math-eval/TAL-SCQ5K huggingface dataset:
Problem: Starting with some gold coins and some empty treasure chests, I tried to put $$9$$ gold coins in each treasure chest, but that left $$2$$ treasure chests empty. So instead I put $$6$$ gold coins in each treasure chest, but then I had $$3$$ gold coins left over. How many gold coins did I have? ． 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$27$$ 
aoVal: C
content: $$45$$ 
aoVal: D
content: $$63$$ 
aoVal: E
content: $$81$$ 
Answer: C
Analysis: Suppose $x$ is the number of treasure chests. Thus the number of gold coins can be represented as $$9(x-2)$$ or $$6x + 3$$. So, $$9(x-2)=6x+3$$, $$x=7$$. There are $$9\times (7-2)=45$$ gold coins. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable
Problem: On a map $4\text{cm}$ represents $50\text{km}$. The distance between town A and town B is $14\text{cm}$. A car leaves town A and travels towards town B at $35$km per hour. How long does it take the car to travel to town B? 
Options:
aoVal: A
content: $4\text{hours}$ 
aoVal: B
content: $5\text{hours}$ 
aoVal: C
content: $10\text{hours}$ 
aoVal: D
content: $14\text{hours}$ 
aoVal: E
content: $18\text{hours}$ 
Answer: B
Analysis: If $$4\textasciitilde\text{cm}$$ represents $$50\textasciitilde\text{km}$$, $$2\textasciitilde\text{cm}$$ represents $$25\textasciitilde\text{km}$$. So, their actual distance apart is $$14\div2\times 25=175\textasciitilde\text{km}$$. $175\div35=5$ hours. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units
Problem: Students guess that Norb\textquotesingle s age is $$24$$, $$28$$, $$30$$, $$32$$, $$36$$, $$38$$, $$41$$, $$44$$, $$47$$, and $$49$$. Norb says, "At least half of you guessed too low, two of you are off by one, and my age is a prime number." How old is Norb? ($$2011$$ AMC $$8$$ problem, Question \#$$21$$) 
Options:
aoVal: A
content: $$29$$ 
aoVal: B
content: $$31$$ 
aoVal: C
content: $$37$$ 
aoVal: D
content: $$43$$ 
aoVal: E
content: $$48$$ 
Answer: C
Analysis: If at least half the guesses are too low, then Norb\textquotesingle s age must be greater than $$36$$.  If two of the guesses are off by one, then his age is in between two guesses whose difference is $$2$$. It could be $$31$$, $$37$$, or $$48$$, but because his age is greater than $$36$$, it can only be $$37$$ or $$48$$.  Lastly, Norb\textquotesingle s age is a prime number so the answer must be $$37$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems
Problem: Joan needs $$250$$ pounds of metal with $$27\textbackslash\%$$ silver. If Joan combines one metal with $$23\textbackslash\%$$ silver, and another with $$43\textbackslash\%$$ silver,how much of each metal does Joan need respectively? 
Options:
aoVal: A
content: $$200$$;$$50$$ 
aoVal: B
content: $$150$$;$$100$$ 
aoVal: C
content: $$100$$;$$150$$ 
aoVal: D
content: $$50$$;$$200$$ 
Answer: A
Analysis: $$\dfrac{43\textbackslash\%-27\textbackslash\%}{27\textbackslash\%-23\textbackslash\%}=\dfrac{16}{4}=\dfrac{4}{1}$$,  $$23\textbackslash\%$$ silver:$$250\times\dfrac{4}{4+1}=200$$,  $$43\textbackslash\%$$ silver:$$250\times\dfrac{4}{4+1}=50$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base
Problem: If I start with $2$, and begin to count in $$3$$s, my $50^{}\text{th}$ number will be~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$148$$ 
aoVal: B
content: $$149$$ 
aoVal: C
content: $$150$$ 
aoVal: D
content: $$151$$ 
aoVal: E
content: $$152$$ 
Answer: B
Analysis: $2+(50-1)\times3=149$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression
Problem: Emma is $9$ years old. Anna is $12$ years old. Peter is older than Emma but younger than Anna. How old is Peter? 
Options:
aoVal: A
content: $$13$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$7$$ 
aoVal: E
content: $$5$$ 
Answer: C
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems
Source: 其它
Problem: Some kangaroos are lining at bakery. Tom is the third kangaroo from the back, and the fifth from the front. How many kangaroos are there lining up in total? 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$6$$ 
aoVal: D
content: $$5$$ 
Answer: B
Analysis: $$3+5-1=7$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: Henderson has $$9$$ sweets more than Flora. After teacher Johnny gave each of them $$7$$ more sweets, they have a total of $$43$$ sweets. How many sweets does Flora has at first? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$17$$ 
aoVal: E
content: $$19$$ 
Answer: B
Analysis: $$43-14-9=20$$  $$20\div2=10$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: If today is a Tuesday, then $$15$$ days ago was a.　 
Options:
aoVal: A
content: Saturday　 
aoVal: B
content: Sunday　 
aoVal: C
content: Monday　 
aoVal: D
content: Wednesday　 
Answer: C
Analysis: Today is Tues. $$14$$ days ago was Tues. $$15$$ days ago was Mon. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: In a jar of red, green, and blue marbles, all but $$6$$ are red marbles, all but $$8$$ are green, and all but $$4$$ are blue. How many marbles are in the jar? 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: $$10$$ 
Answer: D
Analysis: Suppose there are $$x$$ red marbles, $$y$$ green marbles and $$z$$ blue marbles. Thus, we can get  $$\begin{cases} x+y=4① \textbackslash\textbackslash{} y+z=6②\textbackslash\x+z=8③\end{cases}$$,  ①$$+$$②$$+$$③: $$2x+2y+2z=18$$, $$x+y+z=9$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems
Problem: In a jar of red, green, and blue marbles, all but $$16$$ are red marbles, all but $$18$$ are green, and all but $$14$$ are blue. How many marbles are in the jar? ． 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$18$$ 
aoVal: C
content: $$20$$ 
aoVal: D
content: $$24$$ 
aoVal: E
content: $$36$$ 
Answer: D
Analysis: Suppose there are $$x$$ red marbles, $$y$$ green marbles and $$z$$ blue marbles. Thus, we can get  $$\begin{cases} x+y=14① \textbackslash\textbackslash{} y+z=16②\textbackslash\x+z=18③\end{cases}$$,  ①$$+$$②$$+$$③: $$2x+2y+2z=48$$, $$x+y+z=24$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems
Problem: Sanjay let me finish his box of mints.  He had eaten $$\frac{5}{8}$$ of them.  If $$36$$ mints were left for me, how many mints were there in the box at the start? 
Options:
aoVal: A
content: $$96$$ 
aoVal: B
content: $$58$$ 
aoVal: C
content: $$68$$ 
aoVal: D
content: $$36$$ 
aoVal: E
content: $$56$$ 
Answer: A
Analysis: $36\div(1-\dfrac{5}{8})=96$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base
Problem: Calculate:  $\frac{1}{1\times 7}+\frac{1}{7\times 13}+\frac{1}{13\times 19} + \cdots +\frac{1}{1207\times 1213}$ 
Options:
aoVal: A
content: $\frac{1212}{1213}$ 
aoVal: B
content: $\frac{303}{1213}$ 
aoVal: C
content: $\frac{202}{1213}$ 
aoVal: D
content: $\frac{1212}{6065}$ 
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: There are $$300$$ students in Think Primary School. Three-tenths of the students are in year $$5$$ and three-fifths of the year $$5$$ students are girls. How many year $$5$$ girls are there in Think Primary School? 
Options:
aoVal: A
content: $$36$$ 
aoVal: B
content: $$48$$ 
aoVal: C
content: $$54$$ 
aoVal: D
content: $$60$$ 
aoVal: E
content: $$90$$ 
Answer: C
Analysis: $$300\times\frac{3}{10}\times\frac{3}{5}=54$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages
Source: 其它
Problem: The five-digit number $411A2$ is a multiple of $9$. What digit does A represent? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$1$$ 
aoVal: C
content: $$2$$ 
aoVal: D
content: $$3$$ 
aoVal: E
content: None of the above 
Answer: B
Analysis: From the Divisibility Rule of $9$, the sum of the digit of 411A2 must be divisible by $9$.  $4 + 1 + 1+ 4 + 2 = 8 + A$  Hence A = $1$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division
Source: 其它
Problem: Iron Man\textquotesingle s flying speed is $$12,250$$km/h, which is $$25$$ times the speed of a regular airplane. What is the speed of the airplane? 
Options:
aoVal: A
content: $$490$$km/h 
aoVal: B
content: $$500$$km/h 
aoVal: C
content: $$4900$$km/h 
aoVal: D
content: $$5000$$km/h 
aoVal: E
content: $$245$$km/h 
Answer: A
Analysis: The speed of the airplane is~$12250\div25=490$km/h. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples
Problem: I am threading blue and purple beads onto a necklace in the ratio $$2 : 5$$. I use $$98$$ beads in total. How many more purple beads than blue do I use? 
Options:
aoVal: A
content: $$7$$ 
aoVal: B
content: $$35$$ 
aoVal: C
content: $$42$$ 
aoVal: D
content: $$14$$ 
aoVal: E
content: $$49$$ 
Answer: C
Analysis: The ratio $$2 : 5$$ means that $$2$$ in $$7$$ beads are blue and $$5$$ in $$7$$ purple. Since $$98 \div 7 = 14$$, there are $$28$$ blue and $$70$$ purple beads, hence $$70 - 28 = 42$$ more purple than blue. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio
Problem: If Pip was 10 years old 5 years ago, how old will he be 7 years from now? 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$14$$ 
aoVal: C
content: $$16$$ 
aoVal: D
content: $$22$$ 
aoVal: E
content: $$18$$ 
Answer: D
Analysis: $$10+5+7=22$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems
Source: 其它
Problem: Harry planted some trees around a $20$m by $20$m square garden. If there are trees planted at each of the $4$ corners, and the distance between every $2$ trees is $5$m, at least how many trees did Harry plant? 
Options:
aoVal: A
content: $$16$$ 
aoVal: B
content: $$18$$ 
aoVal: C
content: $$20$$ 
aoVal: D
content: $$22$$ 
Answer: A
Analysis: $20 \div 5 = 4$ intervals on each side  $4+1=5$ trees on each side  $4\times5-4=16$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Circular Paths->Planting Trees (circular path)
Source: 其它
Problem: There is a basket of peaches. Three students take turns to take peaches. Sana takes $2$ less than the half of peaches. Joann takes $2$ more than half of the remaining peaches. Now, there are $5$ peaches in the basket. How many peaches are there in the basket at beginning? 
Options:
aoVal: A
content: $$20$$ 
aoVal: B
content: $$22$$ 
aoVal: C
content: $$24$$ 
aoVal: D
content: $$28$$ 
aoVal: E
content: $$18$$ 
Answer: C
Analysis: $$5+2=7$$  $7+7=14$  $14-2=12$  $12+12=24$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: Mother\textquotesingle s Day in $$2020$$ was May $$10$$th, which was Sunday. Father\textquotesingle s Day in $$2020$$ was June $$21$$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: Andy has $$6$$ candies.  Bob has twice as many candies as Andy.  Chloe has $$4$$ times as many candies as Andy.  How many candies do they have altogether? 
Options:
aoVal: A
content: $$24$$ 
aoVal: B
content: $$35$$ 
aoVal: C
content: $$42$$ 
aoVal: D
content: $$48$$ 
Answer: C
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples
Problem: James wants to make $5$ cakes. Each day he makes one cake. He made the first cake on Tuesday. What day of the week will it be when he makes the last cake? (Adapted from 2011 Math Kangaroo Problem, Level 3-4, Question \#2) 
Options:
aoVal: A
content: Wednesday 
aoVal: B
content: Thursday 
aoVal: C
content: Friday 
aoVal: D
content: Saturday 
aoVal: E
content: Sunday 
Answer: D
Analysis: Count day by day directly. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Source: 其它
Problem: Half a loaf of bread costs $$6$$ pence more than one-fourth of a loaf of bread. How many pence does a whole loaf of bread cost? ($$1998$$ Math Kangaroo Problem, Level $$3-4$$, Question \#$$14$$) 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$12$$ 
aoVal: C
content: $$18$$ 
aoVal: D
content: $$24$$ 
aoVal: E
content: $$30$$ 
Answer: D
Analysis: One-fourth of a loaf of bread is "$$1$$ unit". Half a loaf of bread is "$$2$$ units".  One-fourth of a loaf of bread: $$6 \div (2-1) =6$$. A whole loaf of bread: $$6 \times 4 =24$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base
Problem: Many years ago, $$1^{\text{st}}$$ of May was a Friday. Which day of the week was $$23^{\text{rd}}$$ of May in that year? 
Options:
aoVal: A
content: Thursday 
aoVal: B
content: Friday 
aoVal: C
content: Saturday 
aoVal: D
content: Sunday 
aoVal: E
content: Monday 
Answer: C
Analysis: First Friday: 　　　$$1^{\text{st}}$$ of May  Second Friday: 　　$$8^{\text{th}}$$ of May  Third Friday: 　　　$$15^{\text{th}}$$ of May  Fourth Friday: 　　$$22^{\text{nd}}$$ of May  $$23^{\text{rd}}$$ of May was a \textbf{Saturday} in that year. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: There are stools and chairs in the room. Each stool has $$3$$ legs, and each chair has $$4$$ legs. Altogether there are $$17$$ legs. How many chairs are there in the room? 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$2$$ 
aoVal: E
content: $$1$$ 
Answer: D
Analysis: If there are five stools, the chairs have $17-3\times5=2$ legs, which is not applicable. If there are four stools, the chairs have $17-3\times4=5$~ legs, which is also not applicable. If there are three stools, the chairs have $17-3\times3=8$ legs, which implies that there are $8\div4=2$ chairs and is applicable according to the question. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis
Problem: The cost of my algebra book is $$200\textbackslash\%$$ of that of my geometry book.  The cost of my geometry book is $$\frac{4}{3}$$ that of my calculus book. If my calculus book costs ＄$$21$$, how much do all $$3$$ books cost together? 
Options:
aoVal: A
content: ＄$$28$$ 
aoVal: B
content: ＄$$56$$ 
aoVal: C
content: ＄$$84$$ 
aoVal: D
content: ＄$$105$$ 
Answer: D
Analysis: The cost of the calculus book is ＄$$21$$. The cost of my geometry book is ＄$$21\times \left(\frac{4}{3}\right)=$$＄$$28$$. My algebra book costs ＄$$28 \times2 =$$＄$$56$$. All $$3$$ books cost ＄$$21+$$＄$$28 +$$＄$$56 =$$＄$$105$$ in total. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base
Problem: There are $$18$$ chocolates in Swee Tuth\textquotesingle s box, $$2$$ each of $$9$$ flavours. She likes only $$6$$ of the flavours. If she picks a chocolate at random, what is the probability of her getting one she doesn\textquotesingle t like? 
Options:
aoVal: A
content: $$\frac{2}{9}$$ 
aoVal: B
content: $$\frac{1}{3}$$ 
aoVal: C
content: $$\frac{4}{9}$$ 
aoVal: D
content: $$\frac{1}{2}$$ 
aoVal: E
content: $$\frac{2}{3}$$ 
Answer: B
Analysis: Out of $$18$$ chocolates there are $$6\times2=12$$ of the flavours that she likes. So the probability of Swee Tuth getting one she doesn\textquotesingle t like is $$\frac{6}{18} =\frac{1}{3}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate
Problem: Maddie is $$2$$ years older than Lola, and Lola is $$6$$ years younger than Ellie.  How much older is Ellie than Maddie? 
Options:
aoVal: A
content: $$2$$ years 
aoVal: B
content: $$3$$ years 
aoVal: C
content: $$4$$ years 
aoVal: D
content: $$5$$ years 
aoVal: E
content: $$6$$ years 
Answer: C
Analysis: Ellie is $$6$$ years older than Lola, and Maddie is $$2$$ years older than Lola. Therefore Ellie is $$4$$ years older than Maddie. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems
Problem: Some students are going to an amusement park. If each student carries $9$ bottles of water in his or her backpack, there will be $2$ students carrying nothing; if one of the students carries $2$ bottles of water and the rest students carry $8$ bottles each, all the bottles of water can be carried to the park. There are~\uline{~~~~~~~~~~}~bottles of water in total that need to be carried. 
Options:
aoVal: A
content: $$80$$ 
aoVal: B
content: $$90$$ 
aoVal: C
content: $$92$$ 
aoVal: D
content: $$102$$ 
Answer: B
Analysis: Solve the problem as a problem of surplus and shortage. If each student carries $9$ bottles, there will be a shortage of $9\times2=18$ bottles;  if each student carries $8$ bottles, there will be a shortage of $8-2=6$ bottles. Therefore, there are $(18-6)\div(9-8)=12$ students and $12\times9-18=90$ bottles of water. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Distribution Conversion Problems
Problem: In a certain calendar year, there are more Mondays than Fridays, and more Sundays than Wednesdays. Which day of the week is $$1^{}\text{st}$$ March in that year? 
Options:
aoVal: A
content: Monday　 
aoVal: B
content: Tuesday　 
aoVal: C
content: Wednesday　 
aoVal: D
content: Thursday　 
aoVal: E
content: Friday　 
aoVal: F
content: Saturday　 
aoVal: G
content: Sunday　 
Answer: D
Analysis: Nil 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: A worm is staying at the bottom of a well with a depth of $$13$$ metres. If it climbs up $$4$$ metres in the daytime and slips down $$1$$ metres at night, which day will it climb up to the ground? 
Options:
aoVal: A
content: The $$4$$th day 
aoVal: B
content: The $$5$$th day 
aoVal: C
content: The $$6$$th day 
aoVal: D
content: The $$7$$th day 
Answer: A
Analysis: It climbs up $$4$$ metres in the day time and slips down $$1$$ metre at night, so it climbs up $$3$$ metres in a whole day. For the first $$3$$ days, it climbs $$9$$ metres. During the day time of the forth day, it climbs $$4$$ metres and reaches the ground. Then it needs four days to climb up to the ground. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems
Problem: A jacket was on sale. The original price was ＄$$180$$, and Peter bought it at ＄$$135$$. What was the discount rate? 
Options:
aoVal: A
content: $$135\textbackslash\%$$ 
aoVal: B
content: $$180\textbackslash\%$$ 
aoVal: C
content: $$75\textbackslash\%$$ 
aoVal: D
content: $$25\textbackslash\%$$ 
Answer: D
Analysis: $$1-135\div180=25\textbackslash\%$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts
Problem: Justin said to his mom, "If I had planted three times as many flowers as I planted, I would have planted $48$ more flowers than I have planted now." How many flowers did Justin plant? 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$23$$ 
aoVal: C
content: $$24$$ 
aoVal: D
content: $$22$$ 
Answer: C
Analysis: $48\div(3-1)=24$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple
Source: 其它
Problem: Ella and George are lining up for dinner. Ella is sitting in the fifth from the front of the line, and George is sitting at the sixth from the end of the line. George and Ella are standing together. How many people are there in total?~(adapted from 2001 Math Kangaroo Problem, Level 3-4, Question \#13) 
Options:
aoVal: A
content: $$12$$ 
aoVal: B
content: $$11$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: $$8$$ 
Answer: C
Analysis: $5 + 6 - 1 = 10$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line
Problem: There are $20$ children lining up outside a theme park. John is the $14$\textsuperscript{th}~ person counting from the front of the line and Mary is the $2$\textsuperscript{th}~person counting from the back of the line. How many children are standing in line between John and Mary? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: D
Analysis: Mary is the $$20-2+1=19$$\textsuperscript{th} person in the line, so there are $$19-14-1=4$$ children are between them. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: A mixture of $80$ liters of paint is $20 \textbackslash\%$ red tint, $30 \textbackslash\%$ yellow tint and $50 \textbackslash\%$ water. $20$ liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (adapted from 2007 AMC 8, Question \#17 ) 
Options:
aoVal: A
content: $$33$$ 
aoVal: B
content: $$36$$ 
aoVal: C
content: $$39$$ 
aoVal: D
content: $$42$$ 
aoVal: E
content: $$44$$ 
Answer: E
Analysis: The original mixture contains $80 \times 30\textbackslash\% = 24$ liters of yellow tint.  $$20$$ liters of yellow tint is added to the mixture, the new mixture now has $24+20=44$ liters of yellow tint.  New percent of yellow =$\frac{44}{80+20} =44\textbackslash\% $ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems
Source: 其它
Problem: Calculate: $1^{3}+2^{3}+3^{3}+\cdots +17^{3}+18^{3}$ 
Options:
aoVal: A
content: $$4447881$$ 
aoVal: B
content: $$23409$$ 
aoVal: C
content: $$12654$$ 
aoVal: D
content: $$29241$$ 
aoVal: E
content: None of the above 
Answer: D
Analysis: D 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples
Source: 其它
Problem: A $30\textbackslash\%$ sugar solution contains $12$ g of pure sugar. How many g of solution are there? 
Options:
aoVal: A
content: $30$ g 
aoVal: B
content: $40$ g 
aoVal: C
content: $50$ g 
aoVal: D
content: $60$ g 
Answer: B
Analysis: $$12\div30\textbackslash\%=40$$ g. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems