math-eval/TAL-SCQ5K huggingface dataset:
Problem: There are $$7$$ numbers with an average of $$79$$. After eliminating a number, the average of the remaining numbers is $$84$$. What is the eliminated number? 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$19$$ 
aoVal: C
content: $$29$$ 
aoVal: D
content: $$49$$ 
aoVal: E
content: $$60$$ 
Answer: D
Analysis: $(84-79)\times6=30$, $79-30=49$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems 
Source: 其它
Problem: If today is Saturday, what day of the week will be 100 days later? 
Options:
aoVal: A
content: Sunday 
aoVal: B
content: Friday 
aoVal: C
content: Monday 
aoVal: D
content: Thursday 
Answer: C
Analysis: $$100\div7=14$$$$\cdots \cdots 2$$,  So 2 days later is Monday. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates
Problem: Some zoo animals are standing in an array to prepare for the Zoo Olympics. The fox, Bob, finds that no matter whether he counts from front to back, back to front, left to right, or right to left, he is always the $$3$$\textsuperscript{rd} in line. How many animals are there in the array?~\uline{~~~~~~~~~~}~ 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$25$$ 
aoVal: D
content: $$36$$ 
Answer: C
Analysis: $$3+3-1=5$$.  Since each row and column has $$5$$ animals, there are $$5\times5=25$$ animals in total. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number of People in a Rectangular Array
Problem: The sum of two natural numbers is equal to $$77$$. If the first number is multiplied by $$8$$ and the second by $$6$$, then those products are equal. The larger of these numbers is~\uline{~~~~~~~~~~}~. ($$2004$$ Math Kangaroo Problems, Level $$5-6$$, Question \#$$20$$) 
Options:
aoVal: A
content: $$23$$ 
aoVal: B
content: $$33$$ 
aoVal: C
content: $$43$$ 
aoVal: D
content: $$44$$ 
aoVal: E
content: $$54$$ 
Answer: D
Analysis: Suppose one of the numbers is $x$. $8x=6(77-x)$, $x=33$. Thus, these two numbers are $33$ and $44$. The larger one is $44$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple->Problems of Sum and Multiplication with Indirect Multiples
Problem: Mother\textquotesingle s Day in $$2020$$ was May $$10$$\textsuperscript{th}, which was Sunday. Father\textquotesingle s Day in $$2020$$ was June $$21$$\textsuperscript{st}. On what day did Father\textquotesingle s Day 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 $$42 \div 7 = 6$$, which means the Father\textquotesingle s Day fell on Sunday as well. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: Zosia is drawing kangaroos.The first one is blue, the next one green, the one after it red, the fourth one yellow, and then again blue, green, red, yellow, and so on, in the same order. What color will the seventeenth kangaroo be? (2003 Math Kangaroo Problem, Level 3-4, Question \#4) 
Options:
aoVal: A
content: $$$$Blue 
aoVal: B
content: $$$$Green 
aoVal: C
content: $$$$Red 
aoVal: D
content: $$$$Black 
aoVal: E
content: $$$$Yellow 
Answer: A
Analysis: $17\div4=4R1$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation
Problem: Ella says:" I can run $18\text{km}$ every hour."  Vivian says: " Haha, I am the faster runner because I can run $100\text{m}$ every $21\text{s}$."  Vivian\textquotesingle s statement is~\uline{~~~~~~~~~~}~because it only takes Ella~\uline{~~~~~~~~~~}~$\text{s}$ to run $100\text{m}$. 
Options:
aoVal: A
content: correct, 200 
aoVal: B
content: correct, 60 
aoVal: C
content: wrong, 20 
aoVal: D
content: wrong, 10 
Answer: C
Analysis: $\frac{18km}{1h}=\frac{18000m}{3600s}=5m/s$  $100\div 5=20s$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate
Source: 其它
Problem: Anna, Bridgit and Carol run in a $$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$$ metres behind Anna. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Problem: There were $$31$$ runners competing in a race. The number of runners who finished before John is four times smaller than the number of runners who finished later than John. At what place did John finish? ($$1998$$ Math Kangaroo Problem, Level $$3-4$$, Question \#$$13$$) 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$20$$ 
aoVal: E
content: $$21$$ 
Answer: B
Analysis: $$(31-1) \div (4+1) = 6$$  $$6+1=7$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple
Problem: Mike has a bookcase with three layers, and the ratio of books placed on the upper, middle and lower layers is $$5:6:4$$. Given that there are $$240$$ books on the middle level,  books should be removed from middle level and added to the lower level so that the number of books on each level can be exactly the same. 
Options:
aoVal: A
content: $$48$$ 
aoVal: B
content: $$40$$ 
aoVal: C
content: $$60$$ 
aoVal: D
content: $$80$$ 
Answer: B
Analysis: Lower level: $$240\div6\times4=160$$,  The number of books to be added to the lower level: $$(240-160)\div2=40$$.  So, the answer is $$\text{B}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with an Invariant Part
Problem: Tom and Jerry have to mail $$2000$$ envelopes for a new marketing campaign. Jerry can mail $$120$$ envelopes per hour. With Tom\textquotesingle s help, they can get the job done in $$10$$ hours. How long will it take Tom to finish the job by himself? 
Options:
aoVal: A
content: $$24$$ 
aoVal: B
content: $$25$$ 
aoVal: C
content: $$30$$ 
aoVal: D
content: $$80$$ 
Answer: B
Analysis: Working together: $$2000\div10=200$$ envelopes per hour.  Tom: $$200-120=80$$ envelops per hour, $$2000\div80=25$$ hours. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems
Problem: A series of colored lanterns are arranged in the pattern: red, red, red, yellow, yellow, red, red, red, yellow, yellow $\cdots$ The $$50$$\textsuperscript{th} lantern is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: red 
aoVal: B
content: yellow 
Answer: B
Analysis: Since $$50\div(3+2)=10$$ which has no remainder, the $$50^{\text{th}}$$ colored lantern is yellow. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation
Problem: In a farm, there is an equal number of cows, sheep, and chickens. These animals have $250$ legs in total. How many sheep are there? 
Options:
aoVal: A
content: $$18$$ 
aoVal: B
content: $$23$$ 
aoVal: C
content: $$25$$ 
aoVal: D
content: $$33$$ 
aoVal: E
content: $$38$$ 
Answer: C
Analysis: Group $1$ of each kind of animals together, and there are $4+4+2=10$ legs in each group. There are $250\div10=25$ groups, so there are $25$ sheep. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems
Source: 其它
Problem: If Kelly was 12 years old 4 years ago, how old will she be 8 years from now? 
Options:
aoVal: A
content: $$21$$ 
aoVal: B
content: $$14$$ 
aoVal: C
content: $$26$$ 
aoVal: D
content: $$22$$ 
aoVal: E
content: $$24$$ 
Answer: E
Analysis: $$12+4+8=24$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems
Source: 其它
Problem: There are $$20$$ students in a class lining up for recess. Mike is the $$7$$\textsuperscript{th} counting from front to back. How many students are behind Mike? What is his position counting from back to front? 
Options:
aoVal: A
content: $$12$$, $$13^{\rm th}$$ 
aoVal: B
content: $$13$$, $$14^{\rm th}$$ 
aoVal: C
content: $$13$$, $$12^{\rm th}$$ 
aoVal: D
content: $$14$$, $$13^{\rm th}$$ 
Answer: B
Analysis: The number of students behind Mike plus the position of Mike equals the total number of students in the class. So there are $$13$$ students behind Mike: $$20-7=13$$. However Mike is not included in these $$13$$ students, which means Mike is the $$14$$\textsuperscript{th} student counting from back to front. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Order of one Character
Problem: The ratio of your pears to oranges is $$3:7$$, and you have $$15$$ pears. How many oranges do you have? 
Options:
aoVal: A
content: $$7$$ 
aoVal: B
content: $$15$$ 
aoVal: C
content: $$21$$ 
aoVal: D
content: $$35$$ 
Answer: D
Analysis: $$3:7=15:x→\dfrac{3}{7}=\dfrac{15}{x}→3x=105→x=35$$ or $$3$$ multiply by $$5$$ equals $$15$$, so if we multiply $$5$$ by $$7$$, we get $$35$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio
Problem: $$10$$ trees are planted at equal distance along a river. The distance between the $$1^{st}$$ and the $$3^{rd}$$ tree is $$20$$ metres. What is the distance between the $$7^{th}$$ and $$9^{th}$$ tree? 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$50$$ 
aoVal: D
content: $$70$$ 
aoVal: E
content: $$90$$ 
Answer: B
Analysis: They are having the same number of intervals. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems
Source: 其它
Problem: The average of John and Leo's ages is Kelly's age. The average of Kelly and Mila's ages is Leo's age. Of the four children, John is the youngest and Mila the oldest. The average of John and Mila's ages is 11.  What is the total of the ages of Kelly and Leo? 
Options:
aoVal: A
content: $$14$$ 
aoVal: B
content: $$16$$ 
aoVal: C
content: $$18$$ 
aoVal: D
content: $$20$$ 
aoVal: E
content: $$22$$ 
Answer: E
Analysis: PMC 2019 21 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems 
Source: 其它
Problem: Marcus has $$75$$ toy cars. $$\frac{1}{5}$$ of his toy cars are black, $$\frac{2}{15}$$ of the remainder are white, and the rest are grey. He hasmore black toy cars than white toy cars. 
Options:
aoVal: A
content: $$7$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$11$$ 
Answer: A
Analysis: $75\div5=15$ toy cars are black.  $15\times4=60$ toy cars are white or grey.  $60\div15\times2=8$ toy cars are white.  He has $15-8=7$ more black toy cars than white toy cars. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base
Problem: Miya is $3$ years old this year, and her brother is $3$ years older than her. How old her brother will be $2$ years later?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$7$$) 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$9$$ 
Answer: D
Analysis: When Miya is $3$, her brother is $6$, so $2$~years later, her brother is  $8$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages
Problem: Five years ago, Jennifer\textquotesingle s age was five times Jason\textquotesingle s age. Now, Jennifer\textquotesingle s age is four times Jason\textquotesingle s age. How old is Jennifer now? 
Options:
aoVal: A
content: $$20$$ 
aoVal: B
content: $$60$$ 
aoVal: C
content: $$80$$ 
aoVal: D
content: $$100$$ 
aoVal: E
content: None of the above 
Answer: C
Analysis: Let Jason\textquotesingle s age five years ago be 1 unit. Then Jennifer\textquotesingle s age was 5 units.  Now, Jason\textquotesingle s age is 1 unit + 5 and Jennifer\textquotesingle s age is 5 units + 5. We also know that Jennifer\textquotesingle s age is four times Jason\textquotesingle s age or 4 x (1 unit + 5) = 4 units + 20.  Then:~  5 units + 5 = 4 units + 20  5 units - 4 units = 20 - 5  1 unit = 15  Jennifer is 5 units + 5 = 5x15 + 5 = 80 years old now. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems
Source: 其它
Problem: The number of weeks in $$139$$ days is most nearly equal to． 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$14$$ 
aoVal: C
content: $$19$$ 
aoVal: D
content: $$20$$ 
Answer: D
Analysis: The number of weeks in $$139$$ days is most nearly $$140\div 7=20$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division
Problem: When Patience asked her Granddad how old he was, he answered, "I am $$34$$ now and will be $$33$$ on my birthday." She looked confused so he added, "After being $$50$$ for a year I started counting backwards on each birthday. " How old will he actually be on his birthday?　 
Options:
aoVal: A
content: $$33$$ 
aoVal: B
content: $$34$$ 
aoVal: C
content: $$56$$ 
aoVal: D
content: $$67$$ 
aoVal: E
content: $$83$$ 
Answer: D
Analysis: When Granddad would have claimed to be $$49$$ he was actually $$51$$, $$48$$ when he was actually $$52$$- in every case his claimed age and his real age have a total of  $$100$$. So this year his age is $$100-33=67$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems
Problem: Calculate: $1^{2}+2^{2}+3^{2}+\cdots +20^{2}+21^{2}$ 
Options:
aoVal: A
content: $$231$$ 
aoVal: B
content: $$2870$$ 
aoVal: C
content: $$3311$$ 
aoVal: D
content: $$53361$$ 
aoVal: E
content: None of the above 
Answer: C
Analysis: C 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples
Source: 其它
Problem: In the window of Bradley\textquotesingle s Bicycle Bazaar there are some unicycles, some bicycles and some tricycles. Laura sees that there are seven saddles in total, thirteen wheels in total and more bicycles than tricycles.  How many unicycles are in the window? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: B
Analysis: JMC 2017 22 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems
Source: 其它
Problem: Red and green dragons lived in a cave. Each red dragon had $$6$$ heads, $$8$$ legs, and $$2$$ tails. Each green dragon had $$8$$ heads, $$6$$ legs, and $$4$$ tails. There were $$44$$ tails altogether, and there were $$6$$ less green legs than red heads. How many red dragons lived in the cave? ($$2003$$ Math Kangaroo Problems, Level $$5-6$$, Question \#$$29$$) 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: $$10$$ 
Answer: C
Analysis: Suppose there are $x$ red dragons and $y$ green dragons. $2x+4y=44$ and $6x-6y=6$. We can get that $y=7$ and $x=8$. Thus, there are $8$ red dragons. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis->Basic Type->Non-typical Types
Problem: There are $$20$$ students in a class lining up for recess. Mike is the $$7$$\textsuperscript{th} counting from front to back. How many students are behind Mike? What is his position counting from back to front? 
Options:
aoVal: A
content: $$12$$, $$13$$ 
aoVal: B
content: $$13$$, $$14$$ 
aoVal: C
content: $$13$$, $$12$$ 
aoVal: D
content: $$14$$, $$13$$ 
Answer: B
Analysis: The number of students behind Mike plus the position of Mike equals the total number of students in the class. So there are $$13$$ students behind Mike: $$20-7=13$$. However Mike is not included in these $$13$$ students, which means Mike is the $$14$$\textsuperscript{th} student counting from back to front. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Order of one Character
Problem: A bookstore purchases $$20$$ story books for ＄$$820$$. If the bookstore wants to earn ＄$$12$$ for each book, what is the selling price of each book? 
Options:
aoVal: A
content: ＄$$50$$ 
aoVal: B
content: ＄$$51$$ 
aoVal: C
content: ＄$$52$$ 
aoVal: D
content: ＄$$53$$ 
Answer: D
Analysis: $$\frac{820}{20}+12=41+12=53$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable
Problem: Henry starts to read a $$290$$-page book on a Monday. He reads four pages every day except on Sundays when he reads $$25$$ pages. He will read the book starting from page~\uline{~~~~~~~~~~}~next Monday. 
Options:
aoVal: A
content: $$24$$ 
aoVal: B
content: $$49$$ 
aoVal: C
content: $$50$$ 
aoVal: D
content: $$240$$ 
Answer: C
Analysis: $$25+6\times 4=49$$，$$49+1=50$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division
Problem: There are $$10$$ blind boxes on the desk, and each blind box contains two toys. Now there are $$16$$ toys in hands. How many blind boxes remain？(adapted from $$2010$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$15$$) 
Options:
aoVal: A
content: $$2$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$3$$ 
Answer: A
Analysis: $$16$$ toys means $$8$$ blind boxes are opened.  There are $$10$$-$$8$$=$$2$$ blind boxes that have not been opened. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method
Problem: A salt solution is made by mixing $$8$$ ounces of pure salt and $$32$$ ounces of water. Find the percent concentration of the solution. 
Options:
aoVal: A
content: $$10\textbackslash\%$$ 
aoVal: B
content: $$15\textbackslash\%$$ 
aoVal: C
content: $$20\textbackslash\%$$ 
aoVal: D
content: $$25\textbackslash\%$$ 
Answer: C
Analysis: $$8\div(8+32)=20\textbackslash\%$$.  ~~ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems
Problem: The speed of high-speed train is approximately $$350$$ kilometers per hour, while the walking speed of a person is approximately $$5$$ meters per second.  Approximately, how many times is the speed of a high-speed train faster than the walking speed of a person?． 
Options:
aoVal: A
content: $$2 $$ 
aoVal: B
content: $$20 $$ 
aoVal: C
content: $$70 $$ 
aoVal: D
content: $$200 $$ 
aoVal: E
content: $$700$$ 
Answer: B
Analysis: The speed of high-speed train is approximately $$350$$ kilometers per hour, which is approximately $$100$$ meters per second. So its speed is roughly $$20$$ times faster than $$5$$ $$ meters per second. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples
Problem: If February is a month that contains Friday $$13^{}\text{th}$$, what day of the week is February $$1$$st?． 
Options:
aoVal: A
content: Sunday　 
aoVal: B
content: Monday　 
aoVal: C
content: Wednesday　 
aoVal: D
content: Thursday　 
aoVal: E
content: Saturday　 
Answer: A
Analysis: We can count backward by days or by weeks. Count a few weeks back to find that February $$6$$ is a Friday. Then count a few days back to find that February $$1$$ is a Sunday. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: Grandpa suggested dividing all the peanuts between the family members in the following way: one person would get $5$ kilos, two people would get $4$ kilos each, four people would get $2$ kilos each, one person would get $6$ kilos, and one person would not get any peanuts. Grandma suggested dividing the peanuts equally among all of the family members. How many people would get more peanuts in grandma\textquotesingle s suggestion than grandpa\textquotesingle s? (adapted from 2005 Math Kangaroo Problem, Level 5-6, Question \#14) 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
aoVal: E
content: $$7$$ 
Answer: C
Analysis: Grandma\textquotesingle s suggestion: $(1\times 5 + 2\times 4+4\times 2+1\times 6+1\times 0)\div(1+2+4+1+1) = 27\div9=3$  Thus, there are $4+1=5$ people get more peanuts. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems 
Source: 其它
Problem: Study the pattern below. The $$100^{}\rm {th}$$ letter is  .  $$A A B B C A A B B C A A B B C A A \cdots$$ 
Options:
aoVal: A
content: $$A$$ 
aoVal: B
content: $$B$$ 
aoVal: C
content: $$C$$ 
Answer: C
Analysis: $$100$$~$\div$ $$5$$ = $$20$$ $$R0$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation
Problem: Given that May $2$nd of a given year is a Thursday, what day is May $29$th of the same year? 
Options:
aoVal: A
content: Saturday 
aoVal: B
content: Wednesday 
aoVal: C
content: Thursday 
aoVal: D
content: Tuesday 
Answer: B
Analysis: $29-2=27$ days later, it will be May $29$th. $27\div7=3R6$, which means May $29$th is Wednesday. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems
Source: 其它
Problem: A $$16$$-quart radiator is filled with water.Four quarts are removed and replaced with pure antifreeze liquid.Then four quarts of the mixture are removed and replaced with pure antifreeze.This is done a third and a fourth time.The fractional part of the final mixture that is water is． 
Options:
aoVal: A
content: $$\frac{81}{256}$$ 
aoVal: B
content: $$\frac{27}{64}$$ 
aoVal: C
content: $$\frac{37}{64}$$ 
aoVal: D
content: $$\frac{175}{256}$$ 
Answer: A
Analysis: After the first time:$$1\times \frac{12}{16}+0\times \frac{4}{16}=\frac{3}{4}$$.  After the second time:$$\frac{3}{4}\times \frac{12}{16}+0 \times \frac{4}{16}= \frac{9}{16}$$.  After the third time:$$\frac{9}{16}\times \frac{12}{16}+0 \times \frac{4}{16}= \frac{27}{64}$$.  After the fourth time:$$\frac{27}{64}\times \frac{12}{16}+0 \times \frac{4}{16}= \frac{81}{256}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants
Problem: On a map of the Andes, if $2$ $\text{cm}$ represents $6000$ $\text{km}$, then  ~represents $300$ $\text{km}$ . 
Options:
aoVal: A
content: $$0.1$$ 
aoVal: B
content: $$0.5$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$20$$ 
Answer: A
Analysis: If $2$ $\text{cm}$ represents $6000\text{km}$, $1\text{cm}$ represents $3000\text{km}$, and $0.1\text{cm}$ represents $300\text{km}$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units