dataset_name
stringclasses 4
values | dataset_version
timestamp[s] | qid
stringlengths 1
5
| queId
stringlengths 32
32
| competition_source_list
sequence | difficulty
stringclasses 5
values | qtype
stringclasses 1
value | problem
stringlengths 6
1.51k
| answer_option_list
list | knowledge_point_routes
sequence | answer_analysis
sequence | answer_value
stringclasses 7
values |
|---|---|---|---|---|---|---|---|---|---|---|---|
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8955 | 20475d6f4e4947128f5e7cd35367a37f | [] | 1 | single_choice | Rina bought a handbag for＄$$60$$ at a discount of $$20\textbackslash\%$$. Ana paid＄$$67.5$$ for the same handbag. What was the discount rate given to Ana? | [
[
{
"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->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"Original price: $$60\\div \\left( 1-20\\textbackslash\\% \\right)=75$$. Discount for Ana: $$\\left( 75-67.5 \\right)\\div 75=10\\textbackslash\\%$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8956 | 677587cf2d7f445d86998360b3f47c1a | [
"其它"
] | 1 | single_choice | SASMO 2014 P2 Q5 What number between 37 and 47 is exactly divisible by both 2 and 3? | [
[
{
"aoVal": "A",
"content": "$$38$$ "
}
],
[
{
"aoVal": "B",
"content": "$$39$$ "
}
],
[
{
"aoVal": "C",
"content": "$$42$$ "
}
],
[
{
"aoVal": "D",
"content": "$$44$$ "
}
],
[
{
"aoVal": "E",
"content": "$$45$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division"
] | [
"6 x 7 = 42 "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8957 | 4784020f2a3e4415885b7617f7078071 | [] | 1 | single_choice | If each fork costs ＄$$6$$, each spoon costs ＄$$7$$, and each knife costs ＄$$8$$, what is the total cost of $$3$$ forks, $$4$$ spoons, and $$5$$ knives? | [
[
{
"aoVal": "A",
"content": "＄$$40$$ "
}
],
[
{
"aoVal": "B",
"content": "＄$$46$$ "
}
],
[
{
"aoVal": "C",
"content": "＄$$80$$ "
}
],
[
{
"aoVal": "D",
"content": "＄$$86$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"$$3$$ forks cost ＄$$6\\times3 =$$＄$$18$$. $$4$$ spoons cost ＄$$7\\times4 =$$＄$$28$$. $$5$$ knives cost ＄$$8\\times5 = $$＄$$40$$. They cost a total of ＄$$18+$$＄$$28+$$＄$$40 =$$＄$$86$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8966 | 289af981df934f3d9d58674d7c64a6f4 | [] | 2 | single_choice | A given month has $$31$$ days, and it has four Mondays and four Thursdays. What day of the week is the $$20^{\rm th}$$ of this month? | [
[
{
"aoVal": "A",
"content": "$$$$Wednesday$$$$. "
}
],
[
{
"aoVal": "B",
"content": "Thursday "
}
],
[
{
"aoVal": "C",
"content": "Friday "
}
],
[
{
"aoVal": "D",
"content": "Sunday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"It implies that there are four Mondays, four Tuesdays, four Wednesdays, and four Thursdays. Similarly, there are five Fridays, five Saturdays, and five Sundays. The first day of the month therefore must be a Friday. $$20\\div7=2\\text{ R }6$$. The $$20^{\\rm th}$$ day of this month is a Wednesday, which is the $$6^{\\rm th}$$ day after Friday, inclusive. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8973 | 677f5e71abcc4006a14a6ee86b9457de | [
"其它"
] | 1 | single_choice | Grandpa suggested dividing all the peanuts between the family members in the following way: one person would get $5$ kilos, two people would get $4$ kilos each, four people would get $2$ kilos each, one person would get $6$ kilos, and one person would not get any peanuts. Grandma suggested dividing the peanuts equally among all of the family members. How many people would get more peanuts in grandma\textquotesingle s suggestion than grandpa\textquotesingle s? | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"Grandma\\textquotesingle s suggestion: $(1\\times 5 + 2\\times 4+4\\times 2+1\\times 6+1\\times 0)\\div(1+2+4+1+1) = 27\\div9=3$ Thus, there are $4+1=5$ people get more peanuts. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8976 | 2070e8e9ad71476dbea8bb6468c3e317 | [
"其它"
] | 1 | single_choice | Anna is $$10$$ years old and the age of her mother is $$4$$ times that of Anna. How old will Anna\textquotesingle s mother be when Anna\textquotesingle s mother is twice as old as Anna? (Math kangaroo Problem, Level $$5-6$$) | [
[
{
"aoVal": "A",
"content": "$$40$$ "
}
],
[
{
"aoVal": "B",
"content": "$$50$$ "
}
],
[
{
"aoVal": "C",
"content": "$$60$$ "
}
],
[
{
"aoVal": "D",
"content": "$$70$$ "
}
],
[
{
"aoVal": "E",
"content": "$$80$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Varying Multiples in Age Problems"
] | [
"The age difference between them is $(4-1)\\times10=30$, which stays the same forever. Then, when Anna\\textquotesingle s mother is twice as old as Anna, Anna should be $30$ years old, then her mom should be $30\\times2=60$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8977 | 4c2228c414cf4507a3502274c27fd237 | [] | 1 | single_choice | If $$2$$ watermelons can serve $$15$$ people, I need watermelons for $$60$$ people. | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"
] | [
"If $$2$$ melons can serve $$15$$ people, I need $$4\\times2=8$$ melons for $$4\\times15=60$$ people. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8978 | b50af7cb22704ba892f668c342921d09 | [] | 1 | single_choice | On Kellin\textquotesingle s $$13$$th birthday, Allen was four times her age. On Kellin\textquotesingle s $$24$$th birthday, how old was Allen? | [
[
{
"aoVal": "A",
"content": "$$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$$th birthday, so Allen\\textquotesingle s age at that time was $$52 +11 =63$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8979 | 20791ee4e06a4edeb45dba05f9d73b43 | [] | 1 | single_choice | A glass contains $$240$$ $$\rm ml$$ of water. The water takes up $$\frac 23$$ of the volume of the glass. What is the volume of the glass, in milliliters? | [
[
{
"aoVal": "A",
"content": "$$60$$ "
}
],
[
{
"aoVal": "B",
"content": "$$100$$ "
}
],
[
{
"aoVal": "C",
"content": "$$120$$ "
}
],
[
{
"aoVal": "D",
"content": "$$270$$ "
}
],
[
{
"aoVal": "E",
"content": "$$360$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"$$240\\div \\frac 23=360$$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8980 | 2cfb178f3aaa4fada6f4dd78cc5ecbfe | [] | 1 | single_choice | At the pumpkin festival, Mike brought a $10$ pounds pumpkin. Mary\textquotesingle s pumpkin weighed $5$ pounds more than Mike\textquotesingle s. How many pounds is Mary\textquotesingle s pumpkin？(adapted from $$2009$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$) | [
[
{
"aoVal": "A",
"content": "$$28$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$15$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"Mary\\textquotesingle s pumpkin weighs $5$ pounds more than Mike\\textquotesingle s, so it\\textquotesingle s $10 + 5 = 15$ pounds. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8986 | 20804e21e09e41e2a1f201f42c1be6b1 | [] | 1 | single_choice | Water makes up $$84\textbackslash\%$$ of the weight of Kubus the Camel when he is thirsty. After he drinks, Kubus weighs $$800$$ kg and water makes up $$85\textbackslash\%$$ of his weight. What is the weight of Kubus the Camel when he is thirsty? ($$2001$$ Math Kangaroo Problem, Level $$9-10$$, Question \#$$16$$) | [
[
{
"aoVal": "A",
"content": "$$672$$ kg "
}
],
[
{
"aoVal": "B",
"content": "$$680$$ kg "
}
],
[
{
"aoVal": "C",
"content": "$$715$$ kg "
}
],
[
{
"aoVal": "D",
"content": "$$720$$ kg "
}
],
[
{
"aoVal": "E",
"content": "$$750$$ kg "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"
] | [
"The ratio between the thirsty Kubus and the water he drank: $$(100-85):(85-84)=15:1$$. So, the weight of the thirsty Kubus is: $$800 \\times \\frac{15}{15+1}=750$$ kg. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8988 | abd318c6c36b4d00b6031180aefc4c83 | [
"其它"
] | 1 | single_choice | Arthur decided to lose weight. On the first month, he lost $2$ kg. He decided that each month he would be losing twice as much kilograms as the month before. How many kilograms did Arthur lose in total in the first three monthes? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Geometric Progression"
] | [
"$2 + 4 + 8 = 14$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8991 | 35c5f540168c42ddb87900669a7fbb40 | [] | 1 | single_choice | How many tens must be added to $$215$$ to make $$985$$?~\uline{~~~~~~~~~~}~tens | [
[
{
"aoVal": "A",
"content": "$$770$$ "
}
],
[
{
"aoVal": "B",
"content": "$$77$$ "
}
],
[
{
"aoVal": "C",
"content": "$$120$$ "
}
],
[
{
"aoVal": "D",
"content": "$$1200$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with Invariant Sums",
"Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Addition and Subtraction of Whole Numbers->Adding and Subtracting within 10000->Subtraction of 3-digit Numbers"
] | [
"$$985-215=770$$ $$770\\div 10=77$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9000 | 50b5773e9ccb47b2ae6a76de4e2c1136 | [] | 1 | single_choice | Determine whether 2008 is a common year or a leap year. | [
[
{
"aoVal": "A",
"content": "a common year "
}
],
[
{
"aoVal": "B",
"content": "a leap year "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"
] | [
"$2008\\div4=502$, so 2008 is a leap year. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9003 | 995395a086b94524b656f12ccfb2ecb1 | [] | 1 | single_choice | A $$15\textbackslash\%$$ sugar solution contains $$18$$ grams of pure sugar. How many grams of solution are there? | [
[
{
"aoVal": "A",
"content": "$$90$$ grams "
}
],
[
{
"aoVal": "B",
"content": "$$100$$ grams "
}
],
[
{
"aoVal": "C",
"content": "$$120$$ grams "
}
],
[
{
"aoVal": "D",
"content": "$$150$$ grams "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"
] | [
"$$18\\div15\\textbackslash\\% = 120$$ grams. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9005 | 3a4302374beb4b9bb287f025c6c9b910 | [] | 1 | single_choice | If $$19^{}\text{th}$$March is Monday, what day of the week is $$1$$\textsuperscript{st~}March ? | [
[
{
"aoVal": "A",
"content": "Sunday "
}
],
[
{
"aoVal": "B",
"content": "Monday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Thursday "
}
],
[
{
"aoVal": "E",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"There are 19 days between $$19^{}\\text{th}$$March and~ $$1$$\\textsuperscript{st~}March. Apart from $19$\\textsuperscript{th} March itself, there are $18$ days, 18 days = 2 week and 4 days. Therefore,~~$$1$$\\textsuperscript{st~}March is Thursday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9010 | 75545ef04b054c9d9bb0a3389f39b2f4 | [
"其它"
] | 2 | single_choice | Elsa started to raise some chicken in her farm in January. The number of chicken triples every month, while she goes to the market to sell $81$ chicken every month. On April when she came back from the market, she found she had no chicken left. How many chicken did she raise in January? | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$35$$ "
}
],
[
{
"aoVal": "C",
"content": "$$40$$ "
}
],
[
{
"aoVal": "D",
"content": "$$45$$ "
}
],
[
{
"aoVal": "E",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems"
] | [
"$81 \\div 3 = 27$ $(81 + 27) \\div 3 = 36$ $(36 + 81) \\div 3 = 39$ $(39 + 81) \\div 3 = 40$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9015 | 554dcd8cf4db44bba1c2c303814e25c1 | [] | 1 | single_choice | Mariam had ＄$$4y$$. After buying some cloth at ＄$$7$$ per metre, she had ＄$$y$$ left. How many metres of cloth did she buy? | [
[
{
"aoVal": "A",
"content": "$$\\frac{3y}{7}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{5y}{7}$$ "
}
],
[
{
"aoVal": "C",
"content": "$21y$ "
}
],
[
{
"aoVal": "D",
"content": "$$35y$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"
] | [
"Amount of money she spent to buy the cloth $$\\rightarrow$$＄$$4y-$$＄$$y$$ $$=$$＄$$3y$$, Length of cloth she bought $$\\rightarrow$$＄$$3y\\div $$＄$$7/\\text{m}$$ $$= \\frac{3y}{7}\\text{m}$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9016 | 755716b534644524b64070f2d8e89dd2 | [] | 1 | single_choice | A pencil is one dollar, and a pencil box is two dollars more expensive than a pencil. Jimmy has seven dollars and bought a pencil box. How many pencils can Jimmy buy？(adapted from $$2009$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$) | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$1$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2$$ "
}
],
[
{
"aoVal": "E",
"content": "$$4$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"A pencil box costs two dollars more than a pencil, so it\\textquotesingle s $1+2=3$ dollars. $7-3=4$. So~He can buy $4\\div1=4$~pencils. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9019 | b9ae7f6da3644676a43ed238be442a9b | [] | 1 | single_choice | The February of a given year has five Fridays. What day of the week was January $$31$$\textsuperscript{th~}of that year? | [
[
{
"aoVal": "A",
"content": "Friday "
}
],
[
{
"aoVal": "B",
"content": "Saturday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Thursday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"There are seven days in a week. In order to have five Fridays, a month has at least $$4\\times 7+1=29$$ days. Since February has at most $$29$$ days, the $$1$$\\textsuperscript{st} and $$29$$\\textsuperscript{th} days of this February must be Friday, which means that January $$31$$ is Thursday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9023 | 35e07a8c8c474bb2a06eab793f4ba4e7 | [
"其它"
] | 1 | single_choice | George takes 4 minutes to go from 1st floor to 3rd floor. He just realised that he forgot his water bottle on the 5th floor. He is now on the 2nd floor. How long would it take him to get his watter bottle? | [
[
{
"aoVal": "A",
"content": "4 minutes "
}
],
[
{
"aoVal": "B",
"content": "5 minutes "
}
],
[
{
"aoVal": "C",
"content": "6 minutes "
}
],
[
{
"aoVal": "D",
"content": "8 minutes "
}
],
[
{
"aoVal": "E",
"content": "None of the above. "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications"
] | [
"2 gaps between 1st to 3rd floor. hence, 4/2=2 minutes per gap. Moving from 2nd to 5th floor, 3 gaps -\\textgreater{} 3 gaps x 2 minutes per gap = 6 minutes. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9027 | 35e3d08db3384991b74d8f9237c114bf | [] | 1 | single_choice | Billy has three times as many llamas as lambs. Milly has twice as many lambs as llamas. They have $$17$$ animals in total. How many of the animals are llamas? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
],
[
{
"aoVal": "E",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Indefinite Equation Word Problems"
] | [
"Let Billy have $$b$$ lambs and $$3b$$ llamas. Let Milly have $$m$$ llamas and $$2m$$ lambs. Therefore, as they have $$17$$ animals in total, $$4b + 3m= 17$$. The only positive integer solution of this equation is $$b= 2$$, $$m= 3$$. So the number of llamas is $$3b + m = 3 \\times 2 + 3 = 6 + 3 = 9$$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9033 | 28ebd08f7b9a4fd2b5a29dba55cdf4fc | [] | 1 | single_choice | If $$15^{}\text{th}$$March is Monday, what day of the week is $$26$$\textsuperscript{th} March ? | [
[
{
"aoVal": "A",
"content": "Sunday "
}
],
[
{
"aoVal": "B",
"content": "Monday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Friday "
}
],
[
{
"aoVal": "E",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"There are 11 days between $$15^{}\\text{th}$$March and~ $$26$$\\textsuperscript{th} March. 11 days = 1 week and 4 days. Therefore,~~$$26$$\\textsuperscript{th} March is Friday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9041 | b517757aafc849dbb93583a85b080fcc | [] | 1 | single_choice | Sarah is $$1.14\text{m}$$ tall. Benny is $$0.23\text{m}$$ taller than Sarah. What is the total height of the $$2$$ children? Round off your answer to $$1$$ decimal place. | [
[
{
"aoVal": "A",
"content": "$$1.4\\text{m}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2.1\\text{m}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2.5\\text{m}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2.6\\text{m}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"Benny\\textquotesingle s height $$=1.14+0.23=1.37\\text{m}$$ Total heights of the $$2$$ children $$=1.14+1.37=2.51=2.5\\text{m}$$ (rounded to $$1$$ d.p.) "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9042 | 28f475c9f7064d948dbcba7b4fd41806 | [] | 1 | single_choice | There are~ $$30$$ students in Pat\textquotesingle s math class. If there are twice as many girls as boys in the class, how many boys are in the class? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"
] | [
"There are $$30$$ students in Pat\\textquotesingle s math class. With twice as many girls as boys, the class has $$20$$ girls and $$10$$ boys. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9046 | b078bb4dea3142b3bf27f3707db62f84 | [] | 2 | single_choice | Lily\textquotesingle s family used $$21$$ tons of water in the first two months, and an average of $$31$$ tons of water on the remaining three tests. The average tons of water for the five months was~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "$$120$$ "
}
],
[
{
"aoVal": "B",
"content": "$$22$$ "
}
],
[
{
"aoVal": "C",
"content": "$$23$$ "
}
],
[
{
"aoVal": "D",
"content": "$$27$$ "
}
],
[
{
"aoVal": "E",
"content": "$$25$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"Total tons of water: $$21\\times 2+31\\times 3=135$$ Average tons of water: $$135\\div 5=27$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9051 | 24dccd6fe9dd4c5fa0cc77f021a04cd3 | [
"其它"
] | 1 | single_choice | Mr.Smith wants to cut a wood into $5$ pieces. It takes him $2$ minutes to cut a piece. How many minutes will he use to cut? | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
],
[
{
"aoVal": "E",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"Mr.Smith needs to cut $5-1=4$ times, which means he needs to use $4 \\times 2 = 8$ minutes to cut. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9057 | 70d29f5e0a8140f88ef9becfaac2134f | [] | 1 | single_choice | Paul had eight $$\textbackslash$5$$-notes at first. He exchanged all his money for $$\textbackslash$2$$-notes only. How many notes did he have in the end? | [
[
{
"aoVal": "A",
"content": "$$16$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$40$$ "
}
],
[
{
"aoVal": "D",
"content": "$$80$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"
] | [
"He has $=\\textbackslash$5\\times8=\\textbackslash$40$ Number of $\\textbackslash$2$-notes $=\\textbackslash$40\\div\\textbackslash$2=20$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9060 | b07b758fc37a43aa9d4d5e8bdd4b1a62 | [] | 1 | single_choice | Farmer Dunphy has $$16$$ metres of fencing. He wants to make a closed rectangular pen. He uses a long wall for one of the sides. Each side of the pen is a whole number in metres. What is the largest area that the pen can be? | [
[
{
"aoVal": "A",
"content": "$$25\\text{m}^{2}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$27\\text{m}^{2}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$30\\text{m}^{2}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$28\\text{m}^{2}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$32\\text{m}^{2}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems Combined with Geometry->Tile Word Problems"
] | [
"$a+2b=16$, when $$a=2b=8$$, the largest area is $$8\\times (8\\div 2)=32$$ m\\textsuperscript{2}. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9061 | 3a6defe4b99d44a5a66f0b24ebb999cc | [
"其它"
] | 1 | single_choice | In how many places do we need to break a wooden stick in order to get $$5$$ pieces? (1999 Math Kangaroo Problem, Level 3-4, Question \#3) | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "It depends on how long the stick is. "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Planting no Trees on either Side (straight line type)->Sawing Woods"
] | [
"$5-1=4$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9063 | 5563eea1e50e4ccf8b4987951670c614 | [] | 1 | single_choice | Tom starts a savings account with ＄$$4,000$$ at a bank. The interest rate is $$2\textbackslash\%$$ per year. How much interest will he earn in his savings account at the end of the second year? | [
[
{
"aoVal": "A",
"content": "＄$$160$$ "
}
],
[
{
"aoVal": "B",
"content": "＄$$161.6$$ "
}
],
[
{
"aoVal": "C",
"content": "＄$$4,160$$ "
}
],
[
{
"aoVal": "D",
"content": "＄$$4,161.6$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Interest Problems"
] | [
"$$4000\\times \\left( 1+2\\textbackslash\\% \\right)\\times \\left( 1+2\\textbackslash\\% \\right)-4000=161.6$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9069 | 3a738576173341b9950fffbfcfd02524 | [] | 1 | single_choice | If there are $$8$$ pencils in each box, how many pencils are in $$80$$ boxes? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$88$$ "
}
],
[
{
"aoVal": "C",
"content": "$$640$$ "
}
],
[
{
"aoVal": "D",
"content": "$$808$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"There are $$80 \\times8 = 640$$ pencils in $$80$$ boxes. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9075 | 2d5ac1ffd2554acda68a9b3ace5b117c | [] | 1 | single_choice | At which of~ these times is the angle between the minute hand and the hour hand of a clock equal to $$150^{}\circ$$? | [
[
{
"aoVal": "A",
"content": "$$9\\text{pm}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8\\text{pm}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6\\text{pm}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5\\text{pm}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$4\\text{pm}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems"
] | [
"At all the times given, the minute hand is pointing to $$12$$. When the minute hand is pointing to $$12$$ and the angle between the hands is $$150^{}\\circ$$, the hour hand has turned $$\\frac{150}{360}= \\frac{5}{12}$$ of a complete turn. Therefore the hour hand will point at $$5$$ and the time will be $$5\\text{pm}$$. (There are other times when the angle between the hands is $$150^{}\\circ$$ but, of these, only at $$7\\text{pm}$$ does the minute hand point to $$12$$ and $$7\\text{pm}$$ is not one of the times given.) "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9076 | 3608fd0cae9f4f0db6c5f54de02cf476 | [
"其它"
] | 1 | single_choice | Lisa is buying potatoes at a grocery store. She can either spend $10$ dollars on a $25\text{-lb}$ bag or $15$ dollars on a $35\text{-lb}$ bag. Whic is the cheaper one? | [
[
{
"aoVal": "A",
"content": "The $25\\text{-lb}$ bag "
}
],
[
{
"aoVal": "B",
"content": "The $35\\text{-lb}$ bag "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"
] | [
"$$\\frac{10}{25}\\textasciitilde\\textbackslash$ \\text{/lb}=0.4\\textasciitilde\\textbackslash$ \\text{/lb}$$ $$\\frac{15}{35}\\textasciitilde\\textbackslash$ \\text{/lb}=0.43\\textasciitilde\\textbackslash$ \\text{/lb}$$ $$\\frac{10}{25}\\textless\\frac{15}{35}$$ So, the answer is $$A$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9077 | 3ee1252200a043d69102ff1f19852b07 | [] | 1 | single_choice | Ali is arranging the books on his bookshelves. He puts half his books on the bottom shelf and two-thirds of what remains on the second shelf. Finally he splits the rest of his books over the other two shelves so that the third shelf contains four more books than the top shelf. There are three books on the top shelf. How many books are on the bottom shelf？ | [
[
{
"aoVal": "A",
"content": "$$60$$ "
}
],
[
{
"aoVal": "B",
"content": "$$50$$ "
}
],
[
{
"aoVal": "C",
"content": "$$40$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30$$ "
}
],
[
{
"aoVal": "E",
"content": "$$20$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"Since Ali places half his books on the bottom shelf and $$\\frac{2}{3}$$ of the remainder on the second shelf, he places $$\\frac{2}{3}\\times\\frac{1}{2}=\\frac{1}{3}$$ of his books on the second shelf, leaving $$\\left(1-\\frac{1}{2}-\\frac{1}{3}\\right) =\\frac{1}{6}$$~ of his books for the top two shelves. There are three books on the top shelf and four more, so seven books, on the third shelf. Therefore these $$10$$ books represent $$\\frac{1}{6}$$ of the total number of books on the bookshelves. Hence there are $$60$$ books on the bookshelves and half of these, or $$30$$ books, on the bottom shelf. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9082 | 50e2bc1b9981451da4850b2d0760b083 | [
"其它"
] | 1 | single_choice | Given that May $2$nd of a given year is a Thursday, what day is May $29$th of the same year? | [
[
{
"aoVal": "A",
"content": "Saturday "
}
],
[
{
"aoVal": "B",
"content": "Wednesday "
}
],
[
{
"aoVal": "C",
"content": "Thursday "
}
],
[
{
"aoVal": "D",
"content": "Tuesday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems"
] | [
"$29-2=27$ days later, it will be May $29$\\textsuperscript{th}. $27\\div7=3R6$, which means May $29$\\textsuperscript{th}~is Wednesday. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9084 | 31ade8e5fd1f4d89b81e3361fb8b5d2c | [] | 1 | single_choice | Given that August $$15$$th of a given year is a Friday, What day is June $$10$$th of the same year? | [
[
{
"aoVal": "A",
"content": "Monday "
}
],
[
{
"aoVal": "B",
"content": "Tuesday "
}
],
[
{
"aoVal": "C",
"content": "Friday "
}
],
[
{
"aoVal": "D",
"content": "Sunday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"$$30-10+31+15=$$ $66\\div7=9r3$ $$$$Tuesday$$$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9088 | ff313a6edc9f448b9cc424174c60b323 | [] | 1 | single_choice | The selling price of a television is＄$$4800$$ and its profit percentage is $$20\textbackslash\%$$. If the cost of the television is not changed, how much should it be sold for if the profit percentage has to be $$75\textbackslash\%$$? | [
[
{
"aoVal": "A",
"content": "$$6000$$ dollars "
}
],
[
{
"aoVal": "B",
"content": "$$6500$$ dollars "
}
],
[
{
"aoVal": "C",
"content": "$$7000$$ dollars "
}
],
[
{
"aoVal": "D",
"content": "$$8000$$ dollars "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"$$\\frac{4800}{\\left( 1+20\\textbackslash\\% \\right)}=4000$$ dollars, $$4000\\times \\left( 1+75\\textbackslash\\% \\right)=7000$$ dollars. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9101 | a2ad6165be134ef2875c1798789d5958 | [] | 1 | single_choice | The upper shelf of a bookshelf has $$143$$ books. The lower shelf has $$39$$ books. How many books should be taken from the upper shelf to the lower shelf so that both shelves will have the same number of books? | [
[
{
"aoVal": "A",
"content": "$$52$$ "
}
],
[
{
"aoVal": "B",
"content": "$$104$$ "
}
],
[
{
"aoVal": "C",
"content": "$$91$$ "
}
],
[
{
"aoVal": "D",
"content": "$$46$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"
] | [
"$$143-39=104$$, $$104$$~$\\div$ $$2$$ = $$52$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9106 | 252a169e54b4429abc423fb95a4c13c2 | [
"其它"
] | 1 | single_choice | If Pip was 18 years old 5 years ago, how old will he be 7 years from now? | [
[
{
"aoVal": "A",
"content": "$$22$$ "
}
],
[
{
"aoVal": "B",
"content": "$$24$$ "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30$$ "
}
],
[
{
"aoVal": "E",
"content": "$$32$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"$$18+5+7=30$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9107 | 632a2a9dfa734f2097ac608766cdd02f | [] | 1 | single_choice | My dad, Burly Ird, says he has to moan at me two school mornings in every three to get me out of bed. In a twelve-week term, with five schooldays each week, on how many mornings will he moan at me? | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$35$$ "
}
],
[
{
"aoVal": "C",
"content": "$$36$$ "
}
],
[
{
"aoVal": "D",
"content": "$$40$$ "
}
],
[
{
"aoVal": "E",
"content": "$$42$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"The number of moaning mornings is $$\\frac{2}{3}\\times 12 \\times 5 = 40$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9109 | 2949882443274602ad9ff0fffe5be4cb | [
"其它"
] | 2 | single_choice | In one year, there were 5 Sundays in February. What day of the week was 3\textsuperscript{rd~}Feb ? | [
[
{
"aoVal": "A",
"content": "Saturday "
}
],
[
{
"aoVal": "B",
"content": "Monday "
}
],
[
{
"aoVal": "C",
"content": "Tuesday "
}
],
[
{
"aoVal": "D",
"content": "Wednesday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"
] | [
"Normally, there are 28 days in February, which has 4 Sundays at most. Therefore, it could be the leap year with 29 days in February. If there are 5 Sundays, the first day in Februray should be Sunday, so Feb 3rd is Tuesday. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9116 | 6c5027bfc900405a96a3262d907d3162 | [
"其它"
] | 1 | single_choice | The cost of a computer is $3500$ dollars and the profit percentage is $12\textbackslash\%$ for each computer. Find the price of the computer. | [
[
{
"aoVal": "A",
"content": "$$3850$$ dollars "
}
],
[
{
"aoVal": "B",
"content": "$$3920$$ dollars "
}
],
[
{
"aoVal": "C",
"content": "$$4200$$ dollars "
}
],
[
{
"aoVal": "D",
"content": "$$4550$$ dollars "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts->Calculating Price from Cost and Profit"
] | [
"The price of the computer is: $3500\\times(1+12\\textbackslash\\%)=3920$ dollars. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9119 | 9972583aedc84488b67fca5cb1ffab6a | [] | 1 | single_choice | Given that March $$26$$\textsuperscript{th}, $$2021$$ was Friday, what day was April $$20$$\textsuperscript{th}, $$2021$$? $\textasciitilde$ | [
[
{
"aoVal": "A",
"content": "Monday "
}
],
[
{
"aoVal": "B",
"content": "Tuesday "
}
],
[
{
"aoVal": "C",
"content": "Thursday "
}
],
[
{
"aoVal": "D",
"content": "Wednesday "
}
],
[
{
"aoVal": "E",
"content": "Friday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"Counting from March $$26$$\\textsuperscript{th}, $$2021$$, after $31-26=5$ days it was March $$31$$\\textsuperscript{st}, $$2021$$. After $20$ days it was April $$20$$\\textsuperscript{th}, $$2021$$. In total, there were $5+20=25$ days. $25\\div 7 =3R4$, which means April $$20$$\\textsuperscript{th}, $$2021$$ was Tuesday. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9124 | 757d78c55cce4dec843aca99df10cd82 | [] | 1 | single_choice | Tom, Joanna and Jacky each come up with a number. The sum of the three numbers is $$360$$. Tom\textquotesingle s number is twice Joanna\textquotesingle s number, and Joanna\textquotesingle s number is three times Jacky\textquotesingle s number. What are these three numbers? | [
[
{
"aoVal": "A",
"content": "$$36$$ "
}
],
[
{
"aoVal": "B",
"content": "$$108$$ "
}
],
[
{
"aoVal": "C",
"content": "$$216$$ "
}
],
[
{
"aoVal": "D",
"content": "$$360$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"
] | [
"Jacky\\textquotesingle s number is ``$$1$$'', so Joanna\\textquotesingle s number is ``$$3$$'', and Tom\\textquotesingle s number is ``$$6$$''. Jacky\\textquotesingle s number: $$360 \\div (6 +3+1) =36$$. Joanna\\textquotesingle s number: $$36 \\times 3=108$$. Tom\\textquotesingle s number: $$36 \\times 6 =216$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9132 | 47f70782f7f14c2baa01838dc586e7da | [] | 1 | single_choice | ( $$2004$$ AMC $$8$$ Problem, Question \#$$12$$) Niki usually leaves her cell phone on. If her cell phone is on but she is not actually using it, the battery will last for $$24$$ hours. If she is using it constantly, the battery will last for only $$3$$ hours. Since the last recharge, her phone has been on $$9$$ hours, and during that time she has used it for $$60$$ minutes. If she doesn\textquotesingle t use it any more but leaves the phone on, how many more hours will the battery last? | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14$$ "
}
],
[
{
"aoVal": "E",
"content": "$$15$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Simple Work Word Problems"
] | [
"When not being used, the cell phone uses up $$\\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}$$ more hours without being used. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9137 | 31de0d7a18ae4cf68af276242e97c24c | [] | 1 | single_choice | Mike bought five ice creams. He had three brothers and he gave each brother an ice cream. How many ice creams was left?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$3$$) | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2$$ "
}
],
[
{
"aoVal": "E",
"content": "$$0$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"
] | [
"Each brother gets one ice cream, and three brothers need three ice cream, so Mike has $5-3=2$~ice cream left. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9138 | 70f10ebca60b4f78b3596722ccc3a9d5 | [
"其它"
] | 1 | single_choice | Elmp visits the Sesame Street Park every Wednesday. If the 1st of January 2017 was Sunday and February has 28 days, what was the last date in March 2017 in which Elmo visited Sesame Street Park? | [
[
{
"aoVal": "A",
"content": "28th March "
}
],
[
{
"aoVal": "B",
"content": "29th March "
}
],
[
{
"aoVal": "C",
"content": "30th March "
}
],
[
{
"aoVal": "D",
"content": "31st March "
}
],
[
{
"aoVal": "E",
"content": "None of the above. "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems"
] | [
"Draw the calendar out. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9139 | 633400457b2a47cfa9363f17f1286353 | [
"其它"
] | 0 | single_choice | A construction team is going to build a road of $50$ miles. The plan is that it finishes $30$\% of the road in the first month, $40$\% of the road in the second month and $30$\% of the road in the third month. How many miles can be built after two months? | [
[
{
"aoVal": "A",
"content": "$$15$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$30$$ "
}
],
[
{
"aoVal": "D",
"content": "$$35$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$30$\\%+$40$\\%=$70$\\%, $50 \\times 70$\\%=$35$ After two months, $35$ miles of road can be built. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9140 | 7a1e1572638c473891ceef59b339554f | [
"其它"
] | 1 | single_choice | Kate bought $$2$$ apple pies and Lucy bought $$4$$ cupcakes. They each paid the same amount of money and together they paid $$16$$ dollars. How many dollars does $$1$$ cupcake cost? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
],
[
{
"aoVal": "E",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Applying Division"
] | [
"$4$ cupcakes cost $16\\div2=8$ dollars, so one cupcake cost $8\\div4=2$ dollars. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9144 | 31e38582c22d45a8b73fdd680db87bbc | [] | 1 | single_choice | Esther made $$18$$ paper stars and she made $$3$$ times as many paper stars as Amy. How many paper stars did Amy make? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"
] | [
"omitted "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9152 | 3ab230920c8a448a935224efb4bbd275 | [] | 2 | single_choice | In a class of pupils, $80\textbackslash\%$ participated in basketball, $85\textbackslash\%$ participated in football, $74\textbackslash\%$ participated in softball and $68\textbackslash\%$ participated in squash. Find the minimum percentage of pupils who participated in all the four sports events. | [
[
{
"aoVal": "A",
"content": "$7\\textbackslash\\%$ "
}
],
[
{
"aoVal": "B",
"content": "$10\\textbackslash\\%$ "
}
],
[
{
"aoVal": "C",
"content": "$12\\textbackslash\\%$ "
}
],
[
{
"aoVal": "D",
"content": "$15\\textbackslash\\%$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"
] | [
"Least percentage of pupils who participated in both basketball and football $=80\\textbackslash\\%+ 85\\textbackslash\\%-100\\textbackslash\\% =65\\textbackslash\\%$, Least percentage of pupils who participated in basketball, football and softball $=65\\textbackslash\\%+74\\textbackslash\\%-100\\textbackslash\\% =39\\textbackslash\\%$, Least percentage of pupils who participated in basketball, football, softball and squash $=39\\textbackslash\\%+ 68\\textbackslash\\%-100\\textbackslash\\% = 7\\textbackslash\\%$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9156 | e368d6c3bc1b423a838f92958f48a055 | [] | 1 | single_choice | Simon has two identical aquariums. There are $$26$$ quarts of water in one, and $$42$$ quarts of water in the other. How many quarts of water does Simon need to pour from the second aquarium into the first in order to have the same amount of water in both? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Giving and Receiving"
] | [
"Difference: $42-26=16$ Move: Half of $16=8$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9157 | 2974fbb221394803aa3e2851d02d7c6a | [] | 1 | single_choice | In $$20$$ years, Li will be $$3$$ times as old as he is now. How old will he be in $$10$$ years? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$30$$ "
}
],
[
{
"aoVal": "D",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->When..., When... Type Age Problems"
] | [
"In $$20$$ years, Li will be $$3$$ times his age now, so $$20$$ must be twice his age now. Thus, Li is $$10$$ now and will be $$20$$ in $$10$$ years. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9160 | c30d76211ffc4b33b74ecb40481a3f80 | [] | 1 | single_choice | When Paul is $$4$$ years old, his brother Peter is $$7$$ years old. How old is Paul when Peter is $$10$$ years old? Paul is~\uline{~~~~~~~~~~}~years old. | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"
] | [
"We can find their age difference is $$7-4=3$$. It will never change. So when Peter is $$10$$ years old, Paul is $$10-3=7$$ years old. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9175 | 2dcf32ee240746e991d76e0c3e410ed7 | [
"其它"
] | 1 | single_choice | If Paul gives $$6$$ candies to Billy, they will have the same number of candies. At beginning, Paul has $$17$$ candies. How many candies does Billy have, originally? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
],
[
{
"aoVal": "E",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"Their difference: $$6+6=12$$ Billy: $$17-12=5$$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9177 | 7ec7203e832d43a4ae2c712cd4fd38c3 | [] | 1 | single_choice | Su Li has the same number of ten-cent and fifty-cent coins. The total value is ＄$$6$$. How many coins does she have in all? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$36$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"$$10u + 50u = 600$$ Thus, $$1u = 10$$, in total we have $$2u=20$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9180 | 366ebcb8e901438dbcaab7f7eae8fb50 | [] | 1 | single_choice | Andy is $18$ years old and his mother is $$54$$ years old now. In how many years\textquotesingle{} time will the sum of their ages be $$90$$? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$14$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$28$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"
] | [
"$$18+54 = 72$$ $$90-72 = 18$$ $$18\\div2=9$$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9191 | 8bb83ae894e1479cae8a829f26b30e09 | [
"其它"
] | 1 | single_choice | Together, Mom Kangaroo and her son Jumper weigh $60$ kilograms. Mom Kangaroo alone weighs $52$ kilograms. How much does Jumper weigh? ($$2019$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$3$$) | [
[
{
"aoVal": "A",
"content": "2 kilograms "
}
],
[
{
"aoVal": "B",
"content": "4 kilograms "
}
],
[
{
"aoVal": "C",
"content": "8 kilograms "
}
],
[
{
"aoVal": "D",
"content": "30 kilograms "
}
],
[
{
"aoVal": "E",
"content": "46 kilograms "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"
] | [
"Jumper\\textquotesingle s weight is Mom Kangaroo and Jumper\\textquotesingle s weight minus the mom\\textquotesingle s weight. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9195 | da31826157214798804ddb8fa2daadca | [
"其它"
] | 0 | single_choice | There are three books, Chinese, Math, and English. Sissy wants to put them in bookcase. How many ways are there for three books to put? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$3$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"List out all the possible ways in order. $C A E$ $C E A$ $A C E$ $A E C$ $E C A$ $E A C $ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9198 | 67e89215e9c9426f941e2f128e8d0841 | [
"其它"
] | 1 | single_choice | Alex had $76. He spent some of it in a shop. Then he gave half of what he had left to Charlie. Charlie spent a quarter of what Alex gave him on lunch. Charlie spent $9 on lunch. How much did Alex spend in the shop? | [
[
{
"aoVal": "A",
"content": "$4 "
}
],
[
{
"aoVal": "B",
"content": "$12 "
}
],
[
{
"aoVal": "C",
"content": "$14 "
}
],
[
{
"aoVal": "D",
"content": "$36 "
}
],
[
{
"aoVal": "E",
"content": "$40 "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"Charlie\\textquotesingle s 1/4 is 9, so Charlie gets 4\\times 9=36 dollars, and Alex is left with 36+36=72 dollars, so he spends 76-72=4 dollars "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9204 | 3aef27b0617f40e3abdf060f4491b2df | [] | 1 | single_choice | Min Ho deposited ＄$$20 000$$ into a bank at the beginning of the year. The annual interest for depositing money into the bank was $$5\textbackslash\%$$. How much did Min Ho have in the bank at the end of the year if he did not take out any money from the bank?． | [
[
{
"aoVal": "A",
"content": "$$\\textbackslash$1000$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\textbackslash$19 000$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\textbackslash$21 000$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\textbackslash$31 000$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"He has $20000 \\times 1.05 = \\textbackslash$21000$ at the end of the year. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9206 | 880a8e37428c4889b5d2b4703cbe3889 | [
"其它"
] | 1 | single_choice | The pages of a book are numbered 1, 2, 3 $\cdots$ . In total, it takes 852 digits to number all the pages of the book. What is the number of the last page? | [
[
{
"aoVal": "A",
"content": "$$215$$ "
}
],
[
{
"aoVal": "B",
"content": "$$314$$ "
}
],
[
{
"aoVal": "C",
"content": "$$320$$ "
}
],
[
{
"aoVal": "D",
"content": "$$329$$ "
}
],
[
{
"aoVal": "E",
"content": "$$422$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem"
] | [
"omitted jmc 2007 \\#24 "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9207 | ac0813321e60496d8537f827af1b9051 | [] | 1 | single_choice | Eddie and Frank can complete a job together in $$15$$ days. Eddie can do it alone in $$20$$ days. Frank can do it alone indays. | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$45$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"
] | [
"$$\\frac{1}{15}-\\frac{1}{20}=\\frac{1}{60}$$, $$1\\div\\frac{1}{60}=60$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9214 | d592b49d1e4542c39fcea7e8ab89cf90 | [] | 1 | single_choice | There are $$600$$ pupils in Pip\textquotesingle s school, with $$30$$ more girls than boys. How many girls are at Pip\textquotesingle s school? | [
[
{
"aoVal": "A",
"content": "$$270$$ "
}
],
[
{
"aoVal": "B",
"content": "$$300$$ "
}
],
[
{
"aoVal": "C",
"content": "$$315$$ "
}
],
[
{
"aoVal": "D",
"content": "$$330$$ "
}
],
[
{
"aoVal": "E",
"content": "$$345$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"
] | [
"Let there be $$g$$ girls in Pip\\textquotesingle s school. Then there are $$(g-30)$$ boys at the school. So $$g+g-30=600$$. Therefore $$2g=630$$, that is $$g=315$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9216 | 67eea995ee504a68a52fff4e078f0adc | [] | 1 | single_choice | A ship was attacked by pirates. One by one the pirates climb a rope to get on the ship. The pirate captain was the $$8$$\textsuperscript{th}~pirate to climb in line, and there were as many pirates in front of him as behind him. How many pirates climbed the rope? (2015 Math Kangaroo Problem, Level 1 - 2, Question \#18) $$\textasciitilde$$ $$\textasciitilde$$ $$\textasciitilde$$ $$\textasciitilde$$ $$\textasciitilde$$ $$\textasciitilde$$ | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
],
[
{
"aoVal": "E",
"content": "$$16$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line"
] | [
"The pirate captain was the $$8$$\\textsuperscript{th}~pirate and there were as many pirates in front of him as behind him, which means there were $$7$$ pirates in front of him and there were also $$7$$ pirates behind him. The total number of pirates is~~$$7+7+1=15$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9221 | ecb8f9ef5d1b4aaa916b9c1ce004c480 | [] | 1 | single_choice | Half a loaf of bread costs $$6$$ pence more than one quarter of a loaf of bread. How many pence does a whole loaf of bread cost? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$24$$ "
}
],
[
{
"aoVal": "E",
"content": "$$30$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"One quarter of a loaf of bread is ``$$1$$.'' Half a loaf of bread is ``$$2$$.'' One quarter of a loaf of bread: $$6 \\div (2-1) =6$$. A whole loaf of bread: $$6 \\times 4 =24$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9222 | 880f4cb118f14f90bfc89ece33e6305f | [
"其它"
] | 1 | single_choice | After Sally takes 20 shots, she has made $40 \textbackslash\%$ of her shots. After she takes 5 more shots, she raises her percentage to $52 \textbackslash\%$. How many of the last 5 shots did she make? (2004 AMC 8, Question\#6) | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
],
[
{
"aoVal": "E",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"Sally made $0.4 * 20=8$ shots originally. Letting $x$ be the number of shots she made, we have $\\frac{8+x}{25}=0.52$. Solving for $x$ gives us $x=5$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9223 | 55c6a4144e5e44aea914f1e2263db0f6 | [] | 1 | single_choice | Seventh grade students from a school line up and form a square array. There are $196$ students in the outermost layer. How many students in total are there in this array? | [
[
{
"aoVal": "A",
"content": "$$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$$. The total number of students in the array was $$50\\times 50=2500$$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9225 | f603b7e6a99c4d2caef7012f7673bc31 | [] | 1 | single_choice | My first day of vacation is May $$10$$. My last day of vacation is May $$20$$ of the same year. How many days of vacation do I have? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$ 10 $$ "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"NA "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9229 | 36a6178cc2984c619773488f7dbaf7b5 | [] | 1 | single_choice | In a jar of red, green, and blue marbles, all but $$6$$ are red marbles, all but $$8$$ are green, and all but $$4$$ are blue. How many marbles are in the jar? ($$2012$$ AMC $$8$$ problem, Question \#$$19$$) | [
[
{
"aoVal": "A",
"content": "$$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$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9231 | b0a8da14729546d38e11e4d003e97fca | [] | 1 | single_choice | After Anna spends $\dfrac{1}{3}$~of her money and loses $\dfrac{1}{2}$~of the remainder, she then has~$\textbackslash$10$ left. She started with． | [
[
{
"aoVal": "A",
"content": "$\\textbackslash$30$ "
}
],
[
{
"aoVal": "B",
"content": "$\\textbackslash$45$ "
}
],
[
{
"aoVal": "C",
"content": "$\\textbackslash$50$ "
}
],
[
{
"aoVal": "D",
"content": "$\\textbackslash$60$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"After Anna spends $\\dfrac{1}{3}$~of her money, she has $\\dfrac{2}{3}$~left. If she loses $\\dfrac{1}{2}$~of this, she has $\\dfrac{1}{3}$~left. Since$\\dfrac{1}{3}=$$\\textbackslash$10$,~$\\dfrac{3}{3}=3\\times$$\\textbackslash$10=$$\\textbackslash$30$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9235 | 43e6c32f5cdd4d81af4f3de94586b61e | [] | 1 | single_choice | Given March $$25$$th of a certain year is Monday, what day of the week would May $$1$$st fall on this year? | [
[
{
"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"
] | [
"The cycle includes seven days, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday. There are in total $$7+30+1=38$$ days from March $$25$$ to May $$1$$. Since $$38\\div7=5 \\text{ R }3$$，$$$$May$$$$ $$1$$ is the $$3^{\\rm rd}$$ day in the cycle, it is a Wednesday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9238 | 3263efa465b14b1ba130f0bc30112c1c | [] | 1 | single_choice | In an arts and crafts class, the students cut out some triangles, quadrilaterals and pentagons. All the shapes combined have $$394$$ sides. Among them, there are $$2$$ pentagons and the number of quadrilaterals is $$82$$ more than that of triangles. How many quadrilaterals are there? | [
[
{
"aoVal": "A",
"content": "$$90$$ "
}
],
[
{
"aoVal": "B",
"content": "$$95$$ "
}
],
[
{
"aoVal": "C",
"content": "$$100$$ "
}
],
[
{
"aoVal": "D",
"content": "$$105$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"
] | [
"Let $$x$$ represent the number of quadrilaterals, thus the number of triangles can be represented as $$(x-82)$$. So we have $$2\\times5+4x +3(x-82)=394$$. implying that $$x =90$$. Therefore there are $$90$$ quadrilaterals. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9241 | 3265fed465f44eda9549816f1eeadb1e | [] | 3 | single_choice | Sam wants to use two kinds of sugar water with concentrations of $$5\textbackslash\%$$ and $$20\textbackslash\%$$ to make a sugar water of $$300$$g with a concentration of $$15\textbackslash\%$$. He correctly calculated the required ratio of the two solutions, but reversed the two bottles of sugar water when preparing them. The actual concentration of the wrongly mixed sugar water is~\uline{~~~~~~~~~~}~$$\textbackslash\%$$. | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12.5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"
] | [
"NA "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9244 | 5ee5a7529d924d24830c90f41fdcde27 | [] | 1 | single_choice | If February contains Friday the $$13^{}\text{th}$$, what day of the week is February $$1$$st?． | [
[
{
"aoVal": "A",
"content": "Sunday "
}
],
[
{
"aoVal": "B",
"content": "Monday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Thursday "
}
],
[
{
"aoVal": "E",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"We can count backward by days or by weeks. Count a few weeks back to find that February $$6$$ is a Friday. Then count a few days back to find that February $$1$$ is a Sunday. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9253 | 3b22152a712a46e3b1f60c74afeca85b | [
"其它"
] | 1 | single_choice | Eddie spends $12$ minutes to climb from the first floor to the third floor at a constant speed. At this speed, how many minutes does Eddie need to climb from the first floor to the sixth floor? | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$36$$ "
}
],
[
{
"aoVal": "D",
"content": "$$42$$ "
}
],
[
{
"aoVal": "E",
"content": "$$48$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"$12 \\div (3 - 1) = 6$ $6 \\times (6 - 1) = 30$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9254 | 5a5b821ef2f24238abcfc4879e7f11b6 | [] | 1 | single_choice | The number of months in a year minus the number of days in a week equals． | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$19$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"The number of months in a year minus the number of days in a week is $$12-7 = 5$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9257 | a2da102de4fb4a178058fd96fd618628 | [
"其它"
] | 2 | single_choice | At the 2018 Tompkins County Fair a vendor is offering a "fair special" on hats. If you buy one hat at the regular price of $\textbackslash$ 30$, you get a second hat at a $40\textbackslash\%$ discount, and a third pair at half the regular price. James took advantage of the "fair special" to buy three hats. What percentage of the $\textbackslash$ 90$ regular price did he save? (adapted from 2013 AMC 8, Question \#12) | [
[
{
"aoVal": "A",
"content": "$$15$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$25$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30$$ "
}
],
[
{
"aoVal": "E",
"content": "$$40$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"First, the amount of money one will pay for three hats without the discount $=\\textbackslash$ 90$. Then, find the amount of money using the discount: $30+0.6 \\times 30+\\frac{1}{2} \\times 30=\\textbackslash$ 63$. Finding the percentage yields $\\frac{63}{90}=70\\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-70\\textbackslash\\%= 30\\textbackslash\\%$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9258 | 68073846e52148b484031f0a491973a2 | [
"其它"
] | 1 | single_choice | Find the average of these numbers: $7,9,5,3,6$ | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"D "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9270 | b550a910f5b0480a9dac345621313a24 | [
"其它"
] | 1 | single_choice | There were some cupcakes in a bakery. First, Jade ate half of the cupcakes. Then, Neil ate half of the remaining cupcakes. Finally, Terry ate $6$ cupcakes and there were $$2$$ cupcakes left. At beginning, how many cupcakes were there in the bakery? | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$32$$ "
}
],
[
{
"aoVal": "C",
"content": "$$48$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$6+2=8$$ $$8+8=16$$ $$16+16=32$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9273 | 6ca03b7ad77243b785d6d66961e437fa | [
"其它"
] | 1 | single_choice | In a zoo, there are three monkeys. The monkeys are all younger than $$5$$ years old. None of them has the same age, and all their ages are whole numbers. The product of their ages is $$8$$. What is the sum of their ages? | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
],
[
{
"aoVal": "E",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"The whole numbers smaller than $$5$$ are: $$1, 2, 3, 4$$ (age cannot be $$0$$) The product of three numbers is $$8$$. $$1\\times2\\times4=8$$ Their sum: $$1+2+4=7$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9275 | e382131f02d0430ab06cb30d744ced61 | [
"其它"
] | 1 | single_choice | After every $$3$$ steps that Pip takes forward, he takes $$2$$ steps backwards. Each step is $$1 $$$$\text{m}$$. Pip starts at one end of a $$100$$ $$\text{m}$$ hall. Pip will first reach the other end after~\uline{~~~~~~~~~~}~steps. | [
[
{
"aoVal": "A",
"content": "$$100$$ "
}
],
[
{
"aoVal": "B",
"content": "$$488$$ "
}
],
[
{
"aoVal": "C",
"content": "$$490$$ "
}
],
[
{
"aoVal": "D",
"content": "$$500$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"
] | [
"3+2=5, 3-2=1 The pattern: Pip move forward 1m in 5 steps $$100-3=97$$ $97\\times5+3=488$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9281 | 48714785331a41c4ba8c40eef02f17b3 | [] | 1 | single_choice | Susan is $6$ years old. Her sister is one year younger and her brother is one year older. What is the sum of the ages of the three siblings? | [
[
{
"aoVal": "A",
"content": "$10$ "
}
],
[
{
"aoVal": "B",
"content": "$15$ "
}
],
[
{
"aoVal": "C",
"content": "$18$ "
}
],
[
{
"aoVal": "D",
"content": "$21$ "
}
],
[
{
"aoVal": "E",
"content": "$30$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"
] | [
"Susan\\textquotesingle s sister is $6-1=5$ years old and her brother is $6+1=7$ years old. The sum of the ages of the three siblings is $5+6+7=18$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9285 | 7ef85e4c918e415693150305c0b9d315 | [] | 1 | single_choice | Peter has $$20$$ grams of a $$20\textbackslash\%$$ salt solution. How many grams of salt should he add to make it a $$25\textbackslash\%$$ solution? | [
[
{
"aoVal": "A",
"content": "$1$ grams "
}
],
[
{
"aoVal": "B",
"content": "$$\\dfrac{4}{3}$$ grams "
}
],
[
{
"aoVal": "C",
"content": "$4$ grams "
}
],
[
{
"aoVal": "D",
"content": "$5$ grams "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"
] | [
"Method $$1$$: Suppose $$x$$ ounces of salt should be added to the solution: $$\\dfrac{20\\times20\\textbackslash\\%+x}{20+x}=25\\textbackslash\\%$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde x=\\dfrac{4}{3}$$. Method $$2$$: $$20\\times(1-20\\textbackslash\\%)\\div(1-25\\textbackslash\\%)-20=\\dfrac{4}{3}$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9293 | 8390112dc36e4b7392c6d60c62a34980 | [] | 2 | single_choice | Bridget bakes $48$ loaves of bread for her bakery. She sells half of them in the morning for ＄$2.50$ each. In the afternoon she sells two thirds of what she has left, and because they are not fresh, she charges only half price. In the late afternoon she sells the remaining loaves at a dollar each. Each loaf costs ＄$0.75$ for her to make. In dollars, what is her profit for the day?($$2014$$ AMC $$10$$A Problem, Question \#$$3$$) | [
[
{
"aoVal": "A",
"content": "$24$ "
}
],
[
{
"aoVal": "B",
"content": "$36$ "
}
],
[
{
"aoVal": "C",
"content": "$44$ "
}
],
[
{
"aoVal": "D",
"content": "$48$ "
}
],
[
{
"aoVal": "E",
"content": "$52$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"
] | [
"She first sells one-half of her $48$ loaves, or $$\\frac{48}{2}=24$$ loaves. Each loaf sells for＄$2.50$, so her total earnings in the morning is equal to$24\\times $＄$2.50=$＄$60$. This leaves $24$ loaves left, and Bridget will sell $\\frac{2}{3}\\times24=16$ of them for a price of＄$\\frac{2.50}{2}=$＄$1.25$. Thus, her total earnings for the afternoon is$16\\times~ $＄$1.25=$＄$20$. Finally, Bridget will sell the remaining $24-16=8$ loaves for a dollar each. This is a total of＄$1\\times~ 8=$＄$8$. The total amount of money she makes is equal to $60+20+8=$＄$88$. However, since Bridget spends＄$0.75$ making each loaf of bread, the total cost to make the bread is equal to＄$0.75\\times 48=$＄$36$. Her total profit is the amount of money she spent subtracted from the amount of money she made, which is $88-36=52\\Rightarrow \\left(\\text{E}\\right)52$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9294 | d10656660c4e405ea503eb7956c53bc4 | [
"其它"
] | 2 | single_choice | At the "Think Flea Market", a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $\textbackslash$ 50$, you get a second pair at a $40 \textbackslash\%$ discount, and a third pair at half the regular price. Owen took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $\textbackslash$ 150$ regular price did he save? (adapted from 2013 AMC 8, Question \#12) | [
[
{
"aoVal": "A",
"content": "$$25$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$33$$ "
}
],
[
{
"aoVal": "D",
"content": "$$40$$ "
}
],
[
{
"aoVal": "E",
"content": "$$45$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"First, find the amount of money one will pay for three sandals without the discount. We have $\\textbackslash$ 50 \\times 3$ sandals $=\\textbackslash$ 150$. Then, find the amount of money using the discount: $50+0.6 \\times 50+\\frac{1}{2} \\times 50=\\textbackslash$ 105$. Finding the percentage yields $\\frac{105}{150}=70 \\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-70 \\textbackslash\\%=(\\text{B}) 30$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9301 | ac2282f76f904dca90a0c7e8c2ccf5da | [] | 2 | single_choice | Tom, Jim and Peter earned £$620$ together for painting a wall. The ratio of Tom\textquotesingle s reward to Jim\textquotesingle s reward is $3:4$. The ratio of Jim\textquotesingle s reward to Peter\textquotesingle s reward is $6:5$. How much money did Tom earn? | [
[
{
"aoVal": "A",
"content": "£$60$ "
}
],
[
{
"aoVal": "B",
"content": "£$180$ "
}
],
[
{
"aoVal": "C",
"content": "£$80$ "
}
],
[
{
"aoVal": "D",
"content": "£$240$ "
}
],
[
{
"aoVal": "E",
"content": "£$200$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"
] | [
"$3:4=9:12$, $6:5=12:10$, their rewards were in the ratio of $9:12:10$. $620\\div(9+12+10)=20$, $20\\times9=180$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9304 | 3faaf71c2f1f43a393c5e1f2d11579d2 | [] | 1 | single_choice | My mom\textquotesingle s birthday is on Sunday, and my dad\textquotesingle s birthday is $$55$$ days after it. What day of the week will my dad\textquotesingle s birthday be? | [
[
{
"aoVal": "A",
"content": "Sunday "
}
],
[
{
"aoVal": "B",
"content": "Monday "
}
],
[
{
"aoVal": "C",
"content": "Tuesday "
}
],
[
{
"aoVal": "D",
"content": "Thursday "
}
],
[
{
"aoVal": "E",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"$$55\\div7=7 \\text{R}6$$. It is Saturday. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9306 | 32b210d9db674e38939be320b24f0679 | [] | 1 | single_choice | John bought some cupcakes, and each of them cost $4$ dollars. He gave the salesperson $20$ dollars and got $4$ dollars as change. How many cupcakes did John buy? (Adapted from 2005 Math Kangaroo Problem, Level 3-4, Question \#3) | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$4$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"
] | [
"$(20-4)\\div4=4$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9310 | 63993175d2174396b7242a4febc1367d | [] | 1 | single_choice | There are two bookshelves, A and B. Shelf A has $$1100$$ books, and shelf B has books $$300$$. We need to take books from shelf A to shelf B, so that books in shelf B is three times more than self A. | [
[
{
"aoVal": "A",
"content": "$$750$$ "
}
],
[
{
"aoVal": "B",
"content": "$$800$$ "
}
],
[
{
"aoVal": "C",
"content": "$$850$$ "
}
],
[
{
"aoVal": "D",
"content": "$$900$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference->Problems Involving Sum and Difference with Two Variables"
] | [
"The sum is unchanged, which is $$1400$$，$$1400\\div \\left( 3+1 \\right)=350$$，$$1100-350=750$$． "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9311 | 4424df0ee64643218fea8a7aa5932035 | [
"其它"
] | 2 | single_choice | A mixture of 45 liters of paint is $20 \textbackslash\%$ red tint, $30 \textbackslash\%$ yellow tint and $50 \textbackslash\%$ water. Five liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (adapted from 2007 AMC 8, Question \#17 ) | [
[
{
"aoVal": "A",
"content": "$$33$$ "
}
],
[
{
"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 . "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9315 | 639b8ea4f783416992f6cfdccd4949aa | [] | 1 | single_choice | Twice my house number, plus $$4$$, is $$18$$. What\textquotesingle s my house number? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$14$$ "
}
],
[
{
"aoVal": "D",
"content": "$$40$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"Twice $$7$$, plus $$4$$ is $$18$$, so $$7$$ is my house number "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9316 | be96db402a8045fa90c6c392337aeafd | [
"其它"
] | 1 | single_choice | Alex is $8$ years older than her two sisters who are twins. The sum of the ages of all three girls is $32$ years old. How old is Alex? ($2007$ Math Kangaroo Problem, Level $5$-$6$, Question \#$9$) | [
[
{
"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 sister is $(32-8) \\div 3 =8$ years old. Thus, Alex is $8 +8 =16$ years old. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9323 | d5aa1f84df8c4225a656f09d58800967 | [] | 2 | single_choice | Jacob and Zain take pencils from a box of $$21$$ pencils without replacing them. On Monday Jacob takes $$\frac{2}{3}$$ of the number of pencils that Zain takes. On Tuesday Jacob takes $$\frac{1}{2}$$ of the number of pencils that Zain takes. On Wednesday morning the box is empty. How many pencils does Jacob take? | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$4$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Indefinite Equation Word Problems"
] | [
"Let the number of pencils Zain takes on Monday and Tuesday be $$x$$ and $$y $$ respectively. Therefore $$x+\\frac{2}{3}x+y+\\frac{1}{2}y=21$$. Hence, when we multiply the equation through by $$6$$ to eliminate the fractions and simplify, we obtain $$10x+9y =126$$. Since $$x$$ and $$y$$ are both positive integers and since the units digit of $$10x$$ is $$0$$, the units digit of $$9y$$ is $$6$$ and hence $$y=4$$. Therefore $$x=9$$ and hence the number of pencils Zain takes is $$9+4=13$$. Therefore the number of pencils Jacob takes is $$21-13= 8$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9325 | da4ab08a7cc64ec8a99b4777c206a407 | [
"其它"
] | 1 | single_choice | The fruit store sold a total of $$33$$ boxes of apples in the first three days of last week, and an average of $$18$$ boxes of apples per day in the last four days. How many boxes of apples did this fruit store sell on average each day last week? | [
[
{
"aoVal": "A",
"content": "$$13$$ "
}
],
[
{
"aoVal": "B",
"content": "$$14$$ "
}
],
[
{
"aoVal": "C",
"content": "$$15$$ "
}
],
[
{
"aoVal": "D",
"content": "$$16$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"$$33+18\\times4=105$$ $$105\\div7=15$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9332 | 4436a5189d4245a9836fd4917b4bb007 | [] | 1 | single_choice | The length of Amy\textquotesingle s string is $$12$$ cm. The length of David\textquotesingle s string is $$24$$ cm. What is the total length of their strings? | [
[
{
"aoVal": "A",
"content": "$$16$$ cm "
}
],
[
{
"aoVal": "B",
"content": "$$26$$ cm "
}
],
[
{
"aoVal": "C",
"content": "$$36$$ cm "
}
],
[
{
"aoVal": "D",
"content": "$$46$$ cm "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"$12+24=36$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9342 | 48a3d7867f584283a9129314bacb8161 | [] | 1 | single_choice | If a construction company can construct a $$1000-$$meter highway in $$5$$ days, how many days does it take to construct a $$2600-$$meter highway at the same rate? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$11$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$13$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with Two Variables"
] | [
"It can construct $$1000\\div5=200$$ meters per day. To construct $$2600$$ meters: $$2600\\div200=13$$ days. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9343 | 68367d59ab1a4d5bbbacd1a5d4bb50e9 | [] | 1 | single_choice | A school bought $$12$$ volleyballs and basketballs in total for ＄$$340$$. Each basketball costs ＄$$30$$. Each volleyball costs ＄$$25$$. How many basketballs did the school buy? | [
[
{
"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 basketballs, $$12\\times $$＄$$30=$$＄$$360$$ the total cost would be ＄$$360$$. ＄$$360-$$＄$$340=$$＄$$20$$ There is a difference of ＄$$20$$. ＄$$30-$$＄$$25=$$＄$$5$$ ＄$$20\\div $$＄$$5=4$$ $$12-4=8$$ The school bought $$8$$ basketballs. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 9346 | b0c894af319c463f86a74ddc5f53f33d | [] | 1 | single_choice | Mariam had ＄$$4y$$. After buying some cloth at ＄$$7$$ per metre, she had ＄$$y$$ left. How many metres of cloth did she buy? | [
[
{
"aoVal": "A",
"content": "$$\\frac{3y}{7}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{5y}{7}$$ "
}
],
[
{
"aoVal": "C",
"content": "$21y$ "
}
],
[
{
"aoVal": "D",
"content": "$$35y$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"
] | [
"Amount of money she spent to buy the cloth $$\\rightarrow$$＄$$4y-$$＄$$y$$ $$=$$＄$$3y$$, Length of cloth she bought $$\\rightarrow$$＄$$3y\\div $$＄$$7/\\text{m}$$ $$= \\frac{3y}{7}\\text{m}$$. "
] | A |
Subsets and Splits