Datasets:

math-eval

/

TAL-SCQ5K

like 48

[]

[ [ { "aoVal": "A", "content": "$$2000$$ " } ], [ { "aoVal": "B", "content": "$$2002$$ " } ], [ { "aoVal": "C", "content": "$$2004$$ " } ], [ { "aoVal": "D", "content": "$$2006$$ " } ], [ { "aoVal": "E", "content": "$$2008$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Sums and Multiples in Age Problems" ]

[ "Given that Granny is $$5$$ times older than each of the three triplets, we know that the age of each triplet is $$120\\div (5+3)= 15$$. So Cara, Cate and Chris were born in $$2004$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "The $15\\text{-ounce}$ bag " } ], [ { "aoVal": "B", "content": "The $20\\text{-ounce}$ bag " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value" ]

[ "$\\frac{8\\text{dollars}}{15\\text{ounces}}$ $\\frac{12\\text{dollars}}{20\\text{ounces}}$ " ]

[]

[ [ { "aoVal": "A", "content": "Sunday　 " } ], [ { "aoVal": "B", "content": "Monday　 " } ], [ { "aoVal": "C", "content": "Wednesday　 " } ], [ { "aoVal": "D", "content": "Thursday　 " } ], [ { "aoVal": "E", "content": "Saturday　 " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time" ]

[ "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. " ]

[]

[ [ { "aoVal": "A", "content": "$$14$$ " } ], [ { "aoVal": "B", "content": "$$15$$ " } ], [ { "aoVal": "C", "content": "$$16$$ " } ], [ { "aoVal": "D", "content": "$$17$$ " } ], [ { "aoVal": "E", "content": "$$18$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction" ]

[ "$$112-64=48$$ $$64-48=16$$ " ]

[]

[ [ { "aoVal": "A", "content": "￡$$2$$ " } ], [ { "aoVal": "B", "content": "￡$$3.60$$ " } ], [ { "aoVal": "C", "content": "￡$$4$$ " } ], [ { "aoVal": "D", "content": "￡$$6$$ " } ], [ { "aoVal": "E", "content": "￡$$12$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems" ]

[ "The initial ratio of the children\\textquotesingle s money is $$3:1:4$$. When Miguel shares half of his portion, the ratio becomee $$3 + 1:1+ 1:4-2=4:2:2=2:1:1$$. Given that Clara now has ￡$$6$$ more than Miguel, Pablo now has ￡$$6$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$2$$ " } ], [ { "aoVal": "B", "content": "$$3$$ " } ], [ { "aoVal": "C", "content": "$$4$$ " } ], [ { "aoVal": "D", "content": "$$5$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division" ]

[ "There $$3$$ groups of $$5$$ buns in $$15$$ buns: $$15\\div 5=3$$, so $$5$$ buns cost $$6\\div 3=$$£$$2$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$6$$ " } ], [ { "aoVal": "B", "content": "$$7$$ " } ], [ { "aoVal": "C", "content": "$$8$$ " } ], [ { "aoVal": "D", "content": "$$9$$ " } ], [ { "aoVal": "E", "content": "$$10$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction" ]

[ "14 - 1 (eagle) - 1 (mother hen) = 12 (chicks) 12 - 5 7 chicks " ]

[]

[ [ { "aoVal": "A", "content": "$$20$$ " } ], [ { "aoVal": "B", "content": "$$35$$ " } ], [ { "aoVal": "C", "content": "$$45$$ " } ], [ { "aoVal": "D", "content": "$$55$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method" ]

[ "$$7$$ out of $$11$$ balls that Elena bought are soccer balls. If there are $$7\\times5 =35$$ soccer balls, then there is a total of $$11\\times5=55$$ balls. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$45$$ " } ], [ { "aoVal": "B", "content": "$$48$$ " } ], [ { "aoVal": "C", "content": "$$50$$ " } ], [ { "aoVal": "D", "content": "$$60$$ " } ], [ { "aoVal": "E", "content": "$$65$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems" ]

[ "Assume the total amount of problems is 100 per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got 90 problems correct by herself, and got 120 problems correct overall. We also know that Zoe had 70 problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $120-90=30$. Therefore Zoe has $30+70=100$ problems out of $200$ problems correct. Thus $\\frac{100}{200} = 50$ percent. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$12$$ " } ], [ { "aoVal": "B", "content": "$$22$$ " } ], [ { "aoVal": "C", "content": "$$24$$ " } ], [ { "aoVal": "D", "content": "$$26$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems" ]

[ "Suppose that Cici will be $x$ years old $4$ years later, Linda will be $$(x+11)$$ years old. $x+(x+11)=37$, so $x=13$. Thus, Linda will be $13+11=24$ years old $3$ years later. " ]

[]

[ [ { "aoVal": "A", "content": "$$ $$Sunday$$ $$ " } ], [ { "aoVal": "B", "content": "$$ $$Tuesday$$ $$ " } ], [ { "aoVal": "C", "content": "$$ $$Thursday$$ $$ " } ], [ { "aoVal": "D", "content": "$$ $$Saturday$$ $$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time" ]

[ "After $$1$$ day, it is Monday; after $$2$$ days, it is Tuesday; after $$3$$ days, it is Wednesday $$\\cdots$$ After $$8$$ days, it is still Monday, and the period is $$7$$ days. $$55\\div 7=7$$(weeks) $$\\rm R$$ $$6$$ (days). The birthday is Saturday. " ]

[]

[ [ { "aoVal": "A", "content": "$$33$$ " } ], [ { "aoVal": "B", "content": "$$36$$ " } ], [ { "aoVal": "C", "content": "$$39$$ " } ], [ { "aoVal": "D", "content": "$$42$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Differences and Multiples in Age Problems" ]

[ "My age, $$27$$, is $$3$$ years less than $$5$$ times my sister\\textquotesingle s age, so $$30$$ is $$5$$ times her age. Thus, my sister is $$6$$. The sum of our ages is $$27+6=33$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$20$$; $$65$$ " } ], [ { "aoVal": "B", "content": "$$13$$; $$52$$ " } ], [ { "aoVal": "C", "content": "$$13$$; $$65$$ " } ], [ { "aoVal": "D", "content": "$$20$$; $$52$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems" ]

[ "Sugar: $$65\\times 20\\textbackslash\\% = 13$$ ounces; Water: $$65 - 13 = 52$$ ounces. " ]

[]

[ [ { "aoVal": "A", "content": "$$8$$ " } ], [ { "aoVal": "B", "content": "$$9$$ " } ], [ { "aoVal": "C", "content": "$$10$$ " } ], [ { "aoVal": "D", "content": "$$12$$ " } ], [ { "aoVal": "E", "content": "$$14$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value" ]

[ "$$3+3+3=9$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$58$$ " } ], [ { "aoVal": "B", "content": "$$68$$ " } ], [ { "aoVal": "C", "content": "$$38$$ " } ], [ { "aoVal": "D", "content": "$$48$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction" ]

[ "$$67-19=48$$ " ]

[]

[ [ { "aoVal": "A", "content": "Thursday " } ], [ { "aoVal": "B", "content": "Saturday " } ], [ { "aoVal": "C", "content": "Sunday " } ], [ { "aoVal": "D", "content": "Tuesday " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time" ]

[ "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. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$6$$ " } ], [ { "aoVal": "B", "content": "$$12$$ " } ], [ { "aoVal": "C", "content": "$$32$$ " } ], [ { "aoVal": "D", "content": "$$30$$ " } ], [ { "aoVal": "E", "content": "$$36$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple" ]

[ "Tom\\textquotesingle s mother is $(86+24-2)\\div3=36$ years old. Tom is $36-24=12$ years old. " ]

[]

[ [ { "aoVal": "A", "content": "$$16$$ " } ], [ { "aoVal": "B", "content": "$$25$$ " } ], [ { "aoVal": "C", "content": "$$36$$ " } ], [ { "aoVal": "D", "content": "$$49$$ " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method" ]

[ "Condition on the number of $$$20$$ note you use. $$4$$ gives $$1$$ possibility, $$3$$ gives $$3$$ possibilities, $$2$$ gives $$5$$ possibilities, $$1$$ gives $$7$$ possibilities, $$0$$ gives $$9$$ possibilities. " ]

[]

[ [ { "aoVal": "A", "content": "$$20$$ " } ], [ { "aoVal": "B", "content": "$$25$$ " } ], [ { "aoVal": "C", "content": "$$35$$ " } ], [ { "aoVal": "D", "content": "$$75$$ " } ], [ { "aoVal": "E", "content": "$$80$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple->Sum and Multiple of Two Variables" ]

[ "$100 \\div (3 + 1)~ \\times 3= 75$ " ]

[]

[ [ { "aoVal": "A", "content": "Sunday " } ], [ { "aoVal": "B", "content": "Monday " } ], [ { "aoVal": "C", "content": "Tuesday " } ], [ { "aoVal": "D", "content": "Wednesday " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time" ]

[ "Since there are 7 days in a week, the day will repeat again after 7 days. Thus, if today is Monday, it will be Monday again a week later. $$22\\div 7=3$$ week R $$1$$. The day after $$22$$ days is the same as the day after $$1$$ day. $$1$$ day after Monday is Tuesday. Therefore, it will be \\textbf{Tuesday} $$22$$ days later. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$11$$ " } ], [ { "aoVal": "B", "content": "$$10$$ " } ], [ { "aoVal": "C", "content": "$$9$$ " } ], [ { "aoVal": "D", "content": "$$8$$ " } ], [ { "aoVal": "E", "content": "$$7$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems " ]

[ "Total points: $$40\\times 25=1000$$. To have as many $100$ points as possible, we should consider there are only two groups of students: everyone gets $5$ points in a group and everyone gets $100$ in the other group. $$10\\times 100=1000$$, so there must be less than $10$ people getting $100$ points. If there are nine $100$s: $$9\\times 100+31\\times 5=1055\\textgreater1000$$, which is impossible. If there are eight $100$s:$$8\\times 100+32\\times 5=960\\textless{}1000$$. Thus, the answer is $$8$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$36$$ " } ], [ { "aoVal": "B", "content": "$$38$$ " } ], [ { "aoVal": "C", "content": "$$40$$ " } ], [ { "aoVal": "D", "content": "$$42$$ " } ], [ { "aoVal": "E", "content": "$$44$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares->Basic Solid Square Problems" ]

[ "It can be seen from the question that Bob and Tick have $8$ rows in front and $11$ rows in the back. There are $20$ rows in total, and there are two people in each row, so there are $40$ people in total. " ]

[]

[ [ { "aoVal": "A", "content": "$$3\\text{kg}$$ " } ], [ { "aoVal": "B", "content": "$$6\\text{kg}$$ " } ], [ { "aoVal": "C", "content": "$$7 \\text{kg}$$ " } ], [ { "aoVal": "D", "content": "$$9\\text{kg}$$ " } ], [ { "aoVal": "E", "content": "$$14 \\text{kg}$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference" ]

[ "It should be a moment\\textquotesingle s work to see that Felix weighs $$3\\text{kg}$$ , and Marmalade $$7\\text{kg}$$ . " ]

[]

[ [ { "aoVal": "A", "content": "$8\\text{cm}$ " } ], [ { "aoVal": "B", "content": "$10\\text{cm}$ " } ], [ { "aoVal": "C", "content": "$15\\text{cm}$ " } ], [ { "aoVal": "D", "content": "$18\\text{cm}$ " } ], [ { "aoVal": "E", "content": "$12\\text{cm}$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units" ]

[ "If $$6\\textasciitilde\\text{cm}$$ represents $$50\\textasciitilde\\text{km}$$, $$3\\textasciitilde\\text{cm}$$ represents $$25\\textasciitilde\\text{km}$$. So, their distance apart on the map is $$125\\div25\\times 3=15\\textasciitilde\\text{cm}$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$18$$ " } ], [ { "aoVal": "B", "content": "$$21$$ " } ], [ { "aoVal": "C", "content": "$$35$$ " } ], [ { "aoVal": "D", "content": "$$42$$ " } ], [ { "aoVal": "E", "content": "$$43$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable" ]

[ "Suppose there are $$x$$ ducks in the yard. Since there is an equal number of pigs, ducks and chickens, $$2x+4x+2x=144$$, $$x=18$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$364$$ " } ], [ { "aoVal": "B", "content": "$$365$$ " } ], [ { "aoVal": "C", "content": "$$366$$ " } ], [ { "aoVal": "D", "content": "$$367$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method" ]

[ "Each week has $$7$$ days, so $$52$$ weeks has $$52 \\times 7 = 364$$ days. " ]

[]

[ [ { "aoVal": "A", "content": "$$3$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$6$$ " } ], [ { "aoVal": "D", "content": "$$7$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts" ]

[ "A fair sells a``combo\" ticket for ＄$$30$$ entry and a ``per ride\" ticket for ＄$$12.50$$ to enter plus ＄$$5$$ per ride. A``per ride\" ticket costs ＄$$12.50+$$ ＄$$15 =$$＄$$27.50$$ for $$3$$ rides and ＄$$12.50 +$$ ＄$$20 = $$＄$$32.50$$ for $$4$$ rides. " ]

[]

[ [ { "aoVal": "A", "content": "$$7$$ " } ], [ { "aoVal": "B", "content": "$$8$$ " } ], [ { "aoVal": "C", "content": "$$11$$ " } ], [ { "aoVal": "D", "content": "$$14$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Simple Work Word Problems" ]

[ "When not being used, the cell phone uses up $$\\dfrac{1}{24}$$ of its battery per hour. When being used, the cell phone uses up $$\\dfrac{1}{3}$$ of its battery per hour. Since Niki\\textquotesingle s phone has been on for $$9$$ hours, of those $$8$$ simply on and~~being used to talk, $$8\\left(\\dfrac{1}{24}\\right)+1\\left(\\dfrac{1}{3}\\right)=\\dfrac{2}{3}$$ of its battery has been used up. To drain the remaining $$\\dfrac{1}{3}$$ the phone can last for $$\\dfrac{\\dfrac{1}{3}}{\\dfrac{1}{24}}=\\boxed{(\\text{B})8}$$ more hours without being used. " ]

[]

[ [ { "aoVal": "A", "content": "$$3$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$5$$ " } ], [ { "aoVal": "D", "content": "$$6$$ " } ], [ { "aoVal": "E", "content": "$$7$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems" ]

[ "It climbs up $$3$$ meters in the day time and slips down $$1$$ meter at night, so it climbs up $$2$$ meters in a whole day. For the first $$4$$ days, it climbs $$8$$ meters. During the day time of the fifth day, it climbs $$3$$ meters and reaches the ground. Then it needs five days to climb up to the ground. " ]

[]

[ [ { "aoVal": "A", "content": "$$18$$ " } ], [ { "aoVal": "B", "content": "$$17$$ " } ], [ { "aoVal": "C", "content": "$$14$$ " } ], [ { "aoVal": "D", "content": "$$11$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Basic Sum and Differences Problems in Age Problems" ]

[ "$20-3\\times2=14$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$94$$ " } ], [ { "aoVal": "B", "content": "$$89$$ " } ], [ { "aoVal": "C", "content": "$$80$$ " } ], [ { "aoVal": "D", "content": "$$79$$ " } ], [ { "aoVal": "E", "content": "$$75$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems" ]

[ "There are $12$ pieces of noodle left, so he takes $12-1=11$ bites of the noodle. Thus, the length of the noodle he ate is $11\\times5=55$ cm. The total length of the entire noodle was $55+24=79$ cm. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$52.5$$ " } ], [ { "aoVal": "B", "content": "$$55$$ " } ], [ { "aoVal": "C", "content": "$$57.5$$ " } ], [ { "aoVal": "D", "content": "$$60$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems" ]

[ "The original mixture contains $25\\times 24\\textbackslash\\% = 6$ liters of yellow tint. $$15$$ liters of yellow tint is added to the mixture, the new mixture now has $6+15=21$ liters of yellow tint. New percent of yellow =$\\frac{21}{25+15} =52.5\\textbackslash\\% $ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$12$$ " } ], [ { "aoVal": "B", "content": "$$13$$ " } ], [ { "aoVal": "C", "content": "$$17$$ " } ], [ { "aoVal": "D", "content": "$$21$$ " } ], [ { "aoVal": "E", "content": "$$22$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Word Problems Involving Comparing and Ordering" ]

[ "Blue: $(50 + 5 - 4) \\div 3 = 17$ Red: $17 + 4 = 21$ " ]

[]

[ [ { "aoVal": "A", "content": "$$48$$ " } ], [ { "aoVal": "B", "content": "$$40$$ " } ], [ { "aoVal": "C", "content": "$$60$$ " } ], [ { "aoVal": "D", "content": "$$80$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with an Invariant Part" ]

[ "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 $$\\text{B}$$. " ]

[]

[ [ { "aoVal": "A", "content": "Wednesday " } ], [ { "aoVal": "B", "content": "Thursday " } ], [ { "aoVal": "C", "content": "Friday " } ], [ { "aoVal": "D", "content": "Saturday " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time" ]

[ "The least common multiple of $3$, $4$ and $5$ is $60$. We know that $60\\div7=8\\ldots\\ldots4$, then the remainder tells us that it will be on Thursday. " ]

[]

[ [ { "aoVal": "A", "content": "Wednesday " } ], [ { "aoVal": "B", "content": "Thursday " } ], [ { "aoVal": "C", "content": "Tuesday " } ], [ { "aoVal": "D", "content": "Friday " } ], [ { "aoVal": "E", "content": "Sunday " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time" ]

[ "$$38\\div7=5 \\text{R} 3$$, three days after Sunday, which is Wednesday. " ]

[]

[ [ { "aoVal": "A", "content": "$$3$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$5$$ " } ], [ { "aoVal": "D", "content": "$$6$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules" ]

[ "For the first $$50\\text{km}$$, they drove at $$50\\text{km/hr}$$-that took $$1\\text{hr}$$. For the other second $$50\\text{km}$$, they drove at $$25\\text{km/hr}$$-that took $$2\\text{hrs}$$ . The trip took $$3\\text{hrs}$$ . " ]

[]

[ [ { "aoVal": "A", "content": "$10\\textbackslash\\%$ " } ], [ { "aoVal": "B", "content": "$12\\textbackslash\\%$ " } ], [ { "aoVal": "C", "content": "$15\\textbackslash\\%$ " } ], [ { "aoVal": "D", "content": "$18\\textbackslash\\%$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems" ]

[ "$$600\\times 8\\textbackslash\\%=48$$ g, $$600-120=480$$ g, $$48\\div 480\\times 100\\textbackslash\\%=10\\textbackslash\\%$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$12$$ " } ], [ { "aoVal": "B", "content": "$$18$$ " } ], [ { "aoVal": "C", "content": "$$16$$ " } ], [ { "aoVal": "D", "content": "$$20$$ " } ], [ { "aoVal": "E", "content": "$$14$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems" ]

[ "The age of each twin is $(32-8) \\div 3 =8$ years old. Thus, Alex is $8 +8 =16$ years old. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$13$$ " } ], [ { "aoVal": "B", "content": "$$35$$ " } ], [ { "aoVal": "C", "content": "$$36$$ " } ], [ { "aoVal": "D", "content": "$$40$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems" ]

[ "There are $8-1=7$ spaces. $7\\times 5=35$. " ]

[]

[ [ { "aoVal": "A", "content": "Tuesday " } ], [ { "aoVal": "B", "content": "Wednesday " } ], [ { "aoVal": "C", "content": "Thursday " } ], [ { "aoVal": "D", "content": "Friday " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time" ]

[ "$$1$$ May is $$6+30+1=37$$ days after March $$25$$. Since $$37\\div7=5 \\text{ R }2$$, $$5$$ weeks after is still Monday and $$2$$ days after that is a Wednesday. " ]

[]

[ [ { "aoVal": "A", "content": "$$120$$ " } ], [ { "aoVal": "B", "content": "$$720$$ " } ], [ { "aoVal": "C", "content": "$$360$$ " } ], [ { "aoVal": "D", "content": "$$300$$ " } ], [ { "aoVal": "E", "content": "$$420$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules" ]

[ "The flying speed is $$120\\div2=60$$ miles/hr, and the flying time is $$11:30-5:30=6$$ hours. So, the total distance is $$60\\times 6=360$$ miles. " ]

[]

[ [ { "aoVal": "A", "content": "$$7.5$$ " } ], [ { "aoVal": "B", "content": "$$8$$ " } ], [ { "aoVal": "C", "content": "$$9.5$$ " } ], [ { "aoVal": "D", "content": "$$10$$ " } ], [ { "aoVal": "E", "content": "$$12$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems " ]

[ "Total revenue: $30\\times 8+50\\times 6+20\\times 13=800$ dollars A bag of assorted candy: $$800\\div 100=8$$ dollars " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$26$ " } ], [ { "aoVal": "B", "content": "$$30$$ " } ], [ { "aoVal": "C", "content": "$$33$$ " } ], [ { "aoVal": "D", "content": "$$39$$ " } ], [ { "aoVal": "E", "content": "$$40$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules" ]

[ "$10+10+10=30$ " ]

[]

[ [ { "aoVal": "A", "content": "$2$ hours " } ], [ { "aoVal": "B", "content": "$3$ hours " } ], [ { "aoVal": "C", "content": "$9$ hours " } ], [ { "aoVal": "D", "content": "$18$ hours " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems" ]

[ "Lee paints the room once in $6$ hours. Pat paints the room twice in $6$ hours. Together, they paint the room $3$ times in $6$ hours. So, it takes them $2$ hours to paint it once together. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "Originally, Ben had $3$ more books than Ken. " } ], [ { "aoVal": "B", "content": "Originally, Ben had $4$ more books than Ken. " } ], [ { "aoVal": "C", "content": "Originally, Ben had $1$ fewer book than Ken. " } ], [ { "aoVal": "D", "content": "Originally, Ben had $9$ more books than Ken. " } ], [ { "aoVal": "E", "content": "Originally, Ben had $7$ more books than Ken. " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems " ]

[ "$4+4-1=7$ " ]

[]

[ [ { "aoVal": "A", "content": "$$4$$ " } ], [ { "aoVal": "B", "content": "$$5$$ " } ], [ { "aoVal": "C", "content": "$$6$$ " } ], [ { "aoVal": "D", "content": "$$7$$ " } ], [ { "aoVal": "E", "content": "$$8$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis" ]

[ "If all were pencils, $10\\times 2= 20$ the total cost would be £$$20$$. $44- 20=24$ The difference is £$$24$$. $8-2=6$ $24\\div 6=4$ John bought $4$ notebooks. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$16$$ " } ], [ { "aoVal": "B", "content": "$$17$$ " } ], [ { "aoVal": "C", "content": "$$18$$ " } ], [ { "aoVal": "D", "content": "$$19$$ " } ], [ { "aoVal": "E", "content": "$$21$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Sum of Ages" ]

[ "$17 + 2 \\times 2 = 21$ " ]

[]

[ [ { "aoVal": "A", "content": "$$148$$ " } ], [ { "aoVal": "B", "content": "$$149$$ " } ], [ { "aoVal": "C", "content": "$$150$$ " } ], [ { "aoVal": "D", "content": "$$151$$ " } ], [ { "aoVal": "E", "content": "$$152$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression" ]

[ "$2+(50-1)\\times3=149$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$$2$$ " } ], [ { "aoVal": "C", "content": "$$3$$ " } ], [ { "aoVal": "D", "content": "$$4$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems" ]

[ "Seven years ago: Jucy : $7$ cat: $$0$$ This year: Jucy : $7+6=13$ cat: $0+7=7$ Nicole : $34-13-7=14$$ $$14-13=1$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$15$$ grams " } ], [ { "aoVal": "B", "content": "$$12$$ grams " } ], [ { "aoVal": "C", "content": "$$9$$ grams " } ], [ { "aoVal": "D", "content": "$$6$$ grams " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants" ]

[ "$$40-40\\times25\\textbackslash\\%\\div40\\textbackslash\\%=40-25=15$$ grams. " ]

[]

[ [ { "aoVal": "A", "content": "$$5$$ " } ], [ { "aoVal": "B", "content": "$$8$$ " } ], [ { "aoVal": "C", "content": "$$9$$ " } ], [ { "aoVal": "D", "content": "$$11$$ " } ], [ { "aoVal": "E", "content": "$$13$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable" ]

[ "$$76=10+10+10+10+10+10+10+6$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$160$$ dollars " } ], [ { "aoVal": "B", "content": "$$180$$ dollars " } ], [ { "aoVal": "C", "content": "$$190$$ dollars " } ], [ { "aoVal": "D", "content": "$$200$$ dollars " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts" ]

[ "$$\\left( 125+25 \\right)\\div \\left( 1-25 \\textbackslash\\% \\right)=200$$ dollars. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$36$ kilograms " } ], [ { "aoVal": "B", "content": "$38$ kilograms " } ], [ { "aoVal": "C", "content": "$40$ kilograms " } ], [ { "aoVal": "D", "content": "$43$ kilograms " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems " ]

[ "$4 \\times 37 + 11 \\times 41+ 161 = 760$ kilograms in total. $760 \\div (4 + 11 + 5) = 38$ kg. " ]

[]

[ [ { "aoVal": "A", "content": "$$10$$ " } ], [ { "aoVal": "B", "content": "$$30$$ " } ], [ { "aoVal": "C", "content": "$$20$$ " } ], [ { "aoVal": "D", "content": "$$15$$ " } ], [ { "aoVal": "E", "content": "$$12$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road" ]

[ "Mary walks a total of $$300+300=600\\rm$$ meters in $$40$$ minutes. Average speed: $600\\div40=15$ m/min " ]

[]

[ [ { "aoVal": "A", "content": "$$192$$ " } ], [ { "aoVal": "B", "content": "$$208$$ " } ], [ { "aoVal": "C", "content": "$$240$$ " } ], [ { "aoVal": "D", "content": "$$270$$ " } ], [ { "aoVal": "E", "content": "$$288$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value" ]

[ "If $$6$$ cans contain $$96$$ teaspoons of sugar, $$1$$ can contains $$96\\div6 = 16$$ teaspoons of sugar. Thus $$15$$ cans contain $$16\\times15 =240$$ teaspoons of sugar. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$6$$\\textsuperscript{th} " } ], [ { "aoVal": "B", "content": "$10$\\textsuperscript{th} " } ], [ { "aoVal": "C", "content": "$8$\\textsuperscript{th} " } ], [ { "aoVal": "D", "content": "$9$\\textsuperscript{th} " } ], [ { "aoVal": "E", "content": "$7$\\textsuperscript{th} " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple" ]

[ "Except for Tomek, there are~$28-1=27$~students. The number of students who received more points than Tomek is~$27\\div(2+1)=9$, so Tomek is in the~$9+1=10^{th}$~place. " ]

[]

[ [ { "aoVal": "A", "content": "Friday " } ], [ { "aoVal": "B", "content": "Saturday " } ], [ { "aoVal": "C", "content": "Sunday " } ], [ { "aoVal": "D", "content": "Monday " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time" ]

[ "$$366$$ days $$=52$$ weeks $$2$$ days. Jan $$1$$ $$1988$$ is $$52$$ weeks $$2$$ days before Jan $$1$$ $$1989$$. This date in $$1988$$ is $$2$$ days before Sunday so it is on a Friday. " ]

[]

[ [ { "aoVal": "A", "content": "$$$145.00$$ " } ], [ { "aoVal": "B", "content": "$$$146.50$$ " } ], [ { "aoVal": "C", "content": "$$$150.00$$ " } ], [ { "aoVal": "D", "content": "$$$151.50$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method" ]

[ "Six algebra books cost $$$12.50 \\times 6 = $75$$. Five geometry books cost $$$14\\times5 = $70$$. All together, they cost a total of $$$145$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$25000$$ " } ], [ { "aoVal": "B", "content": "$$100000$$ " } ], [ { "aoVal": "C", "content": "$$160000$$ " } ], [ { "aoVal": "D", "content": "$$225000$$ " } ], [ { "aoVal": "E", "content": "$$275000$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base" ]

[ "A $$90\\textbackslash\\%$$ decrease means $$10\\textbackslash\\%$$ of $$250000 = 250000 \\div 10 = 25000$$ of the lions remain. " ]

[]

[ [ { "aoVal": "A", "content": "$$60$$ " } ], [ { "aoVal": "B", "content": "$$61$$ " } ], [ { "aoVal": "C", "content": "$$67$$ " } ], [ { "aoVal": "D", "content": "$$70$$ " } ], [ { "aoVal": "E", "content": "$$71$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems " ]

[ "$91\\times5-(100+99+98+97)=61$. " ]

[]

[ [ { "aoVal": "A", "content": "$$x=4$$ " } ], [ { "aoVal": "B", "content": "$$x=5$$ " } ], [ { "aoVal": "C", "content": "$$x=6$$ " } ], [ { "aoVal": "D", "content": "$$x=8$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems" ]

[ "The equation can represents this situation is $$4x-2=22$$, so, $$4x=24$$, $$x=6$$. So, the answer is $$6$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$18$$ " } ], [ { "aoVal": "B", "content": "$$17$$ " } ], [ { "aoVal": "C", "content": "$$16$$ " } ], [ { "aoVal": "D", "content": "$$15$$ " } ], [ { "aoVal": "E", "content": "$$14$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares->Solid Squares->Basic Solid Square Problems" ]

[ "The total: $36+16+1=53$ , Jack\\textquotesingle s location: $$(53-1)\\div2=21$$, so there are $15$ people between Jack and Rose. " ]

[]

[ [ { "aoVal": "A", "content": "$$70$$ " } ], [ { "aoVal": "B", "content": "$$72$$ " } ], [ { "aoVal": "C", "content": "$$75$$ " } ], [ { "aoVal": "D", "content": "$$80$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants" ]

[ "$$30\\times30\\textbackslash\\%+20\\times 20\\textbackslash\\%=9+4=13$$ ounces. $$13\\div10\\textbackslash\\%-(30+20)=80$$ ounces. " ]

[]

[ [ { "aoVal": "A", "content": "$$3$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$6$$ " } ], [ { "aoVal": "D", "content": "$$2$$ " } ], [ { "aoVal": "E", "content": "$$12$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules" ]

[ "$$12\\div3=4$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$33$$ " } ], [ { "aoVal": "B", "content": "$$34$$ " } ], [ { "aoVal": "C", "content": "$$70$$ " } ], [ { "aoVal": "D", "content": "$$97$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable" ]

[ "Since $$100\\div 3=33$$ with remainder $$1$$, it takes my frog $$33$$ jumps to jump $$99\\text{m}$$. It needs $$1$$ more jump, for $$34$$ jumps in all, to go at least $$100\\text{m}$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$1996$$ " } ], [ { "aoVal": "B", "content": "$$1994$$ " } ], [ { "aoVal": "C", "content": "$$1992$$ " } ], [ { "aoVal": "D", "content": "$$1990$$ " } ], [ { "aoVal": "E", "content": "$$1988$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Time" ]

[ "The $10$\\textsuperscript{th}~Math Kangaroo was taking place in $2001$, which means that Alice was $9$ years old in $2001$, so she was born in $1992$. " ]

[]

[ [ { "aoVal": "A", "content": "$$6$$ " } ], [ { "aoVal": "B", "content": "$$12$$ " } ], [ { "aoVal": "C", "content": "$$18$$ " } ], [ { "aoVal": "D", "content": "$$24$$ " } ], [ { "aoVal": "E", "content": "$$30$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base" ]

[ "One-fourth of a loaf of bread is ``$$1$$.'' Half a loaf of bread is ``$$2$$.'' One-fourth of a loaf of bread: $$6 \\div (2-1) =6$$. A whole loaf of bread: $$6 \\times 4 =24$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$3$$ " } ], [ { "aoVal": "B", "content": "$$6$$ " } ], [ { "aoVal": "C", "content": "$$4$$ " } ], [ { "aoVal": "D", "content": "$$5$$ " } ], [ { "aoVal": "E", "content": "$$7$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method" ]

[ "$$9-2-1=6$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$40$$ " } ], [ { "aoVal": "B", "content": "$$77$$ " } ], [ { "aoVal": "C", "content": "$$80$$ " } ], [ { "aoVal": "D", "content": "$$83$$ " } ], [ { "aoVal": "E", "content": "$$87$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems" ]

[ "$70 \\textbackslash\\% \\cdot 10=7$ $80 \\textbackslash\\% \\cdot 20=16$ $90 \\textbackslash\\% \\cdot 30=27$ Adding them up gets $7+16+27=50$. The overall percentage correct would be $\\frac{50}{60}=\\frac{5}{6}=5 \\cdot 16 . \\overline{6}=83 . \\overline{3} \\approx(\\mathbf{D}) 83$. " ]

[]

[ [ { "aoVal": "A", "content": "$$35$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$47$$ " } ], [ { "aoVal": "D", "content": "$$50$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules" ]

[ "$$2021\\div (21+22)=47$$. " ]

[]

[ [ { "aoVal": "A", "content": "$18$ " } ], [ { "aoVal": "B", "content": "$20$ " } ], [ { "aoVal": "C", "content": "$$24$$ " } ], [ { "aoVal": "D", "content": "$30$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units" ]

[ "$12$ is the product of $6$ and $2$.Then multiple $3$ by $6$ is the number of red cards. The total number of cards is $30$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$87.5$$ " } ], [ { "aoVal": "B", "content": "$$90$$ " } ], [ { "aoVal": "C", "content": "$$92.5$$ " } ], [ { "aoVal": "D", "content": "$$95.5$$ " } ], [ { "aoVal": "E", "content": "$$100$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems" ]

[ "Assume the total amount of problems is 100 per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got 80 problems correct by herself, and got 180 problems correct overall. We also know that Zoe had 75 problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $180-80=100$. Therefore Zoe has $100+75=175$ problems out of $200$ problems correct. Thus $\\frac{175}{200} = 87.5$ percent. " ]

[]

[ [ { "aoVal": "A", "content": "$$A$$ comes out even " } ], [ { "aoVal": "B", "content": "$$A$$ makes ＄$$1100$$ on the deal " } ], [ { "aoVal": "C", "content": "$$A$$ makes ＄$$1000$$ on the deal " } ], [ { "aoVal": "D", "content": "$$A$$ loses ＄$$900$$ on the deal " } ], [ { "aoVal": "E", "content": "$$A$$ loses ＄$$1000$$ on the deal " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts" ]

[ "Mr. $$ A$$ sells his home for $$(1 + 10\\textbackslash\\%)\\times 10000$$ dollars$$= 1.1\\times 10000$$ dollars$$ = 11000$$ dollars to Mr. $$ B$$. Then, Mr. $$ B$$ sells it at a price of $$(1- 10\\textbackslash\\%)\\times 11000$$ dollars $$= 0.9\\times 11000$$ dollars $$= 9900$$ dollars, thus $$11000- 9900=\\boxed{ (\\rm B) \\textasciitilde A\\textasciitilde makes\\textasciitilde1100\\textasciitilde on\\textasciitilde the\\textasciitilde deal}$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$200$$ " } ], [ { "aoVal": "B", "content": "$$250$$ " } ], [ { "aoVal": "C", "content": "$$300$$ " } ], [ { "aoVal": "D", "content": "$$400$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems" ]

[ "$120\\div(1-60\\textbackslash\\%)=300$ ounces. " ]

[]

[ [ { "aoVal": "A", "content": "$$$$A " } ], [ { "aoVal": "B", "content": "$$$$B " } ], [ { "aoVal": "C", "content": "$$$$Cain " } ], [ { "aoVal": "D", "content": "$$$$Devi " } ], [ { "aoVal": "E", "content": "$$$$Emily " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Circular Operations" ]

[ "After Amit says \"$$2015$$\", there are $$5102-2015=3087$$ numbers remaining. Thus the counting goes round the table $$3087\\div6= 514$$ times with a remainder of $$3$$, so the last to count is Devi. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$9$$ " } ], [ { "aoVal": "B", "content": "$$10$$ " } ], [ { "aoVal": "C", "content": "$$11$$ " } ], [ { "aoVal": "D", "content": "$$12$$ " } ], [ { "aoVal": "E", "content": "$$13$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems" ]

[ "$10 - 1 = 9$ " ]

[]

[ [ { "aoVal": "A", "content": "$$1:2$$ " } ], [ { "aoVal": "B", "content": "$$1:3$$ " } ], [ { "aoVal": "C", "content": "$$2:3$$ " } ], [ { "aoVal": "D", "content": "$$2:1$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio" ]

[ "If $$6$$ students are wearing jeans, then $$18-6=12$$ are not. The ratio of students wearing jeans to students not wearing jeans is $$6:12=1:2$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$14$$ " } ], [ { "aoVal": "B", "content": "$$15$$ " } ], [ { "aoVal": "C", "content": "$$17$$ " } ], [ { "aoVal": "D", "content": "$$30$$ " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division" ]

[ "There are $99$ $4-3 = 33$-multiples of $3$ less than $100$. $3$ of them are one-digit numbers: $3$, $6$ and $9$. Hence there are $30$ $2$-digit multiples of $3$. Similarly, there are $96 + 6 -1 = 16 -1 = 15$ $2$-digit multiples of $6$. Hence, the answer is 30 - 15 = \\textbf{15.} Answer： \\textbf{(B)} " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$210$$ " } ], [ { "aoVal": "B", "content": "$$40$$ " } ], [ { "aoVal": "C", "content": "$$30$$ " } ], [ { "aoVal": "D", "content": "$$20$$ " } ], [ { "aoVal": "E", "content": "$$10$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems" ]

[ "The efficiency of the first faucet is $\\frac1{70}$ and that of the other two is $\\frac3{70}$. Thus, it takes $1\\div (\\frac1{70}+\\frac3{70}\\times2)=10$ minutes to fill the pool. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$87.5$$ " } ], [ { "aoVal": "B", "content": "$$90$$ " } ], [ { "aoVal": "C", "content": "$$92.5$$ " } ], [ { "aoVal": "D", "content": "$$95.5$$ " } ], [ { "aoVal": "E", "content": "$$100$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems" ]

[ "Assume the total amount of problems is 100 per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got 80 problems correct by herself, and got 180 problems correct overall. We also know that Zoe had 75 problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $180-80=100$. Therefore Zoe has $100+75=175$ problems out of $200$ problems correct. Thus $\\frac{175}{200} = 87.5$ percent. " ]

[]

[ [ { "aoVal": "A", "content": "$$5$$ " } ], [ { "aoVal": "B", "content": "$$6$$ " } ], [ { "aoVal": "C", "content": "$$7$$ " } ], [ { "aoVal": "D", "content": "$$8$$ " } ], [ { "aoVal": "E", "content": "$$9$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules" ]

[ "Every day: $5-1=4$ bottles. $29\\div4=7R1$ But for the last day, the tank can be filled with water without using during the night. " ]

[]

[ [ { "aoVal": "A", "content": "$$20\\textbackslash\\%$$ " } ], [ { "aoVal": "B", "content": "$$24\\textbackslash\\%$$ " } ], [ { "aoVal": "C", "content": "$$25\\textbackslash\\%$$ " } ], [ { "aoVal": "D", "content": "$$30\\textbackslash\\%$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts" ]

[ "$$6500\\div(1+30\\textbackslash\\%)=5000$$, $$1200\\div5000=24\\textbackslash\\%$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$$2$$ " } ], [ { "aoVal": "C", "content": "$$3$$ " } ], [ { "aoVal": "D", "content": "$$4$$ " } ], [ { "aoVal": "E", "content": "$$5$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems" ]

[ "Owen made $0.55 * 20=11$ shots originally. Letting $x$ be the number of shots she made, we have $\\frac{11+x}{25}=0.56$. Solving for $x$ gives us $x=$ (C) 3 " ]

[]

[ [ { "aoVal": "A", "content": "$$30$$ " } ], [ { "aoVal": "B", "content": "$$31$$ " } ], [ { "aoVal": "C", "content": "$$465$$ " } ], [ { "aoVal": "D", "content": "$$496$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem" ]

[ "There are in total $30$ days in Nov. $1+2+3+4+\\cdots+30=(1+30)\\times30\\div2=465$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$79$$ " } ], [ { "aoVal": "B", "content": "$$82$$ " } ], [ { "aoVal": "C", "content": "$$84$$ " } ], [ { "aoVal": "D", "content": "$$86$$ " } ], [ { "aoVal": "E", "content": "$$88$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems" ]

[ "Assume the total amount of problems is $100$ per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got $90$ problems correct by herself, and got $168$ problems correct overall. We also know that Zoe had $80$ problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $168-90=78$. Therefore Zoe has $80+78=158$ problems out of $200$ problems correct. This is (C) $79$ percent. " ]

[]

[ [ { "aoVal": "A", "content": "Sunday　 " } ], [ { "aoVal": "B", "content": "Monday　 " } ], [ { "aoVal": "C", "content": "Wednesday　 " } ], [ { "aoVal": "D", "content": "Friday　 " } ], [ { "aoVal": "E", "content": "Saturday　 " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time" ]

[ "There are 14 days between $$1$$\\textsuperscript{st~}April and $$15^{}\\text{th}$$April. 14 days = 2 week Therefore, $$1$$\\textsuperscript{st~}April is Friday. " ]

[]

[ [ { "aoVal": "A", "content": "$$10$$ " } ], [ { "aoVal": "B", "content": "$$21$$ " } ], [ { "aoVal": "C", "content": "$$20$$ " } ], [ { "aoVal": "D", "content": "$$15$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference" ]

[ "$$(31-11)\\div2=10.$$ " ]

[]

[ [ { "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 " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems" ]

[ "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. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$216$$ " } ], [ { "aoVal": "B", "content": "$$32$$ " } ], [ { "aoVal": "C", "content": "$$72$$ " } ], [ { "aoVal": "D", "content": "$$96$$ " } ], [ { "aoVal": "E", "content": "$$120$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value" ]

[ "Given the product of three numbers, the smaller the difference, the smaller the sum. $6\\times6\\times6=216$, so the answer is $6\\times 12=72.$ " ]

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[ [ { "aoVal": "A", "content": "＄$$28000$$ " } ], [ { "aoVal": "B", "content": "＄$$32000$$ " } ], [ { "aoVal": "C", "content": "＄$$35000$$ " } ], [ { "aoVal": "D", "content": "＄$$42000$$ " } ], [ { "aoVal": "E", "content": "＄$$56000$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems" ]

[ "Method $$1$$：$$Let$$ the income amount be denoted by $$A$$. We know that $$\\frac{A\\left( p+.25 \\right)}{100}=\\frac{28000p}{100}+\\frac{\\left( p+2 \\right)\\left( A-28000 \\right)}{100}$$ We can now try to solve for $$A$$: $$\\left( p+.25 \\right)A=28000p+Ap+2A-28000p-56000$$ $$0.25A=2A-56000$$ $$A=32000$$ so the answer is $$\\boxed{ \\text {B}}$$. Method $$2$$: Let $$A$$, $$T$$ be Kristin\\textquotesingle s annual income and the income tax total, respectively. Notice that　 $$T=p\\textbackslash\\%\\cdot 28000+\\left( p+2 \\right)\\textbackslash\\%\\cdot \\left( A-28000 \\right)$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde$$$$=\\left[ p\\textbackslash\\%\\cdot 28000+p\\textbackslash\\%\\cdot \\left( A-28000 \\right) \\right]+2\\textbackslash\\%\\cdot \\left( A-28000 \\right)$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde$$$$=p\\textbackslash\\%\\cdot A+2\\textbackslash\\%\\cdot \\left( A-28000 \\right)$$ We are also given that $$T=\\left( p+0.25 \\right)\\textbackslash\\%\\cdot A=p\\textbackslash\\%\\cdot A+0.25\\textbackslash\\%\\cdot A$$ Thus, $$p\\textbackslash\\%\\cdot A+2\\textbackslash\\%\\cdot \\left( A-28000 \\right)=p\\textbackslash\\%\\cdot A+0.25\\textbackslash\\%\\cdot A$$ $$2\\textbackslash\\%\\cdot \\left( A-28000 \\right)=0.25\\textbackslash\\%\\cdot A$$ Solve for $$A$$ to obtain $$A=32000$$. $$\\boxed{ \\text {B}}$$ " ]

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[ [ { "aoVal": "A", "content": "$$30$$ " } ], [ { "aoVal": "B", "content": "$$26$$ " } ], [ { "aoVal": "C", "content": "$$20$$ " } ], [ { "aoVal": "D", "content": "$$42$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules" ]

[ "$3$~$\\times$~$10$ = $30$ " ]

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[ [ { "aoVal": "A", "content": "$$5$$ " } ], [ { "aoVal": "B", "content": "$$10$$ " } ], [ { "aoVal": "C", "content": "$$15$$ " } ], [ { "aoVal": "D", "content": "$$20$$ " } ], [ { "aoVal": "E", "content": "$$50$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base" ]

[ "Sleeping for $$50$$ minutes every hour through the day is $$\\frac{5}{6}$$ of every hour and thus $$\\frac{5}{6}$$ of the day. Of $$24$$ hours, $$\\frac{5}{6}$$ is $$20$$ hours. " ]

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[ [ { "aoVal": "A", "content": "$$119$$ " } ], [ { "aoVal": "B", "content": "$$120$$ " } ], [ { "aoVal": "C", "content": "$$121$$ " } ], [ { "aoVal": "D", "content": "$$122$$ " } ], [ { "aoVal": "E", "content": "Non of the above " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction" ]

[ "With $$81$$ sweets wrappers. Peter can exchange for $$\\frac{81}{3}=27$$ more sweets With the additional $$27$$ sweets wrappers, Peter can exchange for $$\\frac{27}{3}=9$$ more sweets. with the~~additional $$9$$ sweets wrappes. Peter can exchange for $$\\frac{9}{3}=3$$ more sweets. with the additional $$3$$ sweets wrappers. Peter can exchange for $$\\frac{3}{3}=1$$ more sweet. Therefore, the largest possible number of sweets Peter could have eaten is $$81+27+9+3+1=121$$. " ]

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[ [ { "aoVal": "A", "content": "$$95$$ " } ], [ { "aoVal": "B", "content": "$$110$$ " } ], [ { "aoVal": "C", "content": "$$120$$ " } ], [ { "aoVal": "D", "content": "$$135$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples" ]

[ "$15\\times6=90$ $90+5=95$ $95+15=110$ " ]

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[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$$4$$ " } ], [ { "aoVal": "C", "content": "$$5$$ " } ], [ { "aoVal": "D", "content": "$$6$$ " } ], [ { "aoVal": "E", "content": "$$9$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems" ]

[ "Two of the pieces of information relate to Chas, so we can try to relate the ages of the others to his age. Given Dave is $$5$$ years older than Chas, but $$3$$ years older than Benu, we can tell that Benu is $$2$$ years older than Chas. Given also that Anilis $$3$$ years younger than Chas, we can say that the sum of the ages of the four children is $$\\left( -3+2+5=4 \\right) $$ more than four times Chas' age. So four times Chas' age plus four is twenty, and so Chas must be four. So Anil is just $$ 1$$ year old. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$205$$ " } ], [ { "aoVal": "B", "content": "$$156$$ " } ], [ { "aoVal": "C", "content": "$$84$$ " } ], [ { "aoVal": "D", "content": "$$35$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems" ]

[ "$240 \\times 35$\\%=$84$, Allen has $84$ fossilized snail shells. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$42$$ " } ], [ { "aoVal": "B", "content": "$$19$$ " } ], [ { "aoVal": "C", "content": "$$9$$ " } ], [ { "aoVal": "D", "content": "$$0$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules" ]

[ "$51-42=9$ " ]

[]

[ [ { "aoVal": "A", "content": "$$10$$ " } ], [ { "aoVal": "B", "content": "$$21$$ " } ], [ { "aoVal": "C", "content": "$$20$$ " } ], [ { "aoVal": "D", "content": "$$15$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference" ]

[ "$$(31-11)\\div2=10.$$ " ]

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[ [ { "aoVal": "A", "content": "$$120$$ " } ], [ { "aoVal": "B", "content": "$$90$$ " } ], [ { "aoVal": "C", "content": "$$85$$ " } ], [ { "aoVal": "D", "content": "$$60$$ " } ], [ { "aoVal": "E", "content": "$$55$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems" ]

[ "Now, Wendy has $30-3-7=20$ stickers. Thus, all of them have $20\\times3=60$ stickers, which is equal to the total number of stickers they had at the beginning. " ]