math-eval/TAL-SCQ5K huggingface dataset:
Problem: Teacher Ying bought some sweets and divided them equally among $$9$$ children. If everyone got $$6$$ sweets, there would still be some sweets remaining. What is the most number of sweets Teacher Ying could have bought? What is the least amount of sweets Teacher Ying could have bought? 
Options:
aoVal: A
content: $$63$$，$$54$$ 
aoVal: B
content: $$63$$，$$55$$ 
aoVal: C
content: $$62$$，$$54$$ 
aoVal: D
content: $$62$$，$$55$$ 
Answer: D
Analysis: $$(\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} )\div 9=6 R (\textbackslash{} \textbackslash{} \textbackslash{} \textbackslash{} )$$  Largest remainder: $$8$$, $$9\times 6+8=62$$  Smallest remainder: $$1$$, $$9\times 6+1=55$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders
Problem: In the class, the teacher gave $4$ numbers:$15, 27, 36, 8$. Billy added another number to make the sum result of these $5$ digits to $100$. Guess what\textquotesingle s the number Billy added ? ( adapted from $$2009$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$5$$) 
Options:
aoVal: A
content: $$13$$ 
aoVal: B
content: $$14$$ 
aoVal: C
content: $$15$$ 
aoVal: D
content: $$16$$ 
aoVal: E
content: $$12$$ 
Answer: B
Analysis: $100-15-27-36-8=14$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Subtraction of Whole Numbers->Subtraction in Horizontal Form
Problem: How many of the following equations are written in function form?  ($1$) $2x-y=3x+1$;~($2$) $2x=-5y+2$;~($3$) $y=7x+12$;~($4$) $y+6=12x-17$;~($5$) $y=x+z+ab$ 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: B
Analysis: Function Form is written as: $y=$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables
Source: 其它
Problem: For how many values of $a$ is it true that the line $y=x+a^{2}-6$ passes through the vertex of the parabola $y=4x^{2}-8x+a^{2}$? (Adapted From 2005 AMC 12B Problem, Question \#8) 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$1$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: infinitely many 
Answer: A
Analysis: We see that the vertex of the quadratic function $y=4x^{2}-8x+a^{2}$ is $\left(1, a^{2}-4\right)$. If $\left(2, a^{2}-1\right)$ will be on the line $y=x+a^{2}-6$, $a^{2} -4=1+a^{2}-6$. Solve for $a$, there is no solution. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: \textbf{Recently you learned that the probability of getting a critical hit on an attack in your favorite game is 15\%. You've noticed that you do 20 attacks per fight. You're interested in figuring out how likely it is that you would get 5 critical hits during a fight. Which of the following distributions should you use to answer this question?} 
Options:
aoVal: A
content: \textbf{A binomial distribution with p = 0.15 and n = 20} 
aoVal: B
content: \textbf{A binomial distribution with p = 0.2 and n = 15} 
aoVal: C
content: \textbf{A geometric distribution with p = 0.15} 
aoVal: D
content: \textbf{A geometric distribution with p = 0.2} 
aoVal: E
content: \textbf{A cumulative geometric distribution with p = 0.15} 
Answer: A
Analysis: \textbf{Binomial distribution: how likely it is to get x successes in n trials given that your probability of success is p}  \textbf{Geometric distribution: how likely is it that I'll have my first critical strike on the 5th attack}  \textbf{Cumulative geometric distribution: how likely is it that I'll have my first critical strike on or before the 5th attack.} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: True or False: It is impossible for the $25$-th percentile to be equal to the mean. 
Options:
aoVal: A
content: True 
aoVal: B
content: False 
Answer: B
Analysis: For example, consider a dataset with the following values: 0, 2, 2, 3, 3. The mean of this dataset is $2$, and the $25$-th percentile is also $2$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: One ticket to a mini concert costs $\textbackslash$20$ at full price. Nicole buys $4$ tickets using a coupon that gives her a $25\textbackslash\%$ discount. Bel buys $5$ tickets using a coupon that gives her a $30\textbackslash\%$ discount. How many more dollars does Bel pay than Nicole? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$15$$ 
aoVal: E
content: $$20$$ 
Answer: C
Analysis: C 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: What is the smallest whole number larger than the perimeter of any triangle with a side of length $7$ and a side of length $15$? (2015 AMC8, Question 8) 
Options:
aoVal: A
content: $$24$$ 
aoVal: B
content: $$29$$ 
aoVal: C
content: $$43$$ 
aoVal: D
content: $$44$$ 
aoVal: E
content: $$57$$ 
Answer: D
Analysis: We know from the triangle inequality that the last side, $s$, fulfills $s\textless7+15$. Adding $7+15$ to both sides of the inequality, we get $s+7+15\textless44$, and because $s+7+15$ is the perimeter of our triangle, (D) 44 is our answer. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities
Source: 其它
Problem: Find the missing number: $$12345 + 123450 = 12345\times $$． 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$11$$ 
aoVal: D
content: $$22$$ 
Answer: C
Analysis: $$12345+123450=12345\times1+12345\times10=12345\times11$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations
Problem: Find the result of $$1\times12\times23\times34\times45\times \cdots \times78\times89$$. What is the sum of its last $2$ digits? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$2$$ 
aoVal: E
content: $$7$$ 
Answer: D
Analysis: $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde1\times12\times23\times34\times45\times \cdots \times78\times89$$  $$=1\times6\times23\times34\times9\times \cdots \times78\times89\times2\times5$$  $$1\times6\times3\times4\times9\times6\times7\times8\times9$$ has the last digit of $2$.  The last two digits are $2$ and $0$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers
Problem: $$2^{2}\times 2^{4} =$$． 
Options:
aoVal: A
content: $$2^{8}$$ 
aoVal: B
content: $$2^{6}$$ 
aoVal: C
content: $$4^{8}$$ 
aoVal: D
content: $$4^{7}$$ 
Answer: B
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers
Problem: A number of students from Fibonacci Middle School are taking part in a community service project. The ratio of $8^{\text {th }}$-graders to $6^{\text {th }}$-graders is $5: 3$, and the the ratio of $8^{\text {th }}$-graders to $7^{\text {th }}$ graders is $8: 5$. What is the smallest number of students that could be participating in the project? 
Options:
aoVal: A
content: $$40$$ 
aoVal: B
content: $$55$$ 
aoVal: C
content: $$79$$ 
aoVal: D
content: $$89$$ 
Answer: D
Analysis: We multiply the first ratio by 8 on both sides, and the second ratio by 5 to get the same number for 8 th graders, in order that we can put the two ratios together: $$ \begin{aligned} \&5: 3=5(8): 3(8)=40: 24 \textbackslash\textbackslash{} \&8: 5=8(5): 5(5)=40: 25 \end{aligned} $$ Therefore, the ratio of 8th graders to 7th graders to 6th graders is $40: 25: 24$. Since the ratio is in lowest terms, the smallest number of students participating in the project is $$ 40+25+24=\text { (E) } 89 $$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions
Source: 其它
Problem: A box has fewer than $50$ cookies in it. The cookies can be divided evenly between $2, 3,$ or $4$ children. However, they cannot be divided evenly between $7$ children because $6$ more cookies would be needed. How many cookies are there in the box? (2021 Math Kangaroo Problem, Level 3-4, Question \#21) 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$24$$ 
aoVal: C
content: $$30$$ 
aoVal: D
content: $$36$$ 
aoVal: E
content: $$48$$ 
Answer: D
Analysis: ~\uline{~~~~~~~~~~}~$\div$ $7=$~\uline{~~~~~~~~~~}~$R1$  $36-1=35$, $35\div7=5$, so the answer is $D$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders
Source: 其它
Problem: Which of the following numbers\textquotesingle{} value does not change after removing all ``$$0$$''s ． 
Options:
aoVal: A
content: $$30.41$$ 
aoVal: B
content: $$3.5260$$ 
aoVal: C
content: $$42.09$$ 
Answer: B
Analysis: Only $$3.5260$$\textquotesingle s $$"0"$$ can be removed without causing other digits to change their places from the original number. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals
Source: 其它
Problem: Gilda has a bag of marbles. She gives $20 \textbackslash\%$ of them to her friend Pedro. Then Gilda gives $10 \textbackslash\%$ of what is left to another friend, Ebony. Finally, Gilda gives $25 \textbackslash\%$ of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself? (2019 AMC 8, Question \#8) 
Options:
aoVal: A
content: $$20$$ 
aoVal: B
content: $33 \frac{1}{3}$ 
aoVal: C
content: $$38$$ 
aoVal: D
content: $$45$$ 
aoVal: E
content: $$54$$ 
Answer: E
Analysis: After Gilda gives $20 \textbackslash\%$ of the marbles to Pedro, she has $80 \textbackslash\%$ of the marbles left. If she then gives $10 \textbackslash\%$ of what\textquotesingle s left to Ebony, she has $(0.8 * 0.9)=72 \textbackslash\%$ of what she had at the beginning. Finally, she gives $25 \textbackslash\%$ of what\textquotesingle s left to her brother, so she has $(0.75 * 0.72)$ (E) 54 . of what she had in the beginning left. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation
Source: 其它
Problem: $$25+35+45=60+$$． 
Options:
aoVal: A
content: $$25$$ 
aoVal: B
content: $$35$$ 
aoVal: C
content: $$45$$ 
aoVal: D
content: $$55$$ 
Answer: C
Analysis: $$25+35+45=(25+35)+45=60+45$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction
Problem: For what positive value of $k$ does the following system of equations have no solutions?~\uline{~~~~~~~~~~}~  $$ \begin{cases} 8 x+6 k y=17 \textbackslash\textbackslash{} k x+12 y=16 \end{cases}$$ 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $\frac{56}{15}$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$8$$ 
Answer: C
Analysis: We want the lines to be parallel and not the same line in order to have 0 solutions. Parallel implies the slopes of the lines are equal, so we have $-\frac{8}{6 k}=-\frac{k}{12}$. Cross multiplying, we get $96=6 k^{2}$, so $k^{2}=$ 16 and our positive solution is then $k=4$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation
Source: 其它
Problem: A little rabbit wants to cross the river. He needs to lay ten stones on the river. At this time, there are five stones on the river. The rabbit moves three stones back for the first time and two stones back for the second time. But the river washes away one stone. How many stones the rabbit still need to move?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$) 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$0$$ 
Answer: A
Analysis: $5+3+2-1=9$，$10-9=1$ 
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: What is the $5^{}\text{th}$ number in the $21^{}\text{st}$ row? 
Options:
aoVal: A
content: $$210$$ 
aoVal: B
content: $$215$$ 
aoVal: C
content: $$231$$ 
aoVal: D
content: $$236$$ 
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: Which of the numbers below is the greatest? ($2003$ Math Kangaroo Problem, Level $9-10$, Question \#$11$) 
Options:
aoVal: A
content: $$22222$$ 
aoVal: B
content: $2222^{2}$ 
aoVal: C
content: $222^{22}$ 
aoVal: D
content: $22^{222}$ 
aoVal: E
content: $2^{2222}$ 
Answer: E
Analysis: $2^{2222}\textgreater2^{2220}=\left (2^{10}\right )^{222}=1024^{222}\textgreater22^{222}$. According to this rule, $\text{E}\textgreater\text{D}\textgreater\text{C}\textgreater\text{B}\textgreater\text{A}$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Power->Application of Powers
Problem: What is the ones digit of the result of $3$\textsuperscript{50}? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$7$$ 
aoVal: E
content: $$9$$ 
Answer: E
Analysis: The ones digits of exponents based on $3$ follow the rule: $3, 9, 7, 1, 3, 9, 7, 1\cdots $  $50\div4=12R2$, which means the ones digit is $9$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers
Source: 其它
Problem: Express $$0.\dot{6}\dot{3}$$ as a fraction. 
Options:
aoVal: A
content: $\dfrac{7}{11}$ 
aoVal: B
content: $\dfrac{57}{90}$ 
aoVal: C
content: $\dfrac{636}{1000}$ 
aoVal: D
content: $\dfrac{63}{100}$ 
Answer: A
Analysis: Let $$x = 0.636363\cdots$$  Multiply by $$100$$, which means move the decimal point two places to the right: $$100x = 63.636363\cdots$$  $$x$$ and $$100x$$ have exactly the same decimal part, so if we subtract, it will disappear: $$100x - x = 63.636363\cdots - 0.636363\cdots$$  Which is: $$99x = 63$$ ,$x=\dfrac{63}{99}=\dfrac{7}{11}$  So there is our answer： $$0.636363\cdots=$$$\dfrac{7}{11}$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals
Source: 其它
Problem: The 2000 Census identified the ethnic breakdown of the state of California to be approximately as follows: White:46％, Latino:32\%, Asian:11\%, Blcak:7\%,and Other:4\%.~Assuming that these are mutually exclusive categories (this is not a realistic assumption), what is the probability that a randomly selected person from the state of California is of Asian or Latino descent? 
Options:
aoVal: A
content: 46\% 
aoVal: B
content: 32\% 
aoVal: C
content: 11\% 
aoVal: D
content: 43\% 
aoVal: E
content: 3.5\% 
Answer: C
Analysis: The correct answer is (c).There are 12 values in the A and E cell out the total of 125. When we are given colwnn E, the total is 63. Of those,28 are C. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables
Source: 其它
Problem: Express $$0.\dot{5}$$ as a fraction . ． 
Options:
aoVal: A
content: $\dfrac{111}{200}$ 
aoVal: B
content: $\dfrac{11}{20}$ 
aoVal: C
content: $\dfrac{5}{9}$ 
aoVal: D
content: $\dfrac{2}{3}$ 
Answer: C
Analysis: Let $$x = 0.555\cdots$$  Multiply by $$10$$ , which means move the decimal point one place to the right: $$10x = 5.555\cdots$$.  $$x$$ and $$10x$$ have exactly the same decimal part, so if we subtract, it will disappear: $$10x - x = 5.555\cdots - 0.555\cdots$$.  Simplify:~ $$9x = 5$$，$x=\dfrac{5}{9}$  So there\textquotesingle s our answer : $$0.555\cdots=$$$\dfrac{5}{9}$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Recurring Decimals
Source: 其它
Problem: Alina writes the numbers $1,2,\cdots ,9$ on a separate cards, one number per card. She wishes to divide the cards into $3$ groups of $3$ cards so that the sum of the numbers in each group will be the same. In how many ways can this be done? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$1$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$3$$ 
aoVal: E
content: $$4$$ 
Answer: A
Analysis: C 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: The ones digit of the fourth power of an integer cannot be． 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
Answer: B
Analysis: The ones digit of a $$4\text{th}$$ power canbe $$0$$, $$1$$, $$5$$, or $$6$$. It can never be $$3$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers
Problem: If a study has three factors, each with three levels, how many treatments are there? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: $$27$$ 
Answer: E
Analysis: The number of values you multiply together is equal to the number of factors in a study. There are three factors, so multiply \_\_x\_\_x\_\_. The values that go into each slot represent the number of levels for each factor. In this case, 3x3x3=27. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: $5+19$ is the same as~\uline{~~~~~~~~~~}~$+8$. 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$15$$ 
aoVal: C
content: $$14$$ 
aoVal: D
content: $$13$$ 
Answer: A
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers
Source: 其它
Problem: $$99\times9=$$． 
Options:
aoVal: A
content: $$990-9$$ 
aoVal: B
content: $$990-90$$ 
aoVal: C
content: $$900-99$$ 
aoVal: D
content: $$900-9$$ 
Answer: D
Analysis: $$99\times9=(100-1)\times9$$. This is slightly less than $$100\times9$$, so it\textquotesingle s $$\text{D}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: Ten balls numbered from $1$ to $10$ are put into a bag. $3$ balls are taken out and numbers on them are added up. The ball with number $5$ is included in the balls that are taken out, and the sum of numbers on the $3$ balls can be divisible by both $3$ and $4$. Which of the following balls is definitely not taken out? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$9$$ 
Answer: C
Analysis: The sum can be divisible by both $3$ and $4$, so the sum is the common multiple of $3$ and $4$.  If the sum is $12$, $12-5=7$, so the sum of the other numbers should be $7$. The other two numbers can be $1$ and $6$ or $3$ and $4$.  If the sum is $24$, $24-5=19$, the other two numbers can only be $10$ and $9$.  If the sum is $36$, it is impossible, because $36-5=31$ and the largest sum of two numbers from $1$ to $10$ is $19$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: In which of the following expressions, the value of the constant is larger than the value of the coefficient of $x$? 
Options:
aoVal: A
content: $$33x-55$$ 
aoVal: B
content: $$-25x-32$$ 
aoVal: C
content: $-\frac{x}{3}-\frac{1}{4}$ 
Answer: C
Analysis: the sign in front is also part of constant or coefficient 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Source: 其它
Problem: There is a rule that the symbol "\#" represents an operation of producing the smaller one of the two numbers (for example, $17$ \# $8 = 8$). Calculate: ($6$ \# $3$ ) $\times$($10$ \# $9$)=~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$18$$ 
aoVal: B
content: $$27$$ 
aoVal: C
content: $$54$$ 
aoVal: D
content: $$60$$ 
Answer: B
Analysis: $6$\#$3=3$, $10$\#$9=9$  $3 \times 9=27$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly
Problem: Let $ a◆b=a+(2\times b)$, then $1◆(2◆3)$ =~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$11$$ 
aoVal: C
content: $$17$$ 
aoVal: D
content: $$36$$ 
Answer: C
Analysis: $1◆(2◆3)=1◆[2+(2\times3)]=1◆8=1+16=17$.  So the answer is $\rm C$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly
Problem: $$111$$ 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
Answer: B
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: \textbf{Which of the following data sets has the largest standard deviation?} 
Options:
aoVal: A
content: \textbf{{100, 101, 102, 103, 104}} 
aoVal: B
content: \textbf{{1000.3, 999.56, 1000.49, 1000, 998.32}} 
aoVal: C
content: \textbf{{1, 1, 1, 1, 1}} 
aoVal: D
content: \textbf{{5, 10, 15, 20, 25}} 
aoVal: E
content: \textbf{{1, 2, 3, 4, 5}} 
Answer: D
Analysis: \textbf{variance is used to measure the spread of data. A, B, C, E are densely distributed.We can verify by calculating the variances out. (A) 2.5, (B) 0.598, (C) 0, (D) 50, (E) 2} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: $$$$Calculate$$$$  $$\frac{1}{2}~ (2019 \times 2018-2018 \times 2017+2017 \times 2016-2016 \times 2015+\cdots$$$$ +5\times4-4\times3 +3\times2-2\times1 )$$． 
Options:
aoVal: A
content: $$1007090$$ 
aoVal: B
content: $$1019090$$ 
aoVal: C
content: $$1028090$$ 
aoVal: D
content: $$1037090$$ 
aoVal: E
content: None of the above 
Answer: B
Analysis: $$\dfrac{1}{2}(2019\times2018-2018\times2017+2017\times2016-2016\times2015+\cdots$$$$+5\times4-4\times3+3\times2-2\times1)$$  $$= \frac{1}{2}\left (2 \times 2018+2 \times 2016+ \cdots +2 \times 4+2 \times 2\right )$$  $=\left (2018+2016+\cdots+4+2\right )=1009\times1010=1019090$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations
Problem: \textbf{Events D and E are independent, with P(D) = 0.6 and P(D and E) = 0.18. Which of the following is true?} 
Options:
aoVal: A
content: \textbf{P(E) = 0.12} 
aoVal: B
content: \textbf{P(E) = 0.4} 
aoVal: C
content: \textbf{P(D or E) = 0.28} 
aoVal: D
content: \textbf{P(D or E) = 0.72} 
aoVal: E
content: \textbf{P(D or E) = 0.9} 
Answer: D
Analysis: \textbf{Since D and E are independent, P(D ∩ E) = P(D)*P(E). So P(E) = 0.3.}  \textbf{P(D ∪ E) = P(D) + P(E) -- P(D ∩ E) = 0.6 +0.3 -0.18 = 0.72} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: 13+4=, 87-17=． 
Options:
aoVal: A
content: 17, 80 
aoVal: B
content: 18, 70 
aoVal: C
content: 9,~~94 
aoVal: D
content: 17, 70 
aoVal: E
content: 20, 80 
Answer: D
Analysis: 13+4=17 , 87-17=70 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction 
Source: 其它
Problem: If $2^{200}\times4^{1000}\times8^{40}=16^{}x$, then $x=$~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$295$$ 
aoVal: B
content: $$520$$ 
aoVal: C
content: $$570$$ 
aoVal: D
content: $$580$$ 
aoVal: E
content: $$620$$ 
Answer: D
Analysis: $2^{200} \times 4^{1000} \times 8^{40}=16^{200 \div 4} \times 16^{1000 \div 2} \times 2^{120}$$=16^{50} \times 16^{500} \times 16^{30}=16^{580}$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers
Problem: What is the 100\textsuperscript{th}~number in the arithmetic sequence $$1$$, $$5$$, $$9$$, $$13$$, $$17$$, $$21$$, $$25$$, $$\cdots$$． 
Options:
aoVal: A
content: $$397$$ 
aoVal: B
content: $$399$$ 
aoVal: C
content: $$401$$ 
aoVal: D
content: $$403$$ 
aoVal: E
content: $$405$$ 
Answer: A
Analysis: $$4$\times$100-3=397$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences