {{3}^{4}}+1 \right)\times \left( {{3}^{8}}+1 \right)\times \left( {{3}^{16}}+1 \right)\times \left( {{3}^{32}}+1 \right)$$  $$=\cdots $$  $$=\left( {{3}^{32}}-1 \right)\times \left( {{3}^{32}}+1 \right)$$  $$={{3}^{64}}-1$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas-> Difference of Two Squares Formula
Problem: Three fourths of a pitcher is filled with pineapple juice. The pitcher is emptied by pouring an equal amount of juice into each of 5 cups. What percent of the total capacity of the pitcher did each cup receive?~ (2020 AMC 8, Question \#5) 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$15$$ 
aoVal: D
content: $$20$$ 
aoVal: E
content: $$25$$ 
Answer: C
Analysis: The pitcher is $\frac{3}{4}$ full, i.e. $75 \textbackslash\%$ full. Therefore each cup receives $\frac{75}{5}=(\mathbf{C}) 15$ percent of the total capacity. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation
Source: 其它
Problem: The solution to the rational equation $$\frac{16}{4-{{x}^{2}}}+\frac{x-2}{x+2}=\frac{x+2}{x-2}$$ is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$x=2$$ 
aoVal: B
content: no solution 
aoVal: C
content: $$x=2$$ or $$x=3$$ 
aoVal: D
content: $$x=3$$ 
Answer: B
Analysis: $$\begin{eqnarray}\frac{16}{4-{{x}^{2}}}+\frac{x-2}{x+2}\&=\&\frac{x+2}{x-2}\textbackslash\textbackslash{} -16+{{(x-2)}^{2}}\&=\&{{(x+2)}^{2}}\textbackslash\textbackslash{} x\&=\&-2\end{eqnarray}$$  After verification, $$x=-2$$ is not a solution.  There is no solution. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: The sum of $$5$$ consecutive numbers is $$500$$. Among all five numbers, what is the smallest value? 
Options:
aoVal: A
content: $$95$$ 
aoVal: B
content: $$96$$ 
aoVal: C
content: $$97$$ 
aoVal: D
content: $$98$$ 
aoVal: E
content: $$99$$ 
Answer: D
Analysis: $$500\div5=100$$(middle number is $$100$$)  $$98, 99, 100, 101. 102$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences
Source: 其它
Problem: What is the product of $63$ and $4$? 
Options:
aoVal: A
content: $$242$$ 
aoVal: B
content: $$252$$ 
aoVal: C
content: $$262$$ 
aoVal: D
content: $$272$$ 
Answer: B
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: What is the last number in Row $12$? 
Options:
aoVal: A
content: $$121$$ 
aoVal: B
content: $$144$$ 
aoVal: C
content: $$169$$ 
aoVal: D
content: $$196$$ 
Answer: B
Analysis: B 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns of Number Tables->Triangle Number Table
Source: 其它
Problem: In multiplying a number by $\dfrac{1}{100}$, the result may be obtained by moving the decimal point of that number． 
Options:
aoVal: A
content: two places to the left 
aoVal: B
content: one place to the left 
aoVal: C
content: two places to the right 
aoVal: D
content: one place to the right 
Answer: A
Analysis: Multiplying a number by $\dfrac{1}{100}$, is the same as dividing by $100$. When dividing by $100$, move the decimal point $2$ places left. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals
Problem: If $$3$$ apples weigh as much as $$4$$ pears, and $$2$$ pears weigh as much as $$5$$ plums, then $$9$$ apples weigh as much as~ \uline{?~} plums. 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$19$$ 
aoVal: C
content: $$27$$ 
aoVal: D
content: $$30$$ 
Answer: D
Analysis: If $$9$$ apples weigh as much as $$12$$ pears, and $$12$$ pears weigh as much as $$30$$ plums, then $$9$$ apples weigh as much as $$30$$ plums. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Problem: Let $P(x)$ be a polynomial such that when $P(x)$ is divided by $x-19$, the remainder is 99 , and when $P(x)$ is divided by $x-99$, the remainder is 19. What is the remainder when $P(x)$ is divided by $(x-19)(x-99)$? (1999 AHSME Problems, Question \#17) 
Options:
aoVal: A
content: $-x+80$ 
aoVal: B
content: $x+80$ 
aoVal: C
content: $-x+118$ 
aoVal: D
content: $x+118$ 
aoVal: E
content: $$0$$ 
Answer: C
Analysis: Since the divisor $(x-19)(x-99)$ is a quadratic, the degree of the remainder is at most linear.  We can write $P(x)$ in the form $$ P(x)=Q(x)(x-19)(x-99)+c x+d $$ where $c x+d$ is the remainder.  By the Remainder Theorem, plugging in 19 and 99 gives us a system of equations:  $$ \begin{aligned} \& 99 c+d=19 \textbackslash\textbackslash{} \& 19 c+d=99\end{aligned} $$  Solving gives us $c=-1$ and $d=118$, thus, our answer is $(\text{C})-x+118$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: $1-2-3+4+5-6-7+8-9=$ 
Options:
aoVal: A
content: $$-6$$ 
aoVal: B
content: $$-7$$ 
aoVal: C
content: $$-8$$ 
aoVal: D
content: $$-9$$ 
aoVal: E
content: $$-10$$ 
Answer: D
Analysis: $(1-2-3+4)+(5-6-7+8)-9=-9$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations
Source: 其它
Problem: Given that $$a\Delta b=a+b-4$$, for example, $$3\Delta 2 = 3 +2-4$$, what is $$3\Delta4$$? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$8$$ 
Answer: A
Analysis: Nil 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition
Source: 其它
Problem: \textbf{Which of the following is/are categorical variable(s)?}  \textbf{I. The mean of Grade 1 boys' heights}  \textbf{II. The colors of jackets in the class}  \textbf{III. The types of pens in a stationary store} 
Options:
aoVal: A
content: I 
aoVal: B
content: II 
aoVal: C
content: III 
aoVal: D
content: I, II 
aoVal: E
content: II, III 
Answer: E
Analysis: \textbf{A categorical variable is defined by the set of groups or categories (qualitative values) that individuals are placed into; it is not a numerical value. The mean of~ Grade 1 boys' heights is a number. The colors of jackets in the class and the types of pens in a stationary store cannot be described by numbers.~} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: A movie ticket costs $17$ dollars and the tax is $a$ dollars. George purchases a movie ticket and writes on his ledgar : " the ticket cost $17+a$ dollars". Is this description accurate? 
Options:
aoVal: A
content: yes 
aoVal: B
content: no 
Answer: B
Analysis: When writing an algebraic expression with units, we need to write it in parentheses. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Source: 其它
Problem: $$\frac{5}{12}\div \frac{25}{24}=$$． 
Options:
aoVal: A
content: $$\frac{2}{5}$$ 
aoVal: B
content: $$\frac{5}{2}$$ 
aoVal: C
content: $$\frac{35}{24}$$ 
aoVal: D
content: $$\frac{5}{12}$$ 
Answer: A
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Problem: Calculate: $${{2}^{2}}\div {{2}^{3}}\times {{2}^{4}}\div {{2}^{5}}\times {{2}^{6}}\div \cdots \div {{2}^{99}}\times {{2}^{100}}=$$~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $${{2}^{48}}$$ 
aoVal: B
content: $${{2}^{49}}$$ 
aoVal: C
content: $${{2}^{50}}$$ 
aoVal: D
content: $${{2}^{51}}$$ 
aoVal: E
content: $${{2}^{1}}$$ 
Answer: D
Analysis: $$({{2}^{100}}\div {{2}^{99}})\times ({{2}^{98}}\div {{2}^{97}})\times \cdot \cdot \cdot \times ({{2}^{6}}\div {{2}^{5}})\times ({{2}^{4}}\div {{2}^{3}})\times {{2}^{2}}={{2}^{51}}$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers
Problem: The next number in the sequence $$1, 3, 7, 13, 21, \cdots$$ is． 
Options:
aoVal: A
content: $$37$$ 
aoVal: B
content: $$35$$ 
aoVal: C
content: $$33$$ 
aoVal: D
content: $$31$$ 
aoVal: E
content: $$29$$ 
Answer: D
Analysis: Difference between the numbers is $$2$$, $$4$$, $$6$$, $$8$$. Next one is $$21+10$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences
Problem: Given that the points $A(-2, y\_1)$, $B(0, y\_2)$ and $C(3, y\_3)$ are all on the graph of $f(x)=-2x^{2}+4x+m$, then the relationship among $y\_1$, $y\_2$ and $y\_3$ is: 
Options:
aoVal: A
content: $y\_2 \textgreater{} y\_3\textgreater y\_1$ 
aoVal: B
content: $y\_1~\textgreater{} y\_3\textgreater y\_2$ 
aoVal: C
content: $y\_2 \textgreater{} y\_1\textgreater y\_3$ 
aoVal: D
content: $y\_3~\textgreater{} y\_2\textgreater y\_1$ 
Answer: A
Analysis: The parabola opens down with axis of symmetry $x=1$. Therefore, point $B$ is closer the axis of symmetry than point $C$, and point $C$ is closer the axis of symmetry than point $A$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Which of the following fraction is smaller than $$\frac{1}{9}$$? 
Options:
aoVal: A
content: $$\frac{1}{6}$$ 
aoVal: B
content: $$\frac{1}{7}$$ 
aoVal: C
content: $$\frac{1}{8}$$ 
aoVal: D
content: $$\frac{1}{10}$$ 
Answer: D
Analysis: With same numerator, the one we split into more portion is smaller 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: \textbf{A statistical test involves the following null and alternative hypotheses.~}  \textbf{H0: $\mu$ = 64}  \textbf{Ha: $\mu$ \textgreater{} 64}  \textbf{Which of the following describes a Type II error?} 
Options:
aoVal: A
content: \textbf{Failing to reject the null hypothesis when the population mean is 64} 
aoVal: B
content: \textbf{Failing to reject the null hypothesis when the population mean is greater than 64} 
aoVal: C
content: \textbf{Rejecting the null hypothesis when the population mean is 64} 
aoVal: D
content: \textbf{Rejecting the null hypothesis when the population mean is greater than 64} 
aoVal: E
content: \textbf{Failing to reject the null hypothesis when the p-value is less than the significance level} 
Answer: B
Analysis: \textbf{Type II error ($\beta$): the error of failing to reject the null hypothesis when it is false.~} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: The sum of the recurring decimals $$0.\overline {62}$$ and $$0.\overline {16}$$ is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$0.\overline{78}$$ 
aoVal: B
content: $$78\textbackslash\%$$ 
aoVal: C
content: $$\frac {78}{100}$$ 
aoVal: D
content: $$0.788$$ 
aoVal: E
content: $0.\overline{46}$ 
Answer: A
Analysis: $0.\overline{62}+0.\overline{16}=0.\overline{78}$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals
Problem: Three members of the Euclid Middle School girls\textquotesingle~softball team had the following conversation.  Ashley: I just realized that our uniform numbers are all $$2-$$digit primes.  Bethany: And the sum of your two uniform numbers is the day of my birthday earlier this month.  Caitlin: That\textquotesingle s funny. The sum of your two uniform numbers is the day of my birthday later this month.  Ashley: And the sum of your two uniform numbers is today\textquotesingle s date.  What number does Caitlin wear?  ($$2014$$ AMC $$8$$ Problem, Question \#$$23$$) 
Options:
aoVal: A
content: $$11$$ 
aoVal: B
content: $$13$$ 
aoVal: C
content: $$17$$ 
aoVal: D
content: $$19$$ 
aoVal: E
content: $$23$$ 
Answer: A
Analysis: The maximum amount of days any given month can have is $$31$$, and the smallest, two-digit primes are $$11$$, $$13$$, and $$17$$. There are a few different sums that can be deduced from the following numbers, which are $$24, 30$$, and $$28$$, all of which represent the three days. Therefore, since Brittany says that the other two people\textquotesingle s uniform numbers add up to her birthday eadier in the month, that means Caitlin and Ashley\textquotesingle s numbers must add up to $$24$$. Similarly, Caitlin says that the other two people\textquotesingle s uniform numbers add up to her birhday later in the month, so the sum must add up to $$30$$. This leaves $$28$$ as today\textquotesingle s date. From this, Caitlin was referring to the uniform numbers $$13$$ and $$17$$ telling us that her number is $$11$$, giving our solution as $$(\text{A})=11$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences
Problem: Given that $$23+25+27 +\ldots+(2k-1)=m^{2}$$, where $$k$$ and $$m$$ are whole  numbers, $$k\textgreater30$$, find the value of $$m$$. 
Options:
aoVal: A
content: $$11$$ 
aoVal: B
content: $$35$$ 
aoVal: C
content: $$41$$ 
aoVal: D
content: $$60$$ 
aoVal: E
content: None of the above 
Answer: D
Analysis: D 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: Which of the following is not equal to $$10$$? 
Options:
aoVal: A
content: $$100\div 10$$ 
aoVal: B
content: $$10 \div1$$ 
aoVal: C
content: $$10\times1$$ 
aoVal: D
content: $$100\times 10$$ 
Answer: D
Analysis: Since $$100 \times 10 = 1000$$, choice $$\text{D}$$ is not equal to $$10$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: What is the remainder when $$16+16+16 +16$$ is divided by $$4$$?　 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$0$$ 
Answer: D
Analysis: Since $$16\div4$$ has remainder $$0$$, the remainder is $$0 + 0+0+0 = 0$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: An amusement park has a collection of scale models, with ratio $1: 45$, of buildings and other sights from around the country. If the height of the One World Trade Center is $1770$ feet. What is the height in feet of its replica to the nearest whole number? (adapted from 2018 AMC 8, Question 1) 
Options:
aoVal: A
content: $$36$$ 
aoVal: B
content: $$37$$ 
aoVal: C
content: $$38$$ 
aoVal: D
content: $$39$$ 
aoVal: E
content: $$41$$ 
Answer: D
Analysis: You can see that since the ratio of real building\textquotesingle s heights to the model building\textquotesingle s height is $1: 45$. If the height of the center is $1770$ feet, to find the height of the model, we divide by $45$ . That gives us $39.3$ which rounds to $39$ . Therefore, to the nearest whole number, the duplicate is (D) $39$ feet. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions
Source: 其它
Problem: Which choice is correct:  $$3.5:2.55=$$~\uline{~~~~~~~~~~}~．$$4.6:1.15=$$~\uline{~~~~~~~~~~}~． 
Options:
aoVal: A
content: $$70:51$$，$$5:2$$ 
aoVal: B
content: $$7:5$$，$$4:1$$ 
aoVal: C
content: $$16:11$$，$$4:1$$ 
aoVal: D
content: $$70:51$$，$$4:1$$ 
Answer: D
Analysis: $$70:51$$，$$4:1$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions
Problem: $$24\times 26\times 28\times 30\times 32=48\times 52\times 56\times 60\times $$． 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$16$$ 
aoVal: D
content: $$64$$ 
Answer: A
Analysis: $$24\times 26\times 28\times 30\times 32=\left(24\times 26\times 28\times 30\right)\times \left(2\times 2\times 2\times 2\right)\times \underline{2}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: How many positive integers can fill the blank in the sentence below? ``One positive integer is~\uline{~~~~~~~~~~}~more than twice another, and the sum of the two numbers is $28$.'' 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: $$10$$ 
Answer: D
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: What is the value of $$5^{4}+5^{4}+5^{4}+5^{4}+5^{4}$$? 
Options:
aoVal: A
content: $$5^{4}$$ 
aoVal: B
content: $$5^{5}$$ 
aoVal: C
content: $$5^{6}$$ 
aoVal: D
content: $$5^{10}$$ 
aoVal: E
content: $$5^{20}$$ 
Answer: B
Analysis: $$5^{1}\cdot5^{4}=5^{1+4}=5^{5}$$,  \uline{Teacher should introduce the formula of $$a^{m}a^{n}=a^{m+n}$$}. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers
Problem: A soccer player computes his win ratio by dividing the number of matches he has won by the total number of matches he has played. At the start of a weekend, his win ratio is exactly~$0.5$. During the weekend, he plays five games, winning three and losing two. At the end of the weekend, his win ratio is greater than~$0.505$. What\textquotesingle s the largest number of matches he could\textquotesingle ve won before the weekend began? 
Options:
aoVal: A
content: $$46$$ 
aoVal: B
content: $$47$$ 
aoVal: C
content: $$48$$ 
aoVal: D
content: $$92$$ 
aoVal: E
content: $$96$$ 
Answer: B
Analysis: Assume she won~$x$~games before the weekend, we obtain the inequality~$\frac{x+3}{2x+5}\gt0.505$~. Solve the inequality, we get~$x\lt47.5$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Three positive integers are equally spaced on a number line. The middle number is $15$, and the largest number is $4$ times the smallest number. What is the smallest of these three numbers? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$7$$ 
aoVal: E
content: $$8$$ 
Answer: C
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Eddie has a card. The number on the card is a neighbouring number of 10, but is not a neighbouring number of 12. What is the number on Eddie\textquotesingle s card?~\uline{~~~~~~~~~~}~ 
Options:
aoVal: A
content: $$11$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$8$$ 
Answer: C
Analysis: $$Omitted.$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers
Source: 其它
Problem: If $$20\times 30$$ is divided by $$40$$, the remainder is． 
Options:
aoVal: A
content: $$30$$ 
aoVal: B
content: $$15$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$0$$ 
Answer: D
Analysis: $$(20\times 30)\div 40=600\div 40=15$$; remainder $$=0$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: Which of the following numbers\textquotesingle{} value does not change after removing all ``$$0$$''s ． 
Options:
aoVal: A
content: $$90.221$$ 
aoVal: B
content: $$4.106$$ 
aoVal: C
content: $$22.990$$ 
Answer: C
Analysis: Only $$22.990$$\textquotesingle s $$"0"$$ can be removed without causing other digits to change their places from the original number. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals
Source: 其它