math-eval/TAL-SCQ5K huggingface dataset:
Problem: Joe writes an expression $\frac59\times\frac9{13}\times\frac{13}{17}\cdots $ Following the pattern, he writes middle fraction is \frac{45}{49}. What is the result of the expression? 
Options:
aoVal: A
content: $\frac5{49}$ 
aoVal: B
content: $\frac5{89}$ 
aoVal: C
content: $\frac5{17}$ 
aoVal: D
content: $\frac1{31}$ 
aoVal: E
content: $\frac5{81}$ 
Answer: B
Analysis: The last fraction should be $\frac{85}{89}$, so the answer is $\frac5{89}.$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: There were three color cups in the shop. At the beginning, there was only one cup of each kind. Later, there were five more blue cups, three more red cups, and one more yellow cup. How many cups were there in total at last?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$) 
Options:
aoVal: A
content: $$11$$ 
aoVal: B
content: $$12$$ 
aoVal: C
content: $$13$$ 
aoVal: D
content: $$14$$ 
aoVal: E
content: $$20$$ 
Answer: B
Analysis: To calculate the total number of cups, do not need to consider the color of the cup. At the beginning, there were three cups. The number at last is $3+5+3+1=12$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition and Subtraction of Whole Numbers->Questions Involving Addition and Subtraction
Problem: One apple, one banana and two peaches together weigh $12$ lbs. One apple and one peach together weigh $5$ lbs. One banana and $2$ peaches together weigh $5$ lbs more than one apple and one peach weigh together. Each peach weighs the same. How many pounds does one banana weigh? 
Options:
aoVal: A
content: $3$ lbs 
aoVal: B
content: $4$ lbs 
aoVal: C
content: $5$ lbs 
aoVal: D
content: $6$ lbs 
Answer: B
Analysis: We can write their relationships as the equations below:  $A+B+P+P=12$  $A+P=5$  $B+P+P=A+P+5$  So, $B+P+P=5+5=10$, $A=12-10=2$, $P=5-2=3$, $B=12-2-3-3=4$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution
Source: 其它
Problem: Suppose that $x$ and $y$ are nonzero real numbers such that $\frac{x+y}{x}=2$, what is the value of $\frac{x}{y}$? 
Options:
aoVal: A
content: $$\frac{1}{3}$$ 
aoVal: B
content: $$-1$$ 
aoVal: C
content: $$1$$ 
aoVal: D
content: $$3$$ 
Answer: B
Analysis: Rearranging, we find $x+y=2x, -x=y, \frac xy = -1$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Victor has $3$ siblings, and his mom is buying them chocolate cake for afternoon tea. His mom decides that all kids should receive the same amount of cake. What percent of the cake will Victor get? 
Options:
aoVal: A
content: $33.3$ 
aoVal: B
content: $$30$$ 
aoVal: C
content: $$25$$ 
aoVal: D
content: $$20$$ 
Answer: C
Analysis: $1\div 4=25\textbackslash\%$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation
Source: 其它
Problem: What is $$y$$ if $$56y=728$$? 
Options:
aoVal: A
content: $$13$$ 
aoVal: B
content: $$12$$ 
aoVal: C
content: $$11$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: $$9$$ 
Answer: A
Analysis: $y = 728 \div 56 = 13$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Problem: If $$x-y = -2$$ and $$y+4x = 12$$, then $$x=$$． 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$3$$ 
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: Think Store is selling boba plushies at $100$ dollars each. The plushies are so in demand that Think Store decides to increase the price of the plushies by $30\textbackslash\%$, but if a students buy $2$ boba plushies at the same time, there is a $40\textbackslash\%$ discount for the second plushie. How much does it costs to buy $2$ plushies? 
Options:
aoVal: A
content: $$260$$ 
aoVal: B
content: $$208$$ 
aoVal: C
content: $$182$$ 
aoVal: D
content: $$200$$ 
Answer: B
Analysis: $100\times (1+30\textbackslash\%)=130$  $130+130\times (1-40\textbackslash\%)=130+78=208$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation
Source: 其它
Problem: The sum of the repeating decimals~$0.\overline{163}$~and~$0.\overline{614}$~is ． 
Options:
aoVal: A
content: $$0.7$$ 
aoVal: B
content: $\dfrac{777}{1000}$ 
aoVal: C
content: $$1$$ 
aoVal: D
content: $\dfrac{7}{9}$ 
Answer: D
Analysis: $0.163163163\cdots+0.614614614\cdots=0.777777777\cdots=\dfrac{7}{9}$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals
Source: 其它
Problem: Four numbers are written in a row. The average of the first two is $21$ , the average of the middle two is $26$ , and the average of the last two is $30$ . What is the average of the first and last of the numbers? (2022 AMC 8 Problems, Question \#16) 
Options:
aoVal: A
content: $$24$$ 
aoVal: B
content: $$25$$ 
aoVal: C
content: $$26$$ 
aoVal: D
content: $$27$$ 
aoVal: E
content: $$28$$ 
Answer: B
Analysis: Note that the sum of the first two numbers is $21 \cdot 2=42$, the sum of the middle two numbers is $26 \cdot 2=52$, and the sum of the last two numbers is $30 \cdot 2=60$.  It follows that the sum of the four numbers is $42+60=102$, so the sum of the first and last numbers is $102-52=50$. Therefore, the average of the first and last numbers is $50 \div 2=$ (B) $25$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Which expression has the same result as $1+2+3+4+2+4+6+8+3+6+9+12+4+8+12+16$? 
Options:
aoVal: A
content: $(1+2+3+4)\times 6$ 
aoVal: B
content: $(1+2+3+4)$\textsuperscript{2} 
aoVal: C
content: $(16+1)\times16\div2$ 
aoVal: D
content: $1\times1+2\times2+3\times2+4\times3+6+8\times2+12\times2+16$ 
aoVal: E
content: $4\times20$ 
Answer: B
Analysis: $(1+2+3+4)\times 1+(1+2+3+4)\times 2+(1+2+3+4)\times 3+(1+2+3+4)\times 4=(1+2+3+4)\times (1+2+3+4)$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers
Source: 其它
Problem: Tyler has entered a buffet line in which he chooses one kind of meat, two different vegetables and one dessert. If the order of food items is not important, how many different meals might he choose?  Meat: beef, chicken, pork  Vegetables: baked beans, corn, potatoes, tomatoes  Dessert: brownies, chocolate cake, chocolate pudding, ice cream~($2001$ AMC $8$ Problem, Question \#$14$) 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$24$$ 
aoVal: C
content: $$72$$ 
aoVal: D
content: $$80$$ 
aoVal: E
content: $$144$$ 
Answer: C
Analysis: $\_3C\_1\times \_4C\_2\times \_4C\_1=72$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: If the value of $$x+2y$$ is $$3$$, then what is the result of $$\frac{1}{2}x+y-1$$?． 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$\frac{1}{2}$$ 
Answer: C
Analysis: $$\frac{1}{2}x+y-1=\frac{1}{2}(x+2y)-1=\frac{3}{2}-1=\frac{1}{2}$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Problem: What is the sum of the digits in the number $$3567$$? (adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$7$$) 
Options:
aoVal: A
content: $$3567$$ 
aoVal: B
content: $$35$$ 
aoVal: C
content: $$22$$ 
aoVal: D
content: $$21$$ 
aoVal: E
content: $356$ 
Answer: D
Analysis: $3+5+6+7=21$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form
Problem: Which of the following is the largest fraction? 
Options:
aoVal: A
content: $$\dfrac{3}{5}$$ 
aoVal: B
content: $$\dfrac{3}{6}$$ 
aoVal: C
content: $$\dfrac{3}{7}$$ 
aoVal: D
content: $$\dfrac{3}{8}$$ 
Answer: A
Analysis: Same numerator, so smaller denominator means larger fraction. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering
Source: 其它
Problem: If I multiply $$333333333333333$$ by $$777777777777777$$ and add the first and last digits of the product, the sum is． 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$11$$ 
Answer: A
Analysis: Just as for $$3\times7$$, $$33\times77$$, and $$333\times777$$, the first digit is a $$2$$, the last digit is a $$1$$, and the sum is $$2+1=3$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers
Problem: If $$5$$ apples cost as much as $$16$$ pineapples, then $$15$$ apples cost as much as pineapples. 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$18$$ 
aoVal: C
content: $$21$$ 
aoVal: D
content: $$48$$ 
Answer: D
Analysis: $$5$$ apples = $$16$$ pineapples  $$5\times3$$ apples = $15$ apples  $$16\times3$$ pineapples = $48$ pineapples 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Problem: Fill in the blank according to the pattern.  $$1, 1, 2, 3, 5, 8, $$~\uline{~~~~~~~~~~}~$$, 21, 34$$ 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$17$$ 
aoVal: C
content: $$13$$ 
aoVal: D
content: $$3$$ 
aoVal: E
content: None of the above 
Answer: C
Analysis: Fibonacci number. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences
Source: 其它
Problem: The outside temperature in a town is $-18$ $^{}o$$C$. What change in the temperature, would bring the outside temperature to $0$ $^{}o$$C$? 
Options:
aoVal: A
content: $-19$ 
aoVal: B
content: $-18$ 
aoVal: C
content: $18$ 
aoVal: D
content: $0$ 
Answer: C
Analysis: The opposite of $-18$ is $18$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Negative Numbers
Source: 其它
Problem: Suppose that $x$ and $y$ are nonzero real numbers such that $\frac{5 x+y}{x-4y}=-1$. What is the value of $\frac{x+3 y}{3 x-y}$? (Adapted From 2017 AMC 10B Problems, Question \#4) 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: $$11$$ 
Answer: C
Analysis: Rearranging, we find $5 x+y=-x+4y$, or $6x=3 y \Longrightarrow y=2x$. Substituting, we can convert the second equation into $$\frac{x+6 x}{3 x-2x}=\frac{7 x}{x}=\text { (C) } 7$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Debbie spent $12$ dollars on a book and a volleyball. The volleyball costed $4$ dollars than the book. How many dollars did she spend on the volleyball? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$7$$ 
aoVal: E
content: $$8$$ 
Answer: E
Analysis: $(12 + 4) \div 2 = 8$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Let $a, b$, and $c$ be three distinct one-digit numbers. What is the maximum value of the sum of the roots of the equation $(x-a)(x-b)+(x-b)(x-c)=0$? 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$15.5$$ 
aoVal: C
content: $$16$$ 
aoVal: D
content: $$16.5$$ 
aoVal: E
content: $$17$$ 
Answer: D
Analysis: Expanding the equation and combining like terms results in $2 x^{2}-(a+2 b+c) x+(a b+b c)=0$. By Vieta\textquotesingle s formula the sum of the roots is $\frac{-[-(a+2 b+c)]}{2}=\frac{a+2 b+c}{2}$. To maximize this expression we want $b$ to be the largest, and from there we can assign the next highest values to $a$ and $c$. So let $b=9, a=8$, and $c=7$. Then the answer is $\frac{8+18+7}{2}= 16.5$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Unary Quadratic Equations
Source: 其它
Problem: For how many integers $x$ is the number $x^{4}-7x^{2}+10$ negative? (  2014 AMC 10B Problems, Question \#20) 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$12$$ 
aoVal: E
content: $$24$$ 
Answer: A
Analysis: Factor the polynomial as $\left(x^{2}-5\right)\left(x^{2}-2\right)$. Since this expression is negative, one term must be negative and the other positive. Also, the first term is obviously smaller than the second, so $x^{2}-5\textless0\textless x^{2}-2$. Solving this inequality, we find $2\textless x^{2}\textless5$. There are exactly $2$ integers $x$ that satisfy this inequality, $\pm 2$. Thus our answer is $(\mathbf{A}) 2$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: In how many different ways can you select two digits out of $$ 0$$, $$1$$, $$ 2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, and $$9$$ and put into the two boxes to make the below equality correct?  $$ 20- \square =22-\square $$ 
Options:
aoVal: A
content: $$7$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: $$12$$ 
Answer: B
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers
Problem: If I round $$1315$$ to the nearest ten, then multiply the result by $$3$$, then round to the nearest hundred, what is my final result? 
Options:
aoVal: A
content: $$3800$$ 
aoVal: B
content: $$3900$$ 
aoVal: C
content: $$3945$$ 
aoVal: D
content: $$3960$$ 
aoVal: E
content: $$4000$$ 
Answer: E
Analysis: If I round $$1315$$ to the nearest ten, I get $$1320$$. Then, I multiply by $$3$$ to get $$3960$$. To the nearest hundred, this is $$4000$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Estimating Large Numbers
Problem: Denise fired a silver rocket and a gold rocket at the same time. The rockets exploded into $20$ stars in total. The gold rocket exploded into $6$ more stars than the silver one. How many stars did the gold rocket explode into? (2021 Math Kangaroo Problem, Level 3-4, Question \#7) 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$13$$ 
aoVal: E
content: $$15$$ 
Answer: D
Analysis: The silver rocket exploded $(20-6)\div2=7$ stars, and the gold rocket exploded $20-7=13$ stars. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: What is the missing number in the box?  $2:3=\boxed{?}:12$ 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$4$$ 
Answer: A
Analysis: $\frac{2}{3}=\frac{8}{12}$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions
Problem: When the number $$789678567456$$ is added to the number $$987876765654$$, how many digits does the sum have? 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$13$$ 
aoVal: C
content: $$24$$ 
aoVal: D
content: $$25$$ 
Answer: B
Analysis: The number $$789678567456$$ is added to the number $$987876765654$$.  Since we carry a $$1$$ when adding the left-most digits, the sum has $$12+1$$ digits. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers
Problem: Two integers are inserted into the list $3,3,8,11,28$ to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers? (2023 AMC 8 Problems, Question \#20) 
Options:
aoVal: A
content: $$56$$ 
aoVal: B
content: $$57$$ 
aoVal: C
content: $$58$$ 
aoVal: D
content: $$60$$ 
aoVal: E
content: $$61$$ 
Answer: D
Analysis: To double the range, we must find the current range, which is $28-3=25$, to then double to: $2(25)=50$. Since we do not want to change the median, we need to get a value less than $8$ (as $8$ would change the mode) for the smaller, making $53$ fixed for the larger. Remember, anything less than $3$ is not beneficial to the optimization. So, taking our optimal values of $7$ and $53$, we have an answer of $7+53=$ (D) $60$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: What is the $5^{th}$ number in the $8^{th}$ row? 
Options:
aoVal: A
content: $$53$$ 
aoVal: B
content: $$54$$ 
aoVal: C
content: $$69$$ 
aoVal: D
content: $$70$$ 
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 a chinese chess competition, children would be awarded $$2$$ marks for every game won, $$1$$ mark will be awarded for every game that ended in a draw and $$0$$ marks will be awarded for every game that ended in a loss. $6$ students participated in the round robin and $5$ of the students\textquotesingle{} scores are as follows: $$7$$, $$6$$, $$5$$, $$4$$, $$3$$. How many marks did the last place student score? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$8$$ 
Answer: C
Analysis: $6$ students will play a total of $5+4+3+2+1=15$ games.  Total score $=15\times2=30$  Last student\textquotesingle s score $=30-7-6-5-4-3=5$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences
Problem: Three (different) numbers are selected from $$0$$, $$1$$, $$3$$ and $$5$$ to form a three-digit number, find the difference between the smallest three-digit number and the largest three-digit number formed. 
Options:
aoVal: A
content: $$401$$ 
aoVal: B
content: $$455$$ 
aoVal: C
content: $$428$$ 
aoVal: D
content: $$431$$ 
aoVal: E
content: $$530$$ 
Answer: C
Analysis: $$531-103=428$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers
Problem: Which of the following numbers is the multiple of $5$? 
Options:
aoVal: A
content: $$11$$ 
aoVal: B
content: $$55$$ 
aoVal: C
content: $$79$$ 
aoVal: D
content: $$2022$$ 
Answer: B
Analysis: $55\div 5 =11$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Problem: Usually, people spend $\frac{1}{4}$ of their sleeping time dreaming. If Poole slept $8$ hours last night, how much time did he spend dreaming yesterday? 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$2$$ 
aoVal: E
content: $$1$$ 
Answer: D
Analysis: $$8\times \frac{1}{4}=2$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: The $$41^{}\text{th}$$ number in the sequence $$7$$, $$11$$, $$15$$, $$19$$, $$\cdots \cdots $$ is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$171$$ 
aoVal: B
content: $$167$$ 
aoVal: C
content: $$164$$ 
aoVal: D
content: $$160$$ 
Answer: B
Analysis: $$7+4\times (41-1)=167$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences
Problem: This regression uses the number of times a new worker has spent practicing task (measured in Number Practice~Rounds) to predict how much time is needed to complete one round of the task (measured in Minutes). What is the equation of the least-squares regression line? 
Options:
aoVal: A
content: $\overset{\frown}{Rounds}=-0.6442+22.94\textbackslash{} Minutes$ 
aoVal: B
content: $\overset{\frown}{Rounds}=22.94+0.5466\textbackslash{} Minutes$ 
aoVal: C
content: $\overset{\frown}{Minutes}=22.94+2.866\textbackslash{} Rounds$ 
aoVal: D
content: $\overset{\frown}{Minutes}=22.94-0.6442\textbackslash{} Rounds$ 
aoVal: E
content: $\overset{\frown}{Minutes}=-0.6442+0.5466\textbackslash{} Rounds$ 
Answer: D
Analysis: From Chapter 6, the correct answer is (d). The slope of the regression line, -0.6442, can be found under "Coef" to the right of "Number of Rounds" .The intercept of the regression line, 22.94, can be found under "Coef" to the right of "Constant." Rounds is the explanatory variable (x) and Time is the response variable (y). 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: $$$$Calculate$$$$  $$\frac{1}{5^{5}+1}+ \frac{1}{5^{5}+5}+ \frac{1}{5^{5}+5^{2}}+ \cdots$$$$ + \frac{1}{5^{5}+5^{8}}+ \frac{1}{5^{5}+5^{9}}+ \frac{1}{5^{5}+5^{10}}$$． 
Options:
aoVal: A
content: $$\frac{11}{6250}$$ 
aoVal: B
content: $$\frac{23}{12500}$$ 
aoVal: C
content: $$\frac{6}{3125}$$ 
aoVal: D
content: $$\frac{13}{6250}$$ 
aoVal: E
content: None of the above 
Answer: A
Analysis: $$\frac{1}{5^{5}+1}+ \frac{1}{5^{5}+5}+ \frac{1}{5^{5}+5^{2}}+ \cdots + \frac{1}{5^{5}+5^{8}}+ \frac{1}{5^{5}+5^{9}}+ \frac{1}{5^{5}+5^{10}}$$  $$=\left ( \frac{1}{5^{5}+1}+ \frac{1}{5^{5}+5^{10}}\right )+\left ( \frac{1}{5^{5}+5}+ \frac{1}{5^{5}+5^{9}}\right )$$$$+\left ( \frac{1}{5^{5}+5^{2}}+ \frac{1}{5^{5}+5^{8}}\right )+\cdots+\left (\dfrac{1}{5^{5}+5^{5}}\right )$$  $$=\left ( \frac{5^{5}+1}{5^{5}\left (5^{5}+1\right )}\right )+\left ( \frac{5^{4}+1}{5^{5}(5^{4}+1)}\right )$$$$+\left ( \frac{5^{3}+1}{5^{5}(5^{3}+1)}\right )+ \cdots +$$ $$\left (\frac{1}{2\left (5\right )^{5}}\right )$$  $$= \left (\frac{5}{5^{5}}\right )+\left ( \frac{1}{2(5)^{5}}\right )= \frac{11}{6250}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Complex Fractions
Problem: \textbf{Research indicates that the standard deviation of typical human body temperature is 0.4 degree Celsius (C). which of the following represents the standard deviation of typical human body temperature in degrees Fahrenheit (F), where $$F=\frac{9}{5}C+32$$?} 
Options:
aoVal: A
content: $$\frac{9}{5}(0.4)+32$$ 
aoVal: B
content: $$\frac{9}{5}(0.4)$$ 
aoVal: C
content: $$\frac{9}{5}(0.4)^{2}$$ 
aoVal: D
content: $$\frac{9}{5}^{2}(0.4)$$ 
aoVal: E
content: $$\frac{9}{5}^{2}(0.4)^{2}$$ 
Answer: B
Analysis: \textbf{Standard deviation for Y=ax+b is SD(Y)=\textbar a\textbar SD(x).} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: On her first day of work, Janabel sold one widget. On day two, she sold three widgets. On day three, she sold five widgets, and on each succeeding day, she sold two more widgets than she had sold on the previous day. How many widgets in total had Janabel sold after working $20$ days? 
Options:
aoVal: A
content: $$39$$ 
aoVal: B
content: $$40$$ 
aoVal: C
content: $$210$$ 
aoVal: D
content: $$400$$ 
aoVal: E
content: $$401$$ 
Answer: D
Analysis: On day $20$, she sold $1+2\times(20-1)=39$  Sum of $20$ days: $(1+39)\times 20\div2=400$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences
Source: 其它
Problem: What is the value of  $\frac{1}{2}$~$\cdot$~$\frac{4}{2}$~$\cdot$~$\frac{3}{5}$ $\ldots$~$\frac{18}{20}$~$\cdot$~$\frac{19}{21}$~$\cdot$ $\frac{20}{22}$ 
Options:
aoVal: A
content: $\dfrac{1}{462}$ 
aoVal: B
content: $\frac{1}{231}$ 
aoVal: C
content: $\frac{1}{132}$ 
aoVal: D
content: $\frac{2}{213}$ 
aoVal: E
content: $\frac{1}{22}$ 
Answer: B
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Which of the following fractions is the largest? 
Options:
aoVal: A
content: $\frac13$ 
aoVal: B
content: $\frac34$ 
aoVal: C
content: $$\frac57$$ 
aoVal: D
content: $\frac79$ 
aoVal: E
content: $\frac8{11}$ 
Answer: D
Analysis: $\frac 79 \textgreater{} \frac 34 \textgreater{} \frac 8{11}\textgreater\frac 57\textgreater\frac 13$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Problem: $$27+11+13$$=~\uline{~~~~~~~~~~}~ 
Options:
aoVal: A
content: $$31$$ 
aoVal: B
content: $$41$$ 
aoVal: C
content: $$50$$ 
aoVal: D
content: $$51$$ 
aoVal: E
content: $$60$$ 
Answer: D
Analysis: $$27+11+13$$  $$=27+13+11$$  $$=40+11$$  $$=51$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction 
Source: 其它