math-eval/TAL-SCQ5K huggingface dataset:
Problem: According to the regulation of the pyramid series, the formula $$1+2+3+4+5+6+5+4+3+2+1=$$． 
Options:
aoVal: A
content: $$6\times6$$ 
aoVal: B
content: $$6\times7$$ 
aoVal: C
content: $$6\times5$$ 
Answer: A
Analysis: ``Pyramid series''$$1+2+3+4+\cdots +\left( n-1 \right)+n+\left( n-1 \right)+\cdots +3+2+1$$  $$={{n}^{2}}$$．  So the answer is $$\text{A}$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables
Problem: Which of the following has a result of $183$? 
Options:
aoVal: A
content: $$103+86$$ 
aoVal: B
content: $$117+76$$ 
aoVal: C
content: $$90+83$$ 
aoVal: D
content: $$82+101$$ 
Answer: D
Analysis: $$103+86=189$$  $$117+76=193$$  $$90+83=173$$  $$82+101=183$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction
Problem: Calculate: $$\frac{1}{4}\times \frac{5}{6}+\frac{3}{7}\times \frac{7}{8}=$$． 
Options:
aoVal: A
content: $$\frac{5}{12}$$ 
aoVal: B
content: $$\frac{5}{16}$$ 
aoVal: C
content: $$\frac{5}{17}$$ 
aoVal: D
content: $$\frac{7}{12}$$ 
aoVal: E
content: $$\frac{11}{12}$$ 
Answer: D
Analysis: $$\frac{1}{4}\times \frac{5}{6}+\frac{3}{7}\times \frac{7}{8}$$=$$\frac{5}{24}+\frac{3}{8}$$=$$\frac{5}{24}+\frac{9}{24}$$=$$\frac{14}{24}$$=$$\frac{7}{12}$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions
Problem: Simplify the following expression: $$a^{2}\times a+b^{2}\times b^{3}$$. 
Options:
aoVal: A
content: $$a^{3}+b^{5}$$ 
aoVal: B
content: $$a^{3}b^{5}$$ 
aoVal: C
content: $$a^{2}+b^{5}$$ 
aoVal: D
content: $$a^{2}+b^{6}$$ 
Answer: A
Analysis: $$a^{2}\times a+b^{2}\times b^{3}=$$$$a^{3}+b^{5}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers
Problem: What is the next number in this sequence?  $$1$$, $$2$$, $$3$$, $$6$$, $$11$$, $$20$$, $$37$$,~\uline{~~~~~~~~~~}~? ． 
Options:
aoVal: A
content: $$47$$ 
aoVal: B
content: $$54$$ 
aoVal: C
content: $$57$$ 
aoVal: D
content: $$68$$ 
aoVal: E
content: $$74$$ 
Answer: D
Analysis: After the first three numbers, each number is the sum of the previous three numbers. So the next number is $$11 + 20 + 37 = 68$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences
Problem: \textbf{Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distribution of Sean's weekly income is approximately normal with mean $\textbackslash$225$ and standard deviation $\textbackslash$25$. The distribution of Evan's weekly income is approximately normal with mean $\textbackslash$240$ and standard deviation $15. Assuming their weekly incomes are independent of each other, which of the following is closest to the probability that Sean will have a greater income than Evan in a randomly selected week?} 
Options:
aoVal: A
content: \textbf{0.067} 
aoVal: B
content: \textbf{0.159} 
aoVal: C
content: \textbf{0.227} 
aoVal: D
content: \textbf{0.303} 
aoVal: E
content: \textbf{0.354} 
Answer: D
Analysis: \textbf{Sean \textasciitilde{} N(225, 25)}  \textbf{Evan \textasciitilde{} N(240, 15)}  \textbf{→}  \textbf{Sean - Evan \textasciitilde{} N(-15, 29.155)}  \textbf{P(Sean-Evan \textgreater{} 0) = 1-P(X\textless0) = 0.303} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: An amusement park has a collection of scale models, with ratio $1: 40$, of buildings and other sights from around the country. The height of empire state building is 1250 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: $$30$$ 
aoVal: B
content: $$31$$ 
aoVal: C
content: $$32$$ 
aoVal: D
content: $$33$$ 
aoVal: E
content: $$34$$ 
Answer: B
Analysis: You can see that since the ratio of real building\textquotesingle s heights to the model building\textquotesingle s height is $1: 40$. We also know that the Empire State Building is 1250 feet, so to find the height of the model, we divide by 40 . That gives us $31.25$ which rounds to 31 . Therefore, to the nearest whole number, the duplicate is (B) 31 feet. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions
Source: 其它
Problem: A basketball is on sale with 35\% off, the discounted price is $$52$$ dollars, the original price of the basketball wasdollars． 
Options:
aoVal: A
content: $$18.2$$ 
aoVal: B
content: $$33.8$$ 
aoVal: C
content: $$80$$ 
aoVal: D
content: $$148$$ 
Answer: C
Analysis: $$x \times 65\textbackslash\% = 52$$  $$x = 80$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Which of these is equal to $$(0.3+0.4 + 0.5 -0.9)\div0.6$$? 
Options:
aoVal: A
content: $$0.02 $$ 
aoVal: B
content: $$0.05 $$ 
aoVal: C
content: $$0.2 $$ 
aoVal: D
content: $$0.5$$ 
aoVal: E
content: $$1$$ 
Answer: D
Analysis: Note that $$(0.3+0.4+0.5 -0.9)\div0.6 =(1.2 -0.9)\div0.6 =0.3\div0.6 = 3\div6$$ $$=0.5$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Four Operations of Decimals
Problem: The ratio of $w$ to $x$ is $4: 3$, the ratio of $y$ to $z$ is $3: 2$, and the ratio of $z$ to $x$ is $1: 6$. What is the ratio of $w$ to $y$? (2020 AMC 10B Problems, Question \#3) 
Options:
aoVal: A
content: $4: 3$ 
aoVal: B
content: $3: 2$ 
aoVal: C
content: $8: 3$ 
aoVal: D
content: $4: 1$ 
aoVal: E
content: $16: 3$ 
Answer: E
Analysis: We need to somehow link all three of the ratios together.  We can start by connecting the last two ratios together by multiplying the last ratio by two. $z: x=1: 6=2: 12$, and since $y: z=3: 2$, we can link them together to get $y: z: x=3: 2: 12$.  Finally, since $x: w=3: 4=12: 16$, we can link this again to get: $y: z: x: w=3: 2: 12: 16$, so $w: y=(\mathbf{E}) 16: 3$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: The digit $9$ in what number represents a value of $0.09$? 
Options:
aoVal: A
content: $$9.012$$ 
aoVal: B
content: $$0.469$$ 
aoVal: C
content: $$51.9$$ 
aoVal: D
content: $$26.49$$ 
Answer: D
Analysis: If the digit $$9$$ represents a value of $$0.09$$, it means the digit $$9$$ is located on the hundredth place on that number, which is the second digit after the decimal point.  Check Lesson 4 Concept 1 on textbook 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals
Source: 其它
Problem: What is the smallest whole number larger than the perimeter of any triangle with a side of length $9$ and a side of length $1$? (adapted from 2015 AMC8, Question 8) 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$19$$ 
aoVal: C
content: $$20$$ 
aoVal: D
content: $$21$$ 
aoVal: E
content: $$22$$ 
Answer: C
Analysis: We know from the triangle inequality that the last side, $s$, fulfills $s\textless9+1=10$. Adding $9+1$ to both sides of the inequality, we get $s+9+1\textless20$, and because $s+9+1$ is the perimeter of our triangle, (C) 20 is our answer. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities
Source: 其它
Problem: The sum of three numbers is $20$. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three numbers? 
Options:
aoVal: A
content: $$18$$ 
aoVal: B
content: $$28$$ 
aoVal: C
content: $$32$$ 
aoVal: D
content: $$40$$ 
aoVal: E
content: $$294$$ 
Answer: B
Analysis: B 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: $$4\times4\times20\times20=80\times$$? 
Options:
aoVal: A
content: $$80$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$2$$ 
Answer: A
Analysis: $$(4\times20)\times (4\times20)=80\times80$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: The number $-11+(-7)$ is equal to: 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$-3$$ 
aoVal: C
content: $$-25$$ 
aoVal: D
content: $$25$$ 
aoVal: E
content: $$-18$$ 
Answer: E
Analysis: $-11+(-7)=-18$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations
Source: 其它
Problem: If $$2x-3=y+5$$ and $$3y-1=5$$, then $$x=$$． 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$7$$ 
Answer: C
Analysis: From $$3y -1=5$$, then we can get $$y=2$$.  Therefore from $$2x-3=2+5$$, we obtain $$x=5$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Problem: Write each of the numbers 0,1,2,3,4,5,6 in the sqaures to make the addition correct. What digit will be in the grey square?  pic 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$5$$ 
aoVal: E
content: $$6$$ 
Answer: D
Analysis: work backwards 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns->Encryption and Decryption
Source: 其它
Problem: What is the product of $125$ and $6$? 
Options:
aoVal: A
content: $$420$$ 
aoVal: B
content: $$1230$$ 
aoVal: C
content: $$750$$ 
aoVal: D
content: $$720$$ 
Answer: C
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: If 5 plates weigh as much as 9 mugs, then 99 mugs weigh as much as~\uline{~~~~~~~~~~}~plates. 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$18$$ 
aoVal: C
content: $$55$$ 
aoVal: D
content: $$50$$ 
Answer: C
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution
Source: 其它
Problem: On the first day of a $7-$day holiday, Judy reads $9$ pages of a book. On the second day, she reads $12$. Then each day later, she reads $3$ pages more than the day before. On the last day of the holiday, she reads the corresponding number of pages and exactly finishes reading the book. How many pages does the book have? 
Options:
aoVal: A
content: $$27$$ 
aoVal: B
content: $$30$$ 
aoVal: C
content: $$120$$ 
aoVal: D
content: $$126$$ 
aoVal: E
content: $$128$$ 
Answer: D
Analysis: Use the formula of arithmetic sequence to solve this problem.  On the last day, she reads $9+6\times3=27$ pages.  The book has $(9+27)\times7 \div2=126$ pages. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences
Source: 其它
Problem: Linda, Alice, Joe, Lily, and Rachel lost their balloons. The numbers on their balloons were all smaller than $8$. The difference between the largest number and the smallest number was $5$. What are their balloon\textquotesingle s numbers? (adapted from $$2021$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$8$$） 
Options:
aoVal: A
content: $7, 5, 4, 3,2$ 
aoVal: B
content: $4, 1, 7,9,6$ 
aoVal: C
content: $6,4,2,5,3$ 
aoVal: D
content: $0,7,4,9,5$ 
aoVal: E
content: $1,8,5,4,6$ 
Answer: A
Analysis: In~ B, D, and E, the largest number more than $8$. In the C, the difference between the largest number and the smallest number is $4$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Subtraction of Whole Numbers->Subtraction in Horizontal Form
Problem: $$8+9+12+17+23+31=$$？． 
Options:
aoVal: A
content: $$100$$ 
aoVal: B
content: $$90$$ 
aoVal: C
content: $$80$$ 
aoVal: D
content: $$70$$ 
aoVal: E
content: $$50$$ 
Answer: A
Analysis: $$=8+12+9+31+23+17$$  $$=20+40+40$$  $$=100$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers
Source: 其它
Problem: $$$$Calculate$$$$  $$\left (403 \frac{3}{5}+183 \frac{5}{11}+155 \frac{3}{13}+118 \frac{12}{17}\right ) \div$$$$ \left~~( \frac{1009}{15}+ \frac{1009}{33}+ \frac{1009}{39}+ \frac{1009}{51}\right )$$. 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$5.5$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$6.5$$ 
aoVal: E
content: None of the above 
Answer: C
Analysis: $$\left (403 \frac{3}{5}+183 \frac{5}{11}+155 \frac{3}{13}+118 \frac{12}{17}\right ) \div$$$$ \left ( \frac{1009}{15}+ \frac{1009}{33}+ \frac{10009}{39}+ \frac{1009}{51}\right )$$  $$=2018\left ( \frac{1}{5}+ \frac{1}{11}+ \frac{1}{13}+ \frac{1}{17}\right ) \div \frac{1000}{3}\left ( \frac{1}{5}+ \frac{1}{11}+ \frac{1}{13}+ \frac{1}{17}\right )$$  $=6$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Fast Calculation in Fractions
Problem: What is the next number in the sequence below?  $$47, 44, 38, 29, 17, \cdots $$ 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$2$$ 
aoVal: E
content: None of the above 
Answer: D
Analysis: The pattern is: $$-3, -6, -9, -12, -15, \cdots $$  Thus, $$17-15=2$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences
Source: 其它
Problem: $10000$ years ago, Owen the fisher traded $3$ fishes for $1$ rabbit from Oscar the hunter. Then, Oscar traded $2$ rabbits for $3$ packs of wheat from Dennis the farmer. How many fishes should Owen give Dennis for a pack of wheat? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
Answer: B
Analysis: fish:rabbit$=3:1$  wheat:rabbit$=3:2$  fish: wheat$=2:1$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions->Simplifying Continued Ratios
Source: 其它
Problem: Harry and Terry are each told to calculate $8-(2+5)$.~Harry gets the correct answer. Terry ignores the parentheses and calculates $8-2+5$.~If Harry\textquotesingle s answer is $H$~and Terry\textquotesingle s answer is $T$, what is $H-T$? (2014 AMC $8$ Problem, Question \#1) 
Options:
aoVal: A
content: $$-10$$ 
aoVal: B
content: $$-6$$ 
aoVal: C
content: $$0$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$10$$ 
Answer: A
Analysis: We have $H=8-7=1$ and $T=8-2+5=11$. Clearly $1-11=-10$, so our answer is $A$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations
Source: 其它
Problem: Two non-zero real numbers, $x$ and $y$, satisfy $(x+y)^{2}=3xy$. Which of the following is a possible value of $$\frac{x+y}{y}-\frac{x-y}{x}$$? (Adapted From 2000 AMC 12 Problems, Question \#11) 
Options:
aoVal: A
content: $-1$ 
aoVal: B
content: $-\frac{1}{2}$ 
aoVal: C
content: $\frac{1}{2}$ 
aoVal: D
content: $1$ 
aoVal: E
content: $$2$$ 
Answer: D
Analysis: Note that $(x+y)^{2} = x^{2}+y^{2}+2xy = 3xy \Rightarrow x^{2}+y^{2} = xy$. Then,  $$\frac{x+y}{y}-\frac{x-y}{x}=\frac{x(x+y)-y(x-y)}{xy}=\frac{{{x}^{2}}+xy-xy+{{y}^{2}}}{xy}=\frac{{{x}^{2}}+{{y}^{2}}}{xy} = 1$$. 
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 8, but is not a neighbouring number of 6. What is the number on Eddie\textquotesingle s card?~\uline{~~~~~~~~~~}~ 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$9$$ 
Answer: D
Analysis: $$Omitted.$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers
Source: 其它
Problem: What percent of $$20$$ is $$50$$? 
Options:
aoVal: A
content: $$40$$ 
aoVal: B
content: $$140$$ 
aoVal: C
content: $$200$$ 
aoVal: D
content: $$250$$ 
Answer: D
Analysis: $$\frac{50}{20}=2.5=2.5\times100\textbackslash\%=250\textbackslash\%$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions
Problem: If $A:B=3:5$, $B:C=3:2$, find $A:B:C$. 
Options:
aoVal: A
content: $3:5:4$ 
aoVal: B
content: $9:15:10$ 
aoVal: C
content: $9:3:10$ 
aoVal: D
content: $8:15:10$ 
Answer: B
Analysis: $A:B=3:5$  $B:C=3:2$  $A:B:C=9:15:10$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions
Source: 其它
Problem: If $A:B=3:5$, $B:C=3:2$, find $A:B:C$=~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $3:5:4$ 
aoVal: B
content: $9:15:10$ 
aoVal: C
content: $9:3:10$ 
aoVal: D
content: $8:15:10$ 
Answer: B
Analysis: $A:B=3:5$  $B:C=3:2$  $A:B:C=9:15:10$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions
Source: 其它
Problem: $$0.1\times 0.2\times 0.3=$$．($1979-1980$ Math League.com contest problem, $7$\textsuperscript{th~}Grade, Question \#$12$) 
Options:
aoVal: A
content: $$0.0006$$ 
aoVal: B
content: $$0.006$$ 
aoVal: C
content: $$0.06$$ 
aoVal: D
content: $$0.6$$ 
Answer: B
Analysis: $$0.1\times 0.2\times 0.3=(0.1\times 0.2)\times 0.3=0.02\times 0.3=0.006$$. Therefore, the answer is $$\rm B$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals
Problem: If $$5$$ plates weigh as much as $$9$$ mugs, then $$45$$ mugs weigh as much as~\uline{~~~~~~~~~~}~plates. 
Options:
aoVal: A
content: $$18$$ 
aoVal: B
content: $$25$$ 
aoVal: C
content: $$72$$ 
aoVal: D
content: $$81$$ 
Answer: B
Analysis: Since $$9$$ mugs $$=5$$ plates  $$45\div9=5$$ times of the above equation.  $$45$$ mugs $$=25$$ plates 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Problem: Find the missing number: $$512\times2 = 32\times $$． 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$16$$ 
aoVal: D
content: $$32$$ 
Answer: D
Analysis: $$512\times2=1024=32\times32$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: Calculate:  $$\left( \frac{5}{8}+\frac{1}{17} \right)\times 8+\frac{9}{17}=$$． 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$6$$ 
Answer: C
Analysis: $$\left( \frac{5}{8}+\frac{1}{17} \right)\times 8+\frac{9}{17}$$  $$=\frac{5}{8}\times 8+\frac{1}{17}\times 8+\frac{9}{17}$$  $$=5+\frac{8}{17}+\frac{9}{17}$$  $$=5+1$$  $$=6$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Problem: A container had $27$ ℓ of longan drink. The drink is made up of three $2$-ℓ\textbf{~}bottles of longan syrup and some water. What is the volume of water used to make the drink? 
Options:
aoVal: A
content: 6ℓ 
aoVal: B
content: 18ℓ 
aoVal: C
content: 21ℓ 
aoVal: D
content: 27ℓ 
Answer: C
Analysis: $$2 \times 3 = 6$$  $$27 - 6 = 21$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Volume and Capacity
Source: 其它
Problem: Express $108:9$ in the simplest form:． 
Options:
aoVal: A
content: $12:1$ 
aoVal: B
content: $24:6$ 
aoVal: C
content: $16:4$ 
aoVal: D
content: $4:1$ 
Answer: A
Analysis: $(108\div9):(9\div9)=12:1$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio
Problem: $$5 + 50 + 500 = 5 \times$$． 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$100$$ 
aoVal: C
content: $$111$$ 
aoVal: D
content: $$550$$ 
Answer: C
Analysis: $$5 + 50 + 500 =555= 5 \times111$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: If $$x+2 = y$$ and $$y+4x = 12$$, then $$x=$$． 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
Answer: A
Analysis: $$x+2=y$$, then $$x=y-2$$. We can get $$y+4(y-2)=12$$, $$y=4$$, $$x=y-2=2$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Problem: In the following Figures $\left (a\right )$ and $\left (b\right )$, each number inside a small triangle is the sum of the numbers inside in the neighbouring small circles. The number inside each circle is either $1$, $2$, $3$, $4$, $5$, $6$, $7$ or $8$.  The sum of whole numbers inside the circles in Figure $\left (a\right )$ is $1+8+8+2+3+5=27$. What is the largest possible sum of whole numbers inside the circles in Figure $\left (b\right )$? 
Options:
aoVal: A
content: $$48$$ 
aoVal: B
content: $$52$$ 
aoVal: C
content: $$56$$ 
aoVal: D
content: $$64$$ 
aoVal: E
content: $$72$$ 
aoVal: F
content: $$74$$ 
aoVal: G
content: $$80$$ 
aoVal: H
content: None of the above 
Answer: B
Analysis: B 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Source: 其它
Problem: Known $$A=\frac{{{3}^{2019}}+1}{{{3}^{2020}}+1}$$，$$B=\frac{{{3}^{2020}}+1}{{{3}^{2021}}+1}$$, compare between $$A$$ and $$B$$． 
Options:
aoVal: A
content: $A=B$ 
aoVal: B
content: $A\textgreater B$ 
aoVal: C
content: $A\textless B$ 
aoVal: D
content: All of the above 
aoVal: E
content: None of the above 
Answer: B
Analysis: $${{3}^{2019}}=a$$，$$A=\frac{a+1}{3a+1}$$，$$B=\frac{3a+1}{9a+1}$$，  $$\frac{1}{A}=\frac{3a+1}{a+1}=\frac{3(a+1)-2}{a+1}=3-\frac{2}{a+1}$$，  $$\frac{1}{B}=\frac{9a+1}{3a+1}=\frac{3(3a+1)-2}{3a+1}=3-\frac{2}{3a+1}$$，  ∴$$\frac{1}{A} ~\textless{} ~\frac{1}{B}$$，  ∴$$A\textgreater B$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Problem: The fraction $$\frac23$$ keeps the same value when both its numerator and denominator are． 
Options:
aoVal: A
content: multiplied by $$2~ $$ 
aoVal: B
content: increased by $$2$$ 
aoVal: C
content: decreased by $$2$$ 
aoVal: D
content: $$ $$squared$$ $$ 
Answer: A
Analysis: The problem is about the basic property of fractions, namely, multiplying or dividing the numerator and denominator by the same number (except $$0$$), the value of the fraction is unchanged. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions
Problem: The original price of a product was $$80$$ dollars, and it\textquotesingle s on sale for 30\% off, this product isdollars cheaper than before． 
Options:
aoVal: A
content: $$7$$ 
aoVal: B
content: $$24$$ 
aoVal: C
content: $$30$$ 
aoVal: D
content: $$56$$ 
Answer: B
Analysis: the new price is $$70\textbackslash\%$$ of the original price，$$so$$ the new price is $$80\times 70\textbackslash\%=56$$；  $$80-56=24$$．  so choose $$\text{B}$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: What is the product of five fractions, whose denominators are $5-1$ in descending order, and the numerators are $1-5$ in ascending order？ 
Options:
aoVal: A
content: $\frac1{25}$ 
aoVal: B
content: $\frac1{2}$ 
aoVal: C
content: $\frac1{5}$ 
aoVal: D
content: $$0$$ 
aoVal: E
content: $$1$$ 
Answer: E
Analysis: $\frac{1\times2\times3\times4\times5}{5\times4\times3\times2\times1}=1$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: Tony and Mary are waiting in line to go shopping. Tony is fifth in line, while Mary is 365th. How many people are standing between Tony and Mary in the line? 
Options:
aoVal: A
content: $$359$$ 
aoVal: B
content: $$360$$ 
aoVal: C
content: $$361$$ 
aoVal: D
content: $$315$$ 
aoVal: E
content: $$314$$ 
Answer: A
Analysis: The question is asking for the number of people between Tony and Mary, which is $$365-5-1=359$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering