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 | 8590 | 26e63fc0e4b240e4b73ae972e71fa5d9 | [] | 1 | single_choice | The sum of two natural numbers is equal to $$77$$. If the first number is multiplied by $$8$$ and the second by $$6$$, then those products are equal. The larger of these numbers is~\uline{~~~~~~~~~~}~. ($$2004$$ Math Kangaroo Problems, Level $$5-6$$, Question \#$$20$$) | [
[
{
"aoVal": "A",
"content": "$$23$$ "
}
],
[
{
"aoVal": "B",
"content": "$$33$$ "
}
],
[
{
"aoVal": "C",
"content": "$$43$$ "
}
],
[
{
"aoVal": "D",
"content": "$$44$$ "
}
],
[
{
"aoVal": "E",
"content": "$$54$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple->Problems of Sum and Multiplication with Indirect Multiples"
] | [
"Suppose one of the numbers is $x$. $8x=6(77-x)$, $x=33$. Thus, these two numbers are $33$ and $44$. The larger one is $44$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8591 | 38ef70c334a54280af6dab68b62e158b | [] | 2 | single_choice | Mother\textquotesingle s Day in $$2020$$ was May $$10$$\textsuperscript{th}, which was Sunday. Father\textquotesingle s Day in $$2020$$ was June $$21$$\textsuperscript{st}. On what day did Father\textquotesingle s Day fall? | [
[
{
"aoVal": "A",
"content": "Thursday "
}
],
[
{
"aoVal": "B",
"content": "Saturday "
}
],
[
{
"aoVal": "C",
"content": "Sunday "
}
],
[
{
"aoVal": "D",
"content": "Tuesday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"It passed $$31-10 + 21 = 42$$ days in total. Since $$42 \\div 7 = 6$$, which means the Father\\textquotesingle s Day fell on Sunday as well. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8593 | 1e1f6144fc514493aaf2b483c05bdd63 | [] | 1 | single_choice | Zosia is drawing kangaroos.The first one is blue, the next one green, the one after it red, the fourth one yellow, and then again blue, green, red, yellow, and so on, in the same order. What color will the seventeenth kangaroo be? (2003 Math Kangaroo Problem, Level 3-4, Question \#4) | [
[
{
"aoVal": "A",
"content": "$$$$Blue "
}
],
[
{
"aoVal": "B",
"content": "$$$$Green "
}
],
[
{
"aoVal": "C",
"content": "$$$$Red "
}
],
[
{
"aoVal": "D",
"content": "$$$$Black "
}
],
[
{
"aoVal": "E",
"content": "$$$$Yellow "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"
] | [
"$17\\div4=4R1$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8594 | 12494b0fc0de4222a618734a6f9671e1 | [
"其它"
] | 1 | single_choice | Ella says:" I can run $18\text{km}$ every hour." Vivian says: " Haha, I am the faster runner because I can run $100\text{m}$ every $21\text{s}$." Vivian\textquotesingle s statement is~\uline{~~~~~~~~~~}~because it only takes Ella~\uline{~~~~~~~~~~}~$\text{s}$ to run $100\text{m}$. | [
[
{
"aoVal": "A",
"content": "correct, 200 "
}
],
[
{
"aoVal": "B",
"content": "correct, 60 "
}
],
[
{
"aoVal": "C",
"content": "wrong, 20 "
}
],
[
{
"aoVal": "D",
"content": "wrong, 10 "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"
] | [
"$\\frac{18km}{1h}=\\frac{18000m}{3600s}=5m/s$ $100\\div 5=20s$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8598 | 15f4f028d9094418b3fc16298497248a | [] | 1 | single_choice | Anna, Bridgit and Carol run in a $$100\text{m}$$ race. When Anna finishes, Bridgit is $$16\text{m}$$ behind her and when Bridgit finishes, Carol is $$25\text{m}$$ behind her. The girls run at constant speeds throughout the race. How far behind was Carol when Anna finished? | [
[
{
"aoVal": "A",
"content": "$$37\\text{m}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$41\\text{m}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50\\text{m}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$55\\text{m}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$60\\text{m}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"Carol finishes $$25$$ metres behind Bridgit, so she travels $$75$$ metres while Bridgit runs $$100$$ metres. Therefore she runs $$3$$ metres for every $$4$$ metres Bridgit runs. When Anna finishes, Bridgit has run $$84$$ metres, so that at that time Carol has run $$\\frac{3}{4}\\times 84$$ metres $$=63$$ metres. Hence Carol finishes $$\\left( 100-63 \\right)$$ metres $$= 37$$ metres behind Anna. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8607 | 160a7249c2ea427ca24a5587eac0136c | [] | 1 | single_choice | There were $$31$$ runners competing in a race. The number of runners who finished before John is four times smaller than the number of runners who finished later than John. At what place did John finish? ($$1998$$ Math Kangaroo Problem, Level $$3-4$$, Question \#$$13$$) | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$21$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"
] | [
"$$(31-1) \\div (4+1) = 6$$ $$6+1=7$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8608 | 1a04c9c5940547c1b91c4482af09cf9b | [] | 1 | single_choice | Mike has a bookcase with three layers, and the ratio of books placed on the upper, middle and lower layers is $$5:6:4$$. Given that there are $$240$$ books on the middle level, books should be removed from middle level and added to the lower level so that the number of books on each level can be exactly the same. | [
[
{
"aoVal": "A",
"content": "$$48$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$60$$ "
}
],
[
{
"aoVal": "D",
"content": "$$80$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with an Invariant Part"
] | [
"Lower level: $$240\\div6\\times4=160$$, The number of books to be added to the lower level: $$(240-160)\\div2=40$$. So, the answer is $$\\text{B}$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8610 | 702400ac7e094faa81be58f565c29a72 | [] | 1 | single_choice | Tom and Jerry have to mail $$2000$$ envelopes for a new marketing campaign. Jerry can mail $$120$$ envelopes per hour. With Tom\textquotesingle s help, they can get the job done in $$10$$ hours. How long will it take Tom to finish the job by himself? | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$25$$ "
}
],
[
{
"aoVal": "C",
"content": "$$30$$ "
}
],
[
{
"aoVal": "D",
"content": "$$80$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"
] | [
"Working together: $$2000\\div10=200$$ envelopes per hour. Tom: $$200-120=80$$ envelops per hour, $$2000\\div80=25$$ hours. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8612 | d08b0be5df684e91b08def2b9c5b3777 | [] | 1 | single_choice | A series of colored lanterns are arranged in the pattern: red, red, red, yellow, yellow, red, red, red, yellow, yellow $\cdots$ The $$50$$\textsuperscript{th} lantern is~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "red "
}
],
[
{
"aoVal": "B",
"content": "yellow "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"
] | [
"Since $$50\\div(3+2)=10$$ which has no remainder, the $$50^{\\text{th}}$$ colored lantern is yellow. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8613 | b4bb2b59517c4a359cc2511ef9f09d2a | [
"其它"
] | 1 | single_choice | In a farm, there is an equal number of cows, sheep, and chickens. These animals have $250$ legs in total. How many sheep are there? | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$23$$ "
}
],
[
{
"aoVal": "C",
"content": "$$25$$ "
}
],
[
{
"aoVal": "D",
"content": "$$33$$ "
}
],
[
{
"aoVal": "E",
"content": "$$38$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems"
] | [
"Group $1$ of each kind of animals together, and there are $4+4+2=10$ legs in each group. There are $250\\div10=25$ groups, so there are $25$ sheep. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8616 | 8748f948746249edbf509ecce70d72e7 | [
"其它"
] | 1 | single_choice | If Kelly was 12 years old 4 years ago, how old will she be 8 years from now? | [
[
{
"aoVal": "A",
"content": "$$21$$ "
}
],
[
{
"aoVal": "B",
"content": "$$14$$ "
}
],
[
{
"aoVal": "C",
"content": "$$26$$ "
}
],
[
{
"aoVal": "D",
"content": "$$22$$ "
}
],
[
{
"aoVal": "E",
"content": "$$24$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"$$12+4+8=24$$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8617 | 2290ac52a3ed4007a91061996bb73f93 | [] | 1 | single_choice | There are $$20$$ students in a class lining up for recess. Mike is the $$7$$\textsuperscript{th} counting from front to back. How many students are behind Mike? What is his position counting from back to front? | [
[
{
"aoVal": "A",
"content": "$$12$$, $$13^{\\rm th}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13$$, $$14^{\\rm th}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$13$$, $$12^{\\rm th}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14$$, $$13^{\\rm th}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Order of one Character"
] | [
"The number of students behind Mike plus the position of Mike equals the total number of students in the class. So there are $$13$$ students behind Mike: $$20-7=13$$. However Mike is not included in these $$13$$ students, which means Mike is the $$14$$\\textsuperscript{th} student counting from back to front. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8621 | a2374a895c0d4c5189040a6113355cd0 | [] | 1 | single_choice | The ratio of your pears to oranges is $$3:7$$, and you have $$15$$ pears. How many oranges do you have? | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ "
}
],
[
{
"aoVal": "C",
"content": "$$21$$ "
}
],
[
{
"aoVal": "D",
"content": "$$35$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"
] | [
"$$3:7=15:x→\\dfrac{3}{7}=\\dfrac{15}{x}→3x=105→x=35$$ or $$3$$ multiply by $$5$$ equals $$15$$, so if we multiply $$5$$ by $$7$$, we get $$35$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8622 | 79692c6b3fc3484c957827b9cabc2191 | [
"其它"
] | 1 | single_choice | $$10$$ trees are planted at equal distance along a river. The distance between the $$1^{st}$$ and the $$3^{rd}$$ tree is $$20$$ metres. What is the distance between the $$7^{th}$$ and $$9^{th}$$ tree? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50$$ "
}
],
[
{
"aoVal": "D",
"content": "$$70$$ "
}
],
[
{
"aoVal": "E",
"content": "$$90$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"They are having the same number of intervals. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8625 | 1e4e6ba34d3c4a658aafadb081495651 | [
"其它"
] | 1 | single_choice | The average of John and Leo's ages is Kelly's age. The average of Kelly and Mila's ages is Leo's age. Of the four children, John is the youngest and Mila the oldest. The average of John and Mila's ages is 11. What is the total of the ages of Kelly and Leo? | [
[
{
"aoVal": "A",
"content": "$$14$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$22$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"PMC 2019 21 "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8636 | b4bf9149351d4af181eb7f29fcc16013 | [] | 1 | single_choice | Marcus has $$75$$ toy cars. $$\frac{1}{5}$$ of his toy cars are black, $$\frac{2}{15}$$ of the remainder are white, and the rest are grey. He hasmore black toy cars than white toy cars. | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$11$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"
] | [
"$75\\div5=15$ toy cars are black. $15\\times4=60$ toy cars are white or grey. $60\\div15\\times2=8$ toy cars are white. He has $15-8=7$ more black toy cars than white toy cars. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8641 | 300193aecaa64ec08f681325c9b5554d | [] | 1 | single_choice | Miya is $3$ years old this year, and her brother is $3$ years older than her. How old her brother will be $2$ years later?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$7$$) | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
],
[
{
"aoVal": "E",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages"
] | [
"When Miya is $3$, her brother is $6$, so $2$~years later, her brother is $8$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8643 | 6b8d401afae44216a0c8d5f60573fc7a | [
"其它"
] | 2 | single_choice | Five years ago, Jennifer\textquotesingle s age was five times Jason\textquotesingle s age. Now, Jennifer\textquotesingle s age is four times Jason\textquotesingle s age. How old is Jennifer now? | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$60$$ "
}
],
[
{
"aoVal": "C",
"content": "$$80$$ "
}
],
[
{
"aoVal": "D",
"content": "$$100$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"Let Jason\\textquotesingle s age five years ago be 1 unit. Then Jennifer\\textquotesingle s age was 5 units. Now, Jason\\textquotesingle s age is 1 unit + 5 and Jennifer\\textquotesingle s age is 5 units + 5. We also know that Jennifer\\textquotesingle s age is four times Jason\\textquotesingle s age or 4 x (1 unit + 5) = 4 units + 20. Then:~ 5 units + 5 = 4 units + 20 5 units - 4 units = 20 - 5 1 unit = 15 Jennifer is 5 units + 5 = 5x15 + 5 = 80 years old now. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8646 | 165075983eeb4c76bb07e2b043a909c7 | [] | 1 | single_choice | The number of weeks in $$139$$ days is most nearly equal to． | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$14$$ "
}
],
[
{
"aoVal": "C",
"content": "$$19$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"The number of weeks in $$139$$ days is most nearly $$140\\div 7=20$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8653 | 272937053dac4edc9665c283ce65b173 | [] | 1 | single_choice | When Patience asked her Granddad how old he was, he answered, "I am $$34$$ now and will be $$33$$ on my birthday." She looked confused so he added, "After being $$50$$ for a year I started counting backwards on each birthday. " How old will he actually be on his birthday? | [
[
{
"aoVal": "A",
"content": "$$33$$ "
}
],
[
{
"aoVal": "B",
"content": "$$34$$ "
}
],
[
{
"aoVal": "C",
"content": "$$56$$ "
}
],
[
{
"aoVal": "D",
"content": "$$67$$ "
}
],
[
{
"aoVal": "E",
"content": "$$83$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"
] | [
"When Granddad would have claimed to be $$49$$ he was actually $$51$$, $$48$$ when he was actually $$52$$- in every case his claimed age and his real age have a total of $$100$$. So this year his age is $$100-33=67$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8654 | 1a54dc2d189d470ebfb5f48a48505e88 | [
"其它"
] | 2 | single_choice | Calculate: $1^{2}+2^{2}+3^{2}+\cdots +20^{2}+21^{2}$ | [
[
{
"aoVal": "A",
"content": "$$231$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2870$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3311$$ "
}
],
[
{
"aoVal": "D",
"content": "$$53361$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples"
] | [
"C "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8655 | 625a19f4d2c14ff0ab7eae0950403c2d | [
"其它"
] | 1 | single_choice | In the window of Bradley\textquotesingle s Bicycle Bazaar there are some unicycles, some bicycles and some tricycles. Laura sees that there are seven saddles in total, thirteen wheels in total and more bicycles than tricycles. How many unicycles are in the window? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
],
[
{
"aoVal": "E",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems"
] | [
"JMC 2017 22 "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8656 | 1a56e8d7729b4ea69eac40eb4a08eb24 | [] | 1 | single_choice | Red and green dragons lived in a cave. Each red dragon had $$6$$ heads, $$8$$ legs, and $$2$$ tails. Each green dragon had $$8$$ heads, $$6$$ legs, and $$4$$ tails. There were $$44$$ tails altogether, and there were $$6$$ less green legs than red heads. How many red dragons lived in the cave? ($$2003$$ Math Kangaroo Problems, Level $$5-6$$, Question \#$$29$$) | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis->Basic Type->Non-typical Types"
] | [
"Suppose there are $x$ red dragons and $y$ green dragons. $2x+4y=44$ and $6x-6y=6$. We can get that $y=7$ and $x=8$. Thus, there are $8$ red dragons. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8663 | 4ff3b135fecb4c29a98ff609e49247fe | [] | 1 | single_choice | There are $$20$$ students in a class lining up for recess. Mike is the $$7$$\textsuperscript{th} counting from front to back. How many students are behind Mike? What is his position counting from back to front? | [
[
{
"aoVal": "A",
"content": "$$12$$, $$13$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13$$, $$14$$ "
}
],
[
{
"aoVal": "C",
"content": "$$13$$, $$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14$$, $$13$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Order of one Character"
] | [
"The number of students behind Mike plus the position of Mike equals the total number of students in the class. So there are $$13$$ students behind Mike: $$20-7=13$$. However Mike is not included in these $$13$$ students, which means Mike is the $$14$$\\textsuperscript{th} student counting from back to front. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8667 | f5b4f2b295d244909283349d8c038fe2 | [] | 1 | single_choice | A bookstore purchases $$20$$ story books for ＄$$820$$. If the bookstore wants to earn ＄$$12$$ for each book, what is the selling price of each book? | [
[
{
"aoVal": "A",
"content": "＄$$50$$ "
}
],
[
{
"aoVal": "B",
"content": "＄$$51$$ "
}
],
[
{
"aoVal": "C",
"content": "＄$$52$$ "
}
],
[
{
"aoVal": "D",
"content": "＄$$53$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"
] | [
"$$\\frac{820}{20}+12=41+12=53$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8670 | 4b6592860cc547908160da24dfd2a2c5 | [] | 1 | single_choice | Henry starts to read a $$290$$-page book on a Monday. He reads four pages every day except on Sundays when he reads $$25$$ pages. He will read the book starting from page~\uline{~~~~~~~~~~}~next Monday. | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$49$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50$$ "
}
],
[
{
"aoVal": "D",
"content": "$$240$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"$$25+6\\times 4=49$$，$$49+1=50$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8671 | 1e978c774dbc4d6e94ac3df23435c53c | [] | 1 | single_choice | There are $$10$$ blind boxes on the desk, and each blind box contains two toys. Now there are $$16$$ toys in hands. How many blind boxes remain？(adapted from $$2010$$ Math Kangaroo Problem, Level $$1-2$$, Question \#$$15$$) | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$3$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"$$16$$ toys means $$8$$ blind boxes are opened. There are $$10$$-$$8$$=$$2$$ blind boxes that have not been opened. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8674 | 3db2ae7af8ff459987310c5c5b2539d8 | [] | 0 | single_choice | A salt solution is made by mixing $$8$$ ounces of pure salt and $$32$$ ounces of water. Find the percent concentration of the solution. | [
[
{
"aoVal": "A",
"content": "$$10\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$25\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"
] | [
"$$8\\div(8+32)=20\\textbackslash\\%$$. ~~ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8675 | 66fb9f92550b4d94af78dd64ca55fddf | [] | 1 | single_choice | The speed of high-speed train is approximately $$350$$ kilometers per hour, while the walking speed of a person is approximately $$5$$ meters per second. Approximately, how many times is the speed of a high-speed train faster than the walking speed of a person?． | [
[
{
"aoVal": "A",
"content": "$$2 $$ "
}
],
[
{
"aoVal": "B",
"content": "$$20 $$ "
}
],
[
{
"aoVal": "C",
"content": "$$70 $$ "
}
],
[
{
"aoVal": "D",
"content": "$$200 $$ "
}
],
[
{
"aoVal": "E",
"content": "$$700$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"
] | [
"The speed of high-speed train is approximately $$350$$ kilometers per hour, which is approximately $$100$$ meters per second. So its speed is roughly $$20$$ times faster than $$5$$ $$ meters per second. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8676 | 34a7f96474264c658adb82fcc362cb8f | [] | 1 | single_choice | If February is a month that contains Friday $$13^{}\text{th}$$, 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 | 8677 | 1ea0df171d7a49d2a7463b2af7d41c84 | [
"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? (adapted from 2005 Math Kangaroo Problem, Level 5-6, Question \#14) | [
[
{
"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 | 8678 | 6b9d71feffca4bfe8c4e21f51a4a31be | [] | 1 | single_choice | Study the pattern below. The $$100^{}\rm {th}$$ letter is . $$A A B B C A A B B C A A B B C A A \cdots$$ | [
[
{
"aoVal": "A",
"content": "$$A$$ "
}
],
[
{
"aoVal": "B",
"content": "$$B$$ "
}
],
[
{
"aoVal": "C",
"content": "$$C$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"
] | [
"$$100$$~$\\div$ $$5$$ = $$20$$ $$R0$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8679 | 59279935ffd3426bb4136d25d0df86f3 | [
"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 $29$th. $27\\div7=3R6$, which means May $29$th is Wednesday. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8680 | 16a25ba9f8e04f189f791913f6b471b6 | [] | 1 | single_choice | A $$16$$-quart radiator is filled with water.Four quarts are removed and replaced with pure antifreeze liquid.Then four quarts of the mixture are removed and replaced with pure antifreeze.This is done a third and a fourth time.The fractional part of the final mixture that is water is． | [
[
{
"aoVal": "A",
"content": "$$\\frac{81}{256}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{27}{64}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{37}{64}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{175}{256}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"
] | [
"After the first time:$$1\\times \\frac{12}{16}+0\\times \\frac{4}{16}=\\frac{3}{4}$$. After the second time:$$\\frac{3}{4}\\times \\frac{12}{16}+0 \\times \\frac{4}{16}= \\frac{9}{16}$$. After the third time:$$\\frac{9}{16}\\times \\frac{12}{16}+0 \\times \\frac{4}{16}= \\frac{27}{64}$$. After the fourth time:$$\\frac{27}{64}\\times \\frac{12}{16}+0 \\times \\frac{4}{16}= \\frac{81}{256}$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8685 | 3dbde30796f94c44b2e263b5bea67847 | [] | 1 | single_choice | On a map of the Andes, if $2$ $\text{cm}$ represents $6000$ $\text{km}$, then ~represents $300$ $\text{km}$ . | [
[
{
"aoVal": "A",
"content": "$$0.1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$0.5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"
] | [
"If $2$ $\\text{cm}$ represents $6000\\text{km}$, $1\\text{cm}$ represents $3000\\text{km}$, and $0.1\\text{cm}$ represents $300\\text{km}$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8692 | a24849a03db44c7f8821c2ead15a0ecd | [] | 1 | single_choice | My sister runs $$10\text{km}$$ per hour, and I run $$2\text{km}$$ in $$15$$ minutes. If we both run for $$2$$ hours, my sister will run$$\text{km}$$ farther than I will. | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"I run $$2\\text{km}$$ in $$15$$ minutes, or $$8\\text{km}$$ in $$1$$ hour. In $$2$$ hours, I will run $$16\\text{km}$$ and my sister will run $$20\\text{km}$$. She will run $$4\\text{km}$$ farther than I will. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8694 | 2bc19d01cb93432f890d95c6f9355ccd | [
"其它"
] | 1 | single_choice | In 2010 about 120 million digital still cameras were sold worldwide. By 2018 this number had decreased by 85\%. About how many million digital still cameras were sold in 2018? | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$28$$ "
}
],
[
{
"aoVal": "C",
"content": "$$38$$ "
}
],
[
{
"aoVal": "D",
"content": "$$48$$ "
}
],
[
{
"aoVal": "E",
"content": "$$58$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"
] | [
"$120\\times（1-85\\textbackslash\\%）=18$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8700 | 2bc5b05b78b54e47b3e54627d8cb3978 | [
"其它"
] | 1 | single_choice | Monica arrived in the Kangaroo Camp on July 25th in the morning and left the camp on August 3rd in the afternoon. How many nights did she sleep in the camp? | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$9$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30$$ "
}
],
[
{
"aoVal": "E",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"
] | [
"July has 31 days. She arrive on morning of July 25. From July 25 to 31, there are 7 nights that she slept in the camp. Then she slepft for 2 days in August, since she left on the afternoon Aug 3 already. Hence, 2=7=9 "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8701 | d099cad18be84975900c73c05f9e8596 | [
"其它"
] | 0 | single_choice | There are three books Chinese, Math, and English. Sissy wants to put them in the bookcase. How many ways are there for the three books to put? List out all the ways. | [
[
{
"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 | 8703 | 4b76669ce26f4c83b9cf2b166fd049e1 | [] | 1 | single_choice | In a fruit stall, there are 25 apples. There are 9 fewer apples than oranges. How many oranges are there in the fruit stall? | [
[
{
"aoVal": "A",
"content": "$$17$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$34$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$25+9=34$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8706 | 2306531494994d67b8623f7603101c79 | [] | 1 | single_choice | On a map of the Andes, if $2$ $\text{cm}$ represents $6000$ $\text{km}$, then ~represents $300$ $\text{km}$ . | [
[
{
"aoVal": "A",
"content": "$$0.1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$0.5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"
] | [
"If $2$ $\\text{cm}$ represents $6000\\text{km}$, $1\\text{cm}$ represents $3000\\text{km}$, and $0.1\\text{cm}$ represents $300\\text{km}$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8707 | de8086cc231940be9a4c3751f6365733 | [] | 1 | single_choice | Chloe has＄$$7$$. She is going to buy $$6$$ pens, and each costs $90$ cents. She also buys a certain number of pencils, and each costs $$50$$ cents. How many pencils at most can she buy? (Adapted from 2007 Math Kangaroo Problem, Level 3-4, Question \#4) | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2$$ "
}
],
[
{
"aoVal": "E",
"content": "$$1$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"$7$ dollars =~ $700$ cents $(700-6\\times90)\\div50=3R10$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8714 | ab912e8d10d44ea89d0e2d0eef45faf5 | [
"其它"
] | 1 | single_choice | Isabella must take four $100$-point tests in her math class. Her goal is to achieve an average grade of $95$ on the tests. Her first two test scores were $97$ and $91$. After seeing her score on the third test, she realized she can still reach her goal. What is the lowest possible score she would have made on the third test? | [
[
{
"aoVal": "A",
"content": "$$90$$ "
}
],
[
{
"aoVal": "B",
"content": "$$92$$ "
}
],
[
{
"aoVal": "C",
"content": "$$95$$ "
}
],
[
{
"aoVal": "D",
"content": "$$96$$ "
}
],
[
{
"aoVal": "E",
"content": "$$97$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"Isabella wants an average grade of $95$ on her $4$ test; this also means that she wants the sum of her test scores to be at least $95\\times 4=380$ (if she goes over this number, she\\textquotesingle ll be over the goal!). She\\textquotesingle s already taken two tests, which sum to $97+91=188$, which means she needs $380-188=192$ more points to achieve her desired average. In order to minimize the score on the third test, we assume that Isabella will receive all $100$ points on the fourth test. Therefore, the lowest score on the third test would be $192-100=92$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8717 | 1ab92ac7213c4fed915c07d69575af43 | [
"其它"
] | 2 | single_choice | \textbf{In the setting of the previous problem, about what percent of the variation in the number of service calls is explained by the linear relation between number of service calls and number of machines?~} | [
[
{
"aoVal": "A",
"content": "86\\% "
}
],
[
{
"aoVal": "B",
"content": "93\\% "
}
],
[
{
"aoVal": "C",
"content": "74\\% "
}
],
[
{
"aoVal": "D",
"content": "None of the above "
}
],
[
{
"aoVal": "E",
"content": "\\textbf{Can't tell from the information given} "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$R^{2} = r^{2} = 0.86^{2} = 0.7396$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8725 | 5010dd64822146b69b2a5055c3572558 | [] | 1 | single_choice | Otto the octopus needs $$2$$ tentacles to juggle up to $$3$$ balls. If Otto uses all $$8$$ tentacles, Otto can juggle up to balls. | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$9$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$24$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"Otto needs $$2$$ tentacles to juggle up to $$3$$ balls. Using $$8=4\\times2$$ tentacles, Otto can juggle up to $$4\\times3 = 12$$ balls. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8737 | 2be566b670084b3fba84deaddf00ce87 | [
"其它"
] | 1 | single_choice | Lucy was $$20$$ years old when Bill was $$12$$. Now, Bill is $$17$$ years old. How old is Lucy? | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13$$ "
}
],
[
{
"aoVal": "C",
"content": "$$21$$ "
}
],
[
{
"aoVal": "D",
"content": "$$23$$ "
}
],
[
{
"aoVal": "E",
"content": "$$25$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"The age difference between Lucy and Bill is $$20~-- 12 = 8$$, which will not change. Thus, Lucy is $$17 + 8 = 25$$ years old. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8745 | b9749b14654d47afb8ff37b26d113196 | [] | 2 | single_choice | Olivia has $32$ clothes, $4$ of them are yellow, $10$ are blue, $13$ are purple, and the others are white. Suddenly the power is off, and it is all black in the room. At least how many clothes should Olivia pick in order to guarantee that she gets $8$ clothes in the same color? | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ "
}
],
[
{
"aoVal": "C",
"content": "$$17$$ "
}
],
[
{
"aoVal": "D",
"content": "$$24$$ "
}
],
[
{
"aoVal": "E",
"content": "$$32$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$4+5+7+7+1=24$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8746 | 9470b5e9b9f141ecaddfddd41f59334c | [] | 1 | single_choice | Jack mixed $20$ grams of sugar with $30$ grams of water. What is the percent concentration of the sugar solution? Then Jack added $50$ grams of water. What is the percent concentration the sugar solution? | [
[
{
"aoVal": "A",
"content": "$$40 \\textbackslash\\% $$; $$20\\textbackslash\\% $$. "
}
],
[
{
"aoVal": "B",
"content": "$$40 \\textbackslash\\% $$; $$25 \\textbackslash\\% $$. "
}
],
[
{
"aoVal": "C",
"content": "$$50 \\textbackslash\\% $$; $$20 \\textbackslash\\% $$. "
}
],
[
{
"aoVal": "D",
"content": "$$50 \\textbackslash\\% $$;~$$25 \\textbackslash\\% $$. "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems->Calculating Solvent from Solution and Solute"
] | [
"$n\\_1=\\frac{20}{20+30}\\times100\\textbackslash\\%=40\\textbackslash\\%$; $n\\_2=\\frac{20}{20+30+50}\\times100\\textbackslash\\%=20\\textbackslash\\%$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8748 | 1af51f519342449c9e0685e658bbc883 | [] | 1 | single_choice | Colin has $$70$$ stamps. He has $$7$$ times as many stamps as Ben. How many more stamps does Colin have than Ben? | [
[
{
"aoVal": "A",
"content": "$$73$$ "
}
],
[
{
"aoVal": "B",
"content": "$$70$$ "
}
],
[
{
"aoVal": "C",
"content": "$$60$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems"
] | [
"$$70 \\div10 = 7$$ $$70-10=60$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8749 | 82ce579b479f4a579f72930e17ba5628 | [] | 1 | single_choice | In a certain year, June $$24$$\textsuperscript{th}~is Thursday. What day is August $$27$$\textsuperscript{th~}in this year? $\textasciitilde$ | [
[
{
"aoVal": "A",
"content": "Monday "
}
],
[
{
"aoVal": "B",
"content": "Tuesday "
}
],
[
{
"aoVal": "C",
"content": "Thursday "
}
],
[
{
"aoVal": "D",
"content": "Friday "
}
],
[
{
"aoVal": "E",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"Counting from June $$24$$\\textsuperscript{th}, after $30-24=6$ days it is June $$30$$\\textsuperscript{st}. After $58$ days it is August $$27$$\\textsuperscript{th}. In total, there are $6+58=64$ days. $64\\div 7 =9R1$, which means August $$27$$\\textsuperscript{th~}is Friday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8750 | 990de1b72a4646019e3b400f1d95497c | [
"其它"
] | 1 | single_choice | A tank filled with 200 litres of water weighs 350kg. The same tank filled with 150 litres of water weighs 315kg. What is the weight of the empty tank? | [
[
{
"aoVal": "A",
"content": "$$120$$kg "
}
],
[
{
"aoVal": "B",
"content": "$$150$$kg "
}
],
[
{
"aoVal": "C",
"content": "$$165$$kg "
}
],
[
{
"aoVal": "D",
"content": "$$210$$kg "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"
] | [
"T + 200L = 350kg $\\cdots $ ① -) T + 150L = 315kg $\\cdots $ ② \\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_ (50L = 35kg) x3 = 150L = 105kg 315kg - 105kg = 210kg "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8751 | 594713f4e0a54955bbbc177e8ebb4478 | [] | 1 | single_choice | Esther made $$8$$ paper stars. Faiza made $$4$$ times as many paper stars as Esther did. Gurmit made $$5$$ times as many paper stars as Esther did, How many paper stars did the three boys make altogether? | [
[
{
"aoVal": "A",
"content": "$$64$$ "
}
],
[
{
"aoVal": "B",
"content": "$$80$$ "
}
],
[
{
"aoVal": "C",
"content": "$$144$$ "
}
],
[
{
"aoVal": "D",
"content": "$$152$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"
] | [
"omitted "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8754 | 172a6dbdb43948c794e913ba773dbe50 | [] | 1 | single_choice | Debbie bought a loaf of bread for $$$4$$. She paid for the bread with a $$$10$$ note. How much change did Debbie receive? ． | [
[
{
"aoVal": "A",
"content": "$$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$$14$$ "
}
],
[
{
"aoVal": "D",
"content": "$$$40$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"$$10-4=6$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8755 | 877194e213ef49bb85a4188c792afc5d | [
"其它"
] | 1 | single_choice | Six rectangles each with a common base width of $2$ have lengths of $1,4,9,16,25$, and 36 . What is the sum of the areas of the six rectangles? (2014 AMC 8, Question \#6) | [
[
{
"aoVal": "A",
"content": "$$91$$ "
}
],
[
{
"aoVal": "B",
"content": "$$93$$ "
}
],
[
{
"aoVal": "C",
"content": "$$162$$ "
}
],
[
{
"aoVal": "D",
"content": "$$182$$ "
}
],
[
{
"aoVal": "E",
"content": "$$202$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"The sum of the areas is equal to $2 \\cdot 1+2 \\cdot 4+2 \\cdot 9+2 \\cdot 16+2 \\cdot 25+2 \\cdot 36$. This is equal to $2(1+4+9+16+25+36)$, which is equal to $2 \\cdot 91$. This is equal to our final answer of (D) 182 . "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8756 | 4701f0a24cb44deb958dd0da2441fe6f | [] | 1 | single_choice | My old printer printed $$13$$ pages in $$3$$ seconds. My new printer prints $$21$$ pages in $$2$$ seconds. In $$6$$ seconds my new printer printsmore pages than my old one could have. | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$27$$ "
}
],
[
{
"aoVal": "D",
"content": "$$37$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"My old printer printed $$13$$ pages in $$3$$ seconds or $$26$$ pages in $$6$$ seconds. My new printer prints $$21$$ pages in $$2$$ seconds or $$63$$ pages in $$6$$ seconds. The difference is $$63 - 26=37$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8780 | 397ac5a098ae4c5dac1059df62e3d786 | [] | 1 | single_choice | March $$12$$th, $$2012$$ was a Monday. What day was May $$1$$st, $$2015$$? | [
[
{
"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->Period of Dates"
] | [
"March $$12$$th, $$2013$$: Tuesday March $$12$$th, $$2014$$: Wednesday March $$12$$th, $$2014$$: Thursday $(31-12)+30+1=50$, $50\\div 7=7\\textbackslash{} \\rm r \\textasciitilde1$, so it was Friday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8785 | a25b23b388c744a6afa341d8d1a09bed | [
"其它"
] | 1 | single_choice | SASMO 2014 P2 Q10 Tim is 8 years old and Sally is 4 years old. How old will Sally be when Tim is 14 years old? | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"8 + 6 = 14 4 + 6 = 10 "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8788 | a25bd2d10423408bbc69d70d7673969b | [
"其它"
] | 1 | single_choice | Pip is 10 years and 2 months old. Bud is 124 months old. Bob has been alive for 3660 days. Who is the oldest? | [
[
{
"aoVal": "A",
"content": "Pip "
}
],
[
{
"aoVal": "B",
"content": "Bud "
}
],
[
{
"aoVal": "C",
"content": "Bob "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"
] | [
"omitted "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8792 | 8b363b447f464faba7b50d1941060b6a | [
"其它"
] | 2 | single_choice | There are some ducks and chickens in a farm. The number of chickens is $10$ more than ducks.The number of ducks is half the number of chicken. How many ducks and chickens are there in the farm? ~ | [
[
{
"aoVal": "A",
"content": "$26$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$33$$ "
}
],
[
{
"aoVal": "D",
"content": "$$39$$ "
}
],
[
{
"aoVal": "E",
"content": "$$40$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$10+10+10=30$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8795 | 350e77ab80a84b6ea8f872e947a0badc | [
"其它"
] | 2 | single_choice | I ate half of an apple pie on Saturday and two thirds of the remainder on Sunday. What fraction of the pie was left for Monday? | [
[
{
"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->Knowing the Base"
] | [
"$(1-\\frac12)\\times(1-\\frac23)=\\frac12\\times\\frac13=\\frac16$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8800 | 67301634161942b49134ba39bd5b96ae | [
"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 $6$ 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 | 8821 | b044bdc50e6948c2939430d6f499c1db | [] | 1 | single_choice | If today is Tuesday, what day was it $$76$$ days ago? | [
[
{
"aoVal": "A",
"content": "$$$$Monday "
}
],
[
{
"aoVal": "B",
"content": "$$$$Tuesday "
}
],
[
{
"aoVal": "C",
"content": "$$$$Wednesday "
}
],
[
{
"aoVal": "D",
"content": "$$$$Thursday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"Today is Tues. $$77$$ days ago was Tues. $$76$$ days ago was Wed. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8822 | 35258801683b477b94c336af438813b8 | [
"其它"
] | 1 | single_choice | There is a piece of wire. First, half of the piece is used. Then, half of the remaining piece is used. Next, $$16$$ meters are used. Finally, $$9$$ meters are left. The original piece of the wire is~\uline{~~~~~~~~~~}~meters long. | [
[
{
"aoVal": "A",
"content": "$$36$$ "
}
],
[
{
"aoVal": "B",
"content": "$$50$$ "
}
],
[
{
"aoVal": "C",
"content": "$$64$$ "
}
],
[
{
"aoVal": "D",
"content": "$$100$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$16 + 9 = 25$$ $$25 + 25 =50$$ $$50 + 50 =100$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8827 | c2cc718040e04ca4a0c83b743af94a37 | [
"其它"
] | 1 | single_choice | Karl is now $10$ years old, and Ala is $3$ years old. How many years from now will Karl be twice as old as Ala? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$1$$ "
}
],
[
{
"aoVal": "E",
"content": "$$3$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"The age difference is equal to $10-3=7$. When the age of Karl is twice the age of Ala, the age of Ala will be equal to the age difference which is $7$. Thus, it will pass $7-3 = 4$ years. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8828 | 1b7ffadac1ea48809002660767616994 | [] | 1 | single_choice | In a certain year, March $$27$$\textsuperscript{th}~is Friday. What day is April $$24$$\textsuperscript{th~}in this year? $\textasciitilde$ | [
[
{
"aoVal": "A",
"content": "Monday "
}
],
[
{
"aoVal": "B",
"content": "Tuesday "
}
],
[
{
"aoVal": "C",
"content": "Thursday "
}
],
[
{
"aoVal": "D",
"content": "Friday "
}
],
[
{
"aoVal": "E",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"Counting from March $$27$$\\textsuperscript{th}, after $31-27=4$ days it is March $$31$$\\textsuperscript{st}. After $24$ days it is April $$24$$\\textsuperscript{th}. In total, there are $4+24=28$ days. $28\\div 7 =4$, which means April $$24$$\\textsuperscript{th~}is Friday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8830 | 23a915e78ec143738053a03e90547b02 | [] | 2 | single_choice | How many digits have to be written in order to write down every number from $$1$$ to $$100$$ inclusive? ($$2007$$ Math Kangaroo Problem, Level $$3-4$$, Question \#$$23$$) | [
[
{
"aoVal": "A",
"content": "$$100$$ "
}
],
[
{
"aoVal": "B",
"content": "$$150$$ "
}
],
[
{
"aoVal": "C",
"content": "$$190$$ "
}
],
[
{
"aoVal": "D",
"content": "$$192$$ "
}
],
[
{
"aoVal": "E",
"content": "$$200$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem->Correspondence between Numbers and Page Numbers->Applying the Total Number of Numbers"
] | [
"$1$-digit numbers: $9\\times1=9$ digits. $2$-digit numbers: $90\\times2=180$ digits. $3$-digit numbers: $1\\times3=3$ digits. Total: $9+180+3=192$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8833 | 1b8a0463db0c4bebaeef07997eace089 | [] | 1 | single_choice | Ten years ago, the sum of the ages of my mother and father was $$71$$. What is the sum of their ages today? | [
[
{
"aoVal": "A",
"content": "$$51$$ "
}
],
[
{
"aoVal": "B",
"content": "$$61$$ "
}
],
[
{
"aoVal": "C",
"content": "$$81$$ "
}
],
[
{
"aoVal": "D",
"content": "$$91$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"
] | [
"Ten years ago, the sum of the ages of my mother and father was $$71$$. Each has aged $$10$$ years, so the sum of their ages is now $$91$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8836 | 30bf13245023460e8997d7111f174a8d | [
"其它"
] | 1 | single_choice | The triplets Adam, Jan and Stas and their sister Marysia who is four years older than them were $24$ years old together three years ago. How old is Marysia today? (2001 Math Kangaroo Problem, Level 5-6, Question \#18) | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
],
[
{
"aoVal": "E",
"content": "$$15$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"Adam, Jan and Stas were $(24-4)\\div4=5$ years old three years ago. Marysia was $5+4=9$ years old. Thus, Marysia is $9+3=12$ years old. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8838 | 50527e768fc64e4a8028f90a9868ed8b | [] | 1 | single_choice | A mother cut a cake into $$12$$ equal slices. Her four children had a slice each and she had one too. Later, a neighbour ate four slices. What percentage of the cake was left at the end of the day? | [
[
{
"aoVal": "A",
"content": "$$5\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$25\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$35\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "E",
"content": "$$50\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"
] | [
"$12-(4\\times1)-1-4=3$ $\\frac{3}{12}\\times100\\textbackslash\\%=25\\textbackslash\\%$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8839 | 30bf68fb808c4f1b8110a71bc503371d | [] | 2 | single_choice | A worm is staying at the bottom of a well with a depth of $$13$$ metres. If it climbs up $$4$$ metres in the daytime and slips down $$1$$ metre at night, which day will it climb up to the ground? | [
[
{
"aoVal": "A",
"content": "The $$4$$th day "
}
],
[
{
"aoVal": "B",
"content": "The $$5$$th day "
}
],
[
{
"aoVal": "C",
"content": "The $$6$$th day "
}
],
[
{
"aoVal": "D",
"content": "The $$7$$th day "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"
] | [
"It climbs up $$4$$ metres in the day time and slips down $$1$$ metre at night, so it climbs up $$3$$ metres in a whole day. For the first $$3$$ days, it climbs $$9$$ metres. During the day time of the forth day, it climbs $$4$$ metres and reaches the ground. Then it needs four days to climb up to the ground. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8854 | b4ece9a28c0f4c7693d6b175f6dd1203 | [] | 2 | single_choice | A bag of toffee is $7$ dollars, a bag of cotton candy is $6$ dollars, and a bag of orange candy is $15$ dollars. Now, the candy shop decides to mix $40$ bags of toffee, $50$ bags of cotton candy, and $10$ bags of orange candy for $100$ bags of assorted candy. What should be the price of the assorted candy in dollars to keep the total revenue unchanged? | [
[
{
"aoVal": "A",
"content": "$$7.3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9.5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
],
[
{
"aoVal": "E",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"Total revenue: $40\\times 7+50\\times 6+10\\times 15=730$ dollars A bag of assorted candy: $$730\\div 100=7.3$$ dollars "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8860 | 8791404a6c9247669ac325195ce17039 | [
"其它"
] | 1 | single_choice | A drawer contains $10$ yellow socks, $8$ blue socks and $4$ pink socks. Bella picks socks from the drawer without looking. What is the smallest number of socks she must pick to make sure she has at least one sock of each colour? | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$19$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Extreme Value of Average"
] | [
"$10+8+1=19$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8861 | b04cc06ceb2f45bcb14bc873262b6eca | [
"其它"
] | 1 | single_choice | Peter has some toy cars, and Paul has $$4$$ more toy cars than Peter. Altogether they have $$36$$ toy cars. How many toy cars does Paul have? | [
[
{
"aoVal": "A",
"content": "$$16$$ "
}
],
[
{
"aoVal": "B",
"content": "$$48$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference->Sum and Differences Problems with multiple Variables"
] | [
"Paul has $$(36 + 4) \\div 2 = 20$$ toy cars. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8864 | 6749543a4c4e483eaa09c7465aa1dfba | [] | 3 | single_choice | There is an equation with all integers in the upper squares, and the answer on the right side is only the approximation of $$\frac{\square }{3}+\frac{\square }{5}+\frac{\square }{7}\approx 1.16$$ after rounding off. The numbers in each of the three upper squares of the equation are~\uline{~~~~~~~~~~}~in order. | [
[
{
"aoVal": "A",
"content": "$1,2,3$ "
}
],
[
{
"aoVal": "B",
"content": "$1,3,5$ "
}
],
[
{
"aoVal": "C",
"content": "$1,4,3$ "
}
],
[
{
"aoVal": "D",
"content": "$2,1,2$ "
}
],
[
{
"aoVal": "E",
"content": "$2,3,5$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"
] | [
"NA "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8869 | 39c3062b5afa4c81857a43ad5d4e3b72 | [
"其它"
] | 1 | single_choice | Nancy has $23$ donuts. She gives one donut to Sana, and then Nancy has $10$ more donuts than Sana. At beginning, how many donuts does Sana have? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$11$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$13$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$23-1=22$$ $$22-10=12$$ $$12-1=11$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8871 | 1fbd323f929a46cf8b4ae86af94d47e5 | [] | 2 | single_choice | Joann\textquotesingle s birthday in $$2020$$ was May $$10$$\textsuperscript{th}, which was Sunday. Elizabeth\textquotesingle s birthday in $$2020$$ was June $$21$$\textsuperscript{st}. What day of the week is Elizabeth\textquotesingle s birthday on? | [
[
{
"aoVal": "A",
"content": "Thursday "
}
],
[
{
"aoVal": "B",
"content": "Saturday "
}
],
[
{
"aoVal": "C",
"content": "Sunday "
}
],
[
{
"aoVal": "D",
"content": "Tuesday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"It passed $$31-10 + 21 = 42$$ days in total. Since $$42 \\div 7 = 6$$, it was Sunday. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8882 | 2c848cf8a3684a8fbbbdb0b22ade62d0 | [] | 1 | single_choice | A sugar solution is made by mixing $$7$$ ounces of sugar and $$21$$ ounces of water. Find the percent concentration of the solution. | [
[
{
"aoVal": "A",
"content": "$$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\\%$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8885 | 8b52eb5b2f384128a9beecce5b84956b | [] | 1 | single_choice | Ellis\textquotesingle s Eel Emporium contains a large tank holding three different types of eel: electric eels, moray eels and freshwater eels. A notice on the tank reads as follows: All the eels are electric eels except for $$12$$ All the eels are moray eels except for $$14$$ All the eels are freshwater eels except for $$16$$ How many eels are in the tank? | [
[
{
"aoVal": "A",
"content": "$$42$$ "
}
],
[
{
"aoVal": "B",
"content": "$$33$$ "
}
],
[
{
"aoVal": "C",
"content": "$$24$$ "
}
],
[
{
"aoVal": "D",
"content": "$$21$$ "
}
],
[
{
"aoVal": "E",
"content": "$$20$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems"
] | [
"Let the number of electric eels be $$x$$, the number of moray eels be $$y $$ and the number of freshwater eels be $$z$$. The information on the notice tells us that $$y + z = 12$$, $$x + z = 14$$ and $$x + y = 16$$. When you add these three equations, you obtain $$2x + 2y + 2z = 42$$ and hence $$x + y + z = 21$$. Therefore the number of eels in the tank is $$21$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8886 | 2c85f85b43c547aa8b4c3517991676de | [
"其它"
] | 1 | single_choice | Tom and Ben played a quiz game. $$2$$ points for a correct answer. Tom got $$5$$ questions right, Ben got $$8$$ questions right. How many more points than Ben did Tom get?~(adapted from $$2021$$ Math kangaroo, Level $$1-2$$, Question \#$$14$$) | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
],
[
{
"aoVal": "E",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"August got $$5\\times2=10$$ points, and Ben got $$8\\times2=16$$ points. $$16-10=6$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8887 | 2c86d070ab8c45b991b7bdfde4be189b | [
"其它"
] | 1 | single_choice | Farmer Baar has 36 sheep, some pink and the rest white. There are twice as many pink sheep as white sheep. How many of the sheep are pink? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$24$$ "
}
],
[
{
"aoVal": "E",
"content": "$$30$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple->Sum and Multiple of Two Variables"
] | [
"$36\\div (1+2)=12, 12\\times2=24$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8888 | 6755c48c72454835b9e9b7c4fbca6f8a | [
"其它"
] | 1 | single_choice | John is 33 years old. His three sons are 5, 6 and 10 years old. In how many years will the three sons together be as old as their father? | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
],
[
{
"aoVal": "E",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"Let x be the number of years needed for the ages of the three sons sum up to be equal to their dad\\textquotesingle s age. Their dad\\textquotesingle s age is then 33+x, while the sum of the sons\\textquotesingle{} age is (5+x) x (6+x)+(10+x)=21+3x. We have the following equation: 21+3x = 33+x 2x = 12 x = 6 "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8892 | 67572310a8bb4d58bf7d1502b5e12761 | [
"其它"
] | 1 | single_choice | In Grade $3$, Amy\textquotesingle s height was $136$ cm. When she was Grade $4$, the doctor said that her height was $15$cm taller than last year. What was her height in Grade $4$? (adapted from $$2019$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$3$$) | [
[
{
"aoVal": "A",
"content": "$15$ cm "
}
],
[
{
"aoVal": "B",
"content": "$137$ cm "
}
],
[
{
"aoVal": "C",
"content": "$151$ cm "
}
],
[
{
"aoVal": "D",
"content": "$161$ cm "
}
],
[
{
"aoVal": "E",
"content": "$167$ cm "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"
] | [
"$136+15=151$ cm "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8897 | 5e26fa34813e424e8e6ee5a179f75bb9 | [] | 1 | single_choice | Blii and Elsa went to see a movie together and sat in the same row. Ela was in the sixth row counting from the front of the room and Elsa was seated in the fourteenth counting from the end. How many rows in their room? (Adapted from 2001 Math Kangaroo Problem, Level 3-4, Question \#13) | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$9$$ "
}
],
[
{
"aoVal": "C",
"content": "$$19$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$21$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line"
] | [
"$6 + 14 - 1 = 19$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8901 | 5074192cee714c75a3a52358dd875594 | [] | 1 | single_choice | Several people buy a boardgame together. If each person pays $60$ dollars, $60$ more dollars are needed for the payment. If each person pays $70$ dollars, $10$ dollars are remaining. How much is the boardgame in dollars? | [
[
{
"aoVal": "A",
"content": "$$600$$ "
}
],
[
{
"aoVal": "B",
"content": "$$480$$ "
}
],
[
{
"aoVal": "C",
"content": "$$690$$ "
}
],
[
{
"aoVal": "D",
"content": "$$550$$ "
}
],
[
{
"aoVal": "E",
"content": "$$720$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems"
] | [
"$$(60+10)\\div (70-60)=7$$ $$60\\times7+60=480$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8905 | 9936982de95b4611810f791046ef4c13 | [] | 1 | single_choice | Farmer Dunphy has $$100$$ metres of fencing. He wants to make a closed rectangular pen. He uses a long wall for one of the sides. Each side of the pen is a whole number in metres. What is the largest area that the pen can be? | [
[
{
"aoVal": "A",
"content": "$$125\\text{m}^{2}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$625\\text{m}^{2}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$1000\\text{m}^{2}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$1250\\text{m}^{2}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$2500\\text{m}^{2}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems Combined with Geometry->Tile Word Problems"
] | [
"$a+2b=100$, when $$a=2b=50$$, the largest area is $$50\\times (50\\div 2)=1250$$ m\\textsuperscript{2}. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8906 | f5d48c82aee34181ac89ab558e8f39c8 | [] | 1 | single_choice | How many fingers are there on a dozen pairs of gloves if each glove has $$5$$ fingers? | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$60$$ "
}
],
[
{
"aoVal": "D",
"content": "$$120$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"There are $$2\\times5 =10$$ fingers on a pair of gloves. $$\\text{A}$$ dozen pairs have $$12 \\times 10 = 120$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8908 | 5e2d2c0604854be086310a7e2f2d567f | [] | 2 | single_choice | Kevin got $$80\textbackslash\%$$ of the problems correct on a $$25-$$problem test, $$ 90\textbackslash\%$$ on a $$40-$$problem test, and $$70\textbackslash\%$$ on a $$10-$$problem test. What percent of all the problems did Kevin answer correctly? (2010 AMC8 Problem, Question \#9) | [
[
{
"aoVal": "A",
"content": "$$64$$ "
}
],
[
{
"aoVal": "B",
"content": "$$75$$ "
}
],
[
{
"aoVal": "C",
"content": "$$80$$ "
}
],
[
{
"aoVal": "D",
"content": "$$84$$ "
}
],
[
{
"aoVal": "E",
"content": "$$86$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"
] | [
"Ryan answered $$(0.8)(25)=20$$ problems correct on the first test, $$(0.9)(40)=36$$ on the second, and $$(0.7)(10)=7$$ on the third. This amounts to a total of $$ 20+36+7=63$$ problems correct. The, total number of problems is $$25+40+10=75$$.Therefore, the percendage is $$\\frac {63}{75}\\to(\\rm D)84$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8912 | 3100e88ffd7d4d76a81d65e1707a67e5 | [] | 1 | single_choice | A teacher distributes scorecards to students. If everyone gets $3$ cards, there will be a shortage of $12$ cards. If everyone gets $2$ cards, all these cards will just be divided. Then, how many students are there in total? | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems"
] | [
"If $2-1=1$ fewer card is given to students, the situation would transfer from \\textquotesingle a shortage of $12$ cards\\textquotesingle~ to \\textquotesingle all cards are just divided\\textquotesingle. So, there are in total $12$ students. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8915 | f5d5e3d976c0471a8ee7c4fe0438c3d3 | [
"其它"
] | 1 | single_choice | SASMO 2015 P2 Q5 Today, Wednesday, 8th of April 2015, is the day of the SASMO competition and your friend says tha the Singapore Math Kangaroo Contest was 14 days ago. On which day was the SMKC? | [
[
{
"aoVal": "A",
"content": "23rd of March, Monday "
}
],
[
{
"aoVal": "B",
"content": "24th of March, Tuesday "
}
],
[
{
"aoVal": "C",
"content": "25th of March, Wednesday "
}
],
[
{
"aoVal": "D",
"content": "26th of March, Thursday "
}
],
[
{
"aoVal": "E",
"content": "27th of March, Friday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"Draw table. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8920 | cc1ff60502104a48a1354527311ba3b2 | [
"其它"
] | 2 | single_choice | Suppose $20 \textbackslash\%$ of $x$ equals $30 \textbackslash\%$ of $y$. What percentage of $y$ is $x$ ? (adapted from 2020 AMC 8, Question 15) | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$35$$ "
}
],
[
{
"aoVal": "C",
"content": "$$75$$ "
}
],
[
{
"aoVal": "D",
"content": "$150$ "
}
],
[
{
"aoVal": "E",
"content": "$$300$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"Since $20 \\textbackslash\\%=\\frac{1}{5}$, multiplying the given condition by 5 shows that $x$ is $30 \\cdot 5=(\\mathbf{C}) 150$ percent of $y$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8922 | 2caaf37b6b6642b4acbdbc5ada15bccd | [] | 1 | single_choice | A shop purchased some tennis rackets at ＄$$100$$ each, and then sold them at ＄$$150$$ each. How much did the shopkeeper earn for $$10$$ rackets? | [
[
{
"aoVal": "A",
"content": "＄$$200$$ "
}
],
[
{
"aoVal": "B",
"content": "＄$$250$$ "
}
],
[
{
"aoVal": "C",
"content": "＄$$300$$ "
}
],
[
{
"aoVal": "D",
"content": "＄$$500$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"$$(150-100)\\times 10 = 500$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8923 | 50802ffd15ed4c4ba440f0fa2e601176 | [] | 1 | single_choice | Jack bought a batch of goods that he hoped to earn a $$50\textbackslash\%$$ profit after selling them. On the first day, he sold $$60\textbackslash\%$$ of his goods at a profit of $$50\textbackslash\%$$. On the second day, he sold all remaining goods for a discount. If the total profit is $$76\textbackslash\%$$ of the planned profit, what was the discount rate? | [
[
{
"aoVal": "A",
"content": "$$20\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$21\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$22\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$24\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"
] | [
"Let the cost for the batch of goods be $$m$$ dollars. Jack finally earned: $$m\\times 50\\textbackslash\\%\\times 92\\textbackslash\\%=0.38m$$. On the first day he earned: $$m\\times 60\\textbackslash\\%\\times 50\\textbackslash\\%=0.30m$$. Profit for the second day: $$0.38m-0.30m=0.08m$$. Profit rate for the second day: $$\\frac{0.08m}{\\left( m-0.6m \\right)}=20\\textbackslash\\%$$. Percentage discount: $$1-\\frac{\\left( 1+20\\textbackslash\\% \\right)}{\\left( 1+50\\textbackslash\\% \\right)}=20\\textbackslash\\%$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8925 | 310dda11c52c4ce5a97b92e7a7b2bdf7 | [
"其它"
] | 1 | single_choice | Paul has $13$ books, and Jenny has $6$ more books than Paul. How many books do Paul and Jenny have together? | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ "
}
],
[
{
"aoVal": "C",
"content": "$$22$$ "
}
],
[
{
"aoVal": "D",
"content": "$$23$$ "
}
],
[
{
"aoVal": "E",
"content": "$$32$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"Jenny has $$13 + 6 = 19$$ books. So, there are $13 + 19 = 32$ books in total. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8926 | c7804702c9c1402f9634b0e57b1d60d5 | [] | 1 | single_choice | In the land of Seuss, a plate of green eggs costs twice as much as a plate of ham. If a plate of ham costs $$5$$￠, how much would $$1$$ pay for $$2$$ plates of green eggs and $$3$$ plates of ham? | [
[
{
"aoVal": "A",
"content": "$$40$$￠ "
}
],
[
{
"aoVal": "B",
"content": "$$35$$￠ "
}
],
[
{
"aoVal": "C",
"content": "$$30$$￠ "
}
],
[
{
"aoVal": "D",
"content": "$$25$$￠ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"
] | [
"Since a plate of green eggs costs twice as much as a plate of ham, a plate of the eggs costs $$10$$￠. The cost of $$2$$ plates of eggs and $$3$$ plates of ham is $$2\\times 10$$￠$$+3\\times 5$$￠$$=20$$￠$$+15$$￠$$=35$$￠. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8930 | 59a124cef42d4c94b831ab0e07e1a800 | [] | 1 | single_choice | The sum of $$2$$ positive whole numbers is $$3$$ times their difference. When the larger is divided by the smaller, the quotient is． | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Difference and Multiple"
] | [
"The sum must be a multiple of $$3$$. There are many examples, e.g., $$2\\And 1$$, $$4\\And 2$$, $$10\\And 5$$, etc. The quotient is always $$2$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8933 | 39ffe4f8bfe241af94c729249f49caca | [] | 1 | single_choice | In a mathematics contest with ten problems, a student gains $$5$$ points for a correct answer and loses $$2$$ points for an incorrect answer. If Olivia answered every problem and her score was $$29$$, how many correct answers did she have? | [
[
{
"aoVal": "A",
"content": "$$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$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8937 | c2e27acf781747ed887f201c3f1902eb | [
"其它"
] | 2 | single_choice | At the 2018 Tompkins County Fair a vendor is offering a "fair special" on shoes. If you buy one pair of shoes at the regular price of $\textbackslash$ 80$, you get a second pair at a $34\textbackslash\%$ discount, and a third pair at half the regular price. James took advantage of the "fair special" to buy three pairs. What percentage of the $\textbackslash$ 240$ regular price did he save? (adapted from 2013 AMC 8, Question \#12) | [
[
{
"aoVal": "A",
"content": "$$28$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$36$$ "
}
],
[
{
"aoVal": "D",
"content": "$$38$$ "
}
],
[
{
"aoVal": "E",
"content": "$$40$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"First, the amount of money one will pay for three hats without the discount $=\\textbackslash$ 240$. Then, find the amount of money using the discount: $80+0.66\\times 80+\\frac{1}{2} \\times 80=\\textbackslash$ 172.8$. Finding the percentage yields $\\frac{172.8}{240}=72\\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-72\\textbackslash\\%= 28\\textbackslash\\%$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8942 | 2032f7b96fcf4f2c8499a135043eda25 | [] | 1 | single_choice | I had $$3$$ dozen socks in my drawer, but I lost $$2$$ pairs. How many socks do I now have in my drawer? | [
[
{
"aoVal": "A",
"content": "$$32$$ "
}
],
[
{
"aoVal": "B",
"content": "$$34$$ "
}
],
[
{
"aoVal": "C",
"content": "$$36$$ "
}
],
[
{
"aoVal": "D",
"content": "$$40$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"I had $$3$$ dozen socks in my drawer, which is $$36$$ socks. When I lost $$2$$ pairs, I lost $$4$$ socks, so I had $$32$$ socks left. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8944 | 2880102c561847a79d4d988e65715c64 | [] | 1 | single_choice | Mike and Jack compete in the long jump. Mike jumps twice as far as Jack once. Mike jumps three times. How many times can jack jump the distance equal to Mike？(adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$6$$) | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
],
[
{
"aoVal": "E",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"We can imagine the distance of Jack\\textquotesingle s long jump as $1$, and the distance of Mike\\textquotesingle s long jump as $2$. The distance that Mike jumps three times is $2$$\\times$$3$=$6$. ~Jack needs to jump $6$$\\div$$1=$$6$ times. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8945 | 5e435ff9ea0444c4b3ad0e90a8861aef | [
"其它"
] | 1 | single_choice | NBA playoffs are held annually. The $62$\textsuperscript{nd~}NBA playoffs were held in $2008$. When Cindy was $7$ years old, the $66$\textsuperscript{th}~NBA playoffs were held. How old is Cindy in $2022$? | [
[
{
"aoVal": "A",
"content": "$$14$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ "
}
],
[
{
"aoVal": "D",
"content": "$$17$$ "
}
],
[
{
"aoVal": "E",
"content": "$$18$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"$66-62+2008=2012$ $7+(2022-2012)=17$ "
] | D |
Subsets and Splits