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stringclasses 4
values | dataset_version
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stringlengths 1
5
| queId
stringlengths 32
32
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sequence | difficulty
stringclasses 5
values | qtype
stringclasses 1
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stringlengths 6
1.51k
| answer_option_list
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sequence | answer_analysis
sequence | answer_value
stringclasses 7
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|---|---|---|---|---|---|---|---|---|---|---|---|
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7099 | ababbc2496cf4ca299c7768e03f1f664 | [] | 1 | single_choice | The Gellers went on a trip. They left home at 9:15 in the morning and arrived at the hotel at 8:22 in the evening. How long did the journey take? | [
[
{
"aoVal": "A",
"content": "$$11$$ hours $$22$$ minutes "
}
],
[
{
"aoVal": "B",
"content": "$$11$$ hours $$15$$ minutes "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ hours $$7$$ minutes "
}
],
[
{
"aoVal": "D",
"content": "$$1$$ hours $$7$$ minutes "
}
],
[
{
"aoVal": "E",
"content": "$$12$$ hours $$7$$ minutes "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$3$h-$15$min + $8$h+$22$min = $11$h$7$min "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7101 | 2c4bbbc9d76b4b24aa16563851ea3c68 | [
"其它"
] | 2 | single_choice | The first student wrote the number $1$ on the board, the second student wrote the number $2$, and the third one and each of the following students wrote a number that was the quotient of the number written just before the last number and the last number. What did the tenth student write? | [
[
{
"aoVal": "A",
"content": "$\\frac1{2^{10}}$ "
}
],
[
{
"aoVal": "B",
"content": "$$256$$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac1{2^{13}}$ "
}
],
[
{
"aoVal": "D",
"content": "$$1024$$ "
}
],
[
{
"aoVal": "E",
"content": "$$2^{34}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"
] | [
"The ten numbers are: $1(2^{0}), 2^{1}, \\frac1{2^{1}}, 2^{2}, \\frac1{2^{3}}, 2^{5} \\frac1{2^{8}}\\cdots$ Thus the tenth exponent is $34$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7103 | 2c4d4abc52684d75a7de4d35aff58f34 | [
"其它"
] | 1 | single_choice | In Think Academy, there are $147$ students. Among these $147$ students, we can guarantee that at least~\uline{~~~~~~~~~~}~students belong to the zodiac sign with the most students. | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13$$ "
}
],
[
{
"aoVal": "C",
"content": "$$14$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
],
[
{
"aoVal": "E",
"content": "$$136$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle"
] | [
"$147\\div12=12R3$, $12+1=13$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7107 | 4bc51a0a3df5449581f73286be1ceaed | [
"其它"
] | 0 | single_choice | From $1$ to $23$, how many integers can be chosen at most to ensure that no two of chosen numbers differ by $4$? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Constructing and Proving"
] | [
"$1, 5, 9, 13, 17, 21$ $2, 6, 10, 14, 18, 22$ $3, 7, 11, 15, 19, 23$ $4, 8, 12, 16, 20$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7141 | 79cafa9675da44d9a363bf7790d92680 | [] | 2 | single_choice | Rose and Kylie are playing a game. Here are the rules： 1. There are $$14$$ marbles placed in a row. 2. The players take turns removing either $1$ or $2$ marbles each turn. 3. Whoever picks the last marble wins the game. Rose starts first and is followed by Kylie. To ensure her victory, how many marbles must Rose take away in the first turn? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"
] | [
"If there are n marbles in total, the first player has a winning strategy for all $$n$$ that is not a multiple of $$3$$. For $$n$$ being a multiple of $$3$$, the second player can always win, regardless of what strategy the first player plays. $$14\\div (1+2)=4 \\textbackslash{} \\text{R} 2$$ Rose should take away the remainder, i.e. two marbles, to make herself the second player when there is a multiple of $3$ marbles left. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7145 | 39eece3590a94e2f9b8f8ee3797e9e36 | [] | 1 | single_choice | The time shown on the electronic clock is $6:08$. How long before the numbers appear again? (adapted from 2007 Math Kangaroo Problem, Level 3 - 4, Question \#16) | [
[
{
"aoVal": "A",
"content": "$$2$$ h $$2$$ min "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ h "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ h $$2$$ min "
}
],
[
{
"aoVal": "D",
"content": "$$2$$ h $$12$$ min "
}
],
[
{
"aoVal": "E",
"content": "$$2$$ h "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$8:06$=$6:08$+$2$h$2$min "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7147 | 47695b12320a4c328444a9e70bd97eaf | [
"其它"
] | 2 | single_choice | We are given a certain number. We double the number and then subtract $1$ from the result. We repeat this operation $4$ more times. If the end result is $2^{6}+1$, then what is the number that we started with? (Adapted from $2005$ Math Kangaroo Problems, Level $11-12$, Question \#$29$) | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "$$3$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"
] | [
"After repeating the operation $4+1=5$ times, the result is $2^{6}+1$. After repeating the operation $4$ times, the result is $(2^{6}+1+1)\\div2=2^{5}+1$. After repeating the operation $3$ times, the result is $2^{4}+1$. $$\\cdots $$ After doing the operation for the first time, the result is $2^{2}+1$. Before we do anything, the number is $2^{1}+1$, which is $3$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7161 | 3e8ddf60b7314b48a659c2bbda5a703b | [
"其它"
] | 2 | single_choice | When number $\overline{OK}$ is divided by $K$, the result will give the same quotient as the divisor and leave the remainder of $O$. The same letter represents the same digit, and different letters represent different digits. Then, what is the product of the two digits, $O$ and $K$? | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$36$$ "
}
],
[
{
"aoVal": "C",
"content": "$$63$$ "
}
],
[
{
"aoVal": "D",
"content": "$$72$$ "
}
],
[
{
"aoVal": "E",
"content": "$$81$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"
] | [
"$89\\div9=9R8$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7176 | b9aa2a9d45f44254b02d73bd48c76cf8 | [
"其它"
] | 0 | single_choice | How many minutes are there in one week? | [
[
{
"aoVal": "A",
"content": "$$7\\times24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7\\times 2\\times 12$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7\\times 12 \\times 60$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7\\times 2 \\times 12 \\times 60$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"One week $$7$$ days. $$24$$ hours per day. $$60$$ minutes per hour. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7182 | 2d17ec0b9ac9477abc3dfbc13e118f7d | [
"其它"
] | 1 | single_choice | We left for a summer camp at $4:32$ PM and got to our destination at $6:11$ PM. How long did we travel? (Adapted from 2015 Math Kangaroo Problem, Level 1--2, Question \#24) | [
[
{
"aoVal": "A",
"content": "$1$ hour $39$ minutes "
}
],
[
{
"aoVal": "B",
"content": "$2$ hours $39$ minutes "
}
],
[
{
"aoVal": "C",
"content": "$2$ hours $21$ minutes "
}
],
[
{
"aoVal": "D",
"content": "$1$ hour $21$ minutes "
}
],
[
{
"aoVal": "E",
"content": "$39$ minutes "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"$6:11$ - $4:43$ = $1$ hour $39$ minutes "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7183 | 24af39fc66024042ab0d4bcec8dfd1fc | [
"其它"
] | 1 | single_choice | Apply this operation to $$(50, 20)$$. What are the last two numbers when the operation stops? | [
[
{
"aoVal": "A",
"content": "$(2,2) "
}
],
[
{
"aoVal": "B",
"content": "$(3,3)$ "
}
],
[
{
"aoVal": "C",
"content": "$(5,5)$ "
}
],
[
{
"aoVal": "D",
"content": "$(7,7)$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Patterns of Figures->Special Changes"
] | [
"E "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7191 | 47baf36c34bf45ba96ac9777f77a18f0 | [
"其它"
] | 2 | single_choice | Amy calculate $47\times86$ wrong. Her teacher says her result which has a difference of $172$ from the correct one. After checking, Amy finds that she writes one of the four digits two multipliers the result as $9$. Which digits does she write incorrectly? | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "It\\textquotesingle s impossible to determine. "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"
] | [
"The difference between the wrong answer and the correct one is $172$. $172\\div86=2$, $172\\div47=3R31$.That means Amy writes neither $ 8$ nor $6$ wrong. Then, compare $49\\times86$ and $97\\times86$, so we can get the correct answer. $49\\times86-47\\times86=172.$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7201 | 28ff2dfc39b64e1189d663f735bfdd38 | [
"其它"
] | 1 | single_choice | Lucy, Maria, and Anna have a meeting at $$12:30$$. Lucy\textquotesingle s walk takes $$10$$ minutes, Maria\textquotesingle s walk takes a quarter of an hour, and Anna\textquotesingle s walk takes $$30$$ minutes. At what time must the person who needs the longest time to get to the meeting leave her house? (Adapted from 2006 Math Kangaroo Problem, Level 1-2, Question \#9) | [
[
{
"aoVal": "A",
"content": "$$12:00$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12:10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12:15$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12:20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$11:50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$12:30$ - $30$ min = $12:00$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7204 | 8b8bbc1f779c4a1e916d7015410c2906 | [] | 1 | single_choice | From Monday to Wednesday Mark always lies. For the rest of the week he tells the truth. One day, Mark said to Mary: $$1$$) "Yesterday I lied." and $$2$$) "Starting the day after tomorrow, I will be lying for two consecutive days." On what day of the week did Mark talk to Mary? | [
[
{
"aoVal": "A",
"content": "Monday "
}
],
[
{
"aoVal": "B",
"content": "Tuesday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Thurday "
}
],
[
{
"aoVal": "E",
"content": "Friday "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions->Complex Reasoning "
] | [
"It was on Monday, so the answer is A. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7210 | 4c5b6cef26e840f69285cf974403a5b6 | [] | 1 | single_choice | Which of the following month has $30$ days? (adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$5$$) | [
[
{
"aoVal": "A",
"content": "$February$ "
}
],
[
{
"aoVal": "B",
"content": "$$June$$ "
}
],
[
{
"aoVal": "C",
"content": "$$July$$ "
}
],
[
{
"aoVal": "D",
"content": "$$October$$ "
}
],
[
{
"aoVal": "E",
"content": "$$December$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Reading the Clock"
] | [
"June has $30$ days. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7212 | 6319041259e74549b3bccf638b9f9c5e | [
"其它"
] | 0 | single_choice | A certain play has two $$45$$-minute parts and an intermission between them. The play started at $$10:50$$ and ended at $$12:40$$. How many minutes long was the intermission? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$25$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"From $$10:50$$ to $$12:40$$ = $$1$$ h $$50$$ min, $$1$$ h $$50$$ min = $$110$$ min, two $$45$$-minute parts = $$90$$ min, and $$110 - 90 = 20$$ min. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7216 | 25146a5fc21041c5b0484c9f3e67789e | [
"其它"
] | 1 | single_choice | The distance between the school and the park is $$2400$$ $\text{m}$. Lily and Candy depart from the school towards the park at the same time, and return immediately after arriving at the park. Lily travels $$47$$ $\text{m/min}$, and Candy travels $$53$$ $\text{m/min}$. They will meet each other for the first time after~\uline{~~~~~~~~~~}~minutes. | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$48$$ "
}
],
[
{
"aoVal": "C",
"content": "$$72$$ "
}
],
[
{
"aoVal": "D",
"content": "$$96$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics"
] | [
"$2400\\times2\\div(53+47)=48$min "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7219 | 70e4d5d7ee9d43098a105e0d1b19928d | [
"其它"
] | 2 | single_choice | If $a,b,c,d,e,f,g,h,j$ represents different digits from $1$ to $9$ such that $a+\frac{b}{c}+\frac{d}{e}\times f-\left(g+\frac{h}{j} \right) = N$, where $N$ is a whole number. What is the value of $\frac{d}{e}\times f$ to maximize $N$? | [
[
{
"aoVal": "A",
"content": "$$36$$ "
}
],
[
{
"aoVal": "B",
"content": "$$56$$ "
}
],
[
{
"aoVal": "C",
"content": "$$63$$ "
}
],
[
{
"aoVal": "D",
"content": "$$72$$ "
}
],
[
{
"aoVal": "E",
"content": "$$90$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Forming a Maximum/Minimum Multi-Digit Numbers with Fixed Sums"
] | [
"D "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7221 | 3efb8d77db7e4e87a8bd7c9b6fe95242 | [
"其它"
] | 1 | single_choice | True or False: A number can\textquotesingle t be equal to its opposite. | [
[
{
"aoVal": "A",
"content": "True "
}
],
[
{
"aoVal": "B",
"content": "False "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"
] | [
"$0$\\textquotesingle s opposite number is $0$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7246 | 7a2e34fbae1e4194b2c2e2433ced2103 | [
"其它"
] | 1 | single_choice | There are two groups of flowers. Group $A$ has $15$ flowers and Group $B$ has $13$ flowers. Cathy and Ivy want to play a game with these flowers. They will take turns to take flowers from the two groups. Each person can take any number of flowers from a group at a time. The person who takes the last flower in two groups will win the game. If Ivy starts the game first, who has the winning strategy? | [
[
{
"aoVal": "A",
"content": "Ivy has the winning strategy. "
}
],
[
{
"aoVal": "B",
"content": "Cathy has the winning strategy. "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"
] | [
"Two groups of flowers are not equal. Thus, Ivy needs to take away 2 flowers from Group A and two groups will have the same amount of flowers. Then, Ivy will become the second mover and she has the winning strategy. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7257 | 5a33c86d6c42411aa78c85ca384bf674 | [] | 1 | single_choice | Bella got up at 8:10. It took 10 minutes to wash and 30 minutes to eat breakfast. At this moment, she began to read. After reading, she went out. She went out at 9:45. How long did she read? | [
[
{
"aoVal": "A",
"content": "$$10$$ minutes "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ minutes "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ minutes "
}
],
[
{
"aoVal": "D",
"content": "$$25$$ minutes "
}
],
[
{
"aoVal": "E",
"content": "$$30$$ minutes "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$$8:10$$+$$10$$min+$$30$$min+reading=$$9:45$$ reading=$$25$$min "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7259 | 5ec6441b45914f0f891da8db07e677d3 | [
"其它"
] | 1 | single_choice | London time is 7 hours behind of Hong Kong time. Mike is planning to have a flight to Hong Kong from London at $$1$$am of $$12$$th June. If the flight takes 13 hours. When will Mike arrive Hong Kong?(In Hong Kong time) | [
[
{
"aoVal": "A",
"content": "$$1$$am $$12$$th June "
}
],
[
{
"aoVal": "B",
"content": "$$9$$pm $$12$$th June "
}
],
[
{
"aoVal": "C",
"content": "$$8$$am $$12$$th June "
}
],
[
{
"aoVal": "D",
"content": "$$7$$am $$12$$th June "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"Because the flight takes 13 hours, Mike will arrive Hong Kong at $$2$$pm of $$12$$th June(London time). As london time is 7 hours behind Hong Kong time, it will be~$2+7=9$pm(Hong Kong time) "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7272 | 9e348306d77e438d8dab7c6c0eb6da2d | [
"其它"
] | 0 | single_choice | Grace was going to meet her friends at the bus station. Right now, it is $8:40$. Grace arrived at the bus station half an hour ago. The trip from her home to the station was $1$ hour long. What time did Grace depart toward the bus station? | [
[
{
"aoVal": "A",
"content": "$7:20$ "
}
],
[
{
"aoVal": "B",
"content": "$7:10$ "
}
],
[
{
"aoVal": "C",
"content": "$7:50$ "
}
],
[
{
"aoVal": "D",
"content": "$8:10$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"Grace arrived at the bus station at $8:10$, and the trip was $1$ hour long, so she departed at $7:10$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7275 | 95000a91fb5644d7983be7e73194ee33 | [
"其它"
] | 1 | single_choice | In the calculation shown below, different letters represent different digits. $AA\times AB=5467$ What is the sum of $A+B$? | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
],
[
{
"aoVal": "E",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"
] | [
"$5467=77\\times71$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7278 | 4cc989e4afa842ffa3b6887ed09cb5f5 | [
"其它"
] | 1 | single_choice | Which of the following number is the opposite number of $-2022$ | [
[
{
"aoVal": "A",
"content": "$$-2022$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2022$$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac{1}{2022}$ "
}
],
[
{
"aoVal": "D",
"content": "$-\\frac{1}{2022}$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"
] | [
"Opposite number is the number with opposite sign "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7291 | 55e0b001051742dcb995d57203e107d3 | [
"其它"
] | 2 | single_choice | In a speed skating competition 10 racers reached in final. Tom overtook 3 racers more than those who overtook him. Which place did Tom end up in? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"9-3= 6/2=3. Tom ended up in 4th place. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7299 | 440def6c64b648f28dadf550fd8188b1 | [
"其它"
] | 0 | single_choice | A certain play has three $30$-minute parts and two intermissions among them. The play started at $8:30$ AM and ended at $10:15$ AM. How long did the intermissions last for in total? | [
[
{
"aoVal": "A",
"content": "$$10 min$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15 min$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20 min$$ "
}
],
[
{
"aoVal": "D",
"content": "$$25 min$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"From $8:30$ to $10:15$ = $1$ hr $45$ min, $1$ hr $45$ min = $105$ min, three $30$-minute parts = $90$ min, $105 - 90$ = $15$ min. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7305 | ac238672079a4f3b8f371b43a3c8580b | [
"其它"
] | 1 | single_choice | Calculate the following. $(220+130-310) \div (99-89) \times (2 \times 3) =$ | [
[
{
"aoVal": "A",
"content": "$$21$$ "
}
],
[
{
"aoVal": "B",
"content": "$$24$$ "
}
],
[
{
"aoVal": "C",
"content": "$$23$$ "
}
],
[
{
"aoVal": "D",
"content": "$$22$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math"
] | [
"$$NA.$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7307 | 5a7dc26bff354dc8abd5201dea88e6a2 | [
"其它"
] | 2 | single_choice | When calculating $54\times 96$, Judy fails to write the correct column multiplication. She writes one of the four digits as $7$ and gets a result which has a difference of $1920$ from the correct one. Which digit does she write incorrectly? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "It\\textquotesingle s impossible to determine. "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"
] | [
"The difference between the wrong answer and the correct one is $1920$, whose ones digit is $0$. That means Judy writes neither $4$ nor $6$ wrong. Then, compare $20\\times54$ and $20\\times96$, so we can get the correct answer. $74\\times96-54\\times96=1920.$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7325 | 5f29d3bcb4664fa89f766454ecd494eb | [
"其它"
] | 1 | single_choice | When calculating $63\times72$ , Judy fails to write the correct column multiplication. She writes one of the four digits as 9 and gets a result which has a difference of 432 from the correct one. Which digit does she write incorrectly? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
],
[
{
"aoVal": "E",
"content": "It\\textquotesingle s impossible to determine. "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"
] | [
"The difference between the wrong answer and the correct one is $432$, whose ones digit is $2$. That means Judy writes neither $2$ nor $3$ wrong. Then, compare $7\\times63$ and $6\\times72$, so we can get the correct answer. $69\\times72-63\\times72=432.$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7329 | 9e628a2fc5f24d70bb2751113efbfdce | [] | 0 | single_choice | Four friends are competing in a math competition. They are Andy, Bob, Cindy and Daisy. The organiser of the competition told you that: ($$1$$) Andy performed better than Bob. ($$2$$) Cindy\textquotesingle s score is higher than Andy\textquotesingle s score. ($$3$$) Daisy\textquotesingle s score is lower than two of her friends. Arrange their scores in descending order. | [
[
{
"aoVal": "A",
"content": "Andy, Bob, Cindy, Daisy "
}
],
[
{
"aoVal": "B",
"content": "Andy, Cindy, Daisy, Bob "
}
],
[
{
"aoVal": "C",
"content": "Cindy, Andy, Daisy, Bob "
}
],
[
{
"aoVal": "D",
"content": "Cindy, Andy, Bob, Daisy "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"The score from highest to lower: First -\\/-\\textgreater{} Cindy Second -\\/-\\textgreater{} Andy Thrid -\\/-\\textgreater{} Daisy Fourth -\\/-\\textgreater{} Bob "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7336 | 3756a720bf354979bd3cb3de78c0f277 | [] | 2 | single_choice | There are $5$ boxes on the table. From left to right, each of them has $8,$ $4,$ $2,$ $1,$ and $5$ balls of the same size, respectively. Every time, Judy can take one ball each from the other four boxes, and then put them into the box with the smallest number of balls. She follows the rules and operates $2023$ times. Now how many balls are there in the first box counting from the left? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$6$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"
] | [
"Without operation: $$8$$, $$4$$, $$2$$, $$1$$, $$5$$ After the first operation: $$7$$, $$3$$, $$1$$, $$5$$, $$4$$ After the second operation: $$6$$, $$2$$, $$5$$, $$4$$, $$3$$ After the third operation: $$5$$, $$6$$, $$4$$, $$3$$, $$2$$ After the fourth operation: $$4$$, $$5$$, $$3$$, $$2$$, $$6$$ After the fifth operation: $$3$$, $$4$$, $$2$$, $$6$$, $$5$$ After the sixth operation: $$2$$, $$3$$, $$6$$, $$5$$, $$4$$ After the seventh operation: $$6$$, $$2$$, $$5$$, $$4$$, $$3$$ We can find that $6-2-5-4-3$ is repeating starting from the second operation. $$（2023-1）\\div5$$R$$2$$ Thus, after the $2023$\\textsuperscript{rd}~operation, the result will be the same as the third one, which means there are $5$ balls in the first box. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7376 | c35aa0f7141841c688e903344eb9d06e | [] | 1 | single_choice | Lily walks to school every day. She leaves home at $7:15$ and arrives at the school at $7:50$. How many minutes does she spend? | [
[
{
"aoVal": "A",
"content": "$$15$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$35$$ "
}
],
[
{
"aoVal": "D",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"$$7:50-7:15=35$$ min "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7380 | 762b8b6abb0f47f7b0d91546faf67f18 | [
"其它"
] | 1 | single_choice | Which of the following number is the opposite number of $12$? | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$-12$$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac{1}{12}$ "
}
],
[
{
"aoVal": "D",
"content": "$-\\frac{1}{12}$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"
] | [
"Opposite number is the number with opposite sign "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7381 | 405fdabb9d1d4ef5924b50baae98cfcd | [
"其它"
] | 1 | single_choice | There is a cube whose six faces are marked with $3$, $4$, $5$, $6$, $7$, and $8$. If the sum of every two numbers that are on the opposite faces are identical, the number on the opposite face of $4$ is~\uline{~~~~~~~~~~}~ | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
],
[
{
"aoVal": "E",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math->Fun Math Problems->Dice"
] | [
"$3+8=4+7=5+6=11$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7382 | 887d626f08cb4b2a960096d277bd9ddc | [
"其它"
] | 1 | single_choice | Math workshops start at $5:00$ PM. Today Allan was $15$ minutes late to the workshop. What time did Allan come? | [
[
{
"aoVal": "A",
"content": "$5:00$ PM "
}
],
[
{
"aoVal": "B",
"content": "$5:05$ PM "
}
],
[
{
"aoVal": "C",
"content": "$5:15$ PM "
}
],
[
{
"aoVal": "D",
"content": "$5:20$ PM "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"$15$ minutes past $5:00$ PM is $5:15$ PM. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7388 | a7c40e109ddb444f91e03488ad86349f | [
"其它"
] | 2 | single_choice | insert pic Seven children are standing in a circle. No two boys are standing next to each other. No three girls are standing next to each other. Which of these is true for the number of girls standing in the circle? | [
[
{
"aoVal": "A",
"content": "only 3 is possible "
}
],
[
{
"aoVal": "B",
"content": "3 and 4 are possible "
}
],
[
{
"aoVal": "C",
"content": "only 4 is possible "
}
],
[
{
"aoVal": "D",
"content": "4 and 5 are possible "
}
],
[
{
"aoVal": "E",
"content": "only 5 is possible "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"\"No two boys stand next to each other\" meaning there are a maximum of 3 boys only. Hence, there are a minimum of 4 girls in the circle. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7395 | 6d24a1659ead4b9e8e1f8a81eb9dff79 | [
"其它"
] | 1 | single_choice | Thirty apples are distributed among 4 children and each of them can get at least one apple. For the kid who gets the most apples, what\textquotesingle s the least possible number of apples he or she can get? | [
[
{
"aoVal": "A",
"content": "$7$ "
}
],
[
{
"aoVal": "B",
"content": "$8$ "
}
],
[
{
"aoVal": "C",
"content": "$9$ "
}
],
[
{
"aoVal": "D",
"content": "$10$ "
}
],
[
{
"aoVal": "E",
"content": "$11$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Simple Pigeonhole Principle Problems"
] | [
"$$30\\div 4=7 \\textbackslash{} \\text{R}2$$, thus for the kid who gets the most apples, he or she can get $$7+1=8$$ apples at least. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7400 | 5698ba755459432ba6b4989eeda8b325 | [] | 1 | single_choice | Ivy, Vivian, and Candy are playing the truth or lie game. The rule is: the person who picks the truth card can only tell the truth, and the person who picks the lie card can only tell a lie. Ivy said: "Vivian and Candy lied." Vivian said: "I didn\textquotesingle t lie." Candy said: "Vivian lied." How many of them told the truth? How many of them told a lie?~\hspace{0pt}~． | [
[
{
"aoVal": "A",
"content": "$2$; $1$ "
}
],
[
{
"aoVal": "B",
"content": "$0$; $3$ "
}
],
[
{
"aoVal": "C",
"content": "$1$; $2$ "
}
],
[
{
"aoVal": "D",
"content": "$3$; $0$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"Vivian and Candy told contradictory information, so one of them told the truth and the other one told the lie. Therefore, Ivy has definitely told the lie. So two people told the lie, and one people told the truth. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7401 | 5b12efa0a9614add892766ff17db9173 | [] | 1 | single_choice | There are six balls numbered with $$1-6$$. Amy distributes them equally among three people and each time she needs the three people give her a digit from the two balls they got, then she will use the three digits to form a three$-$digit number. She does it three times, and the numbers are $$145$$, $$263$$, and $$651$$. Which two numbers below must belong to one person? | [
[
{
"aoVal": "A",
"content": "$4$ and $5$ "
}
],
[
{
"aoVal": "B",
"content": "$2$ and $1$ "
}
],
[
{
"aoVal": "C",
"content": "$2$ and $5$ "
}
],
[
{
"aoVal": "D",
"content": "$$3$$ and $$4$$ "
}
],
[
{
"aoVal": "E",
"content": "$4$ and $6$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"According to $145$ and $651$, we can find that only $4$ and $6$ have changed with each other. So, they belong to one person. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7417 | bedc92899fa747a9a8a06fd7c4f109d5 | [] | 1 | single_choice | There are two piles of bananas, six in one pile and six in the other pile. Mia and Leo take turns to take the bananas from any one of the two piles. The number of bananas they can take is unlimited, but they have to take at least one each turn. Whoever picks the last banana is the winner. If Mia takes the first match, is guarantee to win. | [
[
{
"aoVal": "A",
"content": "Mia "
}
],
[
{
"aoVal": "B",
"content": "Leo "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"
] | [
"The number of matches in the two piles is the same. No matter how many matches Andy takes from one pile, Bob just needs to take the same amount of matches from the other pile. As long as there are matches for Andy to take, Bob can definitely take away the same amount from the other pile. Therefore, Bob will take away the last match and he is guarantee to win. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7419 | 40c340266cd9443bbce87ab9e7193d17 | [
"其它"
] | 1 | single_choice | Ken, Tom and Keven were playing a game together. At $1$ P.M., Ken got a score of $-75$, Tom got a score of $-32$, and Keven got a score of $3$. Half an hour later, Ken\textquotesingle s score was $-1$, Tom\textquotesingle s score was $41$, and Keven\textquotesingle s score was $-62$. Who had the greatest change of score? | [
[
{
"aoVal": "A",
"content": "Ken "
}
],
[
{
"aoVal": "B",
"content": "Tom "
}
],
[
{
"aoVal": "C",
"content": "Keven "
}
],
[
{
"aoVal": "D",
"content": "They had the same change. "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts"
] | [
"The changes of Ken\\textquotesingle s, Tom\\textquotesingle s and Keven\\textquotesingle s scores were $74$, $73$ and $65$, respectively. Ken had the greatest change. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7424 | 958c26347a1e420d8377c5555fac0186 | [
"其它"
] | 1 | single_choice | A certain movie is $$90$$ minutes long. It started at $$5:10\textasciitilde\text{PM}$$. During the movie, there were two commercial breaks, one lasting $$8$$ minutes and one lasting $$5$$ minutes. At what time did the movie finish? (2009 Math Kangaroo Problem, Level 3-4, Question \#8) | [
[
{
"aoVal": "A",
"content": "At $$6:13\\textasciitilde\\text{PM}$$ "
}
],
[
{
"aoVal": "B",
"content": "At $$6:27\\textasciitilde\\text{PM}$$ "
}
],
[
{
"aoVal": "C",
"content": "At $$6:47\\textasciitilde\\text{PM}$$ "
}
],
[
{
"aoVal": "D",
"content": "At $$6:53\\textasciitilde\\text{PM}$$ "
}
],
[
{
"aoVal": "E",
"content": "At $$7:13\\textasciitilde\\text{PM}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$90+8+5=103$ min=$1$ h $43$ min $5:10+$ $1$ h $43$ min $=6:53$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7431 | 6d68357893a744e9831f02817afc6474 | [] | 1 | single_choice | From City A to City B, the train passes through three other stations besides the starting and ending stations.~~The train leaves at 8:10 and arrives at the third station at 13:25. It will run for 45 minutes. How long does it take to reach the terminal? | [
[
{
"aoVal": "A",
"content": "$$4$$hours $$15$$minutes "
}
],
[
{
"aoVal": "B",
"content": "$$5$$hours $$15$$minutes "
}
],
[
{
"aoVal": "C",
"content": "$$5$$hours "
}
],
[
{
"aoVal": "D",
"content": "$$4$$hours $$45$$minutes "
}
],
[
{
"aoVal": "E",
"content": "$$5$$hours $$45$$minutes "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$$13:25$$-$$8:10$$=$4$h $15$min $4$h $15$min+$$45$$min=$5$h "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7440 | 910417331009438495b590c77f4e9fd2 | [] | 1 | single_choice | There are $$3$$ matches on the table. Andy and Bob take turns to pick up $$1$$ to $$2$$ matches each time. The person who picks up the last match will be the winner. If both Andy and Bob were to use the best method and Andy wants to win, he should pick up the matches~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "First "
}
],
[
{
"aoVal": "B",
"content": "Second "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"
] | [
"Andy should go second. Since Bob must pick up either $1$ or $2$ matches when he begins, there will be either $2$ or $1$ match(es) left. Both results lead to Andy\\textquotesingle s victory "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7446 | df2bc983deba4329aaf02e56888db07c | [
"其它"
] | 2 | single_choice | How many real solutions does $\textbar x+\textbar{} x+2\textbar x\textbar\textbar\textbar=1$ have? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"
] | [
"We have to go through slowly and case by case in order to get every solution, then check for extraneous ones. First, we take off the outermost set of absolute value bars, leaving the equations $$ \\left\\textbackslash{\\begin{array}{c} x+\\textbar x+2\\textbar{} x\\textbar\\textbar=1 \\textbackslash\\textbackslash{} x+\\textbar x+2\\textbar{} x\\textbar\\textbar=-1 \\end{array}\\right. $$ Now, moving the $x$ over and taking off the outermost absolute value bars on both equations leaves us with the equations $$ \\left\\textbackslash{\\begin{array}{c} x+2\\textbar x\\textbar=1-x \\textbackslash\\textbackslash{} x+2\\textbar x\\textbar=-1+x \\textbackslash\\textbackslash{} x+2\\textbar x\\textbar=-1-x \\textbackslash\\textbackslash{} x+2\\textbar x\\textbar=1+x \\end{array}\\right. $$ Moving the $x$ over in every equation gives $$ \\left\\textbackslash{\\begin{array}{c} 2\\textbar x\\textbar=1-2 x \\textbackslash\\textbackslash{} 2\\textbar x\\textbar=-1 \\textbackslash\\textbackslash{} 2\\textbar x\\textbar=-1-2 x \\textbackslash\\textbackslash{} 2\\textbar x\\textbar=1 \\end{array}\\right. $$ Obviously, $2\\textbar x\\textbar=-1$ cannot happen, so we can throw out that equation. Now, removing the absolute value bars on the three remaining equations gives us $$ \\left\\textbackslash{\\begin{array}{c} 2 x=1-2 x \\textbackslash\\textbackslash{} 2 x=-1+2 x \\textbackslash\\textbackslash{} 2 x=-1-2 x \\textbackslash\\textbackslash{} 2 x=1+2 x \\textbackslash\\textbackslash{} 2 x=1 \\textbackslash\\textbackslash{} 2 x=-1 \\end{array}\\right. $$ Obviously, $2 x=-1+2 x$ and $2 x=1+2 x$ are not real equations, so we can throw those out leaving us with four final equations. Solving each one, we get that $x=\\frac{1}{2},-\\frac{1}{2}, \\frac{1}{4}$, and $-\\frac{1}{4}$. Plugging in all those values to the original equation tells us that only $\\frac{1}{4}$ is a real solution while the others are all extraneous, so there is only one real solution. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7453 | 6d8e4deaa3124fa2aa967253f581f186 | [
"其它"
] | 1 | single_choice | Fill in the blanks with $$+$$, $$-$$, $$\times$$ or $$\div$$. $$(13-2)$$~\uline{~~~~~~~~~~}~$$4=7$$ | [
[
{
"aoVal": "A",
"content": "$$+$$ "
}
],
[
{
"aoVal": "B",
"content": "$$-$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\times$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\div$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Filling the Symbol in the Equations"
] | [
"$$Nil$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7460 | da9df4a69bdc460e92b74dc208e97e40 | [
"其它"
] | 1 | single_choice | Mr. John plays a game with his two smart students. He says: "I have a $2-$digit prime number. But I tell Andy only the ones digit and tell Fiona only the tens digit." A few moments later, Andy says: "I don\textquotesingle t know what the number is, neither do you." Fiona says: "I didn\textquotesingle t know what the number was before, but now I know it." What is the ones digit of the prime number? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"Andy knows neither of them know the number, which means the ones digit could not be $7.$ Then using elimination, Fiona knows it, which means the tens digit could be $3$ or $6.$ But no matter what it is, the ones digit will always be $1.$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7471 | 4a2600a01d1c41ec8682fad1e82866c0 | [
"其它"
] | 3 | single_choice | Teacher wrote $$10$$ non-zero natural numbers in sequence on the blackboard, where the $$1$$st number is $$16$$, and the sum of any $$3$$ adjacent numbers is $$100$$. The biggest possibility of the $$8$$th number is~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "$$81$$ "
}
],
[
{
"aoVal": "B",
"content": "$$82$$ "
}
],
[
{
"aoVal": "C",
"content": "$$83$$ "
}
],
[
{
"aoVal": "D",
"content": "$$84$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math"
] | [
"Let first 10 numbers be $${{a}\\_{1}}$$、$${{a}\\_{2}}$$、$${{a}\\_{3}}$$、$${{a}\\_{4}}$$、$$\\ldots \\ldots $$、$${{a}\\_{10}}$$. $${{a}\\_{1}}+{{a}\\_{2}}+{{a}\\_{3}}={{a}\\_{2}}+{{a}\\_{3}}+{{a}\\_{4}}$$，$${{a}\\_{1}}={{a}\\_{4}}$$. Therefore, $${{a}\\_{1}}={{a}\\_{4}}={{a}\\_{7}}={{a}\\_{10}}=16$$，$${{a}\\_{8}}=100-{{a}\\_{10}}-{{a}\\_{9}}=100-16-{{a}\\_{9}}=84-{{a}\\_{9}}$$. The maximum value of $${{a}\\_{8}}$$ is $$83$$. For example：$$16$$、$$83$$、$$1$$、$$16$$、$$83$$、$$1$$、$$16$$、$$83$$、$$1$$、$$16$$． "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7476 | 4a3217a4f1c945dbad62c5bf02b6ed16 | [
"其它"
] | 2 | single_choice | Bud played basketball for half an hour and stopped at 10:15. When did Bud start to play basketball？ | [
[
{
"aoVal": "A",
"content": "10:45 "
}
],
[
{
"aoVal": "B",
"content": "9:45 "
}
],
[
{
"aoVal": "C",
"content": "9:30 "
}
],
[
{
"aoVal": "D",
"content": "110:30 "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"10:15 - 30 minutes = 9:45 "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7480 | 4a3cfc0219f145f7a6c5bcd825fb7823 | [] | 1 | single_choice | There are two piles of matches, seven in one pile and seven in the other pile. JoJo and Kevin take turns to take the matches from any pile. The number of matches they can take is unlimited, but they have to take at least one each turn. Whoever picks the last match is the winner. If JoJo takes the first match, is guarantee to win. | [
[
{
"aoVal": "A",
"content": "JoJo "
}
],
[
{
"aoVal": "B",
"content": "Kevin "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"
] | [
"The number of matches in the two piles is the same. No matter how many matches JoJo takes from one pile, Kevin just needs to take the same amount of matches from the other pile. As long as there are matches for JoJo to take, Kevin can definitely take away the same amount from the other pile. Therefore, Kevin will take away the last match and he is guarantee to win. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7485 | 76df50ddc9b8400ebfb9b7572cff4906 | [
"其它"
] | 2 | single_choice | It is Thursday today. Mary\textquotesingle s birthday was sixteen days ago. On what day of the week was Mary\textquotesingle s birthday? | [
[
{
"aoVal": "A",
"content": "Tuesday "
}
],
[
{
"aoVal": "B",
"content": "Wednesday "
}
],
[
{
"aoVal": "C",
"content": "Thursday "
}
],
[
{
"aoVal": "D",
"content": "Friday "
}
],
[
{
"aoVal": "E",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"Fourteen days ago, it was Thursday again. Then, two days before Thursday was Tuesday. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7491 | 4ebdc6ed66474df8be8e12002703e636 | [
"其它"
] | 1 | single_choice | Which of the following number is the opposite number of $-5$? | [
[
{
"aoVal": "A",
"content": "$$-5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac{1}{5}$ "
}
],
[
{
"aoVal": "D",
"content": "$-\\frac{1}{5}$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"
] | [
"Opposite number is the number with opposite sign "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7492 | 696152aaea4c456487583359e0445b64 | [] | 1 | single_choice | The time in Thornsburg is $$6$$ hours ahead of London. The current time in London is $$8:27$$pm of $$15$$th April. What is the time in Thornsburg currently? Choose the answer. | [
[
{
"aoVal": "A",
"content": "$$8:27$$pm $$15$$th April "
}
],
[
{
"aoVal": "B",
"content": "$$14:27$$ $$15$$th April "
}
],
[
{
"aoVal": "C",
"content": "$$2:27$$pm $$15$$th April "
}
],
[
{
"aoVal": "D",
"content": "$$2:27$$am $$16$$th April "
}
],
[
{
"aoVal": "E",
"content": "$$14:27$$am $$15$$th April "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$6$ hours ahead of $08:27$pm is $02:27$am. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7500 | 4ecf165342224a40a4175b574d9d7c8a | [] | 1 | single_choice | Amy has $$18$$ boxes of clay. Bala has $$9$$ boxes of clay. Cindy has $$6$$ boxes of clay. How many boxes of clay do they have altogether? | [
[
{
"aoVal": "A",
"content": "$$35$$ "
}
],
[
{
"aoVal": "B",
"content": "$$32$$ "
}
],
[
{
"aoVal": "C",
"content": "$$33$$ "
}
],
[
{
"aoVal": "D",
"content": "$$34$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math"
] | [
"\\textbf{[Solution]} $$18 + 9 + 6 = 23$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7523 | 7291e285338a46cea0f2db5b9ca4439b | [] | 0 | single_choice | Four friends are competing in a math competition. They are Andy, Bob, Cindy and Daisy. The organiser of the competition told you that: ($$1$$) Andy performed better than Bob. ($$2$$) Cindy\textquotesingle s score is higher than Andy\textquotesingle s score. ($$3$$) Daisy\textquotesingle s score is lower than two of her friends. Rank them from the highest to the lowest. | [
[
{
"aoVal": "A",
"content": "Andy, Bob, Cindy, Daisy "
}
],
[
{
"aoVal": "B",
"content": "Andy, Cindy, Daisy, Bob "
}
],
[
{
"aoVal": "C",
"content": "Cindy, Andy, Daisy, Bob "
}
],
[
{
"aoVal": "D",
"content": "Cindy, Andy, Bob, Daisy "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"The score from highest to lower: First -\\/-\\textgreater{} Cindy Second -\\/-\\textgreater{} Andy Thrid -\\/-\\textgreater{} Daisy Fourth -\\/-\\textgreater{} Bob "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7529 | 5376ee7c5acd4a00b17c7dfcb2e892b0 | [
"其它"
] | 2 | single_choice | $$100$$ squares are placed in a row, each filled up with a digit among $$0$$, $$1$$, $$2$$, $$\cdots $$, $$9$$. Now if a digit appears $$5$$ times or more, all the squares filled up with that digit will be painted red. Find the smallest possible number of red squares. | [
[
{
"aoVal": "A",
"content": "$$60$$ "
}
],
[
{
"aoVal": "B",
"content": "$$64$$ "
}
],
[
{
"aoVal": "C",
"content": "$$68$$ "
}
],
[
{
"aoVal": "D",
"content": "$$72$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle"
] | [
"B "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7531 | e404d8f83eee406799672dc0d4716f25 | [] | 1 | single_choice | Ivy, Vivian, and Candy are playing the truth or lie game. The rule is: the person who picks the truth card can only tell the truth, and the person who picks the lie card must tell a lie. \textbf{Ivy said: "Vivian and Candy lied."} \textbf{Vivian said: "I didn\textquotesingle t lie."} \textbf{Candy said: "Vivian lied."} How many of them told the truth? How many of them told a lie?~\hspace{0pt} | [
[
{
"aoVal": "A",
"content": "$2$; $1$ "
}
],
[
{
"aoVal": "B",
"content": "$0$; $3$ "
}
],
[
{
"aoVal": "C",
"content": "$1$; $2$ "
}
],
[
{
"aoVal": "D",
"content": "$3$; $0$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"Vivian and Candy told contradictory information, so one of them told the truth and the other one told the lie. Therefore, Ivy has definitely told the lie. So two people told the lie, and one people told the truth. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7543 | d1a30fcf1ad94fc4843c709480ef0ba4 | [] | 1 | single_choice | Students $$A$$, $$B$$, $$C$$, $$D$$, $$E$$ and $$F$$ are standing in a row. We know that: $$\quad \quad \quad 1$$) $$D$$ is standing between $$E$$ and $$F$$; $$\quad \quad \quad 2$$) $$C$$ is standing between $$D$$ and $$E$$; $$\quad \quad \quad 3$$) $$B$$ is standing between $$C$$ and $$D$$; and $$\quad \quad \quad 4$$) $$A$$ is standing between $$B$$ and $$C$$. Which of the folowing statements is true? | [
[
{
"aoVal": "A",
"content": "$$A$$ is positioned either at the right end of the row or the left end of the row. "
}
],
[
{
"aoVal": "B",
"content": "$$A$$ is second from one of the ends of the row. "
}
],
[
{
"aoVal": "C",
"content": "$$A$$ is third from one of the ends of the row. "
}
],
[
{
"aoVal": "D",
"content": "The situation described in the problem is impossible. "
}
],
[
{
"aoVal": "E",
"content": "$$E$$ and $$F$$ are right next to $$A$$. "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions->Complex Reasoning "
] | [
"The only true statement here is that $A$ is the third from one of the ends of the row, which is $C$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7547 | 9ab535bf3efb4456808f664dde7a53e2 | [] | 1 | single_choice | Two sixth-grade students play chess with at least $$10$$ fifth-grade students, and each of the two men plays exactly one game against each other. There are three results: $$2$$ points for winning, $$1$$ point for drawing, and $$0$$ point for losing. After the competition, it is known that the sum of the two sixth grade students is $$20$$ points, and each fifth grader has scored $$N$$ points. $$N$$ is~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$14$$ "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ "
}
],
[
{
"aoVal": "D",
"content": "$$18$$ "
}
],
[
{
"aoVal": "E",
"content": "$$20$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition"
] | [
"The number of the fifth-grade student is $$n$$. $$N=[(n+2)\\times(n+1)-20]\\div n= (n^{2}+3n-18)\\div n = n+3-\\frac{18}{n}$$ $$n=18$$ $$N=18+3-1=20$$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7555 | 72d29d8d091447d6b30932fc7eae339e | [] | 1 | single_choice | Lucy, Maria and Anna have a meeting at $$12:30$$. Lucy\textquotesingle s walk takes $$10$$ minutes, Maria\textquotesingle s a quarter of an hour, and Anna\textquotesingle s $$40$$ minutes. At what time must the person who needs the longest time to get to the meeting leave her house? (2006 Math Kangaroo Problem, Level 1-2, Question \#9) | [
[
{
"aoVal": "A",
"content": "$$12:00$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12:10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12:15$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12:20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$11:50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$12:30-40 min=11:50$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7560 | df78d39d224144ea95717e47a4850603 | [] | 0 | single_choice | If you need $$6$$ minutes to cook $$2$$ eggs, you will need minutes to cook $$4$$ eggs in a pot. (The pot can hold $$4$$ eggs.) | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Planning"
] | [
"It takes $$6$$ minutes to cook a $$2$$ raw egg, and of course a $$4$$ raw egg will be cooked in a pot, and it will still take $$6$$ minutes to cook. So choose $$\\text{B}$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7562 | dae4734d9c524fc3b94ea6d4f53205c6 | [] | 0 | single_choice | Four friends are competing in a math competition. They are Andy, Bob, Cindy and Daisy. The organiser of the competition told you that: ($$1$$) Andy performed better than Bob. ($$2$$) Cindy\textquotesingle s score is higher than Andy\textquotesingle s score. ($$3$$) Daisy\textquotesingle s score is lower than two of her friends. Rank them from the highest to the lowest. | [
[
{
"aoVal": "A",
"content": "Andy, Bob, Cindy, Daisy "
}
],
[
{
"aoVal": "B",
"content": "Andy, Cindy, Daisy, Bob "
}
],
[
{
"aoVal": "C",
"content": "Cindy, Andy, Daisy, Bob "
}
],
[
{
"aoVal": "D",
"content": "Cindy, Andy, Bob, Daisy "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"The score from highest to lower: First -\\/-\\textgreater{} Cindy Second -\\/-\\textgreater{} Andy Thrid -\\/-\\textgreater{} Daisy Fourth -\\/-\\textgreater{} Bob "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7564 | 7761fd864ef3449d9cfd19bf18d677df | [
"其它"
] | 1 | single_choice | Two men and two boys are planning to cross a river using a small boat that can only hold either one man or two boys. What is the least possible number of times the boat needs to cross the river in order to bring all four of them to the other side? | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$9$ "
}
],
[
{
"aoVal": "D",
"content": "$$11$$ "
}
],
[
{
"aoVal": "E",
"content": "$$13$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"
] | [
"Two boys cross the river and one of them goes back. A man crosses the river and the other boy goes back. Two boys cross the river and one of them goes back. The other man crosses the river and the other boy goes back. Two boys cross the river. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7567 | 72e90114736b4c97b05adaa3a6e28963 | [
"其它"
] | 1 | single_choice | Math workshop starts at $5:00$ PM. Today Allan was $15$ minutes late to the workshop. What time did Allan come?~ | [
[
{
"aoVal": "A",
"content": "$5:00$ PM "
}
],
[
{
"aoVal": "B",
"content": "$5:05$ PM "
}
],
[
{
"aoVal": "C",
"content": "$5:15$ PM "
}
],
[
{
"aoVal": "D",
"content": "$5:20$ PM "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"$15$ minutes past $5:00$ PM is $5:15$ PM. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7583 | 9adfadec6e7b498ba30884abe3916430 | [
"其它"
] | 2 | single_choice | Andrea needs an hour to get to the shopping center. If she leaves at $4$, she gets there half an hour after the store closes. When does the shopping center close? | [
[
{
"aoVal": "A",
"content": "$3:30$ "
}
],
[
{
"aoVal": "B",
"content": "$5:30$ "
}
],
[
{
"aoVal": "C",
"content": "$5:00$ "
}
],
[
{
"aoVal": "D",
"content": "$4:00$ "
}
],
[
{
"aoVal": "E",
"content": "$4:30$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"If Andrea leaves at $4$ PM, she arrives at the store when it is $5$ PM, and the store closes at $4:30$ PM. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7608 | 89c746b6d3a940419c94774445d47fd4 | [
"其它"
] | 1 | single_choice | Which of the following numbers is the opposite of $-2$? | [
[
{
"aoVal": "A",
"content": "$$-2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac{1}{2}$ "
}
],
[
{
"aoVal": "D",
"content": "$-\\frac{1}{2}$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"
] | [
"Opposite number is the number with opposite sign "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7610 | 80c86721f64545a4abcd3e716244048b | [
"其它"
] | 1 | single_choice | Which of the following calculations shows how to work out the number of seconds in~~24 days? | [
[
{
"aoVal": "A",
"content": "24 \\times 24~ "
}
],
[
{
"aoVal": "B",
"content": "24 \\times 60 "
}
],
[
{
"aoVal": "C",
"content": "24 \\times 24 \\times 60 "
}
],
[
{
"aoVal": "D",
"content": "24 \\times 60 \\times 60 "
}
],
[
{
"aoVal": "E",
"content": "24 \\times 24 \\times 60 \\times 60 "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"1 day = 24 hours，$$1$$ hour = 60 minutes，$$1$$ minute = 60 seconds，$$24$$ days = (24 \\times 24) hours = [(24\\times 24) \\times 60] minutes = 24\\times 24\\times 60\\times 60 seconds "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7613 | 9b1018648d354477b1bf219f22788ce5 | [
"其它"
] | 1 | single_choice | Jacob writes down a three-digit number on a piece of paper. Lisa, Mike, and Henry are guessing the number Jacob writes down. Lisa: "The number is $473$." Mike: "The number is $623$." Henry: "The number is $428$." Among the three digits, each person guesses two of them correctly for both digits and their positions. What is the number Jacob writes down? | [
[
{
"aoVal": "A",
"content": "$$678$$ "
}
],
[
{
"aoVal": "B",
"content": "$$428$$ "
}
],
[
{
"aoVal": "C",
"content": "$$623$$ "
}
],
[
{
"aoVal": "D",
"content": "$$478$$ "
}
],
[
{
"aoVal": "E",
"content": "$$423$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"In the hundreds place, $4$ appears twice, so $4$ is in the hundreds place. In the tens place, $2$ appears twice, so $2$ is in the tens place. In the ones place, $3$ appears twice, so $3$ is in the ones place. Thus, the number Jacob writes down is $423$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7614 | a8bef60f903e469ca1c1c6956334b29d | [
"其它"
] | 1 | single_choice | The math workshop started at $5:00$. Today Leo was $15$ minutes late to the workshop. What time did Leo arrive? | [
[
{
"aoVal": "A",
"content": "$5:00$ "
}
],
[
{
"aoVal": "B",
"content": "$5:05$ "
}
],
[
{
"aoVal": "C",
"content": "$5:15$ "
}
],
[
{
"aoVal": "D",
"content": "$5:20$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"$15$ minutes past $5:00$ ~is $5:15$ . "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7618 | 6197d451b812429e854c567d682bb904 | [
"其它"
] | 1 | single_choice | Which of the following number is the opposite number of $12$ | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$-12$$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac{1}{12}$ "
}
],
[
{
"aoVal": "D",
"content": "$-\\frac{1}{12}$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"
] | [
"Opposite number is the number with opposite sign "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7621 | 7c51eea30ea1493abb337515da4bba3f | [
"其它"
] | 1 | single_choice | What is the missing number in the sequence below? 1, 3, 7, 15, 31,~\uline{~~~~~~~~~~}~ | [
[
{
"aoVal": "A",
"content": "$$63$$ "
}
],
[
{
"aoVal": "B",
"content": "$$47$$ "
}
],
[
{
"aoVal": "C",
"content": "$$57$$ "
}
],
[
{
"aoVal": "D",
"content": "$$59$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Patterns of Figures"
] | [
"1, 3, 7, 15, 31, \\cdots .. 2. 4. 8.~ 16.~ 32 31+32 = 64 "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7632 | 9220b5b802044337852c68fe46e8298e | [
"其它"
] | 0 | single_choice | Grace was going to meet her friends at the bus station. Right now, it is $8:20$. Grace arrived at the bus station half an hour ago. The trip from her home to the station was $1$ hour long. What time did Grace depart toward the bus station? | [
[
{
"aoVal": "A",
"content": "$7:20$ "
}
],
[
{
"aoVal": "B",
"content": "$6:50$ "
}
],
[
{
"aoVal": "C",
"content": "$7:50$ "
}
],
[
{
"aoVal": "D",
"content": "$8:50$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"Grace arrived at the bus station at $7:50$, and the trip was $1$ hour long, so she departed at $6:50$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7633 | b1f3e4f2d0b943058ba679107675e64d | [
"其它"
] | 2 | single_choice | There are $1000$ students in Grade $3$ in Think Academy. Among these $1000$ students, at least how many students were born in the month with the most births? | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$82$$ "
}
],
[
{
"aoVal": "C",
"content": "$$83$$ "
}
],
[
{
"aoVal": "D",
"content": "$$84$$ "
}
],
[
{
"aoVal": "E",
"content": "$$1000$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle"
] | [
"$1000\\div 12=83R4$, $83+1=84$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7635 | 9225431446224ef3b0279551616551b7 | [
"其它"
] | 1 | single_choice | Fill in the blanks with $$+$$, $$-$$, $$\times$$ or $$\div$$. $$(9+6)$$~\uline{~~~~~~~~~~}~$$7=8$$ | [
[
{
"aoVal": "A",
"content": "$$+$$ "
}
],
[
{
"aoVal": "B",
"content": "$$-$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\times$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\div$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Filling the Symbol in the Equations"
] | [
"$$Nil$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7640 | 810772db20954a2199211d0cc1360072 | [
"其它"
] | 1 | single_choice | In the calculation shown below, different letters represent different digits. $AA\times BC\times ABC=ABCABC$ What is the product of $A\times B\times C$? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$21$$ "
}
],
[
{
"aoVal": "D",
"content": "$$13$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"
] | [
"$AA\\times BC=77\\times13=11\\times91$ $A=7, B=1, C=3$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7654 | 73bcab869f0b4bfca174a206a74e5a7b | [
"其它"
] | 1 | single_choice | About the number 325, five boys said: Andrei: "This is a 3-digit number" Boris: "All digits are distinct" Vick: "The sum of the digits is 10" Greg: "The unit digits is 5" Danny: "All digits are odd" Which of the boys was wrong? | [
[
{
"aoVal": "A",
"content": "Andrei "
}
],
[
{
"aoVal": "B",
"content": "Boris "
}
],
[
{
"aoVal": "C",
"content": "Vick "
}
],
[
{
"aoVal": "D",
"content": "Greg "
}
],
[
{
"aoVal": "E",
"content": "Danny "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"2 is not odd. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7668 | a48b341d0e194ece93f480ac24ca84ab | [
"其它"
] | 0 | single_choice | A certain play has two $30$-minute parts and one intermission among them. The play started at $8:00$ and ended at $9:15$. How many minutes long were the intermission? (Adapted from 2010 Math Kangaroo Problem, Level 1-2, Question \#19) | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$25$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"From $8:00$ to $9:15$ = $1$ h $15$ min, $1$ h $15$ min = $75$ min, two $30$-minute parts = $60$ min, $75 - 60$ = $15$ min. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7675 | 85d1a59f332e48fab3f4da5ecbbc64ae | [
"其它"
] | 1 | single_choice | Math workshops start at $5:00$ PM. Today Allan was $15$ minutes late to the workshop. When did Allan come? | [
[
{
"aoVal": "A",
"content": "$5:00$ PM "
}
],
[
{
"aoVal": "B",
"content": "$5:05$ PM "
}
],
[
{
"aoVal": "C",
"content": "$5:15$ PM "
}
],
[
{
"aoVal": "D",
"content": "$5:20$ PM "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"$15$ minutes past $5:00$ PM is $5:15$ PM. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7678 | 9278bd8836594889b36535a8562e84fa | [
"其它"
] | 0 | single_choice | A school has two classes in the morning, each class continues $$45$$ minutes, and there is a break between classes. The first class starts at $$10:00$$, and the second class ends at $$12:00$$. How long does the courseware rest? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30$$ "
}
],
[
{
"aoVal": "E",
"content": "$$35$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"From $$10:00$$ to $$12:00$$ = $$2$$ h = $$120$$ min, two $$45$$-minute parts = $$90$$ min, and $$120 - 90 = 30$$ min. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7685 | b6c8616bb96e4d50b484be3fb2b964b8 | [] | 2 | single_choice | Joseph has $$100$$ mice. Each of them is either white or grey. At least one of the mice is grey, and out of any seven of Joseph\textquotesingle s mice at least four are white. How many grey mice does Joseph have at the most? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$93$$ "
}
],
[
{
"aoVal": "D",
"content": "$$97$$ "
}
],
[
{
"aoVal": "E",
"content": "$$99$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems"
] | [
"The maximum is $3$ since any group of $7$ at most $3$ are grey. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7686 | e91d78a07ae3423a956836feea512e55 | [] | 1 | single_choice | There are $$25$$ matches on the table. John and James take turns to remove $$1$$ to $$3$$ matches each time. The person who removes the last match will be the winner. If both of them were to use the best method and John removes first, then~\uline{~~~~~~~~~~}~will win.~ | [
[
{
"aoVal": "A",
"content": "John "
}
],
[
{
"aoVal": "B",
"content": "James "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"
] | [
"$$25\\div 4=6\\ldots 1$$ John removes $$1$$ match and $$24$$ is a multiple of $$4$$. So, the first player will win the game. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7695 | 97183c487a584339ada9ef0e646c8d4f | [
"其它"
] | 1 | single_choice | Which of the following number is the opposite number of $-5$ | [
[
{
"aoVal": "A",
"content": "$$-5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac{1}{5}$ "
}
],
[
{
"aoVal": "D",
"content": "$-\\frac{1}{5}$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"
] | [
"Opposite number is the number with opposite sign "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7702 | a4c11c820b124473b45673c8ee3e4dba | [
"其它"
] | 1 | single_choice | Which of the following calculations shows how to work out the number of seconds in~~24 days? | [
[
{
"aoVal": "A",
"content": "24 x24~ "
}
],
[
{
"aoVal": "B",
"content": "24 x~60 "
}
],
[
{
"aoVal": "C",
"content": "24 x~24 x~60 "
}
],
[
{
"aoVal": "D",
"content": "24 x~60 x~60 "
}
],
[
{
"aoVal": "E",
"content": "24 x~24 x~60 x~60 "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"1 day = 24 hours，$$1$$ hour = 60 minutes，$$1minute$$ = 60 seconds，$$24$$ days = (24 x 24) hours = [(24x 24) x 60] minutes = 24x 24x 60x 60 seconds "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7708 | 78d21d6d8ae242c2afb74bdfd2c4dfd2 | [
"其它"
] | 1 | single_choice | The numbers $$1$$, $$2$$, $$4$$, $$5$$, $$8$$, $$9$$, $$10$$, $$13$$ and $$16$$ are divided into groups of one or more numbers. The sum of the numbers in each group is the same. What is the largest possible number of groups? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
],
[
{
"aoVal": "E",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"
] | [
"$1+2+4+5+8+9+10+13+16=68$ $2$ groups: sum of each group is $34$, $34=1+16+2+5+10=4+13+8+9$ $4$ groups: sum of each group is $17$, $17=1+16=2+5+10=4+13=8+9$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7712 | 9bd479bde3f541e1ab16904524b04139 | [
"其它"
] | 1 | single_choice | When calculating $63\times72$ , Judy fails to write the correct column multiplication. She writes one of the four digits as $9$ and gets a result which has a difference of $432$ from the correct one. Which digit does she write incorrectly? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
],
[
{
"aoVal": "E",
"content": "It\\textquotesingle s impossible to determine. "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles"
] | [
"The difference between the wrong answer and the correct one is $432$, whose ones digit is $2$. That means Judy writes neither $2$ nor $3$ wrong. Compare $7\\times63$ and $6\\times72$, and we can get the correct answer. $69\\times72-63\\times72=432.$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7719 | cdc8d08ff4184caca59072ad8e3219fe | [
"其它"
] | 2 | single_choice | Given that $$2a+3b=84$$, the largest possible value of $$a\times b$$ is~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "$$270$$ "
}
],
[
{
"aoVal": "B",
"content": "$$272$$ "
}
],
[
{
"aoVal": "C",
"content": "$$294$$ "
}
],
[
{
"aoVal": "D",
"content": "$$296$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Forming a Maximum/Minimum Multi-Digit Numbers with Fixed Sums"
] | [
"Given that an unchanged sum, the smaller the difference the larger the product. $84=42+42$$$\\Rightarrow (2a) \\times (3b)=6ab\\leqslant {{42}^{2}}\\Rightarrow ab\\leqslant 294$$. Thus, the largest possible value of $ab$ is $294$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7720 | edda09bd011c45b48a1617c95f18d1c6 | [
"其它"
] | 1 | single_choice | There is a cube whose six faces are marked with $3$, $4$, $5$, $6$, $7$, and $8$. If the sum of every two numbers that are on the opposite faces are the same, the number on the opposite face of $4$ is~\uline{~~~~~~~~~~}~ | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
],
[
{
"aoVal": "E",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math->Fun Math Problems->Dice"
] | [
"$3+8=4+7=5+6=11$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7723 | bb94c184371e4737b58cc207cf6e3279 | [
"其它"
] | 2 | single_choice | Bob constructs a rectangular building by many $1\times1\times1$ cubes. The volume of the rectangular building is $210$. What is the least sum of all edges of the rectangular building? | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$80$$ "
}
],
[
{
"aoVal": "C",
"content": "$$72$$ "
}
],
[
{
"aoVal": "D",
"content": "$$210$$ "
}
],
[
{
"aoVal": "E",
"content": "$$116$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Problems of Extreme Value with Fixed Products"
] | [
"Given the product, the smaller the difference, the smaller the sum. $210=2\\times3\\times5\\times7$, so the length, the width, and the height are $5,$ $6,$ and $7$. $(5+6+7)\\times4=72.$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7728 | 7d894810f54c420e9e1c34d42d040529 | [
"其它"
] | 1 | single_choice | Apply this operation to $$(7, 28)$$. What are the last two numbers when the operation stops? | [
[
{
"aoVal": "A",
"content": "$(2,2)$ "
}
],
[
{
"aoVal": "B",
"content": "$(3,3)$ "
}
],
[
{
"aoVal": "C",
"content": "$(5,5)$ "
}
],
[
{
"aoVal": "D",
"content": "$(7,7)$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Patterns of Figures->Special Changes"
] | [
"D "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7737 | a08aa7ef26c94c0ca4b5d61fe44e4018 | [
"其它"
] | 1 | single_choice | Lucy, Maria and Anna have a meeting at $$12:30$$. Lucy\textquotesingle s walk takes $$10$$ minutes, Maria\textquotesingle s walk takes a quarter of an hour, and Anna\textquotesingle s walk takes $$40$$ minutes. At what time must the person who needs the longest time to get to the meeting leave her house? | [
[
{
"aoVal": "A",
"content": "$$12:00$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12:10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12:15$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12:20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$11:50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$12:30$ - $40$ min = $11:50$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7743 | a514b68ee2974f5d862b1faf47b024b5 | [
"其它"
] | 1 | single_choice | A talk show has two $$30$$-minute parts and has few commercials between them. The TV show started at $$1:50$$ and ended at $$3:00$$. How many minutes long were the commercials in total? | [
[
{
"aoVal": "A",
"content": "$$30$$ min "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ min "
}
],
[
{
"aoVal": "C",
"content": "$$15$$ min "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ min "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"From $$1:50$$ to $$3:00$$ is $$1$$ h $$10$$ min, and two $$30$$-minute parts = $$60$$ min. $$1$$ hr $$10$$ min = $$70$$ min, and $$70 - 60 = 10$$ min. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7744 | e95baf5c19084439a9756d333322b356 | [
"其它"
] | 0 | single_choice | Vera leaves home at $$9.15$$ a.m. to walk to Derek's house, which takes her $$25$$ minutes. Carl leaves his house $$5$$ minutes after Vera but only takes $$6$$ minutes to get to Derek's house. When Carl arrives, how long will he and Derek have to wait for Vera to arrive? | [
[
{
"aoVal": "A",
"content": "$$11$$ min "
}
],
[
{
"aoVal": "B",
"content": "$$14$$ min "
}
],
[
{
"aoVal": "C",
"content": "$$21$$ min "
}
],
[
{
"aoVal": "D",
"content": "$$24$$ min "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"Vera will arrive at $$9.40$$ a.m. Carl will leave at $$9.20$$ a.m. and arrive at $$9.26$$ a.m. So, Carl and Derek will have to wait for $$14$$ min. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7758 | f297eaf3b38b4bb7998925a448a0546a | [
"其它"
] | 1 | single_choice | The numbers $$1$$, $$5$$, $$8$$, $$9$$, $$10$$, $$12$$, and $$15$$ are divided into groups of one or more numbers. The sum of the numbers in each group is the same. What is the largest possible number of groups? (2016 Math Kangaroo Problem, Level 1-2, Question \#24) | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
],
[
{
"aoVal": "E",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"
] | [
"$1+5+8+9+10+12+15=60$ $2$ groups: sum of each group is $30$, $30=15+5+10=1+8+9+12$ $3$ groups: sum of each group is $20$, $20=15+5=12+8=10+9+1$ $4$ groups: sum of each group is $15$, $15-12=3$, but there is no $3$ in given numbers Thus, the largest possible number of groups is $3$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7759 | f29bb177737a48cb9e356b22515fd819 | [
"其它"
] | 2 | single_choice | Andrea needs an hour to get to the shopping center. If she leaves at $4$ PM, she gets there half an hour after the store closes. If she leaves at $8$ AM, she gets there half an hour before the store opens. What hours is the shopping center open? (2007 Math Kangaroo Problem, Level 1-2, Question \#24) | [
[
{
"aoVal": "A",
"content": "$7:30$ to $4:30$ "
}
],
[
{
"aoVal": "B",
"content": "$8:30$ to $5:30$ "
}
],
[
{
"aoVal": "C",
"content": "$7:30$ to $5:30$ "
}
],
[
{
"aoVal": "D",
"content": "$8:30$ to $4:30$ "
}
],
[
{
"aoVal": "E",
"content": "$9:30$ to $4:30$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"If Andrea leaves at $4$ PM, she arrives at the store when it is $5$ PM, and the store closes at $4:30$ PM. If Andrea leaves at $8$ AM, she arrives at the store when it is $9$ AM, and the store opens at $9:30$ AM. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7763 | f742f5395e1a4c6f8cb4569902f7375c | [] | 1 | single_choice | There are two piles of matches, six in one pile and six in the other pile. Andy and Bob take turns to take the matches from any one of the two piles. The number of matches they can take is unlimited, but they have to take at least one each turn. Whoever picks the last match is the winner. If Andy takes the first match, is guarantee to win. | [
[
{
"aoVal": "A",
"content": "Andy "
}
],
[
{
"aoVal": "B",
"content": "Bob "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"
] | [
"The number of matches in the two piles is the same. No matter how many matches Andy takes from one pile, Bob just needs to take the same amount of matches from the other pile. As long as there are matches for Andy to take, Bob can definitely take away the same amount from the other pile. Therefore, Bob will take away the last match and he is guarantee to win. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7772 | 97f0e8ab3f3e4780aeeb0e313ec8e2c9 | [] | 2 | single_choice | All numbers that are divisible by neither $$5$$ nor $$11$$ were removed from a sequence of consecutive natural numbers from $$1$$ to $$5500$$. A new sequence was formed. How many terms are there in this new sequence? (Adapted from $$2004$$ Math Kangaroo Problems, Level $$9-10$$, Question \#$$30$$) | [
[
{
"aoVal": "A",
"content": "$$1000$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1500$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2500$$ "
}
],
[
{
"aoVal": "D",
"content": "$$3300$$ "
}
],
[
{
"aoVal": "E",
"content": "$$4400$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Number Operation"
] | [
"Method $1$: $5500\\div5=1100$; $5500\\div11=500$; $5500\\div(5\\times11)=100$. $1100+500-100=1500$. Method $2$: In each group formed by $55$ consecutive numbers, $55-(11+5-1)=40$ numbers will be removed. $5500\\div55\\times(55-40)=1500$ numbers will remain in this new sequence. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7773 | f753eab2cf60498295be31efd71e9e21 | [] | 1 | single_choice | A tortoise is running along a $$5$$ metre track. It can run either half a metre or a metre every second. How many different ways can the tortoise finish the track? | [
[
{
"aoVal": "A",
"content": "$$72$$ "
}
],
[
{
"aoVal": "B",
"content": "$$89$$ "
}
],
[
{
"aoVal": "C",
"content": "$$91$$ "
}
],
[
{
"aoVal": "D",
"content": "$$56$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Inductive Recursion"
] | [
"$$1$$,$$2$$,$$3$$,$$5$$,$$8$$,$$13$$,$$21$$,$$34$$,$$55$$,$$89$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7781 | fbfc1e1271cd49c1916e4a65f18d0204 | [] | 1 | single_choice | A cat divides $$24$$ cans of tuna into $$4$$ groups. Each group has at least $$1$$ can of tuna, and the number of cans in each group \uline{cannot be the same}. There are at mostcans of tuna in the group that has the largest number of cans. | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ "
}
],
[
{
"aoVal": "C",
"content": "$$21$$ "
}
],
[
{
"aoVal": "D",
"content": "$$24$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Number Puzzles->Number Puzzles (sign of operations)->Obtaining Maximum/Minimum Values "
] | [
"$$ 1 + 2+3 + 18 = 24$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7782 | 9c8769716d3244b98fd33b96529a612d | [
"其它"
] | 3 | single_choice | Basil has several domino tiles, as shown in the figure. He wants to arrange them in a line according to the well-known "domino rules": in any two tiles that are next to each other, the squares that touch must have the same number of points. What is the largest number of tiles he can arrange in this way? [insert picccc] | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"One possible configuration for 5 dominoes is shown. [pic] "
] | C |
Subsets and Splits