math-eval/TAL-SCQ5K huggingface dataset:
Problem: Which of the following is the largest fraction?  $$\dfrac{2}{6}$$,$$\dfrac{2}{7}$$,$$\dfrac{2}{8}$$,$$\dfrac{2}{9}$$ 
Options:
aoVal: A
content: $$\dfrac{2}{5}$$ 
aoVal: B
content: $$\dfrac{2}{7}$$ 
aoVal: C
content: $$\dfrac{2}{11}$$ 
aoVal: D
content: $$\dfrac{2}{9}$$ 
aoVal: E
content: $$\dfrac{2}{10}$$ 
Answer: A
Analysis: Same numerator, so smaller denominator means larger fraction. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating
Source: 其它
Problem: David measured the length of his garden.  It was $$15$$ metres to the nearest tenth of a metre.  Between what limits was the actual length? 
Options:
aoVal: A
content: $$14.995\leqslant $$ the actual length $$\leqslant 15.005$$ 
aoVal: B
content: $$14.9\leqslant $$ the actual length $$\textless~15.1$$ 
aoVal: C
content: $$14.95\leqslant $$ the actual length $$\textless{} 15.05$$ 
aoVal: D
content: $$14.99\leqslant $$ the actual length $$\textless15.01$$ 
aoVal: E
content: $$14.5\textless$$ the actual length $$\textless15.5$$ 
Answer: C
Analysis: 14.9500000\ldots{}  15.0499999\ldots{} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals->Finding Approximate Values
Problem: There were three piles of plums and a camel wanted to eat some. Each pile had $30$ plums. The camel ate a few plums from the first pile and then ate as many strawberries from the third pile as were left in the first pile. Then it ate some plums in the second plie, and finally there were $5$ plums left in the second pile. How many plums in total did the camel eat? 
Options:
aoVal: A
content: $$30$$ 
aoVal: B
content: $$45$$ 
aoVal: C
content: $$55$$ 
aoVal: D
content: $$65$$ 
aoVal: E
content: $$70$$ 
Answer: C
Analysis: $30 + (30 - 5) = 55$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: In a group of $40$ students, $40\textbackslash\%$ of them can swim. In this group of students, how many of them can swim? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$24$$ 
aoVal: D
content: $$40$$ 
Answer: A
Analysis: $40\times40\textbackslash\%=16$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation
Source: 其它
Problem: $$33$$ hours and $$36$$ minutes $$=$$  minutes. 
Options:
aoVal: A
content: $$1996$$ 
aoVal: B
content: $$2006$$ 
aoVal: C
content: $$2016$$ 
aoVal: D
content: $$2026$$ 
Answer: C
Analysis: $$33$$ hours and $$36$$ minutes $$=33\times60+36$$ minutes $$=2016$$ minutes. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Time
Problem: Polly has more than $90$ candies. The candies cabe divided evenly between $2$, $3$ or $4$, children. However, they cannot be divided evenly between $9$ children because $3$ more candies would be needed. How many candies does she have at least? 
Options:
aoVal: A
content: $$96$$ 
aoVal: B
content: $$132$$ 
aoVal: C
content: $$135$$ 
aoVal: D
content: $$168$$ 
aoVal: E
content: $$171$$ 
Answer: A
Analysis: $9 \times 11 - 3 = 96$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Avril\textquotesingle s father bought 15 books. Avril takes away 8 books. How many books does Avril\textquotesingle s father have left? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$7$$ 
Answer: C
Analysis: $$15-8=7$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: $$8002-2008=$$$$-2009$$. 
Options:
aoVal: A
content: $$9003$$ 
aoVal: B
content: $$9002$$ 
aoVal: C
content: $$8003$$ 
aoVal: D
content: $$8002$$ 
Answer: C
Analysis: $$8002-2008=(8002+1)-(2008+1)=8003-2009$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction
Problem: Find the value of $$\left\textbar{} -19 \right\textbar$$. 
Options:
aoVal: A
content: $$19$$ 
aoVal: B
content: $$-19$$ 
aoVal: C
content: $$23$$ 
aoVal: D
content: $$0$$ 
Answer: A
Analysis: By the definition, we can remove the mimus sign before $$-19$$. We get $$19$$ and choose $$\text{A}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Problem: The ones digit of $$1!\times2!\times3!\times ···\times50!$$ is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$1$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$6$$ 
Answer: A
Analysis: As long as we can find the factor $2$ and $5$, the ones digit is $0$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas
Source: 其它
Problem: Evaluate the following expression:  $$2^{7}+2^{8}+\cdots +2^{19}+2^{20}$$ 
Options:
aoVal: A
content: $$2^{20}-2^{6}$$ 
aoVal: B
content: $$2^{20}-2^{7}$$ 
aoVal: C
content: $$2^{21}-2^{6}$$ 
aoVal: D
content: $$2^{21}-2^{7}$$ 
aoVal: E
content: None of the above 
Answer: D
Analysis: $$1+2+\cdots +2^{20}=2^{21}-1$$  $$1+2+\cdots +2^{6} = 2^{7}-1$$  Subtracting the two equations we have:  $$2^{7}+2^{8}+\cdots +2^{20} = 2^{21}-2^{7}$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Fill iin the missing number.  $$-7\textless{}11+9$$ 
Options:
aoVal: A
content: $$20$$ 
aoVal: B
content: $$30$$ 
aoVal: C
content: $$40$$ 
Answer: A
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers
Problem: Some numbers add up to $4077$ and one of the number is $93$. Double this number. What is the new sum of the these numbers? 
Options:
aoVal: A
content: $$4077$$ 
aoVal: B
content: $$4160$$ 
aoVal: C
content: $$4167$$ 
aoVal: D
content: $$4170$$ 
aoVal: E
content: $$4177$$ 
Answer: D
Analysis: $4077 + 93 = 4170$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction 
Source: 其它
Problem: If the repeating decimal $2.0232323\cdots $ can be written as $\frac{m}{n}$, where the fraction is in its simplest form. Find $m+n$ 
Options:
aoVal: A
content: $$2122$$ 
aoVal: B
content: $$2993$$ 
aoVal: C
content: $$3013$$ 
aoVal: D
content: $$3293$$ 
aoVal: E
content: None of the above 
Answer: B
Analysis: B 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals
Source: 其它
Problem: Think Academy will hold a concert. The stage and seats have been set up. There are $$40$$ benches that can only seat one people each, and there are $$7$$ benches that can seat three people each ,How many people can all the chairs and benches hold? 
Options:
aoVal: A
content: $$40$$ 
aoVal: B
content: $$54$$ 
aoVal: C
content: $$61$$ 
aoVal: D
content: $$70$$ 
Answer: C
Analysis: $$7\times3=21$$~ $21+40=61$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Source: 其它
Problem: There are $20$ balls of the same size in a box.  Lucas says: "$\frac12$ of them are red."  Peter says: "The probability of drawing a green ball without observing them is $\frac15$."  Claire says: "There are three colors of balls in the box: red, light blue, and green."  How many dark blue balls are there in the box? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$10$$ 
Answer: A
Analysis: There is no dark blue ball in the box. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: In order to estimate the value of $x-y$ where $x$ and $y$ are real numbers with $x\textgreater y\textgreater0$, Xiaoli rounded $x$ up by a small amount, rounded $y$ down by the same amount, and then subtracted her rounded values. Which of the following statements is necessarily correct? (2012 AMC 10B Problem, Question \#6) 
Options:
aoVal: A
content: Her estimate is larger than $x-y$ 
aoVal: B
content: Her estimate is smaller than $x-y$ 
aoVal: C
content: Her estimate equals $x-y$ 
aoVal: D
content: Her estimate equals $y-x$ 
aoVal: E
content: Her estimate is $0$ 
Answer: A
Analysis: Let\textquotesingle s define $z$ as the amount rounded up by and down by.  The problem statement tells us that Xiaoli performed the following computation: $(x+z)-(y-z)=x+z-y+z=x-y+2 z$  We can see that $x-y+2 z$ is greater than $x-y$, and so the answer is $A$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: What is the correct ordering of the three numbers $$\dfrac{5}{6}$$, $$\dfrac{7}{8}$$, and $$\dfrac{9}{10}$$, in increasing order? (Adapted from$$2012$$ AMC $$8$$ Problem, Question \#$$4$$) 
Options:
aoVal: A
content: $$\dfrac{9}{10}\textless{} \dfrac{7}{8}\textless\dfrac{5}{6}$$ 
aoVal: B
content: $$\dfrac{5}{6}\textless{} \dfrac{7}{8}\textless{} \dfrac{9}{10}$$ 
aoVal: C
content: $$\dfrac{9}{10}\textless{} \dfrac{5}{6}\textless{} \dfrac{7}{8}$$ 
aoVal: D
content: $$\dfrac{5}{6}\textless{} \dfrac{9}{10}\textless{} \dfrac{7}{8}$$ 
aoVal: E
content: $$\dfrac{7}{8}\textless{} \dfrac{5}{6}\textless{} \dfrac{9}{10}$$ 
Answer: B
Analysis: Instead of finding the LCD, we can subtract each fraction from $$1$$ to get a common numerator. Thus,  $$1- \dfrac{5}{6}= \dfrac{1}{6}$$,  $$1- \dfrac{7}{8}= \dfrac{1}{8}$$,  $$1- \dfrac{9}{10}= \dfrac{1}{10}$$.  All three fractions have the common numerator $$1$$. Now the order of the fractions is obvious. $$\dfrac{1}{6}\textgreater\dfrac{1}{8}\textgreater\dfrac{1}{10}\Rightarrow\dfrac{5}{6}\textless\dfrac{7}{8}\textless\dfrac{9}{10}$$. Therefore, $$\dfrac{5}{6}\textless\dfrac{7}{8}\textless\dfrac{9}{10}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering
Problem: Supposed that $x$ and $y$ are nonzero real numbers such that $\frac{3 x+y}{x-3 y}=-2$. What is the value of $\frac{x+3 y}{3 x-y}$? 
Options:
aoVal: A
content: $$-3$$ 
aoVal: B
content: $$-1$$ 
aoVal: C
content: $$1$$ 
aoVal: D
content: $$2$$ 
aoVal: E
content: $$3$$ 
Answer: D
Analysis: Rearranging, we find $3 x+y=-2 x+6 y$, or $5 x=5 y \Longrightarrow x=y$. Substituting, we can convert the second equation into $\frac{x+3 x}{3 x-x}=\frac{4 x}{2 x}= 2$ More step-by-step explanation:  $$ \begin{aligned} \&\frac{3 x+y}{x-3 y}=-2 \textbackslash\textbackslash{} \&3 x+y=-2(x-3 y) \textbackslash\textbackslash{} \&3 x+y=-2 x+6 y \textbackslash\textbackslash{} \&5 x=5 y \textbackslash\textbackslash{} \&x=y \textbackslash\textbackslash{} \&\frac{x+3 y}{3 x-y}=\frac{1+3(1)}{3(1)-1}=\frac{4}{2}=2 \end{aligned} $$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Proportional Equations
Source: 其它
Problem: A binomial event has n = 60 trials. The probability of success on each trial is 0.4. Let X be the count of successes of the vent during the 60 trials. Whart are the $$\mu\_x$$ and $$\sigma\_x$$? 
Options:
aoVal: A
content: 24, 3.49 
aoVal: B
content: 24, 14.4 
aoVal: C
content: 4.90, 3.79 
aoVal: D
content: 4.90, 14.4 
aoVal: E
content: 2.4, 3.79 
Answer: A
Analysis: $$\mu\_X = 60 * 0.4 = 24$$  $$\sigma\_X = \sqrt{60*0.4*0.6} = 3.79$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Observe the sequence below and fill in the blank.  $$2, 1, 3, 4, 7, $$~\uline{~~~~~~~~~~}~$$,18, 29, 47$$ 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$11$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$14$$ 
aoVal: E
content: $$15$$ 
Answer: B
Analysis: The sum of the previous two number. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences
Problem: Which of the following is not an algebraic expression? 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $x=y$ 
aoVal: C
content: $\frac{1}{h}$ 
aoVal: D
content: $123xyzabc$ 
Answer: B
Analysis: equation is not algebraic expression 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Source: 其它
Problem: Emily sees a ship traveling at a constant speed along a straight section of a river. She walks parallel to the riverbank at a uniform rate faster than the ship. She counts $210$ equal steps walking from the back of the ship to the front. Walking in the opposite direction, she counts $42$ steps of the same size from the front of the ship to the back. In terms of Emily\textquotesingle s equal steps, what is the length of the ship? (2021 Fall AMC 10A Problems, Question \#11) 
Options:
aoVal: A
content: $$70$$ 
aoVal: B
content: $$84$$ 
aoVal: C
content: $$98$$ 
aoVal: D
content: $$105$$ 
aoVal: E
content: $$126$$ 
Answer: A
Analysis: Let $x$ be the length of the ship. Then, in the time that Emily walks $210$ steps, the ship moves $210-x$ steps. Also, in the time that Emily walks $42$ steps, the ship moves $x-42$ steps. Since the ship and Emily both travel at some constant rate, $\frac{210}{210-x}=\frac{42}{x-42}$. Dividing both sides by $42$ and cross multiplying, we get $5(x-42)=210-x$, so $6 x=420$, and $x=70$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Fill in the operation sign "$$+$$" or~"$$-$$" in the circles below to make the number statement true.  $$5$$ 　$$5$$ 　$$5$$ 　$$5$$　$$5$$ 　$$5=0$$ 
Options:
aoVal: A
content: $$+$$；$$-$$；$$+$$；$$-$$；$$+$$ 
aoVal: B
content: $$-$$；$$+$$；$$-$$；$$+$$；$$-$$ 
aoVal: C
content: $$+$$；$$+$$；$$+$$；$$-$$；$$-$$ 
aoVal: D
content: I don\textquotesingle t know o(╥﹏╥)o 
Answer: B
Analysis: $$5-5+5-5+5-5=0$$．  Option$$\text{B}$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas
Problem: \textbf{At a certain restaurant, the distribution of wait times between ordering a meal and receiving the meal has mean 11.4 minutes and standard deviation 2.6 minutes. The restaurant manager wants to find the probability that the mean wait time will be greater than 12.0 minutes for a random sample of 84 customers. Assuming the wait times among customers are independent, which of the following describes the sampling distribution of the sample mean wait time for random samples of size 84 ?} 
Options:
aoVal: A
content: \textbf{~Approximately normal with mean 11.4 minutes and standard deviation 2.6 minutes} 
aoVal: B
content: \textbf{~Approximately normal with mean 11.4 minutes and standard deviation $\frac{2.6}{\sqrt{84}}$ minute~} 
aoVal: C
content: \textbf{Approximately normal with mean 12.0 minutes and standard deviation 2.6 minutes} 
aoVal: D
content: \textbf{Binomial with mean 84(0.41) minutes and standard deviation 84(0.41)(0.59) minutes~} 
aoVal: E
content: \textbf{Binomial with mean 84(0.5) minutes and standard deviation 84(0.5)(0.5) minutes} 
Answer: B
Analysis: \textbf{For a sufficiently large n, the sampling distribution of $$\bar\_{X}$$ is approximately normal, with mean $\mu\_{\bar\_{X}}=\mu$ and standard deviation $\sigma\_\bar\_{X}=\sqrt{\frac{\sigma}{\sqrt{n}}}$} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Anna and Bella are celebrating their birthdays together. Five years ago, when Bella turned $6$ years old, she received a newborn kitten as a birthday present. Today the sum of the ages of the two children and the kitten is $30$ years. How many years older than Bella is Anna? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: C
Analysis: \uline{NA} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Which calculation has the greatest value? 
Options:
aoVal: A
content: $$2\times \left( 0+2+2 \right)$$ 
aoVal: B
content: $$2-0-2-2$$ 
aoVal: C
content: $$2\times 0\times 2\times 2$$ 
aoVal: D
content: $$2+0+2+2$$ 
Answer: A
Analysis: A 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations
Problem: The result of $\frac12\times \frac23\times \frac34$ is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$\frac 1{3}$$ 
aoVal: B
content: $$\frac 14$$ 
aoVal: C
content: $$\frac 12$$ 
aoVal: D
content: $$\frac {3}{4}$$ 
aoVal: E
content: $$\frac {1}{8}$$ 
Answer: B
Analysis: We notice that a lot of terms can be canceled. In fact, every term in the numerator except for the $$1$$ and every term in the denominator except for the $$4$$ will be canceled out, so the answer is $$\frac 1{4}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions->Multiplication of Fractions
Problem: Dave bought $3$ packets of chips at $2.40$ dollars each and $3$ cans of soft drink at $70$ cents each. How much did he spend altogether? 
Options:
aoVal: A
content: $3.10$ dollars 
aoVal: B
content: $10.70$ dollars 
aoVal: C
content: $9.30$ dollars 
aoVal: D
content: $8.70$ dollars 
aoVal: E
content: $10.50$ dollars 
Answer: C
Analysis: $2.40$ dollars=$240$ cents  $240\times 3+3\times70=930$ cents=$9.30$ dollars. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: $${{100}^{2}}-{{99}^{2}}=$$． 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$100$$ 
aoVal: C
content: $$199$$ 
aoVal: D
content: $$10$$ 
Answer: C
Analysis: $${{100}^{2}}-{{99}^{2}}=(100+99)\times (100-99)=199$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas-> Difference of Two Squares Formula
Problem: The bookstore has the "Exchanging Sales". One school bag exchanges 3 books, 2 books exchange 6 pens, and 3 pens exchange 6 erasers. One school bag exchangeserasers． 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$12$$ 
aoVal: C
content: $$18$$ 
aoVal: D
content: $$8$$ 
Answer: C
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution
Problem: For how many integers $x$ is the number $x^{4}-51 x^{2}+50$ negative? (2014 AMC 10B Problems, Question \#20) 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$14$$ 
aoVal: E
content: $$16$$ 
Answer: C
Analysis: First, note that $50+1=51$, which motivates us to factor the polynomial as $\left(x^{2}-50\right)\left(x^{2}-1\right)$. 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 $x^{2}-50\textless0\textless x^{2}-1$. Solving this inequality, we find $1\textless x^{2}\textless50$. There are exactly $12$ integers $x$ that satisfy this inequality, $\pm\textbackslash{2,3,4,5,6,7\textbackslash}$. Thus our answer is $(\mathbf{C}) 12$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: $$2015$$ Rosyth School, First Continual Assessment, Primary $$5$$, Question \#$$11$$  What is the value of $$\left( 84\div 7 \right)+7\times 6-3$$? 
Options:
aoVal: A
content: $$33$$ 
aoVal: B
content: $$51$$ 
aoVal: C
content: $$57$$ 
aoVal: D
content: $$111$$ 
Answer: B
Analysis: $84\div7=12$  $7\times6=42$  $$12+42-3=51$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations
Problem: Which of the following fractions is equivalent to $$0.3\dot{8}$$？ 
Options:
aoVal: A
content: $$\frac{7}{18}$$ 
aoVal: B
content: $$\frac{38}{990}$$ 
aoVal: C
content: $$\frac{35}{99}$$ 
aoVal: D
content: $$\frac{19}{45}$$ 
Answer: A
Analysis: $$0.3\dot{8}=\frac{38-3}{90}$$  $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde=\frac{35}{90}$$  $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde=\frac{7}{18}$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals
Source: 其它
Problem: $$100\div \dfrac{2}{3}=$$~\uline{~~~~~~~~~~}~，$$\dfrac{15}{16}\div 5=$$~\uline{~~~~~~~~~~}~． 
Options:
aoVal: A
content: $$\dfrac{200}{3}$$，$$\dfrac{75}{16}$$． 
aoVal: B
content: $$150$$，$$\dfrac{75}{16}$$． 
aoVal: C
content: $$\dfrac{200}{3}$$，$$\dfrac{3}{16}$$． 
aoVal: D
content: $$150$$，$$\dfrac{3}{16}$$． 
Answer: D
Analysis: $$100\div \dfrac{2}{3}=\dfrac{50\times 2}{1}\times \dfrac{3}{2}=150$$．  $$\dfrac{15}{16}\div 5=\dfrac{3\times 5}{16}\times \dfrac{1}{5}=\dfrac{3}{16}$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: Bruce is a talented writer and graphic artist who enjoys both types of work equally. Instead of earning 45,000 dollars as a writer, Bruce now earns 25,000 dollars in accounting profits as a graphic artist using the same computer equipment he would have used as a writer. What is Bruce\textquotesingle s economic profit from choosing to work as a graphic artist? 
Options:
aoVal: A
content: -45,000 dollars 
aoVal: B
content: -20,000 dollars 
aoVal: C
content: 20,000 dollars 
aoVal: D
content: 45,000 dollars 
aoVal: E
content: 70,000 dollars 
Answer: B
Analysis: Economic profit = total revenue - economic costs = total revenue - (explicit costs + implicit costs) 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: If~$\dfrac{3}{5}=\dfrac{M}{45}=\dfrac{60}{N}$ , what is $M+N$? （2008 AMC 8,7） 
Options:
aoVal: A
content: $$27$$ 
aoVal: B
content: $$29$$ 
aoVal: C
content: $$45$$ 
aoVal: D
content: $$105$$ 
aoVal: E
content: $$127$$ 
Answer: E
Analysis: Separate into two equations~$\dfrac{3}{5}=\dfrac{M}{45}$~and~$\dfrac{3}{5}=\dfrac{60}{N}$~and solve for the unknowns.~$M=27$~and $N=100$, therefore $M+N=\boxed{\left( E\right)127}.$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions->Simplifying Continued Ratios
Source: 其它
Problem: How many digits are there in the correct answer to the calculation $$1234123412340\div 1234$$? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: $$12$$ 
Answer: D
Analysis: The correct answer to the calculation $$1234123412340\div1234=1000100010$$.  This has $$10$$ digits. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers
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? 
Options:
aoVal: A
content: $$24$$ 
aoVal: B
content: $$25$$ 
aoVal: C
content: $$26$$ 
aoVal: D
content: $$27$$ 
aoVal: E
content: $$28$$ 
Answer: B
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Compare these fractions.  $$\frac{3}{8}$$~\uline{~~~~~~~~~~}~$$\frac{1}{2}$$, $$\frac{5}{18}$$~\uline{~~~~~~~~~~}~$$\frac{1}{3}$$ 
Options:
aoVal: A
content: $$\textgreater$$, $$\textgreater$$ 
aoVal: B
content: $$\textgreater$$, $$\textless$$ 
aoVal: C
content: $$\textless$$, $$\textgreater$$ 
aoVal: D
content: $$\textless$$, $$\textless$$ 
Answer: D
Analysis: $$\frac{3}{8}\textless\frac{4}{8}$$;~$$\frac{5}{18}\textless\frac{6}{18}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering
Problem: Solve the equation: $30-9x=28-5x$. 
Options:
aoVal: A
content: $x=1$ 
aoVal: B
content: $x=0.5$ 
aoVal: C
content: $x=2$ 
aoVal: D
content: $x=1.5$ 
aoVal: E
content: $x=1.6$ 
Answer: B
Analysis: $30-28=9x-5x$  $2=4x$  $x=0.5$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation
Source: 其它