math-eval/TAL-SCQ5K huggingface dataset:
Problem: There is a tournament at the pool. First, $$13$$ children signed up and then another $$19$$ children signed up. Six teams with an equal number of members each are needed for the tournament. At least how many more children need to sign up so that the six teams can be formed?~ 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: D
Analysis: $$13 + 19 = 32$$; $$32 \div 6 = 5R2$$. There are $$2$$ students left, which means that $$6 - 2 = 4$$ more students are needed to form $6$ teams. 
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: A data set consists of $6$ (not distinct) positive integers: $1,7,5,2,5$, and $X$. The average (arithmetic mean) of the 6 numbers equals a value in the data set. What is the sum of all positive values of $X$? (2022 AMC 10A Problems, Question \#8) 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$26$$ 
aoVal: C
content: $$32$$ 
aoVal: D
content: $$36$$ 
aoVal: E
content: $$40$$ 
Answer: D
Analysis: First, note that $1+7+5+2+5=20$. The mean cannot be $1$ or $2$.  There are $3$ possible cases:  Case 1: the mean is $5$ . $$ X=5 \cdot 6-20=10 \text {. } $$  Case 2: the mean is $7$. $$ X=7 \cdot 6-20=22 \text {. } $$  Case 3: the mean is $X$. $$ \frac{20+X}{6}=X \Rightarrow X=4 \text {. } $$  Hence, the answer is $10+22+4=$ (D) $36$ . 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: The average value of ＄$$2$$, ＄$$4$$, ＄$$6$$, ＄$$8$$, and ＄$$10$$ is~\uline{~~~~~~~~~~}~pennies. 
Options:
aoVal: A
content: $$3000$$ 
aoVal: B
content: $$600$$ 
aoVal: C
content: $$550$$ 
aoVal: D
content: $$500$$ 
Answer: B
Analysis: Average $$=$$(＄$$2+$$＄$$4+$$＄$$6+$$＄$$8+$$＄$$10$$)$$\div 5=$$＄$$6=600$$ pennies. 
Knowledge points: Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability
Problem: Which of the following number is different from the others． 
Options:
aoVal: A
content: $$0.08$$ 
aoVal: B
content: $$8\textbackslash\%$$ 
aoVal: C
content: $$\frac{8}{10}$$ 
aoVal: D
content: Eight percents 
Answer: C
Analysis: $$8\textbackslash\%=0.08$$，  But $$\frac{8}{10}=0.8$$．  So, the answer is $$\text{C}$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions->Converting Between Fractions, Percentage and Decimals
Source: 其它
Problem: An operator $$\star$$ acts on two numbers to give the following outcomes:  $$3\star2=51$$  $$5\star3=82$$  $$6\star1=75$$  $$9\star4=135$$  What is $$7\star5$$ equal to? 
Options:
aoVal: A
content: $$112$$ 
aoVal: B
content: $$121$$ 
aoVal: C
content: $$122$$ 
aoVal: D
content: $$212$$ 
aoVal: E
content: None of the above 
Answer: C
Analysis: $$a\star b=\underbrace{(a+b)}\_{\rm{tens}} \underbrace{(a-b)}\_{\rm{ones}}$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition
Source: 其它
Problem: What value does the hundredth place represent in the number $12.345$? 
Options:
aoVal: A
content: $$0.005$$ 
aoVal: B
content: $$0.04$$ 
aoVal: C
content: $$0.3$$ 
aoVal: D
content: $$2$$ 
Answer: B
Analysis: The hundredth place of a number is the second digit after the decimal point, which is $$4$$. Since the number $$4$$ is on the hundredth place, it represents $$0.04$$.  Check Lesson 4 Concept 1 on textbook 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals
Source: 其它
Problem: \textbf{Suppose a certain scale is not calibrated correctly, and as a result, the mass of any object is displayed as 0.75 kilogram less than its actual mass. What is the correlation between the actual masses of a set of objects and the respective masses of the same set of objects displayed by the scale?} 
Options:
aoVal: A
content: $$-1$$ 
aoVal: B
content: $$-0.75$$ 
aoVal: C
content: $$0$$ 
aoVal: D
content: $$0.75$$ 
aoVal: E
content: $$1$$ 
Answer: E
Analysis: \textbf{Since the actual mass is always 0.75kg more than the displayed mass, they are perfectly correlated.~} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: \textbf{High school students from track teams in the state participated in a training program to improve running times. Before the training, the mean running time for the students to run a mile was 402 seconds with standard deviation 40 seconds. After completing the program, the mean running time for the students to run a mile was 368 seconds with standard deviation 30 seconds. Let X represent the running time of a randomly selected student before training, and let Y represent the running time of the same student after training. Which of the following is true about the distribution of X - Y ?} 
Options:
aoVal: A
content: \textbf{The variables X and Y are independent; therefore, the mean is 34 seconds and the standard deviation is 10 seconds.} 
aoVal: B
content: \textbf{~The variables X and Y are independent; therefore, the mean is 34 seconds and the standard deviation is 50 seconds.} 
aoVal: C
content: \textbf{The variables X and Y are not independent; therefore, the standard deviation is 50 seconds and the mean cannot be determined with the information given.} 
aoVal: D
content: \textbf{The variables X and Y are not independent; therefore, the mean is 34 seconds and the standard deviation cannot be determined with the information given.} 
aoVal: E
content: \textbf{The variables X and Y are not independent; therefore, neither the mean nor the standard deviation can be determined with the information given.} 
Answer: D
Analysis: \textbf{Mean: 402 - 368 = 34}  \textbf{SD: X and Y are not independent, correlation is unknown → SD unknown} 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: There is a number $X.$ Three times the sum of $4$ and number $X$ is $36$. What is the value of number $X$? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$10$$ 
Answer: D
Analysis: $3(4+x)=36, x=8$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation
Source: 其它
Problem: insert pic  Which number is hidden behind the square? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$5$$ 
aoVal: E
content: $$6$$ 
Answer: E
Analysis: triangle: 7-4=3  square: 9-3=6 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns->Encryption and Decryption
Source: 其它
Problem: $$\left( {3+2+1} \right)\times 10=30+20+$$~\uline{~~~~~~~~~~}~ 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$11$$ 
aoVal: C
content: $$33$$ 
aoVal: D
content: $$44$$ 
Answer: A
Analysis: $$\left( {3+2+1} \right)\times 10=60=30+20+10$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Distributive Law of Whole Numbers
Problem: Vivian creates a new operation: $m$@$n=m\times m-n\times n$. What is the value of $11$@$9$? 
Options:
aoVal: A
content: $$99$$ 
aoVal: B
content: $$121$$ 
aoVal: C
content: $$81$$ 
aoVal: D
content: $$40$$ 
aoVal: E
content: $$30$$ 
Answer: D
Analysis: $11^{2}-9^{2}=40$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition
Source: 其它
Problem: How many two-digits positive integers has at least one $8$ as its digit? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$11$$ 
aoVal: D
content: $$18$$ 
aoVal: E
content: $$19$$ 
Answer: D
Analysis: D 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: When Koko and Koala does not sleep, he eats 50 grams of leaves per hour. Yesterday, he slept 20 hours. How many grams of leaves did he eat yesterday? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$50$$ 
aoVal: C
content: $$100$$ 
aoVal: D
content: $$200$$ 
aoVal: E
content: $$400$$ 
Answer: D
Analysis: (24 - 20) x 5 = 200. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion
Source: 其它
Problem: Calculate：$$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}=$$． 
Options:
aoVal: A
content: $$\frac{4}{5}$$ 
aoVal: B
content: $$\frac{5}{6}$$ 
aoVal: C
content: $$\frac{11}{12}$$ 
aoVal: D
content: $$\frac{19}{20}$$ 
Answer: A
Analysis: $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}$$  $$=\frac{30}{60}+\frac{10}{60}+\frac{5}{60}+\frac{3}{60}$$  $$=\frac{48}{60}$$  $$=\frac{4}{5}$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Problem: Two non-zero real numbers, $a$ and $b$, satisfy $a b=a-b$. Which of the following is a possible value of $\frac{a}{b}+\frac{b}{a}-a b$? (2000 AMC 12 Problems, Question \#11) 
Options:
aoVal: A
content: $-2$ 
aoVal: B
content: $\frac{-1}{2}$ 
aoVal: C
content: $\frac{1}{3}$ 
aoVal: D
content: $\frac{1}{2}$ 
aoVal: E
content: $$2$$ 
Answer: E
Analysis: $$\frac{a}{b}+\frac{b}{a}-a b=\frac{a^{2}+b^{2}}{a b}-(a-b)=\frac{a^{2}+b^{2}}{a-b}-\frac{(a-b)^{2}}{(a-b)}=\frac{2 a}{a-b}=\frac{2(a-b)}{a-b}=2 \Rightarrow \text{E}.$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Which of these is closest to $$4$$? 
Options:
aoVal: A
content: $$4.07 $$ 
aoVal: B
content: $$ 3.925 $$ 
aoVal: C
content: $$3.979 $$ 
aoVal: D
content: $$4.12 $$ 
aoVal: E
content: $$4.024$$ 
Answer: C
Analysis: Note that $$4.07-4 = 0.07$$; $$4-3.925 = 0.075$$; $$4-3.979 =0.021$$; $$4.12-4 = 0.12$$ and $$4.024-4 = 0.024$$.  So, of the five options, $$3.979$$ is nearest to $$4$$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering
Problem: What is the unit digit of $23^{2023}$? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$7$$ 
aoVal: E
content: $$9$$ 
Answer: D
Analysis: D 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Nancy bought 17 cones of ice-cream for her three children. Misha ate twice as many cones as Ana. Dan ate more ice-cream than Ana but less than Misha. How many cones of ice-cream did Dan eat? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$7$$ 
aoVal: E
content: $$8$$ 
Answer: B
Analysis: Let x be the number of ice-cream cones that Ana ate.  Then, 2x is the number of cones that Misha ate, and the number of cones that Dan ate is:  17 - x - 2x = 17 - 3x.  It is given that Dan ate more than Misha but less than Ana; therefore,  x \textless{} 17 - 3x \textless{} 2x  4x \textless{} 17 \textless{} 5x  only x=4 satisfies this inequality.  The number of cones that Dan ate is thus 17- 3 x 4 = 5. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities->Solving Inequalities
Source: 其它
Problem: For $\triangle ABC$, all its side lengths are integer. The primeter of $\triangle ABC$ with a side of length $14$ and a side length of $8$ is at least ． 
Options:
aoVal: A
content: $$25$$ 
aoVal: B
content: $$26$$ 
aoVal: C
content: $$27$$ 
aoVal: D
content: $$28$$ 
aoVal: E
content: $$29$$ 
Answer: E
Analysis: We know from the triangle inequality that the last side, $s$, fulfills $s+8\textgreater14$. Therefore, $P\textgreater14+14$. The least integer value of $P$ is $29$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities
Source: 其它
Problem: Gilda has a bag of marbles. She gives $30 \textbackslash\%$ of them to her friend Pedro. Then Gilda gives $25 \textbackslash\%$ of what is left to another friend, Ebony. Finally, Gilda gives $10 \textbackslash\%$ 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? (adapted 2019 AMC 8, Question \#8) 
Options:
aoVal: A
content: $$47.25\textbackslash\%$$ 
aoVal: B
content: $50.25\textbackslash\%$ 
aoVal: C
content: $$65\textbackslash\%$$ 
aoVal: D
content: $$70\textbackslash\%$$ 
Answer: A
Analysis: After Gilda gives $30 \textbackslash\%$ of the marbles to Pedro, she has $70 \textbackslash\%$ of the marbles left. If she then gives $25 \textbackslash\%$ of what\textquotesingle s left to Ebony, she has $(0.75 * 0.70)=52.5 \textbackslash\%$ of what she had at the beginning. Finally, she gives $10 \textbackslash\%$ of what\textquotesingle s left to her brother, so she has $(0.9 * 0.525) =$ (A) $47.25\textbackslash\%$ of what she had in the beginning left. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation
Source: 其它
Problem: If $$a=2$$, $$b=4$$, $${{a}^{2}}+3b=$$． 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$9$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$14$$ 
aoVal: E
content: $$16$$ 
Answer: E
Analysis: $$3^{2}+2\times1.5=12$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Source: 其它
Problem: If $$\left\textbar{} 2x-5 \right\textbar=7$$, $x=$~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$-1$$ or $$6$$ 
aoVal: C
content: $$1$$ or $$-6$$ 
aoVal: D
content: $$1$$ or $$6$$ 
Answer: B
Analysis: $$2x-5=\pm 7$$  $$x=6$$ or $$x=-1$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities->Solving Inequalities
Source: 其它
Problem: A circle is centered at $O$, $AB$ is a diameter and $C$ is a point on the circle with $\angle COB=50^{\circ}$. What is the degree measure of $\angle CAB$? 
Options:
aoVal: A
content: $$20$$ 
aoVal: B
content: $$25$$ 
aoVal: C
content: $$45$$ 
aoVal: D
content: $$50$$ 
aoVal: E
content: $$65$$ 
Answer: B
Analysis: B 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
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 $\left(1, a^{2}-4\right)$ 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: Tiara\textquotesingle s toll pass account has a value of $$$24$$. Each time she uses the toll road, $$$1.4$$ is deducted from the account. When the value drops below $$$10$$, she must add value to the toll pass. Assume there are $$x$$ times Tiara can use the toll road without having to add value to the toll pass. Which inequality can represent the situation? 
Options:
aoVal: A
content: $24-1.4x\geq10$ 
aoVal: B
content: $24-1.4x\textgreater10$ 
aoVal: C
content: $24+1.4x\geq10$ 
aoVal: D
content: $24-1.4x\leq10$ 
Answer: A
Analysis: $24-1.4x\geq10$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities
Source: 其它
Problem: How many $0$s are there in the end of the result of the factorial of $25$? 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$8$$ 
Answer: D
Analysis: We can get $1+1+1+1+2=6$ factor $5$s from $5, 10, 15, 20, 25$ in total, which can make six $10$s after multiplying $2$. Six $10$s means that there should be $6$ $0$s in the end. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas->Factorization
Source: 其它
Problem: From a starting number, Olivia was supposed to subtract $3$, and then divide by $9$, but instead, Olivia subtracted $9$, then divided by $3$, getting $43$. If the correct instructions were followed, what would the result be? 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$34$$ 
aoVal: C
content: $$43$$ 
aoVal: D
content: $$51$$ 
aoVal: E
content: $$138$$ 
Answer: A
Analysis: A 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: What is the product of $$5$$ and $$830$$? 
Options:
aoVal: A
content: $$166$$ 
aoVal: B
content: $$825$$ 
aoVal: C
content: $$835$$ 
aoVal: D
content: $$4150$$ 
Answer: D
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division
Problem: In how many ways can the letters in \textbf{BEEKEEPER} be rearranged so that two or more \textbf{E}s do not appear together? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$24$$ 
aoVal: E
content: $$120$$ 
Answer: D
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: There is some water in a bowl, which is on a electronic scales. Mike pours water into the bowl. After pouring $2$ glasses of water, the sacle shows $300$ grams. After pouring a total of $6$ glasses of water, the scale shows $700$ grams. What is the quality of the water at the start? 
Options:
aoVal: A
content: $$100$$ g 
aoVal: B
content: $$150$$ g 
aoVal: C
content: $$200$$ g 
aoVal: D
content: $$250$$ g 
aoVal: E
content: $$275$$ g 
Answer: A
Analysis: The quality of each glass of water: $(700 - 300) \div (6 - 2) = 100$ g  At first: $300 - 100 \times 2 = 100$ g 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: $\left (876\times543\right ) -\left (543\times876\right )=$． 
Options:
aoVal: A
content: $0$ 
aoVal: B
content: $1$ 
aoVal: C
content: $237834$ 
aoVal: D
content: $475668$ 
Answer: A
Analysis: $\left (876\times543\right ) - \left (543\times876\right ) = \left (876\times543\right ) - (876\times543) = 0$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations
Problem: $$26+24-22+20-18+16-14+12-10+8-6+4-2=$$？． 
Options:
aoVal: A
content: $$48$$ 
aoVal: B
content: $$38$$ 
aoVal: C
content: $$36$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: $$0$$ 
Answer: B
Analysis: $$=26+(24-22)+(20-18)+(16-14)+(12-10)+(8-6)+(4-2)$$  $$=26+2+2+2+2+2+2$$  $$=38$$． 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers
Source: 其它
Problem: Ace and Sam were painting a house. Ace painted $$\frac{3}{10}$$ of the house. Sam painted $$\frac{2}{10}$$ more than Ace. What fraction of the house still needs to be painted? 
Options:
aoVal: A
content: $$\frac{2}{10}$$ 
aoVal: B
content: $$\frac{3}{10}$$ 
aoVal: C
content: $$\frac{5}{10}$$ 
aoVal: D
content: $$\frac{8}{10}$$ 
Answer: A
Analysis: Sam: $$\frac{2}{10}+\frac{3}{10}=\frac{5}{10}$$  Total: $$\frac{5}{10}+\frac{3}{10}=\frac{8}{10}$$  Left: $$\frac{10}{10}-\frac{8}{10}=\frac{2}{10}$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: Which of the following is not an expression? 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$a$$ 
aoVal: C
content: $$a+b=a+b$$ 
aoVal: D
content: $$b-3$$ 
Answer: C
Analysis: Equations are not expressions. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Problem: Which of these pairs of fractions are equivalent? 
Options:
aoVal: A
content: $$3\frac{1}{2}$$ and $$2\frac{1}{4}$$ 
aoVal: B
content: $$1\frac{1}{3}$$ and $$\frac{8}{6}$$ 
aoVal: C
content: $$1\frac{1}{4}$$ and $$\frac{3}{4}$$ 
aoVal: D
content: $$3\frac{3}{9}$$ and $$\frac{9}{9}$$ 
Answer: B
Analysis: $\frac{8}{6}=\frac{4}{3}=1\frac{1}{3}$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions
Problem: Cassandra is helping her mother to pack $$75$$ cupcakes. The boxes that her mother prepare can only fit $$7$$ cupcakes. She must ensure the box is full before she can use the next box. How many boxes she can fill up? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$68$$ 
aoVal: E
content: $$70$$ 
Answer: C
Analysis: $$75\div7=10R5$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers
Source: 其它
Problem: Judy has less than $40$ game coins. The game coins can be divided evenly between $3, 4$ or $6$ students. However, they cannot be divided evenly between $7$ students because $4$ more game coins would be needed. How many game coins does Judy have? 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$18$$ 
aoVal: C
content: $$48$$ 
aoVal: D
content: $$24$$ 
aoVal: E
content: $$35$$ 
Answer: D
Analysis: The game coins can be divided evenly between $3, 4$ or $6$ students, which means the number of game coins should be divisible by $3, 4,$ or $6$, so we can eliminate the options $E$ .  The game coins cannot be divided evenly between $7$ students because $4$ more game coins would be needed, so after the number of game coins plus $4$, the result can be divisible by $7$. Thus, the answer is $24$. 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它
Problem: Calculate $$0.3\dot{8}\div 0.\dot{5}1\dot{8}$$ 
Options:
aoVal: A
content: $$\frac12$$ 
aoVal: B
content: $$\frac23$$ 
aoVal: C
content: $$\frac34$$ 
aoVal: D
content: $$\frac45$$ 
aoVal: E
content: $$\frac56$$ 
Answer: C
Analysis: C 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Fractions
Source: 其它
Problem: How many odd numbers are there?  5, 12, 3, 6, 7, 9, 10, 4 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
Answer: B
Analysis: $$Omitted.$$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers
Source: 其它
Problem: Which of the followings is not an algebraic expression? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$ax+32$$ 
aoVal: C
content: $\frac{2}{y}$+88 
aoVal: D
content: $$x=33y$$ 
Answer: D
Analysis: $D$ is an equation 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions
Source: 其它
Problem: For $\triangle ABC$, all its side lengths are integers. The perimeter of $\triangle ABC$ with a side of length $25$ and a side length of $18$ is at least ． 
Options:
aoVal: A
content: $$25$$ 
aoVal: B
content: $$18$$ 
aoVal: C
content: $$52$$ 
aoVal: D
content: $$51$$ 
aoVal: E
content: $$50$$ 
Answer: D
Analysis: We know from the triangle inequality that the last side, $s$, fulfills $s+18\textgreater25$. Therefore, $P\textgreater25+25$. The least integer value of $P$ is $51$ 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities
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: C
Analysis: C 
Knowledge points: Overseas Competition->Knowledge Point->Calculation Modules
Source: 其它