Datasets:

---

math-eval

/

TAL-SCQ5K

like 56

[]

[ [ { "aoVal": "A", "content": "None　 " } ], [ { "aoVal": "B", "content": "$$\\frac{1}{2}$$ " } ], [ { "aoVal": "C", "content": "$$\\frac{1}{3}$$ " } ], [ { "aoVal": "D", "content": "$$\\frac{2}{3}$$ " } ], [ { "aoVal": "E", "content": "$$\\frac{1}{6}$$ " } ] ]

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

[ "After I eat one half, half of the apple pie is left. Eating two thirds of this half leaves one third of one half of the pie, which is one sixth, for Monday. " ]

[]

[ [ { "aoVal": "A", "content": "$$$30$$ " } ], [ { "aoVal": "B", "content": "$$$25$$ " } ], [ { "aoVal": "C", "content": "$$$20$$ " } ], [ { "aoVal": "D", "content": "$$$15$$ " } ] ]

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

[ "1S + 3B = 75; 1S = 2B; 2B + 3B = 75; 5B = 75; B = 75~$\\div$~5 = 15 1S = 2~$\\times$~15 = 30 " ]

[]

[ [ { "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" ]

[ "$$F=M-4$$ $$M-4+M=10$$ $$M=7$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$51$$ " } ], [ { "aoVal": "B", "content": "$$58.4$$ " } ], [ { "aoVal": "C", "content": "$$255$$ " } ], [ { "aoVal": "D", "content": "$$306$$ " } ], [ { "aoVal": "E", "content": "$$308.8$$ " } ] ]

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

[ "Everyone should pay $10.2\\times5=51$ dollars. $51\\times 6=306$ " ]

[]

[ [ { "aoVal": "A", "content": "$$3:2$$ " } ], [ { "aoVal": "B", "content": "$$2:3$$ " } ], [ { "aoVal": "C", "content": "$$11:6$$ " } ], [ { "aoVal": "D", "content": "$$6:11$$ " } ] ]

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

[ "Women: $$60-24=36$$, Women: Men$$=36:24=3:2$$. " ]

[ "其它" ]

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

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

[ "The efficiency of the first faucet is $\\frac1{36}$ and that of the other two is $\\frac4{36}$. Thus it takes $1\\div (\\frac1{36}+\\frac4{36}\\times2)=4$ hours to fill the pool. " ]

[]

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

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

[ "Three weeks after yesterday, which was a Monday, is a Monday also. Two days after a Monday is a Wednesday. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$70$$ " } ], [ { "aoVal": "B", "content": "$$77$$ " } ], [ { "aoVal": "C", "content": "$$84$$ " } ], [ { "aoVal": "D", "content": "$$91$$ " } ], [ { "aoVal": "E", "content": "$$98$$ " } ] ]

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

[ "$28 \\div (5 - 1) = 7$ $7 \\times (12 - 1) = 77$ " ]

[]

[ [ { "aoVal": "A", "content": "$$15$$ " } ], [ { "aoVal": "B", "content": "$$18$$ " } ], [ { "aoVal": "C", "content": "$$19$$ " } ], [ { "aoVal": "D", "content": "$$20$$ " } ], [ { "aoVal": "E", "content": "$$31$$ " } ] ]

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

[ "The total weight of all the boxes is $15+16+18+19+20+31=119$ kg. The weight of pears is twice that of apples, so excluding the box of orange, the weight of the remaining boxes should be divisible by $3$. Only removing $20$, the remaining weight is divisible by $3$. " ]

[]

[ [ { "aoVal": "A", "content": "＄$$150$$ " } ], [ { "aoVal": "B", "content": "＄$$200$$ " } ], [ { "aoVal": "C", "content": "＄$$250$$ " } ], [ { "aoVal": "D", "content": "＄$$300$$ " } ] ]

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

[ "$$(75-60)\\times 10 = 150$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$80$$ " } ], [ { "aoVal": "B", "content": "$$90$$ " } ], [ { "aoVal": "C", "content": "$$92$$ " } ], [ { "aoVal": "D", "content": "$$102$$ " } ] ]

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

[ "Solve the problem as a problem of surplus and shortage. If each student carries $9$ bottles, there will be a shortage of $9\\times2=18$ bottles; if each student carries $8$ bottles, there will be a shortage of $8-2=6$ bottles. Therefore, there are $(18-6)\\div(9-8)=12$ students and $12\\times9-18=90$ bottles of water. " ]

[]

[ [ { "aoVal": "A", "content": "$$1960$$ " } ], [ { "aoVal": "B", "content": "$$2401$$ " } ], [ { "aoVal": "C", "content": "$$2000$$ " } ], [ { "aoVal": "D", "content": "$$2601$$ " } ], [ { "aoVal": "E", "content": "$$2500$$ " } ] ]

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

[ "The number of students on each side of the outermost layer was $$196\\div 4+1=50$$ students. The total number of students in the array was $$50\\times 50=2500$$. " ]

[]

[ [ { "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" ]

[ "$(31-25+30+1=37$ $37\\div7=5R2$ Exactly $5$ weeks from $25$ Mar, it will also be a Monday; another $2$ days later will be a Wednesday " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$30$$ " } ], [ { "aoVal": "B", "content": "$$35$$ " } ], [ { "aoVal": "C", "content": "$$37$$ " } ], [ { "aoVal": "D", "content": "$$39$$ " } ], [ { "aoVal": "E", "content": "$$40$$ " } ] ]

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

[ "Since $30 \\textbackslash\\%$ of the original 45 liters of paint was yellow, and 5 liters of yellow paint were added to make the new mixture, there are $13.5+5=18.5$ liters of yellow tint in the new mixture. Since only 5 liters of paint were added to the original 45 , there are a total of 50 liters of paint in the new mixture. This gives $ 37\\textbackslash\\%$ of yellow tint in the new mixture, which is (C) 37 . " ]

[]

[ [ { "aoVal": "A", "content": "$$7$$ " } ], [ { "aoVal": "B", "content": "$$8$$ " } ], [ { "aoVal": "C", "content": "$$15$$ " } ], [ { "aoVal": "D", "content": "$$16$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line" ]

[ "The $$8$$\\textsuperscript{th} means there are $$7$$ people in front of him. So there are also $$7$$ people behind him. The total number of pirates can be calculated: $$7+7+1=15$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$6$$ minutes " } ], [ { "aoVal": "B", "content": "$$9$$ minutes " } ], [ { "aoVal": "C", "content": "$$12$$ minutes " } ], [ { "aoVal": "D", "content": "$$18$$ minutes " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

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

[ "$$18\\div3=6$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$12$$ " } ], [ { "aoVal": "B", "content": "$$13$$ " } ], [ { "aoVal": "C", "content": "$$24$$ " } ], [ { "aoVal": "D", "content": "$$26$$ " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

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

[ "132/11 = 12 lanterns 12 lanterns + 1 = 13 lanterns 13 x 2 = 26 lanterns. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$1800$$ m " } ], [ { "aoVal": "B", "content": "$$2100$$ m " } ], [ { "aoVal": "C", "content": "$$2400$$ m " } ], [ { "aoVal": "D", "content": "$$2700$$ m " } ], [ { "aoVal": "E", "content": "$$3000$$ m " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Straight Line Type with Objects on Both Sides->Planting Trees on Both Sides" ]

[ "Each interval is $600\\div2=300$ m. There are $9-1=8$ intervals in total, so the bus route\\textquotesingle s length is $300\\times8=2400$ m. " ]

[]

[ [ { "aoVal": "A", "content": "$$7$$ " } ], [ { "aoVal": "B", "content": "$$8$$ " } ], [ { "aoVal": "C", "content": "$$15$$ " } ], [ { "aoVal": "D", "content": "$$16$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line" ]

[ "The $$8$$\\textsuperscript{th} means there are $$7$$ people in front of him. So there are also $$7$$ people behind him. The total number of pirates can be calculated: $$7+7+1=15$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$148$$ " } ], [ { "aoVal": "B", "content": "$$152$$ " } ], [ { "aoVal": "C", "content": "$$144$$ " } ], [ { "aoVal": "D", "content": "$$140$$ " } ], [ { "aoVal": "E", "content": "$$156$$ " } ] ]

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

[ "$$36\\times 4=144$$, or $$37\\times 4-4=144$$ students. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$48$$ " } ], [ { "aoVal": "B", "content": "$$24$$ " } ], [ { "aoVal": "C", "content": "$$16$$ " } ], [ { "aoVal": "D", "content": "$$12$$ " } ], [ { "aoVal": "E", "content": "$$8$$ " } ] ]

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

[ "$8\\times6\\div4=12$ " ]

[]

[ [ { "aoVal": "A", "content": "$$8$$ " } ], [ { "aoVal": "B", "content": "$$33$$ " } ], [ { "aoVal": "C", "content": "$$38$$ " } ], [ { "aoVal": "D", "content": "$$43$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems->Finding the Working Hours" ]

[ "$$[（38-8）\\times2+6]\\div2=33$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$15$$ " } ], [ { "aoVal": "B", "content": "$$30$$ " } ], [ { "aoVal": "C", "content": "$$45$$ " } ], [ { "aoVal": "D", "content": "$$60$$ " } ], [ { "aoVal": "E", "content": "None of the above " } ] ]

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

[ "A: J: S 20:15:5 = 40 120/40 = 3 oranges per person 3*15= 45 oranges " ]

[ "其它" ]

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

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

[ "There are $40\\div\\frac{84-79}{79-76}=24$ students in class $B.$ There are $(40+24)\\div\\frac{89-81}{81-79}=16$ students in class $C.$ $24:16=3:2$ " ]

[]

[ [ { "aoVal": "A", "content": "$3$~dollars and~$30$~cents " } ], [ { "aoVal": "B", "content": "$4$~dollars and~$80$~cents " } ], [ { "aoVal": "C", "content": "$5$~dollars and~$10$~cents " } ], [ { "aoVal": "D", "content": "$6$~dollars and~$30$~cents " } ], [ { "aoVal": "E", "content": "$8$~dollars and~$10$~cents " } ] ]

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

[ "$4$ dollars and $50$ cents are equal to $450$ cents, so one scoop of ice cream costs $450 \\div 3 = 150$ cents. $$3$$ dollars and $$60$$ cents are equal to $360$ cents, so one cookie costs $360 \\div 2 = 180$ cents. Thus, Ala should pay $ 150 + 180 = 330$ cents for one scoop of ice cream and one cookie. $330$ cents are equal to $3$ dollars and $30$ cents, so the answer is $A$. " ]

[]

[ [ { "aoVal": "A", "content": "$$5$$ " } ], [ { "aoVal": "B", "content": "$$10$$ " } ], [ { "aoVal": "C", "content": "$$13$$ " } ], [ { "aoVal": "D", "content": "$$23$$ " } ] ]

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

[ "$$55-42=13$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$32$$ " } ], [ { "aoVal": "B", "content": "$$33$$ " } ], [ { "aoVal": "C", "content": "$$29$$ " } ], [ { "aoVal": "D", "content": "$$26$$ " } ], [ { "aoVal": "E", "content": "$$24$$ " } ] ]

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

[ "$$(38-2)\\div (1+5)=36\\div 6=6$$ $$6\\times 5+2=32$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$150\\text{kg}$$ " } ], [ { "aoVal": "B", "content": "$$190\\text{kg}$$ " } ], [ { "aoVal": "C", "content": "$$240\\text{kg}$$ " } ], [ { "aoVal": "D", "content": "$$288\\text{kg}$$ " } ], [ { "aoVal": "E", "content": "$$324\\text{kg}$$ " } ] ]

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

[ "$$1-\\frac{1}{4}-\\frac{1}{3} =\\frac{5}{12}$$, $$120\\div\\frac{5}{12}=288\\text{kg}$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$12$$ June " } ], [ { "aoVal": "B", "content": "$$13$$ June " } ], [ { "aoVal": "C", "content": "$$14$$ August " } ], [ { "aoVal": "D", "content": "$$15$$ August " } ] ]

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

[ "Nicole uses $$4\\times2=8$$ ml of mouthwash every day. $$500\\div8=62$$ R $$4$$ So, $$62$$ days after $$12$$ April, the bottle of mouthwash will become empty. There are $$18$$ remaining days in April and $$31$$ days in May. $$62-18-31=13$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$3$$ " } ], [ { "aoVal": "B", "content": "$$3.5$$ " } ], [ { "aoVal": "C", "content": "$$4$$ " } ], [ { "aoVal": "D", "content": "$$4.85$$ " } ], [ { "aoVal": "E", "content": "$$5$$ " } ] ]

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

[ "Total revenue: $25\\times 5+60\\times 3+15\\times 12=485$ dollars A bag of assorted candy: $$485\\div 100=4.85$$ dollars " ]

[]

[ [ { "aoVal": "A", "content": "$$10$$ " } ], [ { "aoVal": "B", "content": "$$18$$ " } ], [ { "aoVal": "C", "content": "$$20$$ " } ], [ { "aoVal": "D", "content": "$$22$$ " } ] ]

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

[ "Jill is now $$14$$. Two years ago, she was $$12$$. Since Jack is now $$6$$ years older than Jill was $$2$$ years ago, Jack is now $$12 + 6= 18$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$167$$ " } ], [ { "aoVal": "B", "content": "$$133$$ " } ], [ { "aoVal": "C", "content": "$$166$$ " } ], [ { "aoVal": "D", "content": "$$433$$ " } ], [ { "aoVal": "E", "content": "$$177$$ " } ] ]

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

[ "$$300-133=167$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$30$$ " } ], [ { "aoVal": "B", "content": "$$40$$ " } ], [ { "aoVal": "C", "content": "$$50$$ " } ], [ { "aoVal": "D", "content": "$$60$$ " } ], [ { "aoVal": "E", "content": "$$80$$ " } ] ]

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

[ "The ratio by weight of carrot: cabbage:yoghurt$$=2:1:0.5$$ which we can double to give $$4:2:1$$. We can see that here $$2$$ represents the amount of cabbage and we want $$2 \\text{kg}$$ of cabbage, so there will be $$4+2+1=7\\text{kg}$$ of coleslaw altogether. Therefore the number of pots is $$7000\\div 175 =40$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$105$$ " } ], [ { "aoVal": "B", "content": "$$98$$ " } ], [ { "aoVal": "C", "content": "$$96$$ " } ], [ { "aoVal": "D", "content": "$$94$$ " } ], [ { "aoVal": "E", "content": "$$90$$ " } ] ]

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

[ "There are $108$ heroes in total. Subtract three heroines to get the number of male heroes. That is $108-3=105$. " ]

[]

[ [ { "aoVal": "A", "content": "$$8$$ " } ], [ { "aoVal": "B", "content": "$$12$$ " } ], [ { "aoVal": "C", "content": "$$24$$ " } ], [ { "aoVal": "D", "content": "$$38$$ " } ], [ { "aoVal": "E", "content": "$$6$$ " } ] ]

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

[ "$(100-2\\times46)\\div(3-2)=8$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$11$$ " } ], [ { "aoVal": "B", "content": "$$12$$ " } ], [ { "aoVal": "C", "content": "$$13$$ " } ], [ { "aoVal": "D", "content": "$$14$$ " } ], [ { "aoVal": "E", "content": "$$15$$ " } ] ]

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

[ "$$2$$ years time, Amanda $$10$$ and sister $$5$$. Total $$15$$. This year, $$15-2-2=11$$. " ]

[]

[ [ { "aoVal": "A", "content": "＄$$100$$ " } ], [ { "aoVal": "B", "content": "＄$$500$$ " } ], [ { "aoVal": "C", "content": "＄$$625$$ " } ], [ { "aoVal": "D", "content": "＄$$1000$$ " } ] ]

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

[ "Every $$4$$ quarters is ＄$$1$$; the number of dollars I have is $$2500\\div 4=$$＄$$625$$. " ]

[]

[ [ { "aoVal": "A", "content": "Yes, she can. " } ], [ { "aoVal": "B", "content": "No, she can\\textquotesingle t. " } ] ]

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

[ "$$15\\times7=105$$，$$105\\textless120$$． " ]

[]

[ [ { "aoVal": "A", "content": "$$30\\text{g}$$ " } ], [ { "aoVal": "B", "content": "$$40\\text{g}$$ " } ], [ { "aoVal": "C", "content": "$$50\\text{g}$$ " } ], [ { "aoVal": "D", "content": "$$120\\text{g}$$ " } ], [ { "aoVal": "E", "content": "$$160\\text{g}$$ " } ] ]

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

[ "Let the mass of one plum and the mass of one cherry be $$p \\text{g}$$ and $$c\\text{g}$$ respectively. Then $$2p +c=80$$ and $$p+c=50$$. We can deduce that $$p=80-50= 30$$, and so four plums weigh $$120 \\text{g}$$. Revise from ($$2017$$ Primary Mathematics Challenge-February, Question \\#$$18$$) " ]

[]

[ [ { "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->Equation Word Problems->Word Problems for Linear Equations with One Variable" ]

[ "Suppose Olivia has $$x$$ correct answers. $$5x-2(10-x)=29$$, $$x=7$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$39$$ " } ], [ { "aoVal": "B", "content": "$$44$$ " } ], [ { "aoVal": "C", "content": "$$ 52 $$ " } ], [ { "aoVal": "D", "content": "$$ 63 $$ " } ], [ { "aoVal": "E", "content": "$$ 74$$ " } ] ]

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

[ "On Kellin\\textquotesingle s $$13$$th birthday, Allen was four times her age, that is $$52$$. It is then eleven years until Kellin\\textquotesingle s $$24$$st birthday, so Allen\\textquotesingle s age at that time was $$52 +11 =63$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$6$$ " } ], [ { "aoVal": "B", "content": "$$8$$ " } ], [ { "aoVal": "C", "content": "$$9$$ " } ], [ { "aoVal": "D", "content": "$$10$$ " } ], [ { "aoVal": "E", "content": "$$12$$ " } ] ]

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

[ "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: $$2x+2y+2z=18$$, $$x+y+z=9$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$23$$ " } ], [ { "aoVal": "B", "content": "$$26$$ " } ], [ { "aoVal": "C", "content": "$$33$$ " } ], [ { "aoVal": "D", "content": "$$35$$ " } ], [ { "aoVal": "E", "content": "$$43$$ " } ] ]

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

[ "$6+7+10\\times2=33$ " ]

[ "其它" ]

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

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

[ "The efficiency of the first faucet is $\\frac1{20}$ and that of the other two is $\\frac3{20}$. Thus it takes $1\\div (\\frac1{20}+\\frac3{20}\\times3)=2$ hours to fill the pool. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$104\\text{kg}$$ " } ], [ { "aoVal": "B", "content": "$$52\\text{kg}$$ " } ], [ { "aoVal": "C", "content": "$$87\\text{kg}$$ " } ], [ { "aoVal": "D", "content": "$$96\\text{kg}$$ " } ], [ { "aoVal": "E", "content": "$$53\\text{kg}$$ " } ] ]

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

[ "$$139-35=104$$ Red kangaroo: $$104 \\div2 = 52$$ Gray kangaroo: $$52+35=87$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "None " } ], [ { "aoVal": "B", "content": "$\\frac12$ " } ], [ { "aoVal": "C", "content": "$\\frac13$ " } ], [ { "aoVal": "D", "content": "$\\frac23$ " } ], [ { "aoVal": "E", "content": "$\\frac16$ " } ] ]

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

[ "$(1-\\frac12)\\times(1-\\frac23)=\\frac12\\times\\frac13=\\frac16$. " ]

[]

[ [ { "aoVal": "A", "content": "$$48$$ " } ], [ { "aoVal": "B", "content": "$$40$$ " } ], [ { "aoVal": "C", "content": "$$32$$ " } ], [ { "aoVal": "D", "content": "$$24$$ " } ], [ { "aoVal": "E", "content": "$$8$$ " } ] ]

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

[ "Initially there are $$48$$ children of whom $$\\frac{3}{8}$$ are boys and $$\\frac{5}{8}$$ are girls, so there are $$18$$ boys and $$30$$ girls. When more boys join, there are still $$30$$ girls but now they form $$\\frac{3}{8}$$ of the total. So the total number of pupils is now $$\\frac{8}{3}\\times30= 80$$, of whom $$80-30=50$$ are boys. Hence the number of boys joining is $$50-18=32$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$4$$ " } ], [ { "aoVal": "B", "content": "$$8$$ " } ], [ { "aoVal": "C", "content": "$$12$$ " } ], [ { "aoVal": "D", "content": "$$16$$ " } ], [ { "aoVal": "E", "content": "$$3$$ " } ] ]

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

[ "The total points is $20\\times5=100.$ If there was one wrong anwser, she would lose $5+7=12$ points. $(20\\times5-4)\\div(7+5)=8$, so she got $20-8=12$ problems correct. " ]

[]

[ [ { "aoVal": "A", "content": "$$\\frac{8}{18}$$ " } ], [ { "aoVal": "B", "content": "$$\\frac{3}{9}$$ " } ], [ { "aoVal": "C", "content": "$$\\frac{4}{9}$$ " } ], [ { "aoVal": "D", "content": "$$\\frac{4}{5}$$ " } ] ]

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

[ "White shirts $$=8$$ Total shirts $$=4+6+8=18$$ Fraction of shirts that are white $$=\\frac{8}{18}=\\frac{4}{9}$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$20\\textbackslash\\% $$ " } ], [ { "aoVal": "B", "content": "$$25\\textbackslash\\%$$ " } ], [ { "aoVal": "C", "content": "$$55\\textbackslash\\%$$ " } ], [ { "aoVal": "D", "content": "$$ 60\\textbackslash\\%$$ " } ], [ { "aoVal": "E", "content": "$$75\\textbackslash\\%$$ " } ] ]

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

[ "Actually, we don\\textquotesingle t need the weight of the empty truck. Suppose the weight of the loaded truck before the first stop is $5x$ kg, and the weight of the feight is $4x$ kg. After the first stop, $4x \\times \\frac14=x$ kg of freight is unloaded. Now, the freight weighs $4x-x=3x$ kg, and the loaded truck weighs $5x-x=4x$ kg. Thus, the percent is $\\frac{3x}{4x}=\\frac34=75\\textbackslash\\%$. " ]

[]

[ [ { "aoVal": "A", "content": "$$8$$ days " } ], [ { "aoVal": "B", "content": "$$18$$ days " } ], [ { "aoVal": "C", "content": "$$20$$ days " } ], [ { "aoVal": "D", "content": "$$80$$ days " } ] ]

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

[ "Jodie has just begun to read a $$160$$-page book. If she reads $$20$$ pages every day, she will finish the book in $$160 \\div 20 =8$$ days. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$4$$ " } ], [ { "aoVal": "B", "content": "$$5$$ " } ], [ { "aoVal": "C", "content": "$$10$$ " } ], [ { "aoVal": "D", "content": "$$16$$ " } ], [ { "aoVal": "E", "content": "$$9$$ " } ] ]

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

[ "Witek has $$(28 - 10) \\div 2 = 9$$ zloty, so Tadek has $$9 + 7 = 16$$ zloty. " ]

[ "其它" ]

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

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

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

[]

[ [ { "aoVal": "A", "content": "$$14$$ " } ], [ { "aoVal": "B", "content": "$$13$$ " } ], [ { "aoVal": "C", "content": "$$12$$ " } ], [ { "aoVal": "D", "content": "$$11$$ " } ], [ { "aoVal": "E", "content": "$$10$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line" ]

[ "$5 + 10 - 2 = 13$ " ]

[ "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. " ]

[]

[ [ { "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->Unitary Method Problems->Applying Multiplication and Division" ]

[ "$$5$$ apples fall down from each trees. \"Each\"~is a sign of division. So, the answer is $$20\\div5=4$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$334$$ " } ], [ { "aoVal": "B", "content": "$$335$$ " } ], [ { "aoVal": "C", "content": "$$336$$ " } ], [ { "aoVal": "D", "content": "$$337$$ " } ] ]

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

[ "The only missing month is February. The sum will be either $$365$$ - $$28$$ or (in leap years) $$366$$ - $$29$$. Both are equal to $$337$$． " ]

[]

[ [ { "aoVal": "A", "content": "$$2$$ " } ], [ { "aoVal": "B", "content": "$$3$$ " } ], [ { "aoVal": "C", "content": "$$4$$ " } ], [ { "aoVal": "D", "content": "$$4.5$$ " } ], [ { "aoVal": "E", "content": "$$5$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Newton's Problem of Cows and Fields" ]

[ "Suppose a cow can eat $1$ m\\textsuperscript{2}~of grass each day. The amount of new grass that grows each day: $(9\\times10-12\\times7)\\div(9-7)=3$ m\\textsuperscript{2}. The amount of grass originally: $$90-9\\times 3=63$$ m\\textsuperscript{2}. $$24$$ cows can eat all grass in $$63\\div \\left( 24\\times1-3 \\right)=3$$ days. " ]

[]

[ [ { "aoVal": "A", "content": "$$17:00$$ " } ], [ { "aoVal": "B", "content": "$$15:55$$ " } ], [ { "aoVal": "C", "content": "$$15:30$$ " } ], [ { "aoVal": "D", "content": "$$15:00$$ " } ], [ { "aoVal": "E", "content": "$$14:40$$ " } ] ]

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

[ "Sam left Exeter three hours before Morgan left London, and travelled $$3\\times 25$$ miles $$=75$$ miles in the three hours to $$13:00$$. So at $$13:00$$, the distance between Sam and Morgan was $$ \\left( {175-75} \\right) $$ miles $$=100$$ miles. Let the time in hours between $$13:00$$ and the time at which Sam and Morgan met be $$t$$. Then $$25t+35t=100$$. So $$t=\\frac{{100}}{{60}}$$ hours $$=100$$ minutes $$=1$$ hour $$40$$ minutes. So Sam and Morgan met at $$14:40$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$4$$ " } ], [ { "aoVal": "B", "content": "$$8$$ " } ], [ { "aoVal": "C", "content": "$$9$$ " } ], [ { "aoVal": "D", "content": "$$10$$ " } ], [ { "aoVal": "E", "content": "$$11$$ " } ] ]

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

[ "$$3+7-1=9$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$150\\text{m}$$ " } ], [ { "aoVal": "B", "content": "$$190\\text{m}$$ " } ], [ { "aoVal": "C", "content": "$$240\\text{m}$$ " } ], [ { "aoVal": "D", "content": "$$288\\text{m}$$ " } ], [ { "aoVal": "E", "content": "$$324\\text{m}$$ " } ] ]

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

[ "The river is $$120\\text{m}$$ wide and represents $$\\left( 1-\\frac{1}{4}-\\frac{1}{3} \\right)=\\frac{5}{12}$$ of the length of the bridge. Therefore $$\\frac{1}{12}$$ of the length of the bridge is $$24\\text{m}$$. Hence the total length of the bridge is $$12\\times 24\\text{m}=288\\text{m}$$. " ]

[]

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

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

[ "Every 12th guest receives both a mask and a balloon. Hence, the 12th, 24th and 36th guest receive both. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$18$$ " } ], [ { "aoVal": "B", "content": "$$13$$ " } ], [ { "aoVal": "C", "content": "$$9$$ " } ], [ { "aoVal": "D", "content": "$$7$$ " } ], [ { "aoVal": "E", "content": "$$5$$ " } ] ]

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

[ "$5$ 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. " ]

[]

[ [ { "aoVal": "A", "content": "$$6$$ " } ], [ { "aoVal": "B", "content": "$$7$$ " } ], [ { "aoVal": "C", "content": "$$8$$ " } ], [ { "aoVal": "D", "content": "$$20$$ " } ], [ { "aoVal": "E", "content": "$$21$$ " } ] ]

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

[ "Before is ``$$1$$'', so after is ``$$4$$'', Before: $$(31-1) \\div (4+1) = 6$$, and John: $$6+1=7$$. " ]

[]

[ [ { "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->Concentration Problems->Solving Concentration Problems with Equations" ]

[ "Solution $$1$$. Say we add $$N$$ ounces of water to the shaving lotion. Since half of an $$9$$ ounce bottle of shaving lotion is alcohol, we know that we have $$\\dfrac{9}{2}$$ ounces of alcohol. We want $$\\dfrac{9}{2}=0.3(9+N)$$ (because we want the amount of alcohol, $$\\dfrac{9}{2}$$, to be $$30\\textbackslash\\%$$, or $$0.3$$, of the total amount of shaving lotion, $$9+N$$). Solving this, we find that $$9=0.6(9+N)\\Rightarrow9=5.4+0.6N\\hspace{0pt}\\Rightarrow3.6=0.6N\\hspace{0pt}\\Rightarrow6=N$$. So, the total amount of water we need to add is $$6$$. Solution $$2$$. The concentration of alcohol after adding $$n$$ ounces of water is $$\\dfrac{4.5}{9+n}$$. To get a solution of $$30\\textbackslash\\%$$ alcohol, we solve $$\\dfrac{4.5}{9+n}=\\dfrac{3}{10}$$ $$45=27+3n$$ $$18=3n$$ $$6=n\\Rightarrow6$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$25$$ " } ], [ { "aoVal": "B", "content": "$$15$$ " } ], [ { "aoVal": "C", "content": "$$30$$ " } ], [ { "aoVal": "D", "content": "$$10$$ " } ], [ { "aoVal": "E", "content": "$$5$$ " } ] ]

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

[ "There are 30 children. 15 of them participated in the \"moving bridge\" contest. This means that the other 15, who did not participate in the \"moving bridge\" surely went down the zip-wire. In fact 20 went down the zip-wire; therefore, 20-15=5 of the 15 \"moving bridges\\textquotesingle{} \" participants must have also gone down the zip-wire. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$11$$ " } ], [ { "aoVal": "B", "content": "$$15$$ " } ], [ { "aoVal": "C", "content": "$$28$$ " } ], [ { "aoVal": "D", "content": "$$33$$ " } ], [ { "aoVal": "E", "content": "$$34$$ " } ] ]

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

[ "Suppose that Lucy will be $x$ years old $3$ years later, Cathy will be $$(x+23)$$ years old. $x+(x+23)=45$, so $x=11$. Thus, Cathy will be $11+23=34$ years old $3$ years later. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$11$$ " } ], [ { "aoVal": "B", "content": "$$15$$ " } ], [ { "aoVal": "C", "content": "$$19$$ " } ], [ { "aoVal": "D", "content": "$$33$$ " } ], [ { "aoVal": "E", "content": "$$34$$ " } ] ]

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

[ "Suppose that Lucy will be $x$ years old $5$ years later, Cathy will be $$(x+13)$$ years old. $x+(x+13)=51$, so $x=19$. Thus, Cathy will be $13+19=32$ years old $5$ years later. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$36 " } ], [ { "aoVal": "B", "content": "$40 " } ], [ { "aoVal": "C", "content": "$34 " } ], [ { "aoVal": "D", "content": "$44 " } ], [ { "aoVal": "E", "content": "$30 " } ] ]

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

[ "40-1*4=36 " ]

[]

[ [ { "aoVal": "A", "content": "$375\\text{km}$ " } ], [ { "aoVal": "B", "content": "$275\\text{km}$ " } ], [ { "aoVal": "C", "content": "$187.5\\text{km}$ " } ], [ { "aoVal": "D", "content": "$75\\text{km}$ " } ] ]

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

[ "If $$2\\textasciitilde\\text{cm}$$ represents $$50\\textasciitilde\\text{km}$$, $$1\\textasciitilde\\text{cm}$$ represents $$25\\textasciitilde\\text{km}$$. So, their actual distance apart is $$7.5\\times 25=187.5\\textasciitilde\\text{km}$$. " ]

[ "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": "$$10$$ " } ], [ { "aoVal": "B", "content": "$$15$$ " } ], [ { "aoVal": "C", "content": "$$20$$ " } ], [ { "aoVal": "D", "content": "$$25$$ " } ], [ { "aoVal": "E", "content": "$$30$$ " } ] ]

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

[ "In $$300$$ seconds ($$5$$ minutes), Cagney will frost $$\\dfrac{300}{30}=10$$ cupcakes, and Lacey will frost $$\\dfrac{300}{60}=5$$ cupcakes. Therefore, working together they will frost $$10+5=\\boxed{(\\text{B})15}$$ cupcakes. " ]

[ "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": "$$0$$ " } ], [ { "aoVal": "B", "content": "$$1$$ " } ], [ { "aoVal": "C", "content": "$$2$$ " } ], [ { "aoVal": "D", "content": "$$3$$ " } ], [ { "aoVal": "E", "content": "$$4$$ " } ] ]

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

[ "The key point is that each kangaroo mother needs to take care of the same number of kangaroo babies. So $6$ (number of kangaroo baby) $$\\div$$ $5$ (number of kangaroo mother)$=1\\ldots\\ldots1$, and the remaining one is taken care of by kangaroo father. " ]

[]

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

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

[ "The number of boys that leave the room must equal the number of boys that remain. Since $$5$$ boys leave, there are $$5$$ boys still in the room for a total of $$10$$ boys. " ]

[]

[ [ { "aoVal": "A", "content": "$2$ dollars and $80$ cents " } ], [ { "aoVal": "B", "content": "$2$ dollars and $70$ cents " } ], [ { "aoVal": "C", "content": "$2$ dollars and $60$ cents " } ], [ { "aoVal": "D", "content": "$2$ dollars and $50$ cents " } ], [ { "aoVal": "E", "content": "$2$ dollars and $40$ cents " } ] ]

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

[ "$$2$$ dollars and $$70$$ cents=$270$ cents $$3$$ dollars and $$40$$ cents=$340$ cents One doll costs $270\\div3=90$ cents. One toy car costs $340\\div2=170$ cents. $170+90=260$ cents = $2$ dollars $60$ cents. " ]

[]

[ [ { "aoVal": "A", "content": "$$1 $$ minute " } ], [ { "aoVal": "B", "content": "$$25 $$ seconds " } ], [ { "aoVal": "C", "content": "$$30$$ seconds " } ], [ { "aoVal": "D", "content": "$$15$$ seconds " } ] ]

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

[ "The distance between them is $$100$$ m, and the difference between their speeds is $$12-8=4000$$ m/h. It takes $$100\\div4000\\times60=1.5$$minutes to catch the burglar, which is $$90$$ seconds " ]

[]

[ [ { "aoVal": "A", "content": "$$20$$\\% " } ], [ { "aoVal": "B", "content": "$25$\\% " } ], [ { "aoVal": "C", "content": "$30$\\% " } ], [ { "aoVal": "D", "content": "$33.3$\\% " } ] ]

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

[ "$$7\\div(7+21)=25\\textbackslash\\%$$. " ]

[]

[ [ { "aoVal": "A", "content": "$$30\\text{g}$$ " } ], [ { "aoVal": "B", "content": "$$40\\text{g}$$ " } ], [ { "aoVal": "C", "content": "$$50\\text{g}$$ " } ], [ { "aoVal": "D", "content": "$$120\\text{g}$$ " } ], [ { "aoVal": "E", "content": "$$160\\text{g}$$ " } ] ]

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

[ "Let the mass of one plum and the mass of one cherry be $$p \\text{g}$$ and $$c\\text{g}$$ respectively. Then $$2p +c=80$$ and $$2c+p=70$$. Hence $$3p +3c=150$$, and $$p+c=50$$. But since $$2p+c=80$$, we can deduce that $$p=80-50= 30$$, and so four plums weigh $$120 \\text{g}$$. " ]

[]

[ [ { "aoVal": "A", "content": "$20$; $12$ " } ], [ { "aoVal": "B", "content": "$13$; $19$ " } ], [ { "aoVal": "C", "content": "$18$; $14$ " } ], [ { "aoVal": "D", "content": "$19$; $13$ " } ] ]

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

[ "Suppose all the animals in the cage are chickens: there should be $$2\\times 32=64$$ legs. However, $$90-64=26$$ legs are missing because we counted $$26\\div2=13$$ rabbits as chickens. Hence, there are $$13$$ rabbits and $$32-13=19$$ chickens. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$40$$ " } ], [ { "aoVal": "B", "content": "$$50$$ " } ], [ { "aoVal": "C", "content": "$$60$$ " } ], [ { "aoVal": "D", "content": "$$70$$ " } ], [ { "aoVal": "E", "content": "$$80$$ " } ] ]

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

[ "The age difference between them is $(4-1)\\times10=30$, which stays the same forever. Then, when Anna\\textquotesingle s mother is twice as old as Anna, Anna should be $30$ years old, then her mom should be $30\\times2=60$. " ]

[]

[ [ { "aoVal": "A", "content": "$$$600$$ " } ], [ { "aoVal": "B", "content": "$$$480$$ " } ], [ { "aoVal": "C", "content": "$$$690$$ " } ], [ { "aoVal": "D", "content": "$$$550$$ " } ], [ { "aoVal": "E", "content": "$$$720$$ " } ] ]

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

[ "Number of students: $$(60+10)\\div (70-60)=7$$ Price of boardgame: $$60\\times7+60=480$$． " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$1$$ " } ], [ { "aoVal": "B", "content": "$$3$$ " } ], [ { "aoVal": "C", "content": "$$4$$ " } ], [ { "aoVal": "D", "content": "$$6$$ " } ], [ { "aoVal": "E", "content": "$$7$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Order of one Character" ]

[ "The sum of the number of skaters that came in before Tom and the number of skaters that came in after him is $10 - 1 = 9$. The number of skaters that came in before Tom was $(9 - 3) \\div 2 = 3$, so Tom was the fourth one. " ]

[]

[ [ { "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->Unitary Method Problems->Unitary Method with One Variable" ]

[ "The total number of children is $$13+19=32$$, To form six teams with the same number of children in each team, we divide $$32$$ by $$6$$, $$32\\div6=5$$$$\\rm R$$$$2$$, The remaining $$2$$ children will need $$4$$ more children to form the sixth team. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$2$$ " } ], [ { "aoVal": "B", "content": "$$3$$ " } ], [ { "aoVal": "C", "content": "$$4$$ " } ], [ { "aoVal": "D", "content": "$$5$$ " } ], [ { "aoVal": "E", "content": "$$6$$ " } ] ]

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

[ "$$12-5-2=5$$ " ]

[]

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

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

[ "There are in total $$21 + 21 = 42$$ days from May $$11$$ to June $$21$$. Since $$42 \\div 7 = 6$$, with no remainder, the Father\\textquotesingle s Day falls on Sunday as well. " ]

[]

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

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

[ "If today is Monday, every $$7$$ days is another Monday. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$36 " } ], [ { "aoVal": "B", "content": "$40 " } ], [ { "aoVal": "C", "content": "$34 " } ], [ { "aoVal": "D", "content": "$44 " } ], [ { "aoVal": "E", "content": "$30 " } ] ]

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

[ "40-1*4=36 " ]

[]

[ [ { "aoVal": "A", "content": "$$12$$ " } ], [ { "aoVal": "B", "content": "$$13$$ " } ], [ { "aoVal": "C", "content": "$$14$$ " } ], [ { "aoVal": "D", "content": "$$15$$ " } ] ]

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

[ "A balloon ride can take \\emph{at most}~$$3$$ people at a time. If $$41$$ people want to fly in the balloon, the least number of rides needed is $$41 \\div3$$, rounded \\emph{up} to $$14$$. " ]

[]

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

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

[ "Fifteen cookies for five dollars means three cookies for one dollar. Six more cookies cost $$2$$ dollars. $$5+2=7$$~ dollars in total. " ]

[]

[ [ { "aoVal": "A", "content": "$$15$$ grams " } ], [ { "aoVal": "B", "content": "$$18$$ grams " } ], [ { "aoVal": "C", "content": "$$20$$ grams " } ], [ { "aoVal": "D", "content": "$$25$$ grams " } ] ]

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

[ "$$10\\times20\\textbackslash\\%+40\\times 25\\textbackslash\\%=12$$ ounces. $$(10+40)-12\\div40\\textbackslash\\%=20$$ ounces. " ]

[]

[ [ { "aoVal": "A", "content": "$$17$$ " } ], [ { "aoVal": "B", "content": "$$21$$ " } ], [ { "aoVal": "C", "content": "$$23$$ " } ], [ { "aoVal": "D", "content": "$$27$$ " } ], [ { "aoVal": "E", "content": "$$42$$ " } ] ]

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

[ "One of my two brothers is $$4$$ years older than the other. If they were the same age, they\\textquotesingle d each be $$19$$. Thus, one is $$17$$ and the other is $$21$$. " ]

[]

[ [ { "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->Equation Word Problems" ]

[ "Let the year be $x$ years ago. $14-x=(41-x)\\div 4$ $4(14-x)=41-x$ $56-4x=41-x$ $15=3x$ $3x=15$ $x=5$ " ]

[ "其它" ]

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

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

[ "The boba that John drinks during weekdays: $$5x$$ The boba that John drinks during weekends: $$2\\times 2 =4$$ The total boba that John drinks during a week: $$5x+4$$ " ]

[]

[ [ { "aoVal": "A", "content": "$$2000$$ " } ], [ { "aoVal": "B", "content": "$$2002$$ " } ], [ { "aoVal": "C", "content": "$$2004$$ " } ], [ { "aoVal": "D", "content": "$$2007$$ " } ], [ { "aoVal": "E", "content": "$$2009$$ " } ] ]

[ "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 $$2007$$. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$100$$ " } ], [ { "aoVal": "B", "content": "$$19$$ " } ], [ { "aoVal": "C", "content": "$$32$$ " } ], [ { "aoVal": "D", "content": "$$20$$ " } ], [ { "aoVal": "E", "content": "Never " } ] ]

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

[ "$$(140-83) \\div (8-5)=19$$ " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$12$$ " } ], [ { "aoVal": "B", "content": "$$20$$ " } ], [ { "aoVal": "C", "content": "$$48$$ " } ], [ { "aoVal": "D", "content": "$$60$$ " } ] ]

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

[ "$1-20$\\%=$80$\\%, $60 \\times 80$\\%=$48$. $48$ bananas are in good condition. " ]

[ "其它" ]

[ [ { "aoVal": "A", "content": "$$6$$ " } ], [ { "aoVal": "B", "content": "$$19$$ " } ], [ { "aoVal": "C", "content": "$$29$$ " } ], [ { "aoVal": "D", "content": "$$49$$ " } ], [ { "aoVal": "E", "content": "$$60$$ " } ] ]

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

[ "$(84-79)\\times6=30$, $79-30=49$. " ]

[]

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

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

[ "$$100\\div7=14$$$$\\cdots \\cdots 2$$, So 2 days later is Monday. " ]

[]

[ [ { "aoVal": "A", "content": "$$12$$ " } ], [ { "aoVal": "B", "content": "$$20$$ " } ], [ { "aoVal": "C", "content": "$$25$$ " } ], [ { "aoVal": "D", "content": "$$36$$ " } ] ]

[ "Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number of People in a Rectangular Array" ]

[ "$$3+3-1=5$$. Since each row and column has $$5$$ animals, there are $$5\\times5=25$$ animals in total. " ]