math-eval/TAL-SCQ5K huggingface dataset:
Problem: Find the least dividend and divisor in each division equation below.  $\textasciitilde$  ~\uline{~~~~~~~~~~}~$$\div$$5$$=4R4$$  $\textasciitilde$  $$22\div$$~\uline{~~~~~~~~~~}~$$=7R1$$ 
Options:
aoVal: A
content: 24,3 
aoVal: B
content: 23,3 
aoVal: C
content: 24,4 
aoVal: D
content: 23,5 
aoVal: E
content: $$23.4$$ 
Answer: A
Analysis: The remainder should be less than the divisor. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders
Problem: At equilibrium in the market of apartments, the consumer surplus is $\textbackslash$ 120,000$ and the producer surplus is $\textbackslash$ 180,000$. The government decide to set a price ceiling. As a result, the consumer surplus becomes $ \textbackslash$ 140,000$ and the producer surplus becomes $\textbackslash$ 140,000$. What is the deadweight loss from the price ceiling? 
Options:
aoVal: A
content: $\textbackslash$140,000$ 
aoVal: B
content: $\textbackslash$60,000$ 
aoVal: C
content: $\textbackslash$40,000$ 
aoVal: D
content: $\textbackslash$20,000$ 
aoVal: E
content: $\textbackslash$0$ 
Answer: D
Analysis: At the equilibrium, the total surplus is the sum of consumer and producer surplus, which is $ \textbackslash$120,000 + \textbackslash$180,000 = \textbackslash$300,000$.  After the price ceiling is imposed, the consumer surplus increases to $\textbackslash$140,000$, while the producer surplus decreases to $\textbackslash$140,000$. The new total surplus is $ \textbackslash$140,000 + \textbackslash$140,000 = \textbackslash$280,000$.  Therefore, the deadweight loss is the difference between the total surplus before and after the price ceiling, which is $\textbackslash$300,000 - \textbackslash$280,000 = \textbackslash$20,000$ . 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Simplify: $$b\left( a+1 \right)-a\left( b-1 \right)$$． 
Options:
aoVal: A
content: $$b+a$$ 
aoVal: B
content: $$2ab+b-a$$ 
aoVal: C
content: $$b-a$$ 
aoVal: D
content: $$ab-1$$ 
Answer: A
Analysis: $$b\left( a+1 \right)-a\left( b-1 \right)=ab+b-ab+a=b+a$$, so the answer is$\text{A}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Source: 其它
Problem: Stefani is ordering fertilizer for her garden. A local garden supply store sells fertilizer by the yard (that really means cubic yard, but that is what they call it).For every yard she orders there is a $\textbackslash$$15charge and ,in addition ,there is a $\textbackslash$$40 delivery charge. ( Total Cost =~$\textbackslash$$15(yard)+~$\textbackslash$$40.)  $\textasciitilde$  If the average order is 4.3 yards with standard deviation of 2.9 yards, what is the mean and standard deviation of the Total Cost of a typical order? 
Options:
aoVal: A
content: mean = $\textbackslash$$4.30; standard deviation =~$\textbackslash$$2.90 
aoVal: B
content: mean = $\textbackslash$$64.50; standard deviation = $\textbackslash$$43.50 
aoVal: C
content: mean = $\textbackslash$$105.50; standard deviation =~$\textbackslash$$43.50 
aoVal: D
content: mean = $\textbackslash$$105.50; standard deviation = $\textbackslash$$83.50 
aoVal: E
content: Cannot be determined because each order may not be independent~ 
Answer: C
Analysis: The correct answer is (c). When using a linear transformation (Total cost 15 (yard)+40), the mean is changed by both the multiplication and addition. But the standard deviation is only changed by the multiplication. Mean = 15(4.3) +40=$\textbackslash$$ 104.50; =15(2.9) =~$\textbackslash$$43.50. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: $$40 \times 50 \times 60 = 4 \times 5\times 6 \times$$． 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$100$$ 
aoVal: C
content: $$456$$ 
aoVal: D
content: $$1000$$ 
Answer: D
Analysis: $$4\times10\times5\times10\times6\times10=4\times5\times6\times10\times10\times10=4\times5\times6\times1000$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: The average of $$4000$$ fours is four times the average of $$2000$$． 
Options:
aoVal: A
content: ones　 
aoVal: B
content: twos　 
aoVal: C
content: fours　 
aoVal: D
content: eights　 
Answer: A
Analysis: The average of $$4000$$ fours is $$4$$; this is $$4$$ times the average of $$2000$$ ones. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: The mean, median, and mode of the $7$ data values $60,100, x, 40,50,200,90$ are all equal to $x$. What is the value of $x$? (2016 AMC 10A Problems, Question \#7) 
Options:
aoVal: A
content: $$50$$ 
aoVal: B
content: $$60$$ 
aoVal: C
content: $$75$$ 
aoVal: D
content: $$90$$ 
aoVal: E
content: $$100$$ 
Answer: D
Analysis: Since $x$ is the mean, $$ \begin{aligned} x \& =\frac{60+100+x+40+50+200+90}{7} \textbackslash\textbackslash{} \& =\frac{540+x}{7} . \end{aligned} $$  Therefore, $7 x=540+x$, so $x=$ (D) $90$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: What is the simplest form of $5$ minutes $: 30$ seconds? 
Options:
aoVal: A
content: $5:30$ 
aoVal: B
content: $1:6$ 
aoVal: C
content: $6:1$ 
aoVal: D
content: $10:1$ 
Answer: D
Analysis: We need to make units same first. $5$ minutes equal to $300$ seconds. Now we could remove the same unit, second. We get $300:30$ and simplify it to $10:1$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Ratio
Problem: Given the symbol $$\otimes $$ defines a new operation and $$3\otimes 3=3\times 4\times 5$$, $$7\otimes 2=7\times 8$$, and $$2\otimes 4=2\times 3\times 4\times 5$$, then $$5\otimes 3=$$~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$190$$ 
aoVal: B
content: $$200$$ 
aoVal: C
content: $$210$$ 
aoVal: D
content: $$220$$ 
aoVal: E
content: Non of the above 
Answer: C
Analysis: $$5\otimes 3=5\times 6\times 7=210$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns
Problem: Observe the sequence $10$, $15$, $20$, $25$, $\cdots$ , the $9$\textsuperscript{th} term is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $45$ 
aoVal: B
content: $50$ 
aoVal: C
content: $55$ 
aoVal: D
content: $60$ 
Answer: B
Analysis: $10+5\times(9-1)=50$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences
Problem: $$(11+ 11 + 11 + 11 + 11 + 11)-(9 + 9 + 9 +9 +9 +9)=$$． 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$102$$ 
Answer: C
Analysis: Rearranging: $$11-9 +\cdots + 11-9 =2+\cdots +2 =2\times6 = 12$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction
Problem: What is the value of $1+3+5+\ldots+2017+2019-2 -4-6-\ldots-2016-2018$? 
Options:
aoVal: A
content: $$-1010$$ 
aoVal: B
content: $$-1009$$ 
aoVal: C
content: $$1008$$ 
aoVal: D
content: $$1009$$ 
aoVal: E
content: $$1010$$ 
Answer: E
Analysis: $1+3+5+\ldots+2017+2019-2 -4-6-\ldots-2016-2018$  $=1+(3-2)+(5-4)+\cdots +(2017-2016)+(2019-2018)$  $=1+1+1+\cdots +1+1$  $=1010$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Grouping in Fast Addition and Subtraction of Whole Numbers
Source: 其它
Problem: Calculate:  $$1\frac{1}{1024}+2\frac{1}{512}+4\frac{1}{256}+\cdots 256\frac{1}{4}+512\frac{1}{2}=$$~\uline{~~~~~~~~~~}~． 
Options:
aoVal: A
content: $$1023\frac{1}{1024}$$ 
aoVal: B
content: $$1023\frac{1023}{1024}$$ 
aoVal: C
content: $$1024$$ 
aoVal: D
content: $$1024\frac{1}{1024}$$ 
aoVal: E
content: $$1024\frac{1023}{1024}$$ 
Answer: B
Analysis: Nil 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions
Problem: Evaluate $$\left(\frac{2017}{2018}+\frac{20172017}{20182018}\right)\div \frac{201720172017}{201820182018}$$. 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: None of the above 
Answer: B
Analysis: B 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: Which digit is smaller? 
Options:
aoVal: A
content: tens 
aoVal: B
content: ones 
aoVal: C
content: we don\textquotesingle t know 
Answer: C
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Evaluate the expression shown below:  $$36 \left( \frac{1}{1\times 6} + \frac{1}{6\times 11} +\frac{1}{11\times 16} + \frac{1}{16\times 21} + \frac{1}{21\times 26} + \frac{1}{26\times 31} + \frac{1}{31\times 36} \right)$$ 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$7$$ 
Answer: E
Analysis: E 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: A container had $27$ ℓ of longan drink. The drink is made up of three $2$-ℓ\textbf{~}bottles of longan syrup and some water. What was the volume of water used to make the drink? 
Options:
aoVal: A
content: 6ℓ 
aoVal: B
content: 18ℓ 
aoVal: C
content: 21ℓ 
aoVal: D
content: 27ℓ 
Answer: C
Analysis: $$2 \times 3 = 6$$  $$27 - 6 = 21$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Units of Volume and Capacity
Source: 其它
Problem: Given that $$a \Omega b=a\times b-3$$, find $$4\Omega 5$$. 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$17$$ 
aoVal: D
content: $$23$$ 
Answer: D
Analysis: Nil 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly
Problem: $$2+4 +6 +8=1+3 +5 +7 +$$~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$1$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$9$$ 
Answer: C
Analysis: $$2+4 +6 +8=1+1+3+1+5+1+7+1=1+3 +5 +7 +4$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction
Problem: $$4x-x-12=51$$ 
Options:
aoVal: A
content: $$x=12.6$$ 
aoVal: B
content: $$x=-12.6$$ 
aoVal: C
content: $$x=21$$ 
aoVal: D
content: $$x=-21$$ 
Answer: C
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable
Source: 其它
Problem: $$8\times9\times10\times11=80\times$$ . 
Options:
aoVal: A
content: $$81$$ 
aoVal: B
content: $$88$$ 
aoVal: C
content: $$90$$ 
aoVal: D
content: $$99$$ 
Answer: D
Analysis: $$8\times9\times10\times11=(8\times10)\times (9\times11)=80\times99$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: The following are the weights (in pounds) of ten people: $100, 115, 135, 140, 180, 197, 230, 250, 260, 270$. Find the $80$-th percentile. 
Options:
aoVal: A
content: $$115$$ 
aoVal: B
content: $$135$$ 
aoVal: C
content: $$250$$ 
aoVal: D
content: $$260$$ 
aoVal: E
content: None of the above 
Answer: E
Analysis: $np=10(0.8)=8$ The $80$-th percentile is $\frac{250+260}{2} = 255$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: What is the sum of all numbers x for which~$\left\textbar{} x^{2}-12x+34\right\textbar=2$ 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$15$$ 
aoVal: C
content: $$18$$ 
aoVal: D
content: $$21$$ 
aoVal: E
content: $$25$$ 
Answer: C
Analysis: $$4+6+8=18$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: 13+4=, 57-17=． 
Options:
aoVal: A
content: 17, 85 
aoVal: B
content: 18, 40 
aoVal: C
content: 9,~ 64 
aoVal: D
content: 17, 40 
aoVal: E
content: 20, 50 
Answer: D
Analysis: 13+4=17 , 57-17=40 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction 
Source: 其它
Problem: A consumer is willing to pay $\textbackslash$12$ for a good, but is able to purchase it for $\textbackslash$10$. What is the consumer surplus in this scenario? 
Options:
aoVal: A
content: $\textbackslash$2$ 
aoVal: B
content: $\textbackslash$10$ 
aoVal: C
content: $\textbackslash$12$ 
aoVal: D
content: $\textbackslash$22$ 
Answer: A
Analysis: The correct answer is A. $\textbackslash$2$, as consumer surplus is calculated as the difference between the maximum price a consumer is willing to pay for a good and the actual price they pay, which is $\textbackslash$12 - \textbackslash$10 = \textbackslash$2$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: If $$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$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables
Problem: $$\frac{1}{2}\times \frac{22}{7}\div \frac{11}{5}$$ 
Options:
aoVal: A
content: $$\frac{5}{7}$$ 
aoVal: B
content: $$\frac{4}{7}$$ 
aoVal: C
content: $$\frac{6}{7}$$ 
aoVal: D
content: $$\frac{3}{7}$$ 
Answer: A
Analysis: $$\frac{1}{2}\times \frac{22}{7}\div \frac{11}{5}=\frac{1}{2}\times \frac{22}{7}\times \frac{5}{11}=\frac{5}{7}$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: What is the \uline{\textbf{average}} amount of sleep adults get each night? 
Options:
aoVal: A
content: 5 hours 
aoVal: B
content: 6 hours 
aoVal: C
content: 10 hours 
aoVal: D
content: 8 hours 
aoVal: E
content: 12 hours 
Answer: D
Analysis: The average amount of sleep an adult gets is 8 hours. Everyone is different, however; where some adults function off of 6 hours, others need at least 9 hours or more to feel healthy and awake. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: (2016) A test has a mean of 80 with a standard deviation of 4. Which of the following scores is within one standard deviation of the mean? 
Options:
aoVal: A
content: $$75$$ 
aoVal: B
content: $$77$$ 
aoVal: C
content: $$86$$ 
aoVal: D
content: $$90$$ 
aoVal: E
content: $$99$$ 
Answer: B
Analysis: 2016, Q 86 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Cristi has to sell 10 glass bells that vary in price: 1 euro, 2 euro, 3 euro, 4 euro, 5 euro, 6 euro, 7 euro, 8 euro, 9 euro, 10 euro. In how many ways can Cristi divide all the grass bells in three packages so that all the packages have the same price? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: Such a division is not possible 
Answer: E
Analysis: 1+2+3+4+5+6+7+8+9+10 = 55 is not divisible by 3. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Distributive Law of Whole Numbers->Applying Distributive Law of Whole Numbers in Division
Source: 其它
Problem: What is the solution of this equation: $$2^{2007}=4^{1003}\cdot x$$? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$\frac{1}{2}$$ 
aoVal: D
content: $$2^{2}$$ 
aoVal: E
content: $$2^{2008}$$ 
Answer: B
Analysis: $$2^{2007}=2^{2006}\cdot x$$, $x=2$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with one Variable->Equations with Whole Number Coefficient
Problem: Which of the following is a solution of $$\begin{cases}x-3=0 \textbackslash\textbackslash{} 3x-2y=7 \end{cases}$$? 
Options:
aoVal: A
content: ($x$,$y$)=($3$,$-1$) 
aoVal: B
content: ($x$,$y$)=($3$,$1$) 
aoVal: C
content: ($x$,$y$)=($-3$,$1$) 
aoVal: D
content: ($x$,$y$)=($-3$,$-1$) 
Answer: B
Analysis: $3-3=0$  $3\cdot3-2\cdot1=9-2=7$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables
Source: 其它
Problem: $$11+ 12 + 13 + 14 + 15 = 1 + 2 + 3 + 4 + 5 +$$． 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$50$$ 
aoVal: C
content: $$60$$ 
aoVal: D
content: $$65$$ 
Answer: B
Analysis: $$1+10 + 2+10 + 3+10 + 4+10 + 5+10 = 1+2+3+4+5 + 50$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction
Problem: How many different three-digit numbers can we make using $6,7,8,$ and $9$? The digits can be repeated. 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$24$$ 
aoVal: C
content: $$32$$ 
aoVal: D
content: $$64$$ 
Answer: D
Analysis: $4\times4\times4=64$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Addition and Subtraction of Decimals
Source: 其它
Problem: What is the cost of eight mugs at £$$2.99$$ each? 
Options:
aoVal: A
content: £$$23.92$$ 
aoVal: B
content: £$$23.98$$ 
aoVal: C
content: £$$24.00$$ 
aoVal: D
content: £$$24.02$$ 
aoVal: E
content: £$$24.08$$ 
Answer: A
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals->Multiplication of Decimals
Problem: Given that $n!$ represent $n$ factorial, with $n!=1\times 2\times 3 \times \cdots \times n$, then how many positive integer divisors of $12!$ are perfect squares? 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$36$$ 
aoVal: C
content: $$198$$ 
aoVal: D
content: $$396$$ 
aoVal: E
content: $$792$$ 
Answer: B
Analysis: B 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Happy Hotel is offering $$40 \textbackslash\%$$ off discount for any bookings. David booked a room, the new price is $$80$$ dollars cheaper than the original price, what was the original price． 
Options:
aoVal: A
content: $$180$$ 
aoVal: B
content: $$200$$ 
aoVal: C
content: $$300$$ 
aoVal: D
content: $$480$$ 
Answer: B
Analysis: $$80\div40\textbackslash\%=200$$．  so choose $$\text{B}$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Which of the following is equivalent to $\sqrt{16a^{16}}$? 
Options:
aoVal: A
content: $4a^{4}$ 
aoVal: B
content: $4a^{8}$ 
aoVal: C
content: $8a^{4}$ 
aoVal: D
content: $8a^{8}$ 
Answer: B
Analysis: $sqrt{16a^{16}}=\sqrt{16}\sqrt{a^{16}}=4(a^{16\times\frac{1}{2}})=4a^{8}$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Calculate:  $$\left(1+\frac 12+\frac 13+\cdots +\frac 1{149}\right)\times \left(\frac 12+\frac 13+\cdots +\frac 1{149}+\frac 1{150}\right)$$$$-\left(1+\frac 12+\frac 13+\cdots +\frac 1{149}+\frac 1{150}\right)\times \left(\frac 12+\frac 13+\cdots +\frac 1{149}\right)=$$~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $\dfrac{1}{149}$ 
aoVal: C
content: $\dfrac{149}{150}$ 
aoVal: D
content: $\dfrac{1}{150}$ 
aoVal: E
content: $$150$$ 
Answer: D
Analysis: Suppose $$\left(\frac 12+\frac 13+\cdots +\frac 1{149}\right)$$ as $$A$$, $$\left(\frac 12+\frac 13+\cdots +\frac 1{150}\right)$$ as $$B$$.  $$(1+A)\times B-(1+B)\times A=B+AB-A-AB=B-A=\frac 1{150}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Fast Calculation in Fractions
Problem: Which of the following is equal to the product shown below?  $$\frac{8}{4} \cdot \frac{12}{8} \cdot \frac{16}{12} \cdot \frac{20}{16} \cdot \cdot \cdot \frac{2024}{2020}$$ 
Options:
aoVal: A
content: $$253$$ 
aoVal: B
content: $$503$$ 
aoVal: C
content: $$1012$$ 
aoVal: D
content: $$4048$$ 
aoVal: E
content: None of the above 
Answer: E
Analysis: E 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: If $$6$$ pens cost as much as $$5$$ pencils, then $$36$$ pens cost as much as pencils. 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$30$$ 
aoVal: C
content: $$21$$ 
aoVal: D
content: $$98$$ 
Answer: B
Analysis: $$6$$ pens = $$5$$ pencils, we use $\times6$ which give us $36$ pens = $30$ pencils 
Knowledge points: Overseas Competition->Knowledge Point->Heuristics Skills-> Equivalent Substitution
Problem: What is the smallest whole number larger than the perimeter of any triangle with a side of length $12$ and a side of length $13$? (adapted from 2015 AMC8, Question 8) 
Options:
aoVal: A
content: $$25$$ 
aoVal: B
content: $$50$$ 
aoVal: C
content: $$51$$ 
aoVal: D
content: $$49$$ 
aoVal: E
content: $$33$$ 
Answer: B
Analysis: We know from the triangle inequality that the last side, $s$, fulfills $s\textless12+13=25$. Adding $12+13$ to both sides of the inequality, we get $s+12+13\textless25$, and because $s+12+13$ is the perimeter of our triangle, (B) 50 is our answer. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities
Source: 其它
Problem: is a factor of $$1\times2\times3\times4\times5\times6\times7\times8\times9\times10$$. 
Options:
aoVal: A
content: $$71$$ 
aoVal: B
content: $$73$$ 
aoVal: C
content: $$75$$ 
aoVal: D
content: $$77$$ 
Answer: C
Analysis: $$1\times2\times3\times4\times5\times6\times7\times8\times9\times10$$ is divisible by $$3$$ and $$25$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: Simplify the expression: $4^{3}+4^{3}+4^{3}+4^{3}$? 
Options:
aoVal: A
content: $4^{12}$ 
aoVal: B
content: $4^{27}$ 
aoVal: C
content: $4^{3}$ 
aoVal: D
content: $4^{4}$ 
Answer: D
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Power
Source: 其它
Problem: Teacher Nicole bought some badges and divided it equally among $8$ children. If everyone got $9$ badges, there would still be some badges remaining. What is the biggest possible and smallest possible number of badges Teacher Nicole could have bought? 
Options:
aoVal: A
content: $$79$$，$$73$$ 
aoVal: B
content: $$80$$，$$73$$ 
aoVal: C
content: $$79$$，$$72$$ 
aoVal: D
content: $$80$$，$$72$$ 
Answer: A
Analysis: ~\uline{~~~~~~~~~~}~$\div 8=9$ $\text{R}$~\uline{~~~~~~~~~~}~  Biggest possible remainder is $7$ while smallest possible remainder is $1$.  Biggest possible number of badges is $$8\times 9+7=79$$, while the least possible number of sweets is $$8\times 9+1=73$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Problem: In a rectangle, what is the ratio of one angle to the sum of all inner angles? 
Options:
aoVal: A
content: 1:2 
aoVal: B
content: 1:3 
aoVal: C
content: 1:4 
aoVal: D
content: 2:5 
Answer: C
Analysis: $90:360=1:4$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions
Source: 其它
Problem: Real numbers $x$ and $y$ satisfy $x^{3}+y^{3}=4$ and $xy = 2$. What is the value of $2xy+\frac{x^{4}}{y^{2}}+\frac{y^{4}}{x^{2}}$? (Adapted From 2020 AMC 10A Problem, Question \#14) 
Options:
aoVal: A
content: $$-2$$ 
aoVal: B
content: $$0$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$-4$$ 
Answer: D
Analysis: $2xy+\frac{x^{4}}{y^{2}}+\frac{y^{4}}{x^{2}} = 2xy+\frac{x^{6}+y^{6}}{x^{2}y^{2}} = \frac{2xyx^{2}y^{2}+x^{6}+y^{6}}{x^{2}y^{2}}= \frac{2x^{3}y^{3}+x^{6}+y^{6}}{x^{2}y^{2}} $  $= \frac{(x^{3}+y^{3})^{2}}{x^{2}y^{2}} =\frac{4^{2}}{4}= 4$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它