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
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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 | 10397 | 9c088d7837d24ea98075f831157ad76b | [] | 1 | single_choice | The original price of a pair of shoes was $$\textbackslash$85$$. Then, it was sold at a discount of $$20\textbackslash\%$$. What was the price of the pair of shoes after the discount? | [
[
{
"aoVal": "A",
"content": "$$$17$$ "
}
],
[
{
"aoVal": "B",
"content": "$$$52$$ "
}
],
[
{
"aoVal": "C",
"content": "$$$68$$ "
}
],
[
{
"aoVal": "D",
"content": "$$$102$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"After discount, price became $100\\textbackslash\\%-20\\textbackslash\\%=80\\textbackslash\\%$ of original price. $\\textbackslash$85\\times80\\textbackslash\\%=\\textbackslash$85\\times0.8=\\textbackslash$68$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10399 | cde0e43354774440b114a5157dbe3234 | [] | 1 | single_choice | Julia has eaten one-quarter of the pizza. What is the ratio of the number of pizza that remain to the number Julia has eaten? | [
[
{
"aoVal": "A",
"content": "$$1:3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3:1 $$ "
}
],
[
{
"aoVal": "C",
"content": "$$1:4 $$ "
}
],
[
{
"aoVal": "D",
"content": "$$4:1$$ "
}
],
[
{
"aoVal": "E",
"content": "$$4:3$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"
] | [
"Julia has eaten one-quarter of the pizza. So three-quarters of the pizza remain. Therefore the required ratio is $$\\frac{3}{4}:\\frac{1}{4}=3:1$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10403 | 8e9e2f64d74747ca880fd85cb9274978 | [] | 1 | single_choice | In a certain quiz show there are the following rules: every participant has $$10$$ points at the beginning and has to answer $$10$$ questions. For each correct answer, the participant earns $$1$$ point, and for each incorrect answer, the participant loses $1$ point. Mrs. Smith had $$14$$ points at the end of this quiz show. How many correct answers did she give? ($$2011$$ Math Kangaroo Problem, Level $$3-4$$, Question \#$$17$$) | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "$$4$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis->Basic Type->Non-typical Types"
] | [
"Full score: $10+10\\times1=20$. Smith gets $(20-14)\\div(1+1)=3$ questions wrong, and $10-3=7$ questions correct. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10406 | edefd62ea9504276a65ab1b548bf88a7 | [] | 1 | single_choice | My mom\textquotesingle s birthday is on Sunday, and my dad\textquotesingle s birthday is $$55$$ days after it. On what day of the week will my dad\textquotesingle s birthday be? ($$1999$$ Math Kangaroo Problem, Levels $$3-4$$, Question \#$$9$$) | [
[
{
"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 | 10411 | 9c16c816a5974dd2be3a013c234de36a | [] | 1 | single_choice | Penelope paid$$$24.58$$ for pens and pencils. If pens cost $$9$$¢ each and pencils cost $$4$$¢ each, at most how many pens did Penelope purchase? | [
[
{
"aoVal": "A",
"content": "$$273$$ "
}
],
[
{
"aoVal": "B",
"content": "$$272$$ "
}
],
[
{
"aoVal": "C",
"content": "$$271$$ "
}
],
[
{
"aoVal": "D",
"content": "$$270$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"Continue subtracting $$4$$¢ from $$2458$$¢ until the difference is a multiple of $$9$$. This happens when the difference is $$2430$$¢ which is $$270 \\times 9$$¢. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10417 | cdec520781e44101b3c283d4c27a22da | [] | 1 | single_choice | The selling price of a sofa set is $$$5500$$ and the profit percentage is $$10\textbackslash\%$$ for each set sold. If the cost of the sofa set is not changed, what is the new profit percentage if raising the profit to $$$1800$$? | [
[
{
"aoVal": "A",
"content": "$$24\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$25\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$30\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$36\\textbackslash\\%$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"$$5500\\div(1+10\\textbackslash\\%)=5000$$, $$1800\\div5000=36\\textbackslash\\%$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10420 | a9af6280af284c15ae306b36b3168743 | [] | 2 | single_choice | A worm is at the bottom of a well with a depth of $$11$$ metres. If it climbs up $$3$$ metres in the day and slips down $$1$$ metre at night, how many days will it take the worm to climb up to the ground? | [
[
{
"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->Periodic Problems->Snail Climbing out of Well Problems"
] | [
"It climbs up $$3$$ meters in the day time and slips down $$1$$ meter at night, so it climbs up $$2$$ meters in a whole day. For the first $$4$$ days, it climbs $$8$$ meters. During the day time of the fifth day, it climbs $$3$$ meters and reaches the ground. Then it needs five days to climb up to the ground. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10422 | bbbfd287b57445c0a7590dfab5553717 | [] | 1 | single_choice | Bowen has $$40$$ ounces of a $$25\textbackslash\%$$ sugar solution. After~\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of the solution is $$40\textbackslash\%$$. (Evaporate: the water turns from liquid into vapor and is no longer in the solution anymore.) | [
[
{
"aoVal": "A",
"content": "$$15$$ ounces "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ ounces "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ ounces "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ ounces "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"
] | [
"$$40-40\\times25\\textbackslash\\%\\div40\\textbackslash\\%=40-25=15$$ ounces. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10424 | b737cad19dc64dfbaa85ceaa74e79e5a | [
"其它"
] | 2 | single_choice | Patrick gets $80 \textbackslash\%$ on a 10 -problem test, $60 \textbackslash\%$ on a 20 -problem test and $50 \textbackslash\%$ on a 30 -problem test. If the three tests are combined into one 60 problem test, which percent is closest to her overall score? (adapted from 2006 AMC 8, Question \#12) | [
[
{
"aoVal": "A",
"content": "$$50$$ "
}
],
[
{
"aoVal": "B",
"content": "$$52$$ "
}
],
[
{
"aoVal": "C",
"content": "$$55$$ "
}
],
[
{
"aoVal": "D",
"content": "$$58$$ "
}
],
[
{
"aoVal": "E",
"content": "$$60$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$80 \\textbackslash\\% \\cdot 10=8$, $60\\textbackslash\\% \\cdot 20=12$, $50\\textbackslash\\% \\cdot 30=15$ Adding them up gets $8+12+15=35$. The overall percentage correct would be $\\frac{35}{60} \\approx 0.58$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10433 | 97a9ebdec7ab46c893d24eda0e309a27 | [
"其它"
] | 1 | single_choice | Gawel lives on the 2\textsuperscript{nd} floor, and Pawel lives in the same building but has to walk up twice as many stairs as Gawel. There are no stairs to the entrance of the building. On which floor does Pawel live? | [
[
{
"aoVal": "A",
"content": "on the $2$\\textsuperscript{nd} floor "
}
],
[
{
"aoVal": "B",
"content": "on the $3$\\textsuperscript{rd} floor "
}
],
[
{
"aoVal": "C",
"content": "on the $4$\\textsuperscript{th} floor "
}
],
[
{
"aoVal": "D",
"content": "on the $5$\\textsuperscript{th} floor "
}
],
[
{
"aoVal": "E",
"content": "on the $6$\\textsuperscript{th} floor "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"Gawel lives on the second floor, so he only needs to walk up one floor. Pawel has to walk up twice as many stairs as Gawel, so he needs to walk up two floors. So, Pawel lives on the $3$\\textsuperscript{rd} floor. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10438 | a9b931c0785247b49f4df88545ba82f2 | [] | 1 | single_choice | Ben stands in line and has $$76$$ people behind him, If there are a total of $$110$$ people in line, how many people are there in front of Ben? | [
[
{
"aoVal": "A",
"content": "$$33$$ "
}
],
[
{
"aoVal": "B",
"content": "$$34$$ "
}
],
[
{
"aoVal": "C",
"content": "$$35$$ "
}
],
[
{
"aoVal": "D",
"content": "$$36$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of one Character in a Line"
] | [
"If there are a total of $$110$$ people in line, subtract those behind Ben and Ben himself: $$110-76-1=33$$, the number in front of Ben. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10441 | dbadb592e634467da36311f413432ebd | [] | 1 | single_choice | A jacket was on sale. The original price was $$$180$$, and Peter bought it at $$$135$$. What was the discount? | [
[
{
"aoVal": "A",
"content": "$$135\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$180\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$75\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$25\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"$$1-135\\div180=25\\textbackslash\\%$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10442 | c05ac13ddb8d4593bc5ed51dd7549cf8 | [] | 1 | single_choice | The sum of two numbers is $$800$$. The smaller number is $$356$$. What is the greater number? | [
[
{
"aoVal": "A",
"content": "$$1156$$ "
}
],
[
{
"aoVal": "B",
"content": "$$556$$ "
}
],
[
{
"aoVal": "C",
"content": "$$454$$ "
}
],
[
{
"aoVal": "D",
"content": "$$444$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples",
"Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Addition and Subtraction of Whole Numbers->Adding and Subtracting within 10000->Subtraction of 3-digit Numbers"
] | [
"$$800-356=444$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10447 | e4d42c8512e64cc6b68b913aeb3e6fb4 | [] | 1 | single_choice | There are $$20$$ chickens and rabbits in the case, and the total number of legs is $$48$$. How many rabbits in this case? | [
[
{
"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->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"
] | [
"If all were rabbits, $20\\times 4= 80$ the total number of legs would be $$$80$$. $80- 48=32$ The difference is $$$32$$. $4-2=2$ $32\\div 2=16$ $20-16=4$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10452 | 8ecc105d859e4a2f8325bb1e2ad92c22 | [] | 1 | single_choice | A sugar solution is made by mixing $$10$$ ounces of sugar and $$15$$ ounces of water. Find the percent concentration of the solution. | [
[
{
"aoVal": "A",
"content": "$$20\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$25\\textbackslash\\%$ "
}
],
[
{
"aoVal": "C",
"content": "$30\\textbackslash\\%$ "
}
],
[
{
"aoVal": "D",
"content": "$40\\textbackslash\\%$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"
] | [
"$$10\\div(10+15)=40\\textbackslash\\%$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10455 | 8ecdb8b6938346debe2cfe5c5b9133f5 | [] | 1 | single_choice | Mother baked $$40$$ cookies. She gave $$8$$ cookies to her friend and packed the rest equally into bottles. She put $$4$$ cookies in each bottle. How many bottles did she use? | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"
] | [
"$$40-8=32$$, $$32\\div4=8$$. Mother used $$8$$ bottles. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10456 | d720019345ed4aeeb7f91d31778c09c3 | [] | 1 | single_choice | Julian started reading a book with $$348$$ pages. He read $$6$$ pages on each day from Monday to Friday and $$11$$ pages on each day on Saturday and Sunday. He started reading on a Thursday. On which day of the week did he finish reading the book? . | [
[
{
"aoVal": "A",
"content": "Friday "
}
],
[
{
"aoVal": "B",
"content": "Saturday "
}
],
[
{
"aoVal": "C",
"content": "Sunday "
}
],
[
{
"aoVal": "D",
"content": "Monday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"Thursday to Sunday $$\\rightarrow 6\\times 2+11\\times 2=34$$ pages $$348-34=314$$ $1$ week (Monday to Sunday) $$\\rightarrow 11\\times 2+6\\times 5=52$$ pages $6$ weeks $$\\rightarrow 52\\times6=312$$ pages After reading another $312$ pages in $6$ weeks, Julian has another $(314 -- 312) = 2$ pages left to read. It will now be a Monday and Julian can finish reading the last $2$ pages. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10457 | c4e4ec253ce148e3bf906a1977b8373e | [
"其它"
] | 0 | single_choice | $5$\% of the students at Hamilton Middle School have red hair. There are $800$ students at Hamilton Middle School. How many students at Hamilton Middle School have red hair? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$400$$ "
}
],
[
{
"aoVal": "D",
"content": "$$760$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$800 \\times 5$\\%=$40$, $40$ students at Hamilton Middle School have red hair. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10459 | c4e86bb85aef417fb519588e6713531d | [] | 1 | single_choice | My pay is the same every day I work. I worked \emph{every} day in $$1992$$, even weekends. In March, I earned $$$930$$. I earned for all of $$1992$$. | [
[
{
"aoVal": "A",
"content": "$$$11346$$ "
}
],
[
{
"aoVal": "B",
"content": "$$$11315$$ "
}
],
[
{
"aoVal": "C",
"content": "$$$10980$$ "
}
],
[
{
"aoVal": "D",
"content": "$$$10950$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"
] | [
"In March, there are $$31$$ days. I earned $$$930 \\div 31$$, which is $$$30$$ each day. For all of $$1992$$, I earned $$366\\times$$ $$$30 =$$$$$10980$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10465 | b2d181c5de0b4a0fa4b055bdc3c6e873 | [] | 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": "$$$$Blue "
}
],
[
{
"aoVal": "B",
"content": "$$$$Green "
}
],
[
{
"aoVal": "C",
"content": "$$$$Red "
}
],
[
{
"aoVal": "D",
"content": "$$$$Black "
}
],
[
{
"aoVal": "E",
"content": "$$$$Yellow "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"
] | [
"A group of the blue one, the green one, the red one, and the yellow one is repeating. $17 \\div 4 = 4R1$, so the seventeenth one is blue. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10466 | c98133a62e8843efbb779f3ec602b5e2 | [
"其它"
] | 1 | single_choice | William is 15 years old, and his sister is 23 years old. How old will his sister be when William is 23 years old? | [
[
{
"aoVal": "A",
"content": "$$23$$ "
}
],
[
{
"aoVal": "B",
"content": "$$31$$ "
}
],
[
{
"aoVal": "C",
"content": "$$38$$ "
}
],
[
{
"aoVal": "D",
"content": "$$26$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"omitted "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10473 | b2da42781e6e4b4198e0a4593b7f7ad9 | [
"其它"
] | 1 | single_choice | Luna, Lily, and Lucy are talking about their ages. $6$ years ago, Luna was born, and Lily was $5$ years old. This year, the sum of ages of these $3$ people is $33$. When Luna was born, how old was Lucy? | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
],
[
{
"aoVal": "E",
"content": "$$11$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"Six years ago, the sum of ages of Luna, Lily, and Lucy was $33-6\\times3=15$. Lucy was $15-0-5=10$ years old. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10474 | 936325f5ecf5482a889b26091b5af6c9 | [] | 1 | single_choice | Jack mixed $200$ g of $10\textbackslash\%$ salt solution, $200$ g of $15\textbackslash\%$ salt solution, and $400$ g of $20\textbackslash\%$ salt solution together. What is the percent concentration of salt solution at this time? | [
[
{
"aoVal": "A",
"content": "$15\\textbackslash\\%$ "
}
],
[
{
"aoVal": "B",
"content": "$16\\textbackslash\\%$ "
}
],
[
{
"aoVal": "C",
"content": "$16.25\\textbackslash\\%$ "
}
],
[
{
"aoVal": "D",
"content": "$17\\textbackslash\\%$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems->Calculating Solution from Solute and Solvent"
] | [
"$$\\frac{200\\times 10\\textbackslash\\%+200\\times 15\\textbackslash\\%+400\\times 20\\textbackslash\\%}{200+200+400}\\times 100\\textbackslash\\%=16.25\\textbackslash\\%$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10475 | ae596e5d7af44eeab02bc76885169b2d | [
"其它"
] | 1 | single_choice | After Sally takes 20 shots, she has made $75 \textbackslash\%$ of her shots. After she takes 10 more shots, she drops her percentage to $60 \textbackslash\%$. How many of the last 5 shots did she make? (adapted from 2004 AMC 8, Question\#6) | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$6$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"Sally made $0.75 * 20=15$ shots originally. Letting $x$ be the number of shots she made, we have $\\frac{15+x}{30}=0.6$. Solving for $x$ gives us $x=3$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10483 | a56163296a6f4ac3966d09884be81f4e | [
"其它"
] | 1 | single_choice | Crystal and Angela had a poem recitation game. Each poem in their game earned $$2$$ points. Crystal recited $$7$$ poems and Angela recited $$11$$ poems. How many more points than Crystal did Angela earn?~(adapted from $$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$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"Angela recited $$11-7=4$$ poems more than Crystal. There are 4$$\\times$$2$$=8$$ points "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10486 | 8f0021b378ce41c8855c0f791d124e8c | [] | 1 | single_choice | A test is with a full score of $100$ points. Five students in a group wants to reach an average of $92$ points. If everyone scores a different whole number, the lowest score among them could be~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "$$60$$ "
}
],
[
{
"aoVal": "B",
"content": "$$61$$ "
}
],
[
{
"aoVal": "C",
"content": "$$66$$ "
}
],
[
{
"aoVal": "D",
"content": "$$70$$ "
}
],
[
{
"aoVal": "E",
"content": "$$71$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"$92\\times5-(100+99+98+97)=66$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10494 | d73cf51af8444246b644a1f460042783 | [] | 1 | single_choice | Given that April $$15$$, $$2011$$ was Friday, what day was May $$11$$, $$2011$$? | [
[
{
"aoVal": "A",
"content": "Thursday "
}
],
[
{
"aoVal": "B",
"content": "Saturday "
}
],
[
{
"aoVal": "C",
"content": "Tuesday "
}
],
[
{
"aoVal": "D",
"content": "Wednesday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"Counting from April $$15$$, $$2011$$, after $30-15=15$ days it will be April $$30$$, $$2011$$. After $11$ days, it will be May $$11$$, $$2011$$. In total, there are $15+11=26$ days. $26\\div 7 =3R5$, which means May $$11$$, $$2011$$ was Wednesday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10498 | d73ec4a0eed1465d867908a527a36beb | [
"其它"
] | 1 | single_choice | The perimeter of a cuboid is $180$. What is the largest volume? | [
[
{
"aoVal": "A",
"content": "$$216$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3375$$ "
}
],
[
{
"aoVal": "C",
"content": "$$720$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9600$$ "
}
],
[
{
"aoVal": "E",
"content": "$$1200$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value"
] | [
"$180\\div12=15$ $15\\times15\\times15=3375$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10500 | ae757d2fd6004d95b219c4ae422bfbde | [] | 2 | single_choice | A worm is staying at the bottom of a well with a depth of $$10$$ metres. If it climbs up $$3$$ metres in the daytime and slips down $$2$$ metres at night, which day will it climb up to the ground? | [
[
{
"aoVal": "A",
"content": "The $$6$$th day "
}
],
[
{
"aoVal": "B",
"content": "The $$7$$th day "
}
],
[
{
"aoVal": "C",
"content": "The $$8$$th day "
}
],
[
{
"aoVal": "D",
"content": "The $$9$$th day "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"
] | [
"omitted "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10501 | a0f632a738ee4d2e937e89a1f7332f30 | [] | 1 | single_choice | A train travels from Exeter to Cambridge at a~ speed of $$55km/h$$. Given that Cambridge is $$420km$$ away from Exeter, How far is the train away from Cambridge after setting off for 5 hours? | [
[
{
"aoVal": "A",
"content": "$$55km$$ "
}
],
[
{
"aoVal": "B",
"content": "$$145km$$ "
}
],
[
{
"aoVal": "C",
"content": "$$275km$$ "
}
],
[
{
"aoVal": "D",
"content": "$$420km$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"
] | [
"$420-\\left( 55\\times5\\right)=420-275=145$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10502 | e05dcc9a48ad4d0a944b7bfcc8c74ac7 | [] | 1 | single_choice | In the teachers\textquotesingle{} lounge there are $$6$$ tables with $$4$$ chairs by each one, $$4$$ tables with $$2$$ chairs by each, and $$3$$ tables with $$6$$ chairs by each. How many chairs are there in the lounge? (2003 Math Kangaroo Problem, Level 3-4, Question \#5) | [
[
{
"aoVal": "A",
"content": "$$40$$ "
}
],
[
{
"aoVal": "B",
"content": "$$25$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50$$ "
}
],
[
{
"aoVal": "D",
"content": "$$36$$ "
}
],
[
{
"aoVal": "E",
"content": "$$44$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications"
] | [
"$6\\times4+4\\times2+3\\times6=50$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10504 | c99f0bff8f63457c9a5609df53658433 | [] | 1 | single_choice | Helga is climbing stairs in such a way that she goes up $$2$$ steps at a time. She is standing on the third step now. On which step will she be after she moves up $$3$$ times? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications"
] | [
"Moving up $3$ times is $6$ steps. Now she is on the third step, after moving up $6$ steps, she is on the ninth step. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10505 | f75a7eb69bd0453e9db239af54a7f45d | [] | 1 | single_choice | If today is Tuesday, what day of the week will be 86 days later? | [
[
{
"aoVal": "A",
"content": "Wednesday "
}
],
[
{
"aoVal": "B",
"content": "Thursday "
}
],
[
{
"aoVal": "C",
"content": "Friday "
}
],
[
{
"aoVal": "D",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"
] | [
"$$86\\div 7=12\\cdots \\cdots 2$$. 2 days later will be Thursday. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10514 | c9a679ccf8b64e3a9347c8fd806e918e | [
"其它"
] | 1 | single_choice | Last month, the price of a couch increased by $\textbackslash$600$. During a sale this month, the couch was offered at a $25\textbackslash\%$ discount. John bought the couch at $\textbackslash$2250$ at the sale. What is the percentage decrease in the cost of the couch as compared to the original price of the couch before the discount? | [
[
{
"aoVal": "A",
"content": "$6.66\\textbackslash\\%$ "
}
],
[
{
"aoVal": "B",
"content": "$5\\textbackslash\\%$ "
}
],
[
{
"aoVal": "C",
"content": "$6.25\\textbackslash\\%$ "
}
],
[
{
"aoVal": "D",
"content": "None of the above. "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages"
] | [
"Price before discount $=\\frac{100}{75}\\times\\textbackslash$2250=\\textbackslash$3000$ Original price of the couch before increase $=\\textbackslash$3000-\\textbackslash$600=\\textbackslash$2400$ Price decrease $=\\textbackslash$2400-\\textbackslash$2250=\\textbackslash$150$ Percentage decrease $=\\frac{\\textbackslash$150}{\\textbackslash$2400}\\times100\\textbackslash\\%=6.25\\textbackslash\\%$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10517 | 9c83810199be4080a9f60044fee7500d | [
"其它"
] | 1 | single_choice | Anna is lining up to get some ice-cream. Counting from the front, she is the $$4$$\textsuperscript{th}~in the line. Counting from the back, she is the $$7$$\textsuperscript{th}. How many people are there lining up?~\uline{~~~~~~~~~~}~ | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$4+7-1=10$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10520 | e9944220da0246b1ad7f10bdfb3b6fc8 | [] | 1 | single_choice | Jerry starts a savings account with $$$7,000$$ at a bank. The interest rate is $$3\textbackslash\%$$ per year. How much interest will he earn in his savings account at the end of the second year? | [
[
{
"aoVal": "A",
"content": "$$$426$$ "
}
],
[
{
"aoVal": "B",
"content": "$$$426.3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$$4,263$$ "
}
],
[
{
"aoVal": "D",
"content": "$$$4,263.6$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Interest Problems"
] | [
"$$7000\\times \\left( 1+3\\textbackslash\\% \\right)\\times \\left( 1+3\\textbackslash\\% \\right)-7000=426.3$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10528 | ae8c396be5174f2f8fcdcba18b3d3a2b | [] | 1 | single_choice | A bookstore purchases some story books at $$$22$$ each. If the bookstore wants to earn $$$11$$ for each book, what is the selling price of each book? | [
[
{
"aoVal": "A",
"content": "$$$22$$ "
}
],
[
{
"aoVal": "B",
"content": "$$$33$$ "
}
],
[
{
"aoVal": "C",
"content": "$$$35$$ "
}
],
[
{
"aoVal": "D",
"content": "$$$44$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"$$22+11=33$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10530 | 93a6c00328e543d9b88560e67193a71f | [] | 1 | single_choice | There are four books on my shelf. The almanac and the dictionary together weigh $$4310\text{g}$$. The biography and the cookbook together weigh $$2325\text{g}$$. If the almanac and the biography together weigh $$2795\text{g}$$, what is the weigh of the cookbook and dictionary together? | [
[
{
"aoVal": "A",
"content": "$$2620\\text{g}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3270\\text{g}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3840\\text{g}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4100\\text{g}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Including and Excluding "
] | [
"The almanac, the dictionary, the biography, and the cookbook together weigh $$4310\\text{g}+2325\\text{g=6635g}$$. Since the almanac and the biography together weigh $$2795\\text{g}$$, the cookbook and the dictionary together weigh $$6635\\text{g}-2795\\text{g=3840g}$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10534 | dbe6b816ea6641e1a04f845ebb5669a8 | [
"其它"
] | 1 | single_choice | There are $72$ balloons in the shop. Pip bought $$\frac49$$ of them. The shop left~\uline{~~~~~~~~~~}~balloons. | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$32$$ "
}
],
[
{
"aoVal": "C",
"content": "$$40$$ "
}
],
[
{
"aoVal": "D",
"content": "$$52$$ "
}
],
[
{
"aoVal": "E",
"content": "$$60$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"
] | [
"$72\\times(1-\\dfrac{4}{9})=32$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10538 | b78ecb605cb649dab9a928b15e9b2fdf | [
"其它"
] | 1 | single_choice | On Monday morning, a snail fell down a well which is $$10$$ meters deep. During the day, it climbs up $$2$$ meters, and during the night it slides down $$1$$ meter. On what day of the week will the snail get out of the well? ($$1998$$ Math kangaroo Problem, Level $$5-6$$, Question \#$$18$$) | [
[
{
"aoVal": "A",
"content": "$$$$Tuesday "
}
],
[
{
"aoVal": "B",
"content": "$$$$Thursday "
}
],
[
{
"aoVal": "C",
"content": "$$$$Saturday "
}
],
[
{
"aoVal": "D",
"content": "$$$$Sunday "
}
],
[
{
"aoVal": "E",
"content": "$$$$Monday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems->Snail Climbing out of Well (completed)"
] | [
"Except the last day, the snail could climb up $2-1=1$ m. Thus, it takes the snail $(10-2)\\div1+1=9$ days to get out of the well. $9$ days from Monday is the next Tuesday. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10539 | b3101b748edd4194976ef37455b0a402 | [] | 3 | single_choice | When one ounce of water is added to a mixture of acid and water, the new mixture is $$20\textbackslash\%$$ acid. When one ounce of acid is added to the new mixture, the result is $$33\frac{1}{3}\textbackslash\%$$ acid. The percentage of acid in the original mixture is ($$1973$$ AHSME Problem, Question \#$$33$$) | [
[
{
"aoVal": "A",
"content": "$$22\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$24\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$25\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "E",
"content": "$$33\\frac{1}{3}\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"
] | [
"Let $$a$$ be the original number of ounces of acid and $$w$$ be the original number of ounces of water. We can write two equations $$\\frac{a}{a+w+1}=\\frac{1}{5}$$ and $$\\frac{a+1}{a+w+2}=\\frac{1}{3}$$. Then cross-multiply to get rid of the fractions. $$5a=a+w+1$$, $$3a+3=a+w+1$$ Solve the system to get $$a=1$$ and $$w=3$$. The percentage of acid in the original mixture is $$\\frac{1}{1+3}=25 \\textbackslash\\% $$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10540 | ffed284d8b6e472c8a514ab7bf225cf4 | [
"其它"
] | 1 | single_choice | Brandon is engaging sprint race on the track. He is in the fifth place now, and there are $8$ players behind him. There are $5$ extra groups signing up for sprint race, and the number of players of each group are idential. How many sprint players are there in total? | [
[
{
"aoVal": "A",
"content": "$$65$$ "
}
],
[
{
"aoVal": "B",
"content": "$$70$$ "
}
],
[
{
"aoVal": "C",
"content": "$$78$$ "
}
],
[
{
"aoVal": "D",
"content": "$$84$$ "
}
],
[
{
"aoVal": "E",
"content": "$$96$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$(5 + 1 + 8) \\times (5 +1) = 84$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10541 | a5916a33a7f847baa3019c693e3e1604 | [
"其它"
] | 1 | single_choice | A shop advertises everything is "half price in today\textquotesingle s sale." In addition, a coupon gives a $25 \textbackslash\%$ discount on sale prices. Using the coupon, the price today represents what percentage off the original price? (adapted from 2012 AMC 8, Question \#8) | [
[
{
"aoVal": "A",
"content": "$$40\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$42.5\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$57.5\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$62.5\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "E",
"content": "$$70\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$75 \\textbackslash\\% \\cdot 50\\textbackslash\\% =37.5\\textbackslash\\%$ $1 -37.5\\textbackslash\\% = 62.5\\textbackslash\\%$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10543 | c525941c815344f69bacc4a3d27a43bb | [] | 1 | single_choice | James can frost a cookie every $$12$$ seconds and Lacey can frost a cookie every $$15$$ seconds. Working together, how many cookies can they frost in $$10$$ minutes? (Adapted from $$2012$$ AMC $$10\rm A$$ Problem, Question \#$$11$$) | [
[
{
"aoVal": "A",
"content": "$$50$$ "
}
],
[
{
"aoVal": "B",
"content": "$$60$$ "
}
],
[
{
"aoVal": "C",
"content": "$$80$$ "
}
],
[
{
"aoVal": "D",
"content": "$$90$$ "
}
],
[
{
"aoVal": "E",
"content": "$$100$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"
] | [
"In $$600$$ seconds ($$10$$ minutes), James will frost $$\\dfrac{600}{12}=50$$ cookies, and Lacey will frost $$\\dfrac{600}{15}=40$$ cookies. Therefore, working together they will frost $$50+40=\\boxed{(\\text{D})90}$$ cookies. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10547 | 93b59f1f08854802ad730f4ebd312f85 | [] | 1 | single_choice | Judy ran for $$16$$ minutes. If her average speed was $$80$$ meters per minute, then how many meters did Judy run? | [
[
{
"aoVal": "A",
"content": "$$800$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$1280$$ "
}
],
[
{
"aoVal": "D",
"content": "$$96$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$80\\times 16 = 1280$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10554 | ee37582cf77a41cf910c2f3b2968ddcc | [
"其它"
] | 1 | single_choice | The length of a rectangle is increased by $10 \textbackslash\%$ and the width is decreased by $10 \textbackslash\%$. What percent of the old area is the new area? (2009 AMC 8, Question \#8) | [
[
{
"aoVal": "A",
"content": "$$90$$ "
}
],
[
{
"aoVal": "B",
"content": "$$99$$ "
}
],
[
{
"aoVal": "C",
"content": "$$100$$ "
}
],
[
{
"aoVal": "D",
"content": "$$101$$ "
}
],
[
{
"aoVal": "E",
"content": "$$110$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"In a rectangle with dimensions $10 \\times 10$, the new rectangle would have dimensions $11 \\times 9$. The ratio of the new area to the old area is $99 / 100=(\\text{B}) 99$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10555 | 93bd7fea0958495c934623020dc4631d | [] | 1 | single_choice | The price ratio of goods $$A$$ to $$B$$ is $$7:2$$. If their prices were increased by $$\textbackslash$60$$ respectively, the price ratio would be $$5:2$$. What are the prices of these two goods? | [
[
{
"aoVal": "A",
"content": "$$\\textbackslash$315$$, $$\\textbackslash$90$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\textbackslash$320$$, $$\\textbackslash$100$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\textbackslash$330$$, $$\\textbackslash$120$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\textbackslash$350$$, $$\\textbackslash$200$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"
] | [
"The price difference between the two goods did not change. Before $\\to$ $$A:B:Difference$$ is $$7:2:5$$ After $\\to$ $$A:B:Difference$$ is $$5:2:3$$ $\\textasciitilde$ Make difference the same number of units in both ratios by finding LCM. Before $\\to$ $$A:B:Difference$$ is $$21:6:15$$ After $\\to$ $$A:B:Difference$$ is $$25:10:15$$ $\\textasciitilde$ Therefore, $$4u=\\textbackslash$60$$ $$1u=$$ $$\\textbackslash$60\\div4=\\textbackslash$15$$ $\\textasciitilde$ The original prices of these two goods were $$A=21u=21\\times15=\\textbackslash$315$$ and $$B=6u=6\\times15=\\textbackslash$90$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10556 | ae9dbe124e1a450d818a809433638948 | [] | 1 | single_choice | Ela and Kasia boarded a super-train. Ela took a seat in the seventeenth car counting from the front of the train, and Kasia was seated in the thirty-fourth car counting from the end. The girls were sitting in the same car. How many cars did the super-train have? (2001 Math Kangaroo Problem, Level 3-4, Question \#13) | [
[
{
"aoVal": "A",
"content": "$$48$$ "
}
],
[
{
"aoVal": "B",
"content": "$$49$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50$$ "
}
],
[
{
"aoVal": "D",
"content": "$$51$$ "
}
],
[
{
"aoVal": "E",
"content": "$$52$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line"
] | [
"$17 + 34 - 1 = 50$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10563 | e07af8769a0f44239de65b126237335b | [] | 1 | single_choice | James had $$10000$$ dollars, and he deposited $$$7000$$ in Bank $$A$$ and $$$3000$$ in Bank $$B$$. At the end of the year, James received an interest of$$$460$$ in total. Given that the sum of the annual interest rates of the two banks is $$10\textbackslash\%$$, find the interest rates of the two banks, respectively. | [
[
{
"aoVal": "A",
"content": "$$2\\textbackslash\\%$$; $$8\\textbackslash\\%$$. "
}
],
[
{
"aoVal": "B",
"content": "$$3\\textbackslash\\%$$; $$7\\textbackslash\\%$$. "
}
],
[
{
"aoVal": "C",
"content": "$$4\\textbackslash\\%$$; $$6\\textbackslash\\%$$. "
}
],
[
{
"aoVal": "D",
"content": "$$5\\textbackslash\\%$$; $$5\\textbackslash\\%$$. "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Interest Problems"
] | [
"Let $$x$$ be the interest rate of bank $$A$$: $$7000x+3000(10\\textbackslash\\%-x)=460$$ $$x=4\\textbackslash\\%$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10565 | a5a47cb9618148d1a9e9b52e8554a746 | [
"其它"
] | 1 | single_choice | Peter has a rope, and he ties some knots, each using $10$-cm rope. He ties $25$ knots in total. After he ties the last knot, the knots divide the rope into pieces~ equally, and the length of each piece is $7$ cm. What is the length of the entire rope? | [
[
{
"aoVal": "A",
"content": "$$425$$ cm "
}
],
[
{
"aoVal": "B",
"content": "$$432$$ cm "
}
],
[
{
"aoVal": "C",
"content": "$$456$$ cm "
}
],
[
{
"aoVal": "D",
"content": "$$478$$ cm "
}
],
[
{
"aoVal": "E",
"content": "$$480$$ cm "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"$25\\times10+(25+1)\\times7=432$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10575 | 984658792f694f81bf6facccd4a5d188 | [] | 1 | single_choice | The scale of a map is:~$\dfrac{3}{4}$ of an inch $$=10$$ miles. If the distance on the map between two towns is $$12$$ inches, the actual distance between the towns is. | [
[
{
"aoVal": "A",
"content": "$$90$$ miles "
}
],
[
{
"aoVal": "B",
"content": "$$120$$ miles "
}
],
[
{
"aoVal": "C",
"content": "$$150$$ miles "
}
],
[
{
"aoVal": "D",
"content": "$$160$$ miles "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with an Invariant Part"
] | [
"Since $$12 \\div \\frac{3}{4}=16$$, the actual distance between the towns is $$16\\times10 = 160$$ miles. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10577 | a139267252094939a90b49c961117584 | [
"其它"
] | 1 | single_choice | Gawel lives on the second floor, and Pawel lives in the same building but has to walk up twice as many stairs as Gawel. There are no stairs to the entrance of the building. On which floor does Pawel live? (2000 Math Kangaroo Problem, Level 3-4, Question \#4) | [
[
{
"aoVal": "A",
"content": "on the $2$\\textsuperscript{nd} floor "
}
],
[
{
"aoVal": "B",
"content": "on the $3$\\textsuperscript{rd} floor "
}
],
[
{
"aoVal": "C",
"content": "on the $4$\\textsuperscript{th} floor "
}
],
[
{
"aoVal": "D",
"content": "on the $5$\\textsuperscript{th} floor "
}
],
[
{
"aoVal": "E",
"content": "on the $6$\\textsuperscript{th} floor "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"Gawel lives on the second floor, so he only needs to walk up one floor. Pawel has to walk up twice as many stairs as Gawel, so he needs to walk up two floors. So, Pawel lives on the $3$\\textsuperscript{rd} floor. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10578 | fffde920e1164d8c8588de40140ad7b6 | [] | 1 | single_choice | I ate half an apple pie on Saturday and two thirds of the remainder on Sunday. What fraction of the pie was left for Monday? | [
[
{
"aoVal": "A",
"content": "None "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{1}{2}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{1}{3}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{2}{3}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$\\frac{1}{6}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Understanding the Base"
] | [
"After I eat one half, half of the apple pie is left. Eating two thirds of this half leaves one third of one half of the pie, which is one sixth, for Monday. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10579 | c9cc5a0689604a1f9ae1c9d863d52205 | [] | 1 | single_choice | The length of Amy\textquotesingle s string is $$35\text{cm}$$. The length of David\textquotesingle s string is $$29\text{cm}$$. What is the total length of both strings? | [
[
{
"aoVal": "A",
"content": "$$54\\text{cm}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$49\\text{cm}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$64\\text{cm}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$65\\text{cm}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$66\\text{cm}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"$$35+29=64$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10584 | b7b0ce88aa204c6793e3bde34b8844b7 | [] | 1 | single_choice | Cici bought $$12$$ pencils and notebooks in total for $$66$$. Each pencil cost $$2$$. Each notebook costs $8$. How many notebooks did Cici buy? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$8$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"
] | [
"$$12\\times2=24$$ $$8-2=6$$ $$66-24=42$$ $$42\\div6=7$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10585 | 9cc1d229e19d4e469f34a717904897e4 | [
"其它"
] | 2 | single_choice | There are oranges, apricots and peaches in a big basket. How many fruits are there in the basket if the peaches and the apricots together are 18, the oranges and the apricots together are 28 and 30 fruits are not apricots? | [
[
{
"aoVal": "A",
"content": "$$46$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$40$$ "
}
],
[
{
"aoVal": "D",
"content": "$$38$$ "
}
],
[
{
"aoVal": "E",
"content": "$$29$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with Two Variables"
] | [
"If we sum up the number of A and P, the result is 18. But if we sum up A and O, result is 28 instead. Hence, there must be 10 more O than P. Note that there are a total of 30 I and P. Therefore, there are (30+10)/2 = 20 Oranges. Total = 20+18=38. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10586 | e51c571ca64e467c9116b6ab49d529bd | [
"其它"
] | 2 | single_choice | Suppose $15 \textbackslash\%$ of $x$ equals $20 \textbackslash\%$ of $y$. What percentage of $x$ is $y$ ? (2020 AMC 8, Question 15) | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$35$$ "
}
],
[
{
"aoVal": "C",
"content": "$$75$$ "
}
],
[
{
"aoVal": "D",
"content": "$133\\frac{1}{3}$ "
}
],
[
{
"aoVal": "E",
"content": "$$300$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"Since $20 \\textbackslash\\%=\\frac{1}{5}$, multiplying the given condition by 5 shows that $y$ is $15 \\cdot 5=(\\mathbf{C}) 75$ percent of $x$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10590 | 9cc7ab7c016f4b148b1f25f35786da84 | [] | 1 | single_choice | The scale of a map is:~$\dfrac{3}{4}$ of an inch $$=10$$ miles. If the distance on the map between two towns is $$12$$ inches, the actual distance between the towns is. | [
[
{
"aoVal": "A",
"content": "$$90$$ miles "
}
],
[
{
"aoVal": "B",
"content": "$$120$$ miles "
}
],
[
{
"aoVal": "C",
"content": "$$150$$ miles "
}
],
[
{
"aoVal": "D",
"content": "$$160$$ miles "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with an Invariant Part"
] | [
"Since $$12 \\div \\frac{3}{4}=16$$, the actual distance between the towns is $$16\\times10 = 160$$ miles. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10591 | e9b5064a25c24cd2bf0d6c299e8ca03d | [
"其它"
] | 1 | single_choice | Five people took the same test and got an average score of $80$. Four of the people scored $80$, $85$, $82$, and $90$, respectively. What is the score of the remaining person? | [
[
{
"aoVal": "A",
"content": "$$80$$ "
}
],
[
{
"aoVal": "B",
"content": "$$76$$ "
}
],
[
{
"aoVal": "C",
"content": "$$73$$ "
}
],
[
{
"aoVal": "D",
"content": "$$63$$ "
}
],
[
{
"aoVal": "E",
"content": "$$56$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"There are $0+5+2+10=17$ points more than the average, so the last score is $80-17=63$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10593 | b33a52152482460fafe6402546ac5608 | [] | 1 | single_choice | It is $4:00$ now. How many minutes does it take for the clock\textquotesingle s hour and minute hands to overlap for the first time? | [
[
{
"aoVal": "A",
"content": "$43\\frac 7{11}$ minutes "
}
],
[
{
"aoVal": "B",
"content": "$10\\frac {10}{11}$ minutes "
}
],
[
{
"aoVal": "C",
"content": "$21\\frac 9{11}$ minutes "
}
],
[
{
"aoVal": "D",
"content": "$22\\frac 9{11}$ minutes "
}
],
[
{
"aoVal": "E",
"content": "$42\\frac 7{11}$ minutes "
}
]
] | [
"Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems"
] | [
"$(30\\times 4)\\div (6-0.5)=120\\div 5.5=\\frac {240}{11}=21\\frac 9{11}$ minutes. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10596 | f7837a9013bf4de0b029c6a76506b96b | [
"其它"
] | 2 | single_choice | Chloe and Zoe are both students in Ms. Demeanor\textquotesingle s math class. Last night they each solved half of the problems in their homework assignment alone and then solved the other half together. Chloe had correct answers to only $80 \textbackslash\%$ of the problems she solved alone, but overall $88 \textbackslash\%$ of her answers were correct. Zoe had correct answers to $90 \textbackslash\%$ of the problems she solved alone. What was Zoe\textquotesingle s overall percentage of correct answers? (2017 AMC 8, Question \#14) | [
[
{
"aoVal": "A",
"content": "$$89$$ "
}
],
[
{
"aoVal": "B",
"content": "$$92$$ "
}
],
[
{
"aoVal": "C",
"content": "$$93$$ "
}
],
[
{
"aoVal": "D",
"content": "$$96$$ "
}
],
[
{
"aoVal": "E",
"content": "$$98$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"Assume the total amount of problems is 100 per half homework assignment, since we are dealing with percentages, and not values. Then, we know that Chloe got 80 problems correct by herself, and got 176 problems correct overall. We also know that Zoe had 90 problems she did correct alone. We can see that the total amount of correct problems Chloe and Zoe did was $176-80=96$. Therefore Zoe has $96+90=186$ problems out of 200 problems correct. This is (C) $93$ percent. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10599 | aa4a715486b7474596d9c7e95e377a90 | [] | 1 | single_choice | Three boxes under my stairs contain apples or pears or both. Each box contains the same number of pieces of fruit. The first box contains all twelve of the apples and one-ninth of the pears. How many pieces of fruit are there in each box? | [
[
{
"aoVal": "A",
"content": "$$14$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$36$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"
] | [
"$(1-\\frac19)\\div2=\\frac49$, $\\frac49-\\frac19=\\frac13$, $12\\div\\frac13=36$, $36\\times\\frac49=16$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10603 | ce616f2455954faaa96cbde1322717a9 | [
"其它"
] | 0 | single_choice | Duckings are walking in a queue when they are following the mother duck. Joey the duckling is the 6th from the front and 8th from the back (including the mother duck). Some of the ducklings at the back moved away from the queue making Joey the middle duckling in the queue. How many ducklings moved away from the queue? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above. "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"total number of duck and ducklings in the queue is 6+(8-1) = 13. if 2 ducklings at the back moved away, it would be 13-2=11 in the queue, and the middle ducking would be 6th from the front, which is Joey\\textquotesingle s position. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10612 | 987373dc98774f7c86d35e1441e74b99 | [] | 1 | single_choice | Every week, Robyn swims while Sam sings. For every $$2$$ of Sam\textquotesingle s songs, Robyn swims $$9$$ lengths. If Robyn swims $$54$$ lengths, how many songs does Sam sing? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
],
[
{
"aoVal": "E",
"content": "$$18$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"Sam sings $$2$$ songs in the time that Robyn swims $$9$$ lengths. The time that she takes for $$54$$ lengths is $$54\\div9 =6$$ times longer, so Sam will sing $$2\\times6 =12$$ songs. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10617 | f79142f6553d444a88d9a79bcc8926be | [] | 1 | single_choice | If today is a Wednesday, then $$22$$ days ago was a. | [
[
{
"aoVal": "A",
"content": "Tuesday "
}
],
[
{
"aoVal": "B",
"content": "Wednesday "
}
],
[
{
"aoVal": "C",
"content": "Thursday "
}
],
[
{
"aoVal": "D",
"content": "Friday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"Today is Wednesday. $$21$$ days ago was Wednesday. $$22$$ days ago was Tuesday. $\\textasciitilde$ or $\\textasciitilde$ $$22\\div7=3$$ weeks $$1$$ day. $$1$$ day before Wednesday was a Tuesday. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10626 | a5e9f61007ce4b08a91e809df6479dae | [
"其它"
] | 1 | single_choice | John drinks $x$ cups of boba everyday on weekdays and $1$ cups of boba everyday on the weekends. Which of the following equations represents how many cups of boba John drinks every week? | [
[
{
"aoVal": "A",
"content": "$x+2$ "
}
],
[
{
"aoVal": "B",
"content": "$5x+2$ "
}
],
[
{
"aoVal": "C",
"content": "$5x+1$ "
}
],
[
{
"aoVal": "D",
"content": "$5x-1$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"
] | [
"The boba that John drinks during weekdays: $$5x$$ The boba that John drinks during weekends: $$2\\times 1 =2$$ The total boba that John drinks during a week: $$5x+2$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10627 | a5eaf0013626467ea2935363c7092d51 | [] | 2 | single_choice | This year Gareth is seven times the age of his son Herbie. In six years\textquotesingle{} time Gareth will be four times as old as Herbie. What is the difference between Gareth\textquotesingle s and Herbie\textquotesingle s ages this year? | [
[
{
"aoVal": "A",
"content": "$$16$$ years "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ years "
}
],
[
{
"aoVal": "C",
"content": "$$24$$ years "
}
],
[
{
"aoVal": "D",
"content": "$$36$$ years "
}
],
[
{
"aoVal": "E",
"content": "$$42$$ years "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"
] | [
"Let Herbie\\textquotesingle s age this year be $$h$$ years. Then Gareth\\textquotesingle s age this year is $$7h$$ years. In $$6$$ years\\textquotesingle{} time, their ages will be $$h+6$$ years and $$7h+6$$ years respectively. We are told that $$7h+6=$$$$4$$$$\\left(h+6\\right)$$. This gives $$7h+6=4h+24$$ so that $$3h=18$$ and $$h=6$$. So the present ages are $$6$$ and $$7\\times 6=42$$, giving a difference of $$36$$ years. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10630 | 988b12940d1a483b9021106328a6f9af | [
"其它"
] | 2 | single_choice | A piece of pasture can feed $$17$$ cow for $$30$$ days or $$19$$ cows for $$24$$ days. If the grass grows at the same speed every day, how many cows can it feed for $$6$$ days? . | [
[
{
"aoVal": "A",
"content": "$$38$$ "
}
],
[
{
"aoVal": "B",
"content": "$$45$$ "
}
],
[
{
"aoVal": "C",
"content": "$$49$$ "
}
],
[
{
"aoVal": "D",
"content": "$$52$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Newton's Problem of Cows and Fields"
] | [
"$17\\times30=510$ $19\\times 24=456$ $510-456=54$ $54\\div(30-24)=9$ $510-30\\times9=240$ $240+6\\times9=294$ $294\\div 6=49$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10632 | e9cf4bb461884fef889224bee10f4fe4 | [] | 1 | single_choice | The month of February of a given year has five Fridays. What day of the week is January $$31$$ of that year? | [
[
{
"aoVal": "A",
"content": "Tuesday "
}
],
[
{
"aoVal": "B",
"content": "Thursday "
}
],
[
{
"aoVal": "C",
"content": "Friday "
}
],
[
{
"aoVal": "D",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"There are seven days in a week; so, in order to have five Fridays, a month has at least $$4\\times7+1=29$$ days. Since February has at most $$29$$ days, the $$1^{\\rm st}$$ and $$29^{\\rm th}$$ days of this February must both be Fridays, which means that January $$31$$ is a Thursday. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10636 | c9f6771fd40b4fc8902b7a92f6c8183c | [
"其它"
] | 1 | single_choice | Several students are singing in a line. Amy is the fourth one from the left. From the right, Amy is the fourth too. How many students are singing? (adapted from $$2019$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$5$$) | [
[
{
"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->Applying Addition and Subtraction"
] | [
"It comes $4+4=8$ when we count Amy twice. The number of all singing students is $4+4-1=7$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10638 | e0a799aa552a40b486e80e925ec45e4f | [] | 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 | 10644 | 9d0887064c8b46eba72e3a62483bdde7 | [] | 1 | single_choice | If six days ago was a Tuesday, then eight days from today is a. | [
[
{
"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"
] | [
"$$6$$ days ago was a Tuesday. Today is Monday. Thus, in $$8$$ days\\textquotesingle{} time, it will be a Tuesday. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10648 | d796f1c92ec148818f18839dab3967ec | [] | 1 | single_choice | In the sequence of letters $$\text{KANGAROOKANGAROOKANG}\cdots$$ the word $$\text{KANGAROO}$$ is repeated indefinitely. What is the $$2017\text{th}$$ letter in this sequence? | [
[
{
"aoVal": "A",
"content": "$$\\text{K}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\text{N}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\text{G}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\text{R}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$\\text{O}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"
] | [
"The sequence $$\\text{KANGAROOKANGAROOKANG}\\cdots$$ repeats every $$8$$ letters. Since $$2017=8\\times252+1$$, the $$2017\\text{th}$$ letter in the sequence is the first of the repeating sequence and hence is $$\\text{K}$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10652 | dc2da65c25c54d129b71d7b3118be4f0 | [] | 1 | single_choice | There are $$30$$ students in your class. The ratio of boys to girls is $$3:2$$. How many boys and girls are there?. | [
[
{
"aoVal": "A",
"content": "$$30$$ and $$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ and $$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ and $$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ and $$18$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"
] | [
"According to the ratio $$3:2$$, we could know the total is $$5$$. Then the number of boys is $$30\\times \\dfrac{3}{5} =18$$.The number of girls is $$30\\times\\dfrac{2}{5}=12$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10658 | a60cbbd068f8408d9d68ee9484f46f9e | [] | 2 | single_choice | A bag contains $$100$$ raffle tickets in red, white and blue. The ratio of red to white tickets is $$5:4$$ and the ratio of white to blue tickets is $$8:7$$. What is the smallest number of tickets that would have to be picked to make sure having selected at least half of \textbf{one} colour? | [
[
{
"aoVal": "A",
"content": "$$48$$ "
}
],
[
{
"aoVal": "B",
"content": "$$49$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50$$ "
}
],
[
{
"aoVal": "D",
"content": "$$51$$ "
}
],
[
{
"aoVal": "E",
"content": "$$52$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"
] | [
"First we must work out the number of tickets of each colour. Let the numbers of red, white and blue tickets be $$r$$, $$w$$ and b respectively; we have $$r : w = 5 : 4$$ and $$w : b = 8 : 7$$. Writing $$r : w$$ as $$10 : 8$$, we can combine the ratios to find $$r : w : b = 10 : 8 : 7$$. Hence for a total of $$100$$ tickets, there must be $$40$$ red, $$32$$ white and $$28$$ blue tickets. Now the largest number of red tickets one can select without having half of them is $$19$$, and likewise $$15$$ and $$13$$ for white and blue tickets. So it would be possible to select $$19 + 15 + 13 = 47$$ tickets and still not have half or more of any particular colour of ticket. However, the very next ticket, the $$48\\text{th}$$, would have to be a red, a white or a blue one, and so one of the colours would now have at least half of its number selected. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10660 | c58214890d604d8db99bc956ffbe80f7 | [
"其它"
] | 1 | single_choice | Alice\textquotesingle s first day in Caterpillar Club was Tuesday. She wants to throw a party on her $40\rm{th}$ day in the club. If Alice attends the club everyday, on which day of the week will the party be? | [
[
{
"aoVal": "A",
"content": "Friday "
}
],
[
{
"aoVal": "B",
"content": "Saturday "
}
],
[
{
"aoVal": "C",
"content": "Sunday "
}
],
[
{
"aoVal": "D",
"content": "Monday "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"40th day = 39th day after first day joining. 39 days/7 = 5 weeks R 4 days. 4 days after Tues is Saturday. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10664 | d7a6e12a2678431da653e1a728b4413f | [
"其它"
] | 2 | single_choice | Jenny is $5$ years old. She has $2$ sisters, Julie and Jas. Julie is $1$ year older than Jas. In two year\textquotesingle s time, their total age will be $18$ years. How old is Julie now? | [
[
{
"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->Age Problems"
] | [
"NA "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10670 | bc88d7782d36425bb43adb817ff31970 | [] | 1 | single_choice | Julia has eaten one-quarters of the pizza. What is the ratio of the number of pizza that remain to the number Julia has eaten? | [
[
{
"aoVal": "A",
"content": "$$1:3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3:1 $$ "
}
],
[
{
"aoVal": "C",
"content": "$$1:4 $$ "
}
],
[
{
"aoVal": "D",
"content": "$$4:1$$ "
}
],
[
{
"aoVal": "E",
"content": "$$4:3$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"
] | [
"Julia has eaten one-quarters of the pizza. So three-quarter of the pizza remain. Therefore the required ratio is $$\\frac{3}{4}:\\frac{1}{4}=3:1$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10673 | ee797a7d0d2f4757b3f9e2597eb9fa8b | [
"其它"
] | 1 | single_choice | A gardener has a box of bulbs to plant in a garden. The garden has three sections. She plants 1/2~of the bulbs in the first section. She plants 3 /4~of the remaining bulbs in the second section. She has 6 bulbs left, which she plants in the third section. How many bulbs were in the box at the start? | [
[
{
"aoVal": "A",
"content": "$$16$$ "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ "
}
],
[
{
"aoVal": "C",
"content": "$$24$$ "
}
],
[
{
"aoVal": "D",
"content": "$$32$$ "
}
],
[
{
"aoVal": "E",
"content": "$$48$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"1-1/2-1/2*3/4=1/8,1/8means 6 bulbs,$$so$$ in total there are 6\\div 1/8=48 bulbs. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10675 | a1a6ebd3fcd142dfafbeece2e0550076 | [] | 1 | single_choice | Will is selling apples at the farmer\textquotesingle s market. After selling $\dfrac{2}{5}$ of them, he has $150$ left. How many apples did Will have to start with? | [
[
{
"aoVal": "A",
"content": "$$250$$ "
}
],
[
{
"aoVal": "B",
"content": "$$375$$ "
}
],
[
{
"aoVal": "C",
"content": "$$90$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"He has $\\dfrac{3}{5}$~remaining after selling $\\dfrac{2}{5}$. We can write the equation as:~$150\\div\\dfrac{3}{5}=250$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10677 | af12f26206f14071a1f9d43ce2ca0f31 | [
"其它"
] | 1 | single_choice | Brandon is engaging sprint race on the track, and he is in the first group. On the track, there are $5$ players in front of him, and there are $8$ players behind him. There are $5$ extra groups signing up for the sprint race, and the number of players of each group are identical. How many sprint players are there in total? | [
[
{
"aoVal": "A",
"content": "$$65$$ "
}
],
[
{
"aoVal": "B",
"content": "$$70$$ "
}
],
[
{
"aoVal": "C",
"content": "$$78$$ "
}
],
[
{
"aoVal": "D",
"content": "$$84$$ "
}
],
[
{
"aoVal": "E",
"content": "$$96$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"There are $5+8+1=14$ players in each group. There are $14\\times 6=84$ players in total. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10682 | ee7e218d93e5439eaddeb236c91c3157 | [] | 1 | single_choice | Niko counted a total of $$60$$ birds perching in three trees. Five minutes later, $$6$$ birds had flown away from the first tree, $$8$$ birds had flown away from the second tree and $$4$$ birds had flown away from the third tree. He noticed that there was now the same number of birds in each tree. How many birds were originally perched in the second tree? | [
[
{
"aoVal": "A",
"content": "$$14$$ "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$21$$ "
}
],
[
{
"aoVal": "E",
"content": "$$22$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"
] | [
"Let the number of birds remaining in each tree be $$x$$. Therefore $$x+6+x+8+x+4= 60$$, which has solution $$x=14$$. Hence the number of birds originally perched in the second tree is $$14 + 8 = 22$$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10684 | b81086188e474252b1190d51efb9ce6a | [
"其它"
] | 1 | single_choice | A tank filled with $200$ litres of water weighs $350\rm{kg}$. The same tank filled with $150$ litres of water weighs $315\rm{kg}$. What is the weight of the empty tank? | [
[
{
"aoVal": "A",
"content": "$$120\\rm{kg}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$150\\rm{kg}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$165\\rm{kg}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$210\\rm{kg}$$ "
}
],
[
{
"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 | 10685 | b398ea3e4400435983e03d93bfa758f3 | [] | 1 | single_choice | A total of $$42$$ chickens and rabbits are caged together. If there are $$124$$ legs in total, how many chickens and rabbits are in the cage, respectively? | [
[
{
"aoVal": "A",
"content": "$20$; $12$ "
}
],
[
{
"aoVal": "B",
"content": "$22$; $20$ "
}
],
[
{
"aoVal": "C",
"content": "$20$; $24$ "
}
],
[
{
"aoVal": "D",
"content": "$19$; $21$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"
] | [
"Suppose all the animals in the cage are chickens: there should be $$2\\times 42=84$$ legs. However, $$124-84=40$$ legs are missing because we counted $$40\\div2=20$$ rabbits. Hence, there are $$20$$ rabbits and $$42-20=22$$ chickens. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10687 | e9f76f1b730c4df2b65ba6c50785a59b | [] | 1 | single_choice | A string $$12$$ meters long is cut into $$6$$ pieces of equal length. What is the sum of the lengths of any $$4$$ of these pieces? | [
[
{
"aoVal": "A",
"content": "$$2\\text{m}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4\\text{m}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6\\text{m}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8\\text{m}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"
] | [
"The string $$12$$ meters long is cut into $$6$$ pieces of length $$2\\text{m}$$. The sum of the lengths of any $$4$$ of these pieces is $$4\\times2\\text{m}=8\\text{m}$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10689 | e0d0c37a8432405cadd318e99d0e3f2f | [] | 1 | single_choice | William plans to take $$16$$ days to drive to New York City from his home. However, since there is heavy traffic, he drives $$20$$ miles less each day and arrives in New York City $$8$$ days later than his plan. What is the distance between William\textquotesingle s home and New York City? | [
[
{
"aoVal": "A",
"content": "$$480$$ miles "
}
],
[
{
"aoVal": "B",
"content": "$$1080$$ miles "
}
],
[
{
"aoVal": "C",
"content": "$$960$$ miles "
}
],
[
{
"aoVal": "D",
"content": "$$720$$ miles "
}
],
[
{
"aoVal": "E",
"content": "$$1200$$ miles "
}
]
] | [
"Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"
] | [
"We set up an equation in terms of $d$ as the distance and $x$ as the speed in miles per day originally. We have $d=16x=24(x-20)$ $16x=24x-480$ $480=8x$ $x=60$ Thus, the distance between William\\textquotesingle s home and New York City is $60\\times16=960$ miles. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10692 | af28b0c4a6b84bd7b5e76fd7560e8894 | [
"其它"
] | 2 | single_choice | Calculate: $1\times 10+2\times 9+3\times 8+ \cdots + 9\times 2+ 10\times 1$ | [
[
{
"aoVal": "A",
"content": "$$200$$ "
}
],
[
{
"aoVal": "B",
"content": "$$140$$ "
}
],
[
{
"aoVal": "C",
"content": "$$210$$ "
}
],
[
{
"aoVal": "D",
"content": "$$180$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples"
] | [
"E "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10693 | dc521414c5e7410e99318378e9567584 | [
"其它"
] | 2 | single_choice | The sum of Ben\textquotesingle s age and Ben\textquotesingle s grandma\textquotesingle s age is $$96$$. Ben\textquotesingle s grandma\textquotesingle s age is three times older than Ben\textquotesingle s age. How old is Ben\textquotesingle s grandma? | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$48$$ "
}
],
[
{
"aoVal": "C",
"content": "$$72$$ "
}
],
[
{
"aoVal": "D",
"content": "$$96$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Sums and Multiples in Age Problems"
] | [
"The sum of Ben\\textquotesingle s age and Ben\\textquotesingle s grandma\\textquotesingle s age is $$96$$. Since grandma is three times older than Ben, on the number line, $96$ can be divided into $$4$$ portions, and each portion is $$96\\div(1+3)=24$$. Ben is $$24$$ years old, and grandma is three times older. $$24\\times 3=72$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10696 | a63e2f1ae6a24e1584f10b7cc05f51eb | [] | 1 | single_choice | Five children divided some cakes equally. What percents of the cakes two of them could get in total? | [
[
{
"aoVal": "A",
"content": "$$5\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$40\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"
] | [
"Five children divided some cake equally. Two of the children totally got $$\\dfrac{2}{5}$$ of the cake and $$\\dfrac{2}{5}=0.4 = 40\\textbackslash\\%$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10697 | a1c95d7cb7b64d73b60f3f6155adfbdd | [] | 1 | single_choice | This year, March $$19$$ falls on a Thursday. What day of the week will it be in $$30$$ days? | [
[
{
"aoVal": "A",
"content": "Wednesday "
}
],
[
{
"aoVal": "B",
"content": "Thursday "
}
],
[
{
"aoVal": "C",
"content": "Friday "
}
],
[
{
"aoVal": "D",
"content": "Saturday "
}
],
[
{
"aoVal": "E",
"content": "Sunday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"$$30\\div4=7 \\text{ R } 2$$, two days after a Thursday is a Saturday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10703 | dc5c776a10254651bfcf64b5a79c6567 | [] | 1 | single_choice | A group of students go apple-picking. On average, each boy picks $30$ apples and each girl picks $20$ apples. The average number of apples picked by everyone in this groups is $26$. If there are $15$ boys, then how many girls are there in the group? | [
[
{
"aoVal": "A",
"content": "$$15$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$23$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"Every boy picks $$30-26=4$$ more than the average, so boys pick $$4\\times 15=60$$ more in total, which is equal to the number that girls picked less than the average in total. Every girl picks $$26-20=6$$ less than the average, so there are $$60\\div 6=10$$ girls. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10704 | a1d482de2f344a069b532edcb9781703 | [] | 1 | single_choice | If $$10^{}\text{th}$$June is Sunday, what day of the week is $$1$$\textsuperscript{st} June? | [
[
{
"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"
] | [
"We can count backward by days or by weeks. There are 9 days in between, that means 1 week and 2 days. Then count a few days back to find that $$1$$\\textsuperscript{st} June is a Friday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10705 | e0e068fe31fb4174add90714c06d682a | [
"其它"
] | 1 | single_choice | The possible grades on an exam are $$5$$, $$4$$, $$3$$, $$2$$, or $$1$$. In a class of $$200$$ students, $$\frac{1}{10}$$ of them got $$5$$s, $$\frac{1}{5}$$ them got $$4$$s, $$25 \textbackslash\% $$ of them got $$3$$s, and $$15 \textbackslash\%$$ of them got $$2$$s. How many students got $$1$$s ? | [
[
{
"aoVal": "A",
"content": "$$40$$ "
}
],
[
{
"aoVal": "B",
"content": "$$60$$ "
}
],
[
{
"aoVal": "C",
"content": "$$80$$ "
}
],
[
{
"aoVal": "D",
"content": "$$100$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$$200\\times \\left( 1-\\frac{1}{10}-\\frac{1}{5}-25 \\textbackslash\\% -15 \\textbackslash\\% ~\\right)=60$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10707 | ea08f2921d884ebbaa3f60fee63388c5 | [
"其它"
] | 1 | single_choice | The average weight of $4$ students in Class $A$ is $37$ kilograms. The average weight of $11$ students in Class $B$ is $41$ kilograms. The total weight of $5$ students in Class $C$ is $161$ kilograms. What is the average weight of the students in the $3$ classes? | [
[
{
"aoVal": "A",
"content": "$36$ kilograms "
}
],
[
{
"aoVal": "B",
"content": "$38$ kilograms "
}
],
[
{
"aoVal": "C",
"content": "$40$ kilograms "
}
],
[
{
"aoVal": "D",
"content": "$43$ kilograms "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"$4 \\times 37 + 11 \\times 41+ 161 = 760$ kilograms in total. $760 \\div (4 + 11 + 5) = 38$ kg. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10710 | dc62d707308842978a8265c0fe0c5873 | [] | 2 | single_choice | In $$2005$$, both John and Mary have the same amount of pocket money per month. In $$2006$$, John had an increase of $$10\textbackslash\%$$ and Mary a decrease of $$10\textbackslash\%$$ in their monthly pocket money. In $$2007$$, John had a decrease of $$10\textbackslash\%$$ and Mary an increase of $$10\textbackslash\%$$ in their monthly pocket money. $\textasciitilde$ John had a~\uline{~~~~~~~~~~}~$\textbackslash\%$ increase/decrease in his pocket money in $2007$ compared to $2005$. Mary had a~\uline{~~~~~~~~~~}~$\textbackslash\%$ increase/decrease in her pocket money in $2007$ compared to $2005$. $\textasciitilde$ Which one of the following statements is correct? | [
[
{
"aoVal": "A",
"content": "Both have the same amount of pocket money now. "
}
],
[
{
"aoVal": "B",
"content": "John has more pocket money now. "
}
],
[
{
"aoVal": "C",
"content": "Mary has more pocket money now. "
}
],
[
{
"aoVal": "D",
"content": "It is impossible to tell who has more pocket money now. "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"
] | [
"Statement $$\\text{A}$$ is correct. In the amount of pocket money that each has be $$x$$. In $$2007$$, John has $$1.1\\times0.9x=0.99x$$ while Mary has $$0.9\\times1.1x=0.99x$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10725 | ced1ab1899bb4ab0a87e05eebd6f681d | [] | 1 | single_choice | Lena the panda has $$30$$ bamboos. She eats $$3$$ bamboos each day. She ate the $$18th$$ bamboo on Tuesday. On which day did she start eating the bamboos? | [
[
{
"aoVal": "A",
"content": "Monday "
}
],
[
{
"aoVal": "B",
"content": "Tuesday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Thursday "
}
],
[
{
"aoVal": "E",
"content": "Friday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Newton's Problem of Cows and Fields->Basic Newton's Problem of Cows and Fields->Finding the Number of Days"
] | [
"NA "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10729 | eeaa1f787e2d46c58bdf5368396322ca | [] | 2 | single_choice | A particular cattle is fed $7 \text{kg}$, $8 \text{kg}$ and $9 \text{kg}$ of special food on Day $1$, $2$ and $3$ respectively by a farmer. From Day $4$ onwards, the amount of food fed to the cattle follows the following rule: (i) if the total amount of food fed to the cattle in the past $3$ days is $24 \text{kg}$ or more, the cattle will be fed $2 \text{kg}$ less than the day before. (ⅱ) if the total amount of food fed to the cattle in the past $3$ days is less than $24 \text{kg}$, the cattle will be fed $1 \text{kg}$ more than the day before. Calculate the minimum number of days for the total amount of food fed to the cattle to exceed $2018 \text{kg}$. | [
[
{
"aoVal": "A",
"content": "$$280$$ "
}
],
[
{
"aoVal": "B",
"content": "$$284$$ "
}
],
[
{
"aoVal": "C",
"content": "$$288$$ "
}
],
[
{
"aoVal": "D",
"content": "$$292$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"
] | [
"Amount of food fed to the cattle follows the pattern: $789756$~ ~ $$789756$$~ ~ $789756$~ ~ $789756\\cdots\\cdots$ Total amount of food fed in the first $6$ days$=42 \\text{kg}$. $2018 =48\\times6+1= 289$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10732 | ca56d0e864174132a7f950ae6cf78ef1 | [] | 1 | single_choice | Emily was $$6$$ years old last year, and her sister was $$6$$ years old six years ago. What is the age difference between Emily and her sister today? (adapted from 2005 Math Kangaroo Problem, Level 1-2, Question \#17) | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$13$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages"
] | [
"Emily was $$6$$ years old last year , which means Emily is $7$ years old this year. Her sister was~ $$6$$ years old six years ago, which tells us her sister is~ $12$ years old this year, so the age difference is $5$ today. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10733 | ced60cfcbf05434cbc9a5637869db5ba | [] | 1 | single_choice | Sinnce $$7^{2}=49$$, its ones\textquotesingle{} digit is a $$9$$. What is the ones\textquotesingle{} digit of $$2^{50}$$? | [
[
{
"aoVal": "A",
"content": "$$0$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders "
] | [
"The ones\\textquotesingle{} digits repeat in groups of four: $$2$$, $$4$$, $$8$$, $$6$$, $$2$$, $$4$$, $$8$$, $$6$$, $$\\cdots $$. The ones\\textquotesingle{} digits of $$2^{48}$$, $$2^{49}$$, $$2\\%{50}$$ are $$6$$, $$2$$, $$4$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10735 | e0fbf303526648a985b397d975797356 | [] | 1 | single_choice | If six days ago was a Tuesday, then eight days from today is a. | [
[
{
"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"
] | [
"$$6$$ days ago was Tues. Today is Mon. In $$8$$ days it will be Tues. "
] | B |