math-eval/TAL-SCQ5K huggingface dataset:
Problem: Speedy Wiggins cycles to school, a journey that takes $$30$$ minutes at $$12$$mph.  How far does he travel to school? 
Options:
aoVal: A
content: $$3$$miles 
aoVal: B
content: $$4$$miles 
aoVal: C
content: $$6$$miles 
aoVal: D
content: $$10$$miles 
aoVal: E
content: $$20$$miles 
Answer: C
Analysis: Cycling at $$12$$ mph, Speedy would go $$12$$ miles in an hour. So in $$30$$ minutes he cycles $$12$$ miles $$\div2 = 6$$ miles. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Problem: Geraint always cycles to work, leaving at $$8$$am every morning. When he averages $$15{\text{km}}/{\text{h}}\textbackslash;$$,he arrives $$10$$ minutes late. However, when he averages $$30{\text{km}}/{\text{h}}\textbackslash;$$, he arrives $$10$$ minutes early. What speed should he average to arrive on time? 
Options:
aoVal: A
content: $$20{\text{km}}/{\text{h}}\textbackslash;$$ 
aoVal: B
content: $$21{\text{km}}/{\text{h}}\textbackslash;$$ 
aoVal: C
content: $$22.5{\text{km}}/{\text{h}}\textbackslash;$$ 
aoVal: D
content: $$24{\text{km}}/{\text{h}}\textbackslash;$$ 
aoVal: E
content: $$25{\text{km}}/{\text{h}}\textbackslash;$$ 
Answer: A
Analysis: Let $$x\text{km}$$ be the distance Geraint cycles and let $$t $$ hours be the time his journey should take if he is to be on time. Since $$\frac{\text{distance}}{\text{speed}}\text{=time}$$, the information in the question tells us that  $$\frac{x}{15}=t+\frac{1}{6}$$ and that $$\frac{x}{30}=t-\frac{1}{6}$$. When we subtract the second equation from the first, we obtain  $$\frac{x}{30}=\frac{2}{6}$$ and so $$x = 10$$. Hence, from the second equation, $$\frac{10}{30}=t-\frac{1}{6}$$ and so $$t=\frac{1}{3}+\frac{1}{6}=\frac{1}{2}$$. Therefore, to arrive on time, Geraint needs to travel $$10\text{km}$$ in~ $$\frac{1}{2}$$ hour, which is an average speed of $$20{\text{km}}/{\text{h}}\textbackslash;$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Problem: Susie Starfish and her five sisters went to the cinema with Ollie Octopus and his four brothers.  They bought a box of popcorn for every arm they had.  How many boxes of popcorn did they buy? 
Options:
aoVal: A
content: $$13$$ 
aoVal: B
content: $$57$$ 
aoVal: C
content: $$62$$ 
aoVal: D
content: $$65$$ 
aoVal: E
content: $$70$$ 
Answer: E
Analysis: There are $$6$$ starfish and $$5$$ octopuses. So the number of boxes $$=6 \times5+5\times8 =70$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division
Problem: A $$12-$$hour clock loses $$10$$ minutes each day. The clock will first return to the correct time in． 
Options:
aoVal: A
content: $$36$$ days 
aoVal: B
content: $$72$$ days 
aoVal: C
content: $$120$$ days 
aoVal: D
content: $$144$$ days 
aoVal: E
content: $60$ days 
Answer: B
Analysis: Clock shows the correct time after a $$12-$$hr loss. With a $$10-$$min. loss daily, it takes $$6$$ days to lose $$1$$ hr \& $$72$$ days to lose $$12$$ hr. 
Knowledge points: Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems
Problem: After a discount of $$30\textbackslash\%$$, the price of a bed is＄$$210$$. Besides, senior citizens are given a further discount of＄$$15$$. What is the percentage discount given to senior citizens for the bed? 
Options:
aoVal: A
content: $$30\textbackslash\%$$ 
aoVal: B
content: $$32\textbackslash\%$$ 
aoVal: C
content: $$35\textbackslash\%$$ 
aoVal: D
content: $$36\textbackslash\%$$ 
Answer: C
Analysis: Original price: $$\frac{210}{(1-30\textbackslash\%)}=300$$.  Selling price after discount: $$210-15=195$$.  Discount rate: $$1-\left( {\frac{195}{300}} \right)=1-65\textbackslash\%=35\textbackslash\%$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts
Problem: Alex had some trading cards. After giving $36$ trading cards to Ben, Alex received another $42$ trading cards from David. If Alex has $241$ trading cards now, how many trading cards does he have at first? 
Options:
aoVal: A
content: $$235$$ 
aoVal: B
content: $$230$$ 
aoVal: C
content: $$225$$ 
aoVal: D
content: $$220$$ 
Answer: A
Analysis: $241-42+36=235$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction
Problem: How many digits have to be written in order to write down every number from $$1$$ to $$110$$? 
Options:
aoVal: A
content: $$110$$ 
aoVal: B
content: $$109$$ 
aoVal: C
content: $$221$$ 
aoVal: D
content: $$222$$ 
aoVal: E
content: $$330$$ 
Answer: D
Analysis: From $$1$$ to $$9$$ there are~$1\times9=9$~digits.  From $$10$$ to $$99$$ there are~$2\times90=180$~digits.  From $$100$$ to $$110$$ there are~$3\times11=33$~digits.  In total, there are$9+180+33=222$~digits 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem->Correspondence between Numbers and Page Numbers->Applying the Total Number of Numbers
Problem: Daniel raises some ducks and dogs. All the ducks and dogs have $18$ legs and $5$ pairs of wings in total. If all the ducks and dogs each lifts one leg off the ground, they lift~\uline{~~~~~~~~~~}~legs in total. 
Options:
aoVal: A
content: $$18$$ 
aoVal: B
content: $$13$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$7$$ 
aoVal: E
content: $$5$$ 
Answer: D
Analysis: $5$ pairs of wings means there are $5$ ducks, so there are $18-5\times2=8$ legs for dogs, which is $8\div4=2$. Thus, there are $2+5=7$ animals and they will lift $7$ legs. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems
Source: 其它
Problem: Lewis drives from London to Brighton at an average speed of $$60\text{mph}$$. On the way back, he gets stuck in traffic and his average speed is only $$40\text{mph}$$. What is his average speed for the whole journey? 
Options:
aoVal: A
content: $$55\text{mph}$$ 
aoVal: B
content: $$50\text{mph}$$ 
aoVal: C
content: $$48\text{mph}$$ 
aoVal: D
content: $$45\text{mph}$$ 
aoVal: E
content: Impossible to determine 
Answer: C
Analysis: Let the distance from London to Brighton be $$d$$ miles. Since time $$=$$ distance $$\div$$ speed, the times Lewis spent on the two parts of his journey are $$\frac{d}{60}$$ hours and $$\frac{d}{40}$$ hours. Hence the total time in hours that he travelled is$$\frac{d}{60}+ \frac{d}{40}= \frac{2d+3d}{120}= \frac{5d}{120}= \frac{d}{24}$$.  Therefore his average speed for the whole journey is $$2d \div \left( \frac{d}{24}\right)\text{mph}=48 \text{mph}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Distance Word Problems->Bus Departure Time Word Problems
Problem: A $$15\textbackslash\%$$ sugar solution contains $$18$$ grams of pure sugar. How many ounces 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: $$18\div15\textbackslash\% = 120$$ grams. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems
Problem: Judy needed to reach the $10$\textsuperscript{th} floor of a building. It took her $40$ seconds to walk from the $1$\textsuperscript{st} floor to the $5$\textsuperscript{th} floor. How many seconds will it take to go from the $3$\textsuperscript{rd}~to the $10$\textsuperscript{th} floor at the same speed? 
Options:
aoVal: A
content: $$60$$ 
aoVal: B
content: $$70$$ 
aoVal: C
content: $$80$$ 
aoVal: D
content: $$90$$ 
aoVal: E
content: $$100$$ 
Answer: B
Analysis: $40 \div (5 - 1) = 10$  $(10 - 3) \times 10 = 70$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems
Source: 其它
Problem: Bill, Sarah and James each has $4$ cookies at beginning. Bill gives James some cookies and James gives Sarah $2$ cookies. How many cookies do they have in total now? 
Options:
aoVal: A
content: $$0$$ 
aoVal: B
content: $$5$$ 
aoVal: C
content: $$10$$ 
aoVal: D
content: $$12$$ 
aoVal: E
content: $$15$$ 
Answer: D
Analysis: Giving cookies to each other won\textquotesingle t affect the sum of their cookies, so there are $$4+4+4=12$$~in total. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: In a class of $$18$$ students, $$6$$ are wearing jeans. What is the ratio of students wearing jeans to students \emph{not} wearing jeans? 
Options:
aoVal: A
content: $$1:2$$ 
aoVal: B
content: $$1:3$$ 
aoVal: C
content: $$2:3$$ 
aoVal: D
content: $$2:1$$ 
Answer: A
Analysis: If $$6$$ students are wearing jeans, then $$18-6=12$$ are not. The ratio of students wearing jeans to students \emph{not} wearing jeans is $$6:12=1:2$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio
Problem: On average, each student has $$14$$ balls. Each of the $$15$$ girls has $$24$$ balls on average. There are $$25$$ boys, and their average number of balls is~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$6$$ 
aoVal: B
content: $$7$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$9$$ 
aoVal: E
content: $$10$$ 
Answer: C
Analysis: $$14\times(15+25)=560$$  $$560-15\times24=200$$  $$200\div25=8$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems 
Source: 其它
Problem: All the animals stand in rows in the magic forest. There is the same number of animals in each row. There are $3$ rows on the left of monkey and $2$ rows on the right of it. In its row, there are $6$ animals in front of it and $2$ animals behind it. How many animals are there in the forest? 
Options:
aoVal: A
content: $$36$$ 
aoVal: B
content: $$40$$ 
aoVal: C
content: $$45$$ 
aoVal: D
content: $$54$$ 
aoVal: E
content: $$63$$ 
Answer: D
Analysis: $(3 + 2 + 1) \times (6 +2 +1) = 54$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: Billy has twice as many basketballs as soccer balls.  Milly has four times as many soccer balls as basketballs.  They have a total of 18 balls.  How many of them are basketballs? 
Options:
aoVal: A
content: $$5$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$7$$ 
aoVal: D
content: $$8$$ 
aoVal: E
content: $$9$$ 
Answer: A
Analysis: Let Billy have $$b$$ soccer balls and $$2b$$ basketballs. Let Milly have $$m$$ basketballs and $$4m$$ soccer balls.  Therefore, as they have $$17$$ balls in total, $$3b + 5m= 18$$. The only positive integer solution of this equation is $$b= 1$$, $$m= 3$$. So the number of basketballs is $$2b + m = 2 \times 1 + 3 = 5$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Indefinite Equation Word Problems
Problem: Kate sold some dresses and Tasha sold $30$ more dresses than Kate. If Tasha sold thrice as many dresses as Kate, how many dresses did Kate sell? 
Options:
aoVal: A
content: $$10$$ 
aoVal: B
content: $$15$$ 
aoVal: C
content: $$30$$ 
aoVal: D
content: $$45$$ 
Answer: B
Analysis: $30\div2=15$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Problem: The hands of a circular clock form aangle at $$6:15$$ P.M. 
Options:
aoVal: A
content: $$82.5^{}\circ$$ 
aoVal: B
content: $$90^{}\circ$$ 
aoVal: C
content: $$97.5^{}\circ$$ 
aoVal: D
content: $$270^{}\circ$$ 
Answer: C
Analysis: At $$6:15$$, hr. hand has moved $$\left(1/4\right)\times 30^{}\circ$$ from $$6$$, so $$\angle =90^{}\circ+30^{}\circ/4=97.5^{}\circ$$. 
Knowledge points: Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems
Problem: White and White Jr. have $$50$$ apples in total, and White has $$10$$ more appled than junior, so White Jr has~\uline{~~~~~~~~~~}~apples． 
Options:
aoVal: A
content: $$15$$ 
aoVal: B
content: $$20$$ 
aoVal: C
content: $$40$$ 
aoVal: D
content: $$60$$ 
Answer: B
Analysis: $$(50-10)\div 2=20$$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples
Problem: Which of these months has 31 days? ． 
Options:
aoVal: A
content: February 
aoVal: B
content: April 
aoVal: C
content: August 
aoVal: D
content: November 
Answer: C
Analysis: omitted 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates
Problem: There are $$50$$ students in your class. The ratio of boys to girls is $$2:3$$. How many boys and girls are there? 
Options:
aoVal: A
content: $$30$$ and $$20$$ 
aoVal: B
content: $$20$$ and $$30$$ 
aoVal: C
content: $$15$$ and $$20$$ 
aoVal: D
content: $$20$$ and $$15$$ 
Answer: B
Analysis: According to the ratio $$2:3$$, we could know the total is $$5$$. Then the number of boys is $$50\times\frac{2}{5}=20$$. The number of girls is $$50\times\frac{3}{5}=30$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio
Problem: Tom has $$20$$ toys in total, and Tim has $$2$$ more toys than Tom. The number of Amanda\textquotesingle s toys is equal to the sum of that of Tom and Tim. How many toys does Amanda have~\uline{~~~~~~~~~~}~. 
Options:
aoVal: A
content: $$39$$ 
aoVal: B
content: $$42$$ 
aoVal: C
content: $$44$$ 
aoVal: D
content: $$47$$ 
aoVal: E
content: None of the above 
Answer: B
Analysis: We know that Tim has $$20+2=22$$ toys. The sum of Tom\textquotesingle s and Tim\textquotesingle s toys is $$20+22=42$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Word Problems Involving Comparing and Ordering
Problem: The upper shelf of a bookshelf has $$143$$ books. The lower shelf has $$39$$ books. How many books should be taken from the upper shelf to the lower shelf so that both shelves will have the same number of books? 
Options:
aoVal: A
content: $$46$$ 
aoVal: B
content: $$52$$ 
aoVal: C
content: $$91$$ 
aoVal: D
content: $$104$$ 
Answer: B
Analysis: $$143-39=104$$,  $$104$$~$\div$ $$2$$ = $$52$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference
Source: 其它
Problem: The length of a rectangle is increased by $30\textbackslash\%$ and the width is decreased by $25\textbackslash\%$. What percent of the old area is the new area? (adapted from 2009 AMC 8, Question \#8) 
Options:
aoVal: A
content: $$90.5$$ 
aoVal: B
content: $$96.5$$ 
aoVal: C
content: $$97.5$$ 
aoVal: D
content: $$98.5$$ 
aoVal: E
content: $$110.5$$ 
Answer: C
Analysis: $1.3 \times 0.75 = 97.5\textbackslash\%$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems
Source: 其它
Problem: What is the greatest number of days that can occur after the first of one month and before the first of the next month? 
Options:
aoVal: A
content: $$27$$ 
aoVal: B
content: $$28$$ 
aoVal: C
content: $$29$$ 
aoVal: D
content: $$30$$ 
Answer: D
Analysis: A month has at most $$31$$ days, Hence, the greatest number of days in that month, after the first, is $$31 -1=30$$. Then, the next day is another $$1\text{st}$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: Water from the first faucet fills the swimming pool in $18$ hours. Water from each of the two other faucets fills the same swimming pool $4$ times faster. In how many hours will the swimming pool be filled if all three faucets are opened? 
Options:
aoVal: A
content: $$1$$ 
aoVal: B
content: $$2$$ 
aoVal: C
content: $$3$$ 
aoVal: D
content: $$4$$ 
aoVal: E
content: $$5$$ 
Answer: B
Analysis: The efficiency of the first faucet is $\frac1{18}$ and that of the other two is $\frac29$.  Thus it takes $1\div (\frac1{18}+\frac29\times2)=2$ hours to fill the pool. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems
Source: 其它
Problem: SASMO 2015 P2 Q4  Susan prepared a plate of cookies for her friends Ashley, Sam, Max and Olivia. Susan tried the first cookie before serving them to her friends. Ashley took 2 cookies and gave 1 to Sam. Max then took 3 cookies, and gave 1 to Olivia and 1 to Susan. If they each ate the cookies they ended up with, who ate the most cookies? 
Options:
aoVal: A
content: Susan 
aoVal: B
content: Ashley 
aoVal: C
content: Sam 
aoVal: D
content: Max 
aoVal: E
content: Olivia 
Answer: A
Analysis: Susan: +1+1  Ashley: +1  Sam: +1  Max: +1  Olivia: +1 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Source: 其它
Problem: The distance between Town A and Town B is $620\text{km}$. Eric drives from Town A to Town B at a speed of $$75\text{km/h}$$ while Chien drives from Town B to Town A at a speed of $$80\text{km/h}$$. How many hours will it take for them to meet each other? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$24$$ 
aoVal: D
content: $$124$$ 
Answer: A
Analysis: As they are driving toward each other, the total speed is $$75+80=155$$ miles per hour. Then the time needed is $$620\div155=4$$ hours. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules
Problem: Elmp vists the Sesame Street Park every Wednesday. If the 1st of January 2017 was Sunday and February has 28 days, what was the last date in March 2017 in which Elmo visited Sesame Street Park? 
Options:
aoVal: A
content: 28th March 
aoVal: B
content: 29th March 
aoVal: C
content: 30th March 
aoVal: D
content: 31st March 
aoVal: E
content: None of the above. 
Answer: B
Analysis: Draw the calendar out. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems
Source: 其它
Problem: Ashley had a basket of apples. Her family took half of the apples after dinner. Next morning, her family took half of the remaining apples. There were $$2$$ apples left in the basket. How many apples were in the basket at first? 
Options:
aoVal: A
content: $$4$$ 
aoVal: B
content: $$6$$ 
aoVal: C
content: $$8$$ 
aoVal: D
content: $$11$$ 
aoVal: E
content: $$16$$ 
Answer: C
Analysis: $2+2=4$  $4+4=8$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems->Giving Half of a Whole
Problem: A series of colored lanterns are arranged in the pattern ``red, red, green, yellow, yellow, red, red, green, yellow, yellow$$\cdots$$'' What color is the $$52^{\text{th}}$$ lantern? 
Options:
aoVal: A
content: red 
aoVal: B
content: green 
aoVal: C
content: yellow 
Answer: A
Analysis: Since $$52\div(3+2)=10r2$$, the $$52^{\text{th}}$$ colored lantern is red. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation
Problem: Jin loves carrots! Yesterday she ate $$\frac{1}{2}$$ of her carrots, and today she ate $$\frac{2}{3}$$ of the remaining carrots. She then discovered that she had $$12$$ carrots left. Yesterday she must have started with  carrots. 
Options:
aoVal: A
content: $$36$$ 
aoVal: B
content: $$48$$ 
aoVal: C
content: $$60$$ 
aoVal: D
content: $$72$$ 
Answer: D
Analysis: If $$12$$ carrots are left after Jin eats $$\frac{2}{3}$$ of today\textquotesingle s carrots, then $$12$$ carrots are $$\frac{1}{3}$$ of the carrots she started with today. So Jin began today with $$36$$ carrots. Since Jin ate $$\frac{1}{2}$$ yesterday, she started with $$2\times36$$ carrots. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base
Problem: This year, March $$19$$\textsuperscript{th} falls on a Thursday. What day of the week will it be in $$30$$ days? 
Options:
aoVal: A
content: Wednesday 
aoVal: B
content: Thursday 
aoVal: C
content: Friday 
aoVal: D
content: Saturday 
aoVal: E
content: Sunday 
Answer: D
Analysis: $$30\div7=4 \text{R} 2$$, two days after Thursday, which is Saturday. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time
Problem: A $70\textbackslash\%$ alcohol solution contains $$120$$ g of water. How many g of solution are there? 
Options:
aoVal: A
content: $$200$$ g 
aoVal: B
content: $$300$$ g 
aoVal: C
content: $$400$$ g 
aoVal: D
content: $$500$$ g 
Answer: C
Analysis: $$120\div(1-70\textbackslash\%)=400$$ g. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems
Problem: It\textquotesingle s summer time! A beverage shop mixes $10$ bottles of apple and $20$ bottles of watermelon juice to make the new blended juice. The costs of a bottle of apple and a bottle of watermelon juice are $8$ and $11$ dollars, respectively. If the size of the bottle does not change, what is the cost of each bottle of the blended juice? 
Options:
aoVal: A
content: $$7$$ 
aoVal: B
content: $$8$$ 
aoVal: C
content: $$9$$ 
aoVal: D
content: $$10$$ 
aoVal: E
content: $$11$$ 
Answer: D
Analysis: Total cost: $$10\times 8+11\times 20=300$$.  There are $$10+20=30$$ bottles, so each bottle of the blended juice should be $$300\div 30=10$$ dollars. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems
Problem: Irene mixes $$100$$ kilograms of dogfood that contains $$50\textbackslash\%$$ rice with $$400$$ kilograms of dogfood that contains $$80\textbackslash\%$$ rice. Find the percent concentration of the rice in the new mixture. 
Options:
aoVal: A
content: $$70\textbackslash\%$$ 
aoVal: B
content: $$72\textbackslash\%$$ 
aoVal: C
content: $$75\textbackslash\%$$ 
aoVal: D
content: $$74\textbackslash\%$$ 
Answer: D
Analysis: $$\dfrac{100\times50\textbackslash\%+400\times80\textbackslash\%}{100+400}=74\textbackslash\%$$. 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems
Problem: Chris and Debbie want to buy the same book, but they do not take enough money. Chris needs $$2$$ dollars and $$30$$ cents more to buy that book. Debbie needs $$3$$ dollars and $$80$$ cents more to buy that book. The sum of their own money is equal to the price of the book. How much is the book? 
Options:
aoVal: A
content: $$2$$ dollars and $$30$$ cents 
aoVal: B
content: $$4$$ dollars and $$60$$ cents 
aoVal: C
content: $$7$$ dollars and $$60$$ cents 
aoVal: D
content: $$3$$ dollars and $$80$$ cents 
aoVal: E
content: $$6$$ dollars and $$10$$ cents 
Answer: E
Analysis: $$2$$ dollars and $$30$$ cents + $$3$$ dollars and $$80$$ = $$6$$ dollars and $$10$$ cents 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems
Source: 其它
Problem: The average cost of a long-distance call in the USA in 1985 was 56 cents per minute, and the average cost of a long-distance call in the USA in 2018 was 2 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (2007 AMC 8, Question \#6) 
Options:
aoVal: A
content: $$90$$ 
aoVal: B
content: $$95$$ 
aoVal: C
content: $$96$$ 
aoVal: D
content: $$97$$ 
aoVal: E
content: $$98$$ 
Answer: C
Analysis: The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $56-2=54$ so the percent decrease is $\frac{54}{56}$ which is about $ 96 \textbackslash\%$ 
Knowledge points: Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems
Source: 其它