math-eval/TAL-SCQ5K huggingface dataset:
Problem: Historians say that William the Conqueror was born in $$1028$$. How many years ago was that? 
Options:
aoVal: A
content: $$790$$ 
aoVal: B
content: $$810$$ 
aoVal: C
content: $$910$$ 
aoVal: D
content: $$990$$ 
aoVal: E
content: $$1010$$ 
Answer: D
Analysis: The number of years from William\textquotesingle s birth is $$2018 - 1028 = 990$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction
Problem: A 20\% increase in the price of milk leads to a 10\% decrease in the quantity of cereal purchased. The cross-price elasticity of demand between milk and cereal is 
Options:
aoVal: A
content: -0.5 and the two goods are substitutes. 
aoVal: B
content: -0.5 and the two goods are complements. 
aoVal: C
content: 0.5 and the two goods are complements. 
aoVal: D
content: -2 and the two goods are substitutes. 
aoVal: E
content: 2 and the two goods are complements. 
Answer: B
Analysis: This is an application of the cross-price elasticity equation: \% change in QDx/\% change in Py. -0.10/0.2 = -0.5. A negative number means the goods are complements. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: If one bag of chips costs $$75$$￠, then three of these bags cost ． 
Options:
aoVal: A
content: $$$0.25$$ 
aoVal: B
content: $$$1.50$$ 
aoVal: C
content: $$$2.25$$ 
aoVal: D
content: $$$3.00$$ 
Answer: C
Analysis: One bag costs $$75$$￠. Three such bags cost $$3\times $0.75=$2.25$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method
Problem: After Sally takes $20$ shots, she has made $40 \textbackslash\%$ of her shots. After she takes $5$ more shots, she raises her percentage to $52 \textbackslash\%$. How many of the last $5$ shots did she make? ( adapted from 2004 AMC 8, Question\#6) 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: E
Analysis: Sally made $0.4 * 20=8$ shots originally. Letting $x$ be the number of shots she made, we have $\frac{8+x}{25}=0.52$. Solving for $x$ gives us $x=5$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems
Source: 其它
Problem: If $$1$$ August falls on Monday, which day of the week will $$12$$ September fall on?  Below is Chris\textquotesingle~answer.  Number of days from 1 Aug to 12 Sept: 31 + 12 = 43  43 $\div$ 7 = 6 R 1  Hence, 12 September is a Tuesday.  Is Chris\textquotesingle s answer correct? If not, what is the correct answer? ． 
Options:
aoVal: A
content: Sunday 
aoVal: B
content: Monday 
aoVal: C
content: Tuesday 
aoVal: D
content: Wednesday 
Answer: B
Analysis: Number of days from $$1$$ August to $$12$$ September  $$=31+12-1$$  $$=42$$  $$42\div 7=6$$ weeks  Therefore, $$12$$ September will fall on \textbf{Monday}. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: The owner of a bicycle store had a sale on bicycles(two-wheelers) and tricycles(three-wheelers). Each cycle had two pedals. When he counted the total number of pedals of the cycles, he got 50 . When he counted the total number of wheels of the cycles, he got 64 . How many tricycles were offered in the sale? 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$14$$ 
aoVal: E
content: $$16$$ 
Answer: D
Analysis: $50\div 2=25$  let $x$ be the number of bicycles, $y$ be the number of tricycles  $2x+3y=64$  $x+y=25$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems
Source: 其它
Problem: Anna, Bridgit and Carol run in a $$100\text{m}$$ race. When Anna finishes, Bridgit is $$16\text{m}$$ behind her and when Bridgit finishes, Carol is $$25\text{m}$$ behind her. The girls run at constant speeds throughout the race. How far behind was Carol when Anna finished? 
Options:
aoVal: A
content: $$37\text{m}$$ 
aoVal: B
content: $$41\text{m}$$ 
aoVal: C
content: $$50\text{m}$$ 
aoVal: D
content: $$55\text{m}$$ 
aoVal: E
content: $$60\text{m}$$ 
Answer: A
Analysis: Carol finishes $$25$$ metres behind Bridgit, so she travels $$75$$ metres while Bridgit runs $$100$$ metres. Therefore she runs $$3$$ metres for every $$4$$ metres Bridgit runs. When Anna finishes, Bridgit has run $$84$$ metres, so that at that time Carol has run $$\frac{3}{4}\times 84$$ metres $$=63$$ metres. Hence Carol finishes $$\left( 100-63 \right)$$ metres $$= 37$$ metres behind Anna. 
Knowledge points: Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road
Problem: If $$6$$ cans of Sweet Stuff Soda all together contain $$96$$ teaspoons of sugar, then there are a total of teaspoons of sugar in $$15$$ cans. 
Options:
aoVal: A
content: $$192$$ 
aoVal: B
content: $$208$$ 
aoVal: C
content: $$240$$ 
aoVal: D
content: $$288$$ 
Answer: C
Analysis: If $$6$$ cans contain $$96$$ teaspoons of sugar, $$1$$ can contains $$96\div6 = 16$$ teaspoons of sugar. Thus $$15$$ cans contain $$16\times15 =240$$ teaspoons of sugar. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value
Problem: Given that January $$1$$st, $$2018$$ was Monday, on what day did January $$1$$st, $$2019$$ fall? 
Options:
aoVal: A
content: Tuesday 
aoVal: B
content: Monday 
aoVal: C
content: Sunday 
aoVal: D
content: Wednesday 
Answer: A
Analysis: $2018$ was a common year which had $365$ days. Thus, January $$1$$st, $$2019$$ fell on one day after Monday, which was Tuesday. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: Three zebras take part in a contest. The winner is the zebra with the most number of stripes. QingLe has $$15$$ stripes, ChenXi has $$3$$ more than QingLe. QingLe has $$5$$ fewer stripes than YueYing. How many stripes does the winner have? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$18$$ 
aoVal: C
content: $$20$$ 
aoVal: D
content: $$21$$ 
aoVal: E
content: $$23$$ 
Answer: C
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Problem: In the yard there is an equal number of pigs, ducks and chickens. Together, they have $$144$$ legs. How many ducks are there in the yard? 
Options:
aoVal: A
content: $$18$$ 
aoVal: B
content: $$21$$ 
aoVal: C
content: $$35$$ 
aoVal: D
content: $$42$$ 
aoVal: E
content: $$43$$ 
Answer: A
Analysis: Suppose there are $$x$$ ducks in the yard. Since there is an equal number of pigs, ducks and chickens, $$2x+4x+2x=144$$, $$x=18$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable
Problem: Paul was going to buy $$4$$ servings of ice cream, but he was $$80$$ cents short. So, he bought $$3$$ servings and had $$30$$ cents left. What was the price of one serving of ice cream? 
Options:
aoVal: A
content: $$70$$ cents 
aoVal: B
content: $$80$$ cents 
aoVal: C
content: $$90$$ cents 
aoVal: D
content: $$1$$ dollar 
aoVal: E
content: $$1$$ dollar $$10$$ cents 
Answer: E
Analysis: $$(80+30)\div (4-3)=110$$ cents $$=1$$ dollar and $$10$$ cents. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems
Problem: A salt solution is made by mixing $100$ g of salt and $400$ g of water. Find the percent concentration of the mixture. 
Options:
aoVal: A
content: $15\textbackslash\%$ 
aoVal: B
content: $20\textbackslash\%$ 
aoVal: C
content: $25\textbackslash\%$ 
aoVal: D
content: $30\textbackslash\%$ 
Answer: B
Analysis: $$100\div \left( 100+400\right) \times 100\textbackslash\% =20\textbackslash\%$$.  ~~ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts->Calculating Price from Cost and Profit
Problem: When $$4$$ kilograms of $$30\textbackslash\%$$ sugar water is mixed with some $$10\textbackslash\%$$ sugar water, it gives a mixture with a sugar concentration of $$26\textbackslash\%$$. How much $$10\textbackslash\%$$ sugar water is needed?~\uline{~~~~~~~~~~}~$$\text{kg}$$ 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: A
Analysis: Use the cross method $$\begin{matrix}30\textbackslash\%10\textbackslash\% \textbackslash\textbackslash{} \searrow \swarrow \textbackslash\textbackslash{} 26 \textbackslash\% \textbackslash\textbackslash{} \swarrow \searrow \textbackslash\textbackslash{} 16 \textbackslash\%4\textbackslash\% \textbackslash\textbackslash\end{matrix}$$ to see that the ratio of $$30\textbackslash\%$$ solution to $$10\textbackslash\%$$ solution is $$4:1$$. Therefore, $$1\text{kg}$$ of $$10\textbackslash\%$$ solution is needed. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems
Problem: Cindy has $$50$$ bookmarks. If she were to give $$6$$ bookmarks to each of her classmates, she would need $$10$$ more bookmarks. How many classmates does Cindy have? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$12$$ 
Answer: C
Analysis: $50+10=60$  $60\div6=10$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems
Problem: A mixture of 30 liters of paint is $25 \textbackslash\%$ red tint, $30 \textbackslash\%$ yellow tint and $45 \textbackslash\%$ water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (2007 AMC 8, Question \#17 ) 
Options:
aoVal: A
content: $$25$$ 
aoVal: B
content: $$35$$ 
aoVal: C
content: $$40$$ 
aoVal: D
content: $$45$$ 
aoVal: E
content: $$50$$ 
Answer: C
Analysis: Since $30 \textbackslash\%$ of the original 30 liters of paint was yellow, and 5 liters of yellow paint were added to make the new mixture, there are $9+5=14$ liters of yellow tint in the new mixture. Since only 5 liters of paint were added to the original 30 , there are a total of 35 liters of paint in the new mixture. This gives $40 \textbackslash\%$ of yellow tint in the new mixture, which is (C) 40 . 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems
Source: 其它
Problem: Josh lives on the $6$\textsuperscript{th} floor. He needs to climb $24$ steps to move from the $2$\textsuperscript{nd~}floor to the $4$\textsuperscript{th} floor. How many steps does he need to climb from the $1$\textsuperscript{st} floor to the $6$\textsuperscript{th} floor? 
Options:
aoVal: A
content: $$72$$ 
aoVal: B
content: $$60$$ 
aoVal: C
content: $$48$$ 
aoVal: D
content: $$36$$ 
aoVal: E
content: $$32$$ 
Answer: B
Analysis: $24 \div 2 \times (6 - 1) = 60$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems
Source: 其它
Problem: Find the exact number of minutes after $3.00 \text{pm}$ when the minute and hour hands are first at $90^{\circ}$ to each other. 
Options:
aoVal: A
content: $$31 \frac{2}{11}$$ 
aoVal: B
content: $$31 \frac{3}{11}$$ 
aoVal: C
content: $$32 \frac{8}{11}$$ 
aoVal: D
content: $$33 \frac{3}{11}$$ 
aoVal: E
content: None of the above 
Answer: C
Analysis: The minute hand rotates $6^{\circ}$ per minute.  The hour hand rotates $\dfrac{1}{60}\times30^{\circ}=\left (\dfrac{1}{2}\right )^{\circ}$ per mimte.  Starting at $3$ O\textquotesingle clock, when the minute and hour hands are next perpendicular:  $$(90+90)\div(6-0.5)=\frac{360}{11}=32 \frac{8}{11}$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Problem: The page numbers of a book are from $$1$$ to $$62$$. Tim adds up the $$62$$ page numbers. In his calculation, he misses a page number and the sum of remaining pages is $$1940$$. What is the missing page number~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$13$$ 
aoVal: C
content: $$14$$ 
aoVal: D
content: $$15$$ 
Answer: B
Analysis: $$\left( 1+62 \right)\times 62\div 2=1953$$  $$1953-1940=13$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression
Problem: Suppose $50\textbackslash\%$ of $x$ equals $30\textbackslash\%$ of $y$. What percentage of $y$ is $x$ ? (adapted from 2020 AMC 8, Question 15) 
Options:
aoVal: A
content: $$40$$ 
aoVal: B
content: $$60$$ 
aoVal: C
content: $$80$$ 
aoVal: D
content: $120$ 
aoVal: E
content: $$200$$ 
Answer: B
Analysis: $50\textbackslash\% \cdot x = 30\textbackslash\% \cdot y$  $ x = 0.6\cdot y$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems
Source: 其它
Problem: Grandma made some cheese dumplings and some blueberry dumplings. Altogether, she made $$31$$ dumplings. If she had made $$11$$ more cheese dumplings, then there would be the same number of blueberry dumplings as cheese dumplings. How many cheese dumplings did grandma make? ($$2009$$ Math Kangaroo Problem, Levels $$1-2$$, Question \#$$19$$) 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$21$$ 
aoVal: C
content: $$20$$ 
aoVal: D
content: $$15$$ 
Answer: A
Analysis: $$(31-11)\div2=10.$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference
Problem: After the game, Owen is thirsty again. This time he gets a mixture of 3 liters of juice, which contain $25 \textbackslash\%$ of apple juice, $30 \textbackslash\%$ of mango juice, and $45 \textbackslash\%$ of water. $0.5$ liters of mango is added to the original mixture. What is the percent of mango in the new mixture? (Adapted from 2007 AMC 8, Question \#17 ) 
Options:
aoVal: A
content: $$2.5$$ 
aoVal: B
content: $$3.5$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$4.5$$ 
aoVal: E
content: $$5$$ 
Answer: C
Analysis: Since $30 \textbackslash\%$ of the original 30 liters of paint was yellow, and 5 liters of yellow paint were added to make the new mixture, there are $9+5=14$ liters of yellow tint in the new mixture. Since only 5 liters of paint were added to the original 30 , there are a total of 35 liters of paint in the new mixture. This gives $40 \textbackslash\%$ of yellow tint in the new mixture, which is (C) 40 . 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems
Source: 其它
Problem: Grandma made some cheese dumplings and some blueberry dumplings. Altogether, she made $$31$$ dumplings. If she had made $$11$$ more cheese dumplings, then there would be the same number of blueberry dumplings as cheese dumplings. How many cheese dumplings did grandma make? 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$21$$ 
aoVal: C
content: $$20$$ 
aoVal: D
content: $$15$$ 
Answer: A
Analysis: $$(31-11)\div2=10.$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference
Problem: Find the exact number of minutes after $3.00 \text{pm}$ when the minute and hour hands are first at $90^{\circ}$ to each other. 
Options:
aoVal: A
content: $$31 \frac{2}{11}$$ 
aoVal: B
content: $$31 \frac{3}{11}$$ 
aoVal: C
content: $$32 \frac{8}{11}$$ 
aoVal: D
content: $$33 \frac{3}{11}$$ 
aoVal: E
content: None of the above 
Answer: C
Analysis: The minute hand rotates $6^{\circ}$ per minute.  The hour hand rotates $\dfrac{1}{60}\times30^{\circ}=\left (\dfrac{1}{2}\right )^{\circ}$ per mimte.  Starting at $3$ O\textquotesingle clock, the minute hand rotates $\left (6t\right )^{\circ}$ and the hour hand rotates ~$$(90+ \frac{1}{2}t)^{ \circ }$$.  When the minute and hour hands are next perpendicular:  $$6t-\left (90+ \frac{1}{2}t\right )=90$$,  $$\frac{11}{2}t=180$$,  $$t= \frac{360}{11}=32 \frac{8}{11}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Problem: Joann\textquotesingle s birthday in $$2020$$ was May $$10$$\textsuperscript{th}, which was Sunday. Elizabeth\textquotesingle s birthday in $$2020$$ was June $$21$$\textsuperscript{st}. On what day did Elizabeth\textquotesingle s birthday fall? 
Options:
aoVal: A
content: Thursday 
aoVal: B
content: Saturday 
aoVal: C
content: Sunday 
aoVal: D
content: Tuesday 
Answer: C
Analysis: It passed $$31-10 + 21 = 42$$ days in total. Since $$42 \div 7 = 6$$, it was Sunday. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: Three zebras take part in a contest. The winner is the zebra with the most number of stripes. Runa has $$15$$ stripes, Zara has $$3$$ more than Runa. Runa has $$5$$ fewer stripes than Biba. How many stripes does the winner have? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$18$$ 
aoVal: C
content: $$20$$ 
aoVal: D
content: $$21$$ 
aoVal: E
content: $$23$$ 
Answer: C
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Problem: Sara is $$5$$ years old and Mike is $$9$$. How old will Sara be when Mike is $$20$$ years old? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$24$$ 
aoVal: D
content: $$28$$ 
aoVal: E
content: $$30$$ 
Answer: A
Analysis: Their difference in age: $$9-5=4$$  When Mike is $$20$$, Sara is $$20-4=16$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: A $$15\textbackslash\%$$ sugar solution contains $$18$$ grams of pure sugar. How many grams of solution are there? 
Options:
aoVal: A
content: $$90$$ grams 
aoVal: B
content: $$100$$ grams 
aoVal: C
content: $$120$$ grams 
aoVal: D
content: $$150$$ grams 
Answer: C
Analysis: $$18\div15\textbackslash\% = 120$$ ounces. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems
Problem: The boundary of a lake is $$600\text{m}$$ long. Trees are planted at regular intervals of $$6\text{m}$$ round the lake. How many trees are planted round the lake? 
Options:
aoVal: A
content: $$99$$ 
aoVal: B
content: $$100$$ 
aoVal: C
content: $$101$$ 
Answer: B
Analysis: In the case of circular tracks,  number of intervals $$=$$ number of trees,  $$600\div 6=100$$,  $$100$$ trees are planted round the lake. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Circular Paths
Problem: Given that January $$1$$st, $$2018$$ was Monday, on what day did January $$1$$st, $$2019$$ fall? 
Options:
aoVal: A
content: Tuesday 
aoVal: B
content: Monday 
aoVal: C
content: Sunday 
aoVal: D
content: Wednesday 
Answer: A
Analysis: $2018$ was a common year which had $365$ days. Thus, January $$1$$, $$2019$$ fell on one day after Monday, which was Tuesday. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: A machine started printing posters at $$9.00 \rm a.m.$$ on Monday at the rate of $$1000$$ posters per hour. After every $$6$$ hours of printing, it was paused for an hour. How many posters were printed by $$\rm 11.00 a.m$$. the next day? 
Options:
aoVal: A
content: $$20000$$ 
aoVal: B
content: $$22000$$ 
aoVal: C
content: $$23000$$ 
aoVal: D
content: $$26000$$ 
Answer: C
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method
Problem: A shop purchased a kind of Lego at ＄$$125$$ each. It then sold them at ＄$$168$$ each. How much did the shopkeeper earn for $$5$$ Legos? 
Options:
aoVal: A
content: ＄$$190$$ 
aoVal: B
content: ＄$$200$$ 
aoVal: C
content: ＄$$210$$ 
aoVal: D
content: ＄$$215$$ 
Answer: D
Analysis: $$(168-125)\times 5 = 215$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method
Problem: Jenny paid $15$ dollars for $3$ books. How many dollars should she pay in total for the same kind of books if she bought $5$ more of them? 
Options:
aoVal: A
content: $$34$$ 
aoVal: B
content: $$37$$ 
aoVal: C
content: $$40$$ 
aoVal: D
content: $$42$$ 
aoVal: E
content: $$44$$ 
Answer: C
Analysis: $$15=3\times5$$, so $5$ dollars for each book  $$3+5=8$$, $8\times5=40$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: There are $3600$ baby chickens on a farm. The number of hens on the farm is $\dfrac{8}{9}$~of the baby chickens, and the number of roosters is $\dfrac{1}{16}$~of the number of hens. How many roosters are there on the farm? 
Options:
aoVal: A
content: $$180$$ 
aoVal: B
content: $$200$$ 
aoVal: C
content: $$100$$ 
aoVal: D
content: $$225$$ 
Answer: B
Analysis: Hens $=$ baby chickens $\times\dfrac{8}{9}$,  Roosters $=$ hens $\times\dfrac{1}{16}$,  We can write the formula as:~$3600\times\dfrac{8}{9}\times\dfrac{1}{16}=3200\times\dfrac{1}{16}=200$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base
Problem: Students in the third grade lined up and formed a square array to perform a dance. Each side of the outermost layer had $37$ students. How many students in total are there on the outermost layer? 
Options:
aoVal: A
content: $$148$$ 
aoVal: B
content: $$152$$ 
aoVal: C
content: $$144$$ 
aoVal: D
content: $$140$$ 
aoVal: E
content: $$156$$ 
Answer: C
Analysis: $$36\times 4=144$$, or $$37\times 4-4=144$$ students. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares
Problem: The mushrooms picked by $2$ white rabbits in $3$ days will be eaten by $3$ gray rabbits in $4$ days. In how many days will $15$ gray rabbits eat up mushrooms picked by $5$ white rabbits in $6$ days? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$6$$ 
Answer: D
Analysis: The mushrooms picked by $2$ white rabbits in $3$ days will be eaten by $3$ gray rabbits in $4$ days, so the mushrooms picked by $1$ white rabbits in $1$ days will be eaten by $1$ gray rabbits in $2$ days.  Thus, the mushrooms picked by $5$ white rabbits in $6$ days will be eaten by $15$ gray rabbits in $4$ days. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Problem: Jimmy\textquotesingle s father brought Jimmy three pet dogs, and Jimmy could only keep one. How many dogs did Jimmy\textquotesingle s father want to take away?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$3$$) 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$3$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$2$$ 
aoVal: E
content: $$0$$ 
Answer: D
Analysis: $3-1=2$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base
Problem: In a garage, the ratio of red cars to black cars is $$8:5$$, and the ratio of black cars to white cars is $$3:4$$. The minimum number of cars in the garage is． 
Options:
aoVal: A
content: $$20$$ 
aoVal: B
content: $$59$$ 
aoVal: C
content: $$74$$ 
aoVal: D
content: $$91$$ 
Answer: B
Analysis: The ratio of red cars to black cars is $$8:5=24:15$$; the ratio of black cars to  white cars is $$3:4 = 15:20$$. The minimum number of cars is $$24+15+20 =59$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems