math-eval/TAL-SCQ5K huggingface dataset:
Problem: In a class of pupils, $80\textbackslash\%$ participated in basketball, $85\textbackslash\%$ participated in football, $74\textbackslash\%$ participated in softball and $68\textbackslash\%$ participated in squash. Find the minimum percentage of pupils who participated in all the four sports events. 
Options:
aoVal: A
content: $7\textbackslash\%$ 
aoVal: B
content: $10\textbackslash\%$ 
aoVal: C
content: $12\textbackslash\%$ 
aoVal: D
content: $15\textbackslash\%$ 
aoVal: E
content: None of the above 
Answer: A
Analysis: Least percentage of pupils who participated in both basketball and football  $=80\textbackslash\%+ 85\textbackslash\%-100\textbackslash\% =65\textbackslash\%$,  Least percentage of pupils who participated in basketball, football and softball  $=65\textbackslash\%+74\textbackslash\%-100\textbackslash\% =39\textbackslash\%$,  Least percentage of pupils who participated in basketball, football, softball and squash  $=39\textbackslash\%+ 68\textbackslash\%-100\textbackslash\% = 7\textbackslash\%$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate
Problem: Simon has two identical aquariums. There are $$26$$ quarts of water in one, and $$42$$ quarts of water in the other. How many quarts of water does Simon need to pour from the second aquarium into the first in order to have the same amount of water in both? 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$16$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$8$$ 
Answer: D
Analysis: Difference: $42-26=16$  Move: Half of $16=8$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Giving and Receiving
Problem: In $$20$$ years, Li will be $$3$$ times as old as he is now. How old will he be in $$10$$ years? 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$30$$ 
aoVal: D
content: $$50$$ 
Answer: B
Analysis: In $$20$$ years, Li will be $$3$$ times his age now, so $$20$$ must be twice his age now. Thus, Li is $$10$$ now and will be $$20$$ in $$10$$ years. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->When..., When... Type Age Problems
Problem: When Paul is $$4$$ years old, his brother Peter is $$7$$ years old. How old is Paul when Peter is $$10$$ years old?  Paul is~\uline{~~~~~~~~~~}~years old. 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$8$$ 
Answer: B
Analysis: We can find their age difference is $$7-4=3$$. It will never change. So when Peter is $$10$$ years old, Paul is $$10-3=7$$ years old. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems
Problem: If Paul gives $$6$$ candies to Billy, they will have the same number of candies. At beginning, Paul has $$17$$ candies. How many candies does Billy have, originally? 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$9$$ 
Answer: A
Analysis: Their difference: $$6+6=12$$  Billy: $$17-12=5$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: Su Li has the same number of ten-cent and fifty-cent coins. The total value is ＄$$6$$. How many coins does she have in all? 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$36$$ 
aoVal: D
content: $$60$$ 
aoVal: E
content: None of the above 
Answer: B
Analysis: $$10u + 50u = 600$$  Thus, $$1u = 10$$, in total we have $$2u=20$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method
Problem: Andy is $18$ years old and his mother is $$54$$ years old now. In how many years\textquotesingle{} time will the sum of their ages be $$90$$? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$14$$ 
aoVal: C
content: $$18$$ 
aoVal: D
content: $$28$$ 
Answer: A
Analysis: $$18+54 = 72$$  $$90-72 = 18$$  $$18\div2=9$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems
Problem: Together, Mom Kangaroo and her son Jumper weigh $60$ kilograms. Mom Kangaroo alone weighs $52$ kilograms. How much does Jumper weigh? ($$2019$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$3$$) 
Options:
aoVal: A
content: 2 kilograms 
aoVal: B
content: 4 kilograms 
aoVal: C
content: 8 kilograms 
aoVal: D
content: 30 kilograms 
aoVal: E
content: 46 kilograms 
Answer: C
Analysis: Jumper\textquotesingle s weight is Mom Kangaroo and Jumper\textquotesingle s weight minus the mom\textquotesingle s weight. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction
Source: 其它
Problem: There are three books, Chinese, Math, and English. Sissy wants to put them in bookcase. How many ways are there for three books to put? 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$4$$ 
aoVal: D
content: $$3$$ 
Answer: A
Analysis: List out all the possible ways in order.  $C A E$  $C E A$  $A C E$  $A E C$  $E C A$  $E A C $ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: Alex had $76.  He spent some of it in a shop.  Then he gave half of what he had left to Charlie.  Charlie spent a quarter of what Alex gave him on lunch.  Charlie spent $9 on lunch.  How much did Alex spend in the shop? 
Options:
aoVal: A
content: $4 
aoVal: B
content: $12 
aoVal: C
content: $14 
aoVal: D
content: $36 
aoVal: E
content: $40 
Answer: A
Analysis: Charlie\textquotesingle s 1/4 is 9, so Charlie gets 4\times 9=36 dollars, and Alex is left with 36+36=72 dollars, so he spends 76-72=4 dollars 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: Min Ho deposited ＄$$20 000$$ into a bank at the beginning of the year. The annual interest for depositing money into the bank was $$5\textbackslash\%$$. How much did Min Ho have in the bank at the end of the year if he did not take out any money from the bank?． 
Options:
aoVal: A
content: $$\textbackslash$1000$$ 
aoVal: B
content: $$\textbackslash$19 000$$ 
aoVal: C
content: $$\textbackslash$21 000$$ 
aoVal: D
content: $$\textbackslash$31 000$$ 
Answer: C
Analysis: He has $20000 \times 1.05 = \textbackslash$21000$ at the end of the year. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts
Problem: The pages of a book are numbered 1, 2, 3 $\cdots$ . In total, it takes 852 digits to number all the pages of the book. What is the number of the last page? 
Options:
aoVal: A
content: $$215$$ 
aoVal: B
content: $$314$$ 
aoVal: C
content: $$320$$ 
aoVal: D
content: $$329$$ 
aoVal: E
content: $$422$$ 
Answer: C
Analysis: omitted  jmc 2007 \#24 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem
Source: 其它
Problem: Eddie and Frank can complete a job together in $$15$$ days. Eddie can do it alone in $$20$$ days. Frank can do it alone indays. 
Options:
aoVal: A
content: $$30$$ 
aoVal: B
content: $$40$$ 
aoVal: C
content: $$45$$ 
aoVal: D
content: $$60$$ 
Answer: D
Analysis: $$\frac{1}{15}-\frac{1}{20}=\frac{1}{60}$$,  $$1\div\frac{1}{60}=60$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems
Problem: There are $$600$$ pupils in Pip\textquotesingle s school, with $$30$$ more girls than boys. How many girls are at Pip\textquotesingle s school? 
Options:
aoVal: A
content: $$270$$ 
aoVal: B
content: $$300$$ 
aoVal: C
content: $$315$$ 
aoVal: D
content: $$330$$ 
aoVal: E
content: $$345$$ 
Answer: C
Analysis: Let there be $$g$$ girls in Pip\textquotesingle s school. Then there are $$(g-30)$$ boys at the school. So $$g+g-30=600$$. Therefore $$2g=630$$, that is $$g=315$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference
Problem: A ship was attacked by pirates. One by one the pirates climb a rope to get on the ship. The pirate captain was the $$8$$\textsuperscript{th}~pirate to climb in line, and there were as many pirates in front of him as behind him. How many pirates climbed the rope? (2015 Math Kangaroo Problem, Level 1 - 2, Question \#18)  $$\textasciitilde$$  $$\textasciitilde$$  $$\textasciitilde$$  $$\textasciitilde$$  $$\textasciitilde$$  $$\textasciitilde$$ 
Options:
aoVal: A
content: $$7$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$12$$ 
aoVal: D
content: $$15$$ 
aoVal: E
content: $$16$$ 
Answer: D
Analysis: The pirate captain was the $$8$$\textsuperscript{th}~pirate and there were as many pirates in front of him as behind him, which means there were $$7$$ pirates in front of him and there were also $$7$$ pirates behind him. The total number of pirates is~~$$7+7+1=15$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line
Problem: Half a loaf of bread costs $$6$$ pence more than one quarter of a loaf of bread. How many pence does a whole loaf of bread cost? 
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 quarter of a loaf of bread is ``$$1$$.'' Half a loaf of bread is ``$$2$$.''  One quarter 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: 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? (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: Seventh grade students from a school line up and form a square array. There are $196$ students in the outermost layer. How many students in total are there in this array? 
Options:
aoVal: A
content: $$1960$$ 
aoVal: B
content: $$2401$$ 
aoVal: C
content: $$2000$$ 
aoVal: D
content: $$2601$$ 
aoVal: E
content: $$2500$$ 
Answer: E
Analysis: The number of students on each side of the outermost layer was $$196\div 4+1=50$$. The total number of students in the array was $$50\times 50=2500$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares
Problem: My first day of vacation is May $$10$$. My last day of vacation is May $$20$$ of the same year. How many days of vacation do I have? 
Options:
aoVal: A
content: $$9$$ 
aoVal: B
content: $$ 10 $$ 
aoVal: C
content: $$11$$ 
aoVal: D
content: $$12$$ 
Answer: C
Analysis: NA 
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? ($$2012$$ AMC $$8$$ problem, Question \#$$19$$) 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: $$12$$ 
Answer: C
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: After Anna spends $\dfrac{1}{3}$~of her money and loses $\dfrac{1}{2}$~of the remainder, she then has~$\textbackslash$10$ left. She started with． 
Options:
aoVal: A
content: $\textbackslash$30$ 
aoVal: B
content: $\textbackslash$45$ 
aoVal: C
content: $\textbackslash$50$ 
aoVal: D
content: $\textbackslash$60$ 
Answer: A
Analysis: After Anna spends $\dfrac{1}{3}$~of her money, she has $\dfrac{2}{3}$~left. If she loses $\dfrac{1}{2}$~of this, she has $\dfrac{1}{3}$~left. Since$\dfrac{1}{3}=$$\textbackslash$10$,~$\dfrac{3}{3}=3\times$$\textbackslash$10=$$\textbackslash$30$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base
Problem: Given March $$25$$th of a certain year is Monday, what day of the week would May $$1$$st fall on this year? 
Options:
aoVal: A
content: Sunday 
aoVal: B
content: Monday 
aoVal: C
content: Tuesday 
aoVal: D
content: Wednesday 
Answer: D
Analysis: The cycle includes seven days, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday. There are in total $$7+30+1=38$$ days from March $$25$$ to May $$1$$. Since $$38\div7=5 \text{ R }3$$，$$$$May$$$$ $$1$$ is the $$3^{\rm rd}$$ day in the cycle, it is a Wednesday. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: In an arts and crafts class, the students cut out some triangles, quadrilaterals and pentagons. All the shapes combined have $$394$$ sides. Among them, there are $$2$$ pentagons and the number of quadrilaterals is $$82$$ more than that of triangles. How many quadrilaterals are there? 
Options:
aoVal: A
content: $$90$$ 
aoVal: B
content: $$95$$ 
aoVal: C
content: $$100$$ 
aoVal: D
content: $$105$$ 
Answer: A
Analysis: Let $$x$$ represent the number of quadrilaterals, thus the number of triangles can be represented as $$(x-82)$$.  So we have $$2\times5+4x +3(x-82)=394$$. implying that $$x =90$$. Therefore there are $$90$$ quadrilaterals. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable
Problem: Sam wants to use two kinds of sugar water with concentrations of $$5\textbackslash\%$$ and $$20\textbackslash\%$$ to make a sugar water of $$300$$g with a concentration of $$15\textbackslash\%$$. He correctly calculated the required ratio of the two solutions, but reversed the two bottles of sugar water when preparing them. The actual concentration of the wrongly mixed sugar water is~\uline{~~~~~~~~~~}~$$\textbackslash\%$$. 
Options:
aoVal: A
content: $$8$$ 
aoVal: B
content: $$10$$ 
aoVal: C
content: $$12.5$$ 
aoVal: D
content: $$15$$ 
aoVal: E
content: None of the above 
Answer: B
Analysis: NA 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems
Problem: If February contains Friday the $$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$$ is a Sunday. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: Eddie spends $12$ minutes to climb from the first floor to the third floor at a constant speed. At this speed, how many minutes does Eddie need to climb from the first floor to the sixth floor? 
Options:
aoVal: A
content: $$24$$ 
aoVal: B
content: $$30$$ 
aoVal: C
content: $$36$$ 
aoVal: D
content: $$42$$ 
aoVal: E
content: $$48$$ 
Answer: B
Analysis: $12 \div (3 - 1) = 6$  $6 \times (6 - 1) = 30$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems
Source: 其它
Problem: The number of months in a year minus the number of days in a week equals． 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$19$$ 
Answer: A
Analysis: The number of months in a year minus the number of days in a week is $$12-7 = 5$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction
Problem: At the 2018 Tompkins County Fair a vendor is offering a "fair special" on hats. If you buy one hat at the regular price of $\textbackslash$ 30$, you get a second hat at a $40\textbackslash\%$ discount, and a third pair at half the regular price. James took advantage of the "fair special" to buy three hats. What percentage of the $\textbackslash$ 90$ regular price did he save? (adapted from 2013 AMC 8, Question \#12) 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$25$$ 
aoVal: D
content: $$30$$ 
aoVal: E
content: $$40$$ 
Answer: D
Analysis: First, the amount of money one will pay for three hats without the discount $=\textbackslash$ 90$. Then, find the amount of money using the discount: $30+0.6 \times 30+\frac{1}{2} \times 30=\textbackslash$ 63$. Finding the percentage yields $\frac{63}{90}=70\textbackslash\%$ To find the percent saved, we have $100 \textbackslash\%-70\textbackslash\%= 30\textbackslash\%$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems
Source: 其它
Problem: Find the average of these numbers: $7,9,5,3,6$ 
Options:
aoVal: A
content: $$3$$ 
aoVal: B
content: $$4$$ 
aoVal: C
content: $$5$$ 
aoVal: D
content: $$6$$ 
Answer: D
Analysis: D 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems 
Source: 其它
Problem: There were some cupcakes in a bakery. First, Jade ate half of the cupcakes. Then, Neil ate half of the remaining cupcakes. Finally, Terry ate $6$ cupcakes and there were $$2$$ cupcakes left. At beginning, how many cupcakes were there in the bakery? 
Options:
aoVal: A
content: $$24$$ 
aoVal: B
content: $$32$$ 
aoVal: C
content: $$48$$ 
aoVal: D
content: $$12$$ 
Answer: B
Analysis: $$6+2=8$$  $$8+8=16$$  $$16+16=32$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: In a zoo, there are three monkeys. The monkeys are all younger than $$5$$ years old. None of them has the same age, and all their ages are whole numbers. The product of their ages is $$8$$. What is the sum of their ages? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$9$$ 
Answer: C
Analysis: The whole numbers smaller than $$5$$ are: $$1, 2, 3, 4$$ (age cannot be $$0$$)  The product of three numbers is $$8$$.  $$1\times2\times4=8$$  Their sum: $$1+2+4=7$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: After every $$3$$ steps that Pip takes forward, he takes $$2$$ steps backwards. Each step is $$1 $$$$\text{m}$$. Pip starts at one end of a $$100$$ $$\text{m}$$ hall. Pip will first reach the other end after~\uline{~~~~~~~~~~}~steps. 
Options:
aoVal: A
content: $$100$$ 
aoVal: B
content: $$488$$ 
aoVal: C
content: $$490$$ 
aoVal: D
content: $$500$$ 
Answer: B
Analysis: 3+2=5, 3-2=1  The pattern: Pip move forward 1m in 5 steps  $$100-3=97$$  $97\times5+3=488$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems
Source: 其它
Problem: Susan is $6$ years old. Her sister is one year younger and her brother is one year older. What is the sum of the ages of the three siblings? 
Options:
aoVal: A
content: $10$ 
aoVal: B
content: $15$ 
aoVal: C
content: $18$ 
aoVal: D
content: $21$ 
aoVal: E
content: $30$ 
Answer: C
Analysis: Susan\textquotesingle s sister is $6-1=5$ years old and her brother is $6+1=7$ years old. The sum of the ages of the three siblings is $5+6+7=18$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems
Problem: Peter has $$20$$ grams of a $$20\textbackslash\%$$ salt solution. How many grams of salt should he add to make it a $$25\textbackslash\%$$ solution? 
Options:
aoVal: A
content: $1$ grams 
aoVal: B
content: $$\dfrac{4}{3}$$ grams 
aoVal: C
content: $4$ grams 
aoVal: D
content: $5$ grams 
Answer: B
Analysis: Method $$1$$:  Suppose $$x$$ ounces of salt should be added to the solution:  $$\dfrac{20\times20\textbackslash\%+x}{20+x}=25\textbackslash\%$$  $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde x=\dfrac{4}{3}$$.  Method $$2$$:  $$20\times(1-20\textbackslash\%)\div(1-25\textbackslash\%)-20=\dfrac{4}{3}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems
Problem: Bridget bakes $48$ loaves of bread for her bakery. She sells half of them in the morning for ＄$2.50$ each. In the afternoon she sells two thirds of what she has left, and because they are not fresh, she charges only half price. In the late afternoon she sells the remaining loaves at a dollar each. Each loaf costs ＄$0.75$ for her to make. In dollars, what is her profit for the day?($$2014$$ AMC $$10$$A Problem, Question \#$$3$$) 
Options:
aoVal: A
content: $24$ 
aoVal: B
content: $36$ 
aoVal: C
content: $44$ 
aoVal: D
content: $48$ 
aoVal: E
content: $52$ 
Answer: E
Analysis: She first sells one-half of her $48$ loaves, or $$\frac{48}{2}=24$$ loaves. Each loaf sells for＄$2.50$, so her total earnings in the morning is equal to$24\times $＄$2.50=$＄$60$. This leaves $24$ loaves left, and Bridget will sell $\frac{2}{3}\times24=16$ of them for a price of＄$\frac{2.50}{2}=$＄$1.25$. Thus, her total earnings for the afternoon is$16\times~ $＄$1.25=$＄$20$. Finally, Bridget will sell the remaining $24-16=8$ loaves for a dollar each. This is a total of＄$1\times~ 8=$＄$8$. The total amount of money she makes is equal to $60+20+8=$＄$88$. However, since Bridget spends＄$0.75$ making each loaf of bread, the total cost to make the bread is equal to＄$0.75\times 48=$＄$36$. Her total profit is the amount of money she spent subtracted from the amount of money she made, which is $88-36=52\Rightarrow \left(\text{E}\right)52$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems
Problem: At the "Think Flea Market", a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $\textbackslash$ 50$, you get a second pair at a $40 \textbackslash\%$ discount, and a third pair at half the regular price. Owen took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $\textbackslash$ 150$ regular price did he save? (adapted from 2013 AMC 8, Question \#12) 
Options:
aoVal: A
content: $$25$$ 
aoVal: B
content: $$30$$ 
aoVal: C
content: $$33$$ 
aoVal: D
content: $$40$$ 
aoVal: E
content: $$45$$ 
Answer: B
Analysis: First, find the amount of money one will pay for three sandals without the discount. We have $\textbackslash$ 50 \times 3$ sandals $=\textbackslash$ 150$. Then, find the amount of money using the discount: $50+0.6 \times 50+\frac{1}{2} \times 50=\textbackslash$ 105$. Finding the percentage yields $\frac{105}{150}=70 \textbackslash\%$ To find the percent saved, we have $100 \textbackslash\%-70 \textbackslash\%=(\text{B}) 30$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems
Source: 其它