dataset_name stringclasses 4
values | dataset_version timestamp[s] | qid stringlengths 1 5 | queId stringlengths 32 32 | competition_source_list list | difficulty stringclasses 5
values | qtype stringclasses 1
value | problem stringlengths 6 1.51k | answer_option_list list | knowledge_point_routes list | answer_analysis list | answer_value stringclasses 7
values |
|---|---|---|---|---|---|---|---|---|---|---|---|
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1567 | 9da6fccd5d7c46ac920031ceebd5b866 | [] | 1 | single_choice | Express $$\frac{7}{8}$$ as a decimal. | [
[
{
"aoVal": "A",
"content": "$$0.725$$ "
}
],
[
{
"aoVal": "B",
"content": "$$0.785$$ "
}
],
[
{
"aoVal": "C",
"content": "$$0.825$$ "
}
],
[
{
"aoVal": "D",
"content": "$$0.875$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules",
"Overseas In-curriculum->Knowledge Point->Knowing Numbers->Decimals->Converting Between Fractions and Decimals->Converting Fractions to Decimals"
] | [
"Perform long division. $7\\div8=0.875$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1568 | 6705c414205b424a9575a3f6bf86ff8a | [] | 1 | single_choice | How many minutes is it from $$22:45$$ today to $$00:35$$ tomorrow? | [
[
{
"aoVal": "A",
"content": "$$90 $$ "
}
],
[
{
"aoVal": "B",
"content": "$$ 100 $$ "
}
],
[
{
"aoVal": "C",
"content": "$$ 110 $$ "
}
],
[
{
"aoVal": "D",
"content": "$$120 $$ "
}
],
[
{
"aoVal": "E",
"... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"It is $$75$$ minutes from $$22:45$$ to midnight and then another $$35$$ minutes from midnight until $$00:35$$. So the required number of minutes is $$75 + 35 = 110$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1572 | 1ab1a1575a38447299682886540a2baa | [] | 1 | single_choice | How many of the following statements are correct? Statement $1$: The probability of a certain event to happen is $$1$$. Statement $2$: Indefinite events include impossible events. Statement $3$: The probability of an impossible event to happen is $$0$$. Statement $4$: The probability of an indefinite event to happe... | [
[
{
"aoVal": "A",
"content": "$$0$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2$$ "
}
],
[
{
"aoVal": "D",
"content": "$$3$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"Impossible events are definite events. $$\\text{Statement 2}$$ is wrong. $$\\text{Statement 1}$$, $$\\text{Statement 3}$$, and $$\\text{Statement 4}$$ are right. Thus, the answer is $$\\text{D}$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1576 | 1ab9073e2c8f4e4e95cbf3d80c638a88 | [] | 1 | single_choice | There are $$38$$ students in the class. Each student is in either math club or music club or both. Given that among students in this class, $$26$$ students are in the math club, and $$18$$ students are in the music club, there are~\uline{~~~~~~~~~~}~students in the math club only and not in the music club. | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$19$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$21$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"$$26+18-38=6$$, $$26-6=20$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1578 | c75b143de0a249769a802eb010ea57b8 | [
"其它"
] | 1 | single_choice | What is the sum of the smallest $4$-digit number and the largest $1$-digit number? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$109$$ "
}
],
[
{
"aoVal": "C",
"content": "$$999$$ "
}
],
[
{
"aoVal": "D",
"content": "$$1009$$ "
}
],
[
{
"aoVal": "E",
"conten... | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"$9+1000=1009$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1579 | 3dd195b54ee647e3b0582f566e631227 | [] | 2 | single_choice | There are some pieces of candy on a table. You are challenged by your friend to play the following game: The two players take turns taking some candy. Every turn, you can take away either $$1$$, $$2$$, $$3$$, $$4$$ or $$5$$ pieces from the table. The person who takes away the final piece of candy from the table wins. I... | [
[
{
"aoVal": "A",
"content": "$$13$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$21$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"Only $$18$$ is one of the multiples of $$5+1$$, and the second player can ensure victory. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1580 | 304c78f2d1664d75a8d94f02948b37ce | [] | 1 | single_choice | How many of the following statements are current? Statement $1$: The probability of an indefinite event to happen is between $$0$$ and $$1$$. Statement $2$: The probability of an impossible event to happen is $$0$$. Statement $3$: The probability of a certain event to happen is $$1$$. Statement $4$: Indefinite even... | [
[
{
"aoVal": "A",
"content": "$$0$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2$$ "
}
],
[
{
"aoVal": "D",
"content": "$$3$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"Impossible events are definite events. $$\\text{Statement 4}$$ is wrong. $$\\text{Statement 1}$$, $$\\text{Statement 2}$$, and $$\\text{Statement 3}$$ are right. Thus, the answer is $$\\text{D}$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1582 | d53e329cb40d46fb8583c10a5464bc0a | [] | 2 | single_choice | Between them, the two four-digit integers $$M$$ and $$N$$ contain all ten digits from $$1$$ to $$8$$. What is the least possible difference between $$M$$ and $$N$$? | [
[
{
"aoVal": "A",
"content": "$$123$$ "
}
],
[
{
"aoVal": "B",
"content": "$$247$$ "
}
],
[
{
"aoVal": "C",
"content": "$$427$$ "
}
],
[
{
"aoVal": "D",
"content": "$$472$$ "
}
],
[
{
"aoVal": "E",
"conte... | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value in Enumeration Problems"
] | [
"The first digits of the two numbers will need to be as close as possible to each other. Since they cannot be equal, they will have to differ by $$1$$; say they are $$n$$ and $$n + 1$$. The difference between the two numbers will then be minimised by making the four digits after $$n + 1$$ as small as possible and t... | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1585 | 593ad6ab1b4b4c7aa94b43d7dc9de025 | [] | 1 | single_choice | Eddie reads at least one chapter of a book with $$16$$ chapters each day. If he is asked to read a different number of chapters each day, this book can be finished reading for at most~\uline{~~~~~~~~~~}~days. | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$16$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"
] | [
"$$16=1+2+3+4+6$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1587 | 990883c520024355a82e294e65a222d5 | [] | 2 | single_choice | A chess singles tournament had $10$ players. Each player played with every other player only once. $2$ points are earned for winning a game, $0$ points are earned for losing a game, and $1$ point is earned by each player in a tie. After the tournament, the judge finds that the sum of these $10$ players\textquotesingle{... | [
[
{
"aoVal": "A",
"content": "$$180$$ "
}
],
[
{
"aoVal": "B",
"content": "$$100$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"There are $$10$$ players, so there are $$10\\times9\\div2=45$$ games in total. The sum of the points of two players in each game must be $2$. Thus, the sum of all points earned by $10$ players in $45$ games is $2\\times45=90$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1590 | 1eef58703ef840aca99d77cba17a1232 | [
"其它"
] | 1 | single_choice | Hilla can make $9$ burgers every hour. In a day, she makes burgers for $6$ hours. How many burgers can she make? | [
[
{
"aoVal": "A",
"content": "$$15$$ "
}
],
[
{
"aoVal": "B",
"content": "$$72$$ "
}
],
[
{
"aoVal": "C",
"content": "$$45$$ "
}
],
[
{
"aoVal": "D",
"content": "$$54$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"
] | [
"$6\\times9=54$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1595 | 34e18200ccc94f538e6eec3df0880ba4 | [] | 1 | single_choice | Only $$1$$ of the $$3$$ boys Abel, Ben and Charles can swim. Abel says, "I can swim." Ben says, "I cannot swim." Charles says, "Abel cannot swim." Only $$1$$ boy is telling the truth. Who can swim? | [
[
{
"aoVal": "A",
"content": "Abel "
}
],
[
{
"aoVal": "B",
"content": "Ben "
}
],
[
{
"aoVal": "C",
"content": "Charles "
}
],
[
{
"aoVal": "D",
"content": "more information needed "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"Only $$1$$ of the $$3$$ boys can swim. Only $$1$$ of the $$3$$ boys is telling the truth! Since Abel and Cain contradict each other, there must be one who is telling the truth! If Abel is true, Ben is lying and Ben can swim. Then we have $$2$$ boys (Abel and Ben) who can swim. Contradiction. Hence, Cain is tru... | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1598 | d9e385fcc1f4411d8d5cbbb56e2c16c3 | [] | 1 | single_choice | Abby, Bret, Carl, and Dana are sitting in a row of four seats numbered $$1$$ to $$4$$. Joe looks at them and says: "Bret is next to Carl." "Abby is between Bret and Carl." However, all of Joe\textquotesingle s statements are false. Bret is actually sitting in the seat $$3$$. Who is sitting in seat the $$2$$? ． | [
[
{
"aoVal": "A",
"content": "Abby "
}
],
[
{
"aoVal": "B",
"content": "Bret "
}
],
[
{
"aoVal": "C",
"content": "Carl "
}
],
[
{
"aoVal": "D",
"content": "Dana "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"We know that Carl does not sit next to Bret, so he must sit in seat $$1$$. Since Abby is not between Bret and Carl, she must sit in seat $$4$$. Finally, Dana has to take the last seat available, which is $$2$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1602 | 2348d3ed80f0430db07814eb49059cf2 | [
"其它"
] | 1 | single_choice | In numbers 30 to 90, there are some two-digit numbers in which the sum of the tens digit and the ones digit is 13. How many of such numbers are there?~\uline{~~~~~~~~~~}~ | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"
] | [
"49, 58, 67, 76, 85 "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1604 | 307019b435fa4c3fb617b6c72a1ae02b | [
"其它"
] | 1 | single_choice | A top hat contains $$3$$ red chips and $$2$$ green chips. Chips are drawn randomly, one at a time without replacement, until all $$3$$ of the reds are drawn or until both green chips are drawn. What is the probability that the $$3$$ reds are drawn? | [
[
{
"aoVal": "A",
"content": "$$\\frac{3}{10}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{2}{5}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{1}{2}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{3}{5}$$ "
}
],
[
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability"
] | [
"There are two ways of ending the game, either you picked out all the red chips or you picked out all the green chips. We can pick out $3$ red chips, $3$ red chips and $1$ green chip, $2$ green chips, $2$ green chips and $1$ red chip, and $2$ green chips and $2$ red chips. Because order is important in this problem... | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1607 | 30745a2d2ec5416f9de7435ca7b477a4 | [] | 1 | single_choice | Ali, Barb, and Cal were all born on April $$1$$, in different years. This coming April $$1$$, if I add all their ages together, I\textquotesingle ll get $$9$$. On that day, Ali\textquotesingle s age could not be． | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$1$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"Ali, Barb, and Cal \\emph{were} all born on April $$1$$, in \\emph{different} years. This coming Apr $$1$$, if I add all their ages, I\\textquotesingle ll get $$9$$. Since the youngest possible ages are $$1$$ and $$2$$, the oldest possible age is $$6$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1608 | 3972f893d1ee46548e5263dcefee3d7d | [] | 1 | single_choice | Sophia's average score on six tests is $$82$$. Her average scores on the $$7^{}\text{th}$$ and $$8^{}\text{th}$$ tests is $$98$$. What is her average score on all eight tests? ． | [
[
{
"aoVal": "A",
"content": "$$86$$ "
}
],
[
{
"aoVal": "B",
"content": "$$88$$ "
}
],
[
{
"aoVal": "C",
"content": "$$90$$ "
}
],
[
{
"aoVal": "D",
"content": "$$94$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"Sophia\\textquotesingle s total score on the first six tests is $$6\\times82=492$$. Her total score on all eight tests is $$492+2\\times98=688$$, and her average score is $$688\\div8=86$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1609 | 1f1df9e818064915906918e1d35d7c0d | [] | 1 | single_choice | There are $$10$$ boys in Pat\textquotesingle s math class. If there are twice as many girls as boys in the class, how many girls are there in the class? | [
[
{
"aoVal": "A",
"content": "$$50$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$30$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"
] | [
"girls = $10\\times2=20$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1613 | 27ae9ac7c26e4fc5929f456a790b2611 | [
"其它"
] | 1 | single_choice | There are three boxes labeled $$A$$, $$B$$, and $$C$$. Box $$A$$ contains $$1$$ red ball and $$4$$ white balls. Box $$B$$ contains $$2$$ red balls and $$3$$ white balls. Box $$C$$ contains $$3$$ red balls. All the balls are the same except for the color. Oscar randomly selects one box and then randomly selects one ball... | [
[
{
"aoVal": "A",
"content": "$$\\frac{6}{13}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{2}{5}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{8}{13}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{8}{15}$$ "
}
],
[... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"$$\\frac{1}{3}\\times \\frac{1}{5}+\\frac{1}{3}\\times \\frac{2}{5}+\\frac{1}{3}=\\frac{8}{15}$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1614 | 2c0e0ff33b394d04939f900ffd4069e7 | [
"其它"
] | 1 | single_choice | Matt had to deliver flyers to all houses numbered from 25 to 57. How many houses got th flyers? | [
[
{
"aoVal": "A",
"content": "$$31$$ "
}
],
[
{
"aoVal": "B",
"content": "$$32$$ "
}
],
[
{
"aoVal": "C",
"content": "$$33$$ "
}
],
[
{
"aoVal": "D",
"content": "$$34$$ "
}
],
[
{
"aoVal": "E",
"content":... | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"L - F +1 "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1617 | 9db9f389feed49da9466ee914232281b | [
"其它"
] | 1 | single_choice | Which of the following expression doesn\textquotesingle t mean the sum of 6 + 6 + 6 + 6 + 6? | [
[
{
"aoVal": "A",
"content": "$$6+6+6+6+6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5+6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5\\times 6$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"
] | [
"By the meaning of multiplication, $$5\\times 6$$ means the sum of five $$6$$\\textquotesingle s. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1621 | 2363fce3f68a40fea59c731f165c7aa0 | [] | 1 | single_choice | How many thousands of seconds are there in $$365$$ days? | [
[
{
"aoVal": "A",
"content": "$$31536$$ "
}
],
[
{
"aoVal": "B",
"content": "$$525600$$ "
}
],
[
{
"aoVal": "C",
"content": "$$1892160$$ "
}
],
[
{
"aoVal": "D",
"content": "$$3536000$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"$$365$$ days have $$365\\times24\\times60\\times60\\div1000=31536$$ thousand seconds． "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1622 | 2365ee15594a41aba5678ac2435010b5 | [
"其它"
] | 1 | single_choice | There is a box contains $7$ chips numbered $1$, $2$, $3$, $4$, $5$, $6$, and $7$. A chip is drawn randomly from the box. What is the probability that the number on the chip is an even number? (adapted from 2015 AMC 8 Problem, Question \#7) | [
[
{
"aoVal": "A",
"content": "$\\frac17$ "
}
],
[
{
"aoVal": "B",
"content": "$\\frac37$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac57$ "
}
],
[
{
"aoVal": "D",
"content": "$\\frac47$ "
}
],
[
{
"aoVal": "E",
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"$2$, $4$, and $6$ are even numbers. Thus, the probability is $\\frac37$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1623 | 50325552e3904b0282a3ff972b178cca | [] | 2 | single_choice | Four children were born at City Hospital yesterday. Assume each child is equally likely to be a boy or a girl. Which of the following outcomes is most likely? | [
[
{
"aoVal": "A",
"content": "all $4$ are boys "
}
],
[
{
"aoVal": "B",
"content": "all $4$ are girls "
}
],
[
{
"aoVal": "C",
"content": "$2$ are girls and $2$ are boys "
}
],
[
{
"aoVal": "D",
"content": "$3$ are of one gender... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"
] | [
"Nil "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1625 | 9916d162cdb74e5bb9a3b52b5e6011f0 | [
"其它"
] | 1 | single_choice | Which of the following statements is a certain event? | [
[
{
"aoVal": "A",
"content": "$3$ is a factor of $98765$. "
}
],
[
{
"aoVal": "B",
"content": "The sum of the interior angles of a triangle is $180$°. "
}
],
[
{
"aoVal": "C",
"content": "The age difference between Michael and Candy will increase in $1... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"$A$ is an impossible event. $C$ is an impossible event. $D$ is a random event. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1628 | 1b416ed35aec4c8eaae1050204f876ab | [] | 1 | single_choice | Eddie reads at least one chapter of a $$15-$$chapter book each day. If he is asked to read a different number of chapters each day, this book can be read for at most~\uline{~~~~~~~~~~}~days. | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"
] | [
"$$15=1+2+3+4+5$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1631 | 398a037a8d4840c58952677dcfd35257 | [] | 1 | single_choice | Seven girls and three boys are standing in a line randomly. What is the probability that three boys are next to each other? | [
[
{
"aoVal": "A",
"content": "$\\dfrac{1}{15}$ "
}
],
[
{
"aoVal": "B",
"content": "$\\dfrac{2}{15}$ "
}
],
[
{
"aoVal": "C",
"content": "$\\dfrac{1}{5}$ "
}
],
[
{
"aoVal": "D",
"content": "$\\dfrac{4}{15}$ "
}
],
[
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"
] | [
"$\\dfrac{A\\_8^{8}\\times A\\_3^{3}}{A\\_{10}^{10}}=\\dfrac{6}{90}=\\dfrac{1}{15}$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1632 | b4e3317cfb8b4449a3a5d4fe5aae6904 | [
"其它"
] | 0 | single_choice | What is the value of the following sum? $$902+804+700+609+508+403+307+201+106$$ | [
[
{
"aoVal": "A",
"content": "$$4450$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4540$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4500$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4505$$ "
}
],
[
{
"aoVal": "E",
"c... | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"
] | [
"simple math calculation "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1635 | 8fe026582403482ca9b5d36f7d7a5087 | [] | 1 | single_choice | A candy store sells some assorted candies. Each bag of assorted candies is made up of $2$ kilograms of toffee and $3$ kilograms of fruit drops. The price of toffee is $\textbackslash$6$ per kg, and the price of fruit drops is $\textbackslash$1$ per kg. How much is the cost of the assorted candies per kilogram? | [
[
{
"aoVal": "A",
"content": "$$\\textbackslash$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\textbackslash$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\textbackslash$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\textbackslash$7$$... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"The assorted candy weighs $2+3=5$ kg and is priced at $2\\times6+3\\times1=\\textbackslash$15$ in total. Therefore, each kilogram of the assorted candy is priced at $15\\div5=3$ dollars. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1636 | abaa0a6e489c46c5bd6a1de0b6cc0d3f | [
"其它"
] | 2 | single_choice | How many positive integers from $1$ to $100$ do not have $2,3$ or $5$ as its factors? | [
[
{
"aoVal": "A",
"content": "$$23$$ "
}
],
[
{
"aoVal": "B",
"content": "$$25$$ "
}
],
[
{
"aoVal": "C",
"content": "$$26$$ "
}
],
[
{
"aoVal": "D",
"content": "$$28$$ "
}
],
[
{
"aoVal": "E",
"content":... | [
"Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle"
] | [
"C "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1639 | 7e47fcd395f94abda3db528bf96663ef | [] | 1 | single_choice | Elson finished reading a storybook last week. He read an average of $19$ pages per day for the first four days of the week. He read an average of $25$ pages per day from Friday to Saturday. He did not read on Sunday. How many pages on average did Elson read per day throughout the entire week? | [
[
{
"aoVal": "A",
"content": "$$21$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$19$$ "
}
],
[
{
"aoVal": "D",
"content": "$$18$$ "
}
],
[
{
"aoVal": "E",
"content":... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"$(19\\times4+25\\times2)\\div7=18$ pages. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1641 | 4731ba56e521440f9160d5d0679428c3 | [
"其它"
] | 1 | single_choice | There are $6$ more red fish than yellow fish in Joann\textquotesingle s aquarium. Joann buys $8$ new red fish and $3$ new yellow fish. How many more red fish than yellow fish are in the aquarium now? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$9$$ "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
],
[
{
"aoVal": "E",
"content": "... | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"$8-3=5$ $6+5=11$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1644 | be2edf07b2f44cc2bf7bfbc0b43cb4f1 | [
"其它"
] | 1 | single_choice | Three children have $$10$$ balloons in total, and each of them has a different number of balloons. Joann has the most balloons, and at least how many balloons should she have? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$... | [
"Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Splitting Whole Numbers"
] | [
"$10=1+2+7=1+3+6=1+4+5=2+3+5$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1645 | 42b39fadca61484aa4552c3b10fd8352 | [] | 2 | single_choice | Molly, Dolly, Sally, Elly and Kelly are sitting on a park bench. Molly is not sitting on the far right and Dolly is not sitting on the far left. Sally is not sitting at either end. Kelly is not sitting next to Sally and Sally is not sitting next to Dolly. Elly is sitting to the right of Dolly but not necessarily next t... | [
[
{
"aoVal": "A",
"content": "Molly "
}
],
[
{
"aoVal": "B",
"content": "Dolly "
}
],
[
{
"aoVal": "C",
"content": "Sally "
}
],
[
{
"aoVal": "D",
"content": "Kelly "
}
],
[
{
"aoVal": "E",
"content":... | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Conditions"
] | [
"The question tells us that Sally is not sitting at either end. This leaves three possible positions for Sally, which we will call positions $$2$$, $$3$$ and $$4$$ from the left-hand end. Were Sally to sit in place $$2$$, neither Dolly nor Kelly could sit in places $$1$$ or $$3$$ as they cannot sit next to Sally an... | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1647 | 5053a7942b514916bbea8bbd86d3475b | [] | 1 | single_choice | There are $$20$$ red balls, $$2$$ black balls, and 1 white ball in a cloth bag. They are of identical shape, size and quality except for color. Take out 1 ball at random. Among the following statements, which one is true? | [
[
{
"aoVal": "A",
"content": "The probability of taking out a black ball is the smallest. "
}
],
[
{
"aoVal": "B",
"content": "It\\textquotesingle s impossible to take out a white ball. "
}
],
[
{
"aoVal": "C",
"content": "The probability of taking out... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"The number of red balls in the bag is the most compared with other colored balls. If we take out one ball at random, the probability of taking out a red ball is larger. So $$\\text{C}$$ is the answer. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1657 | 674a40172e3f47be898041cd1f36a5b6 | [] | 1 | single_choice | Joshua took a $$3$$ hours $$20$$ minutes train ride from Town $$X$$ to Town $$Y$$. The train departed at $$7:55$$ am, but stopped for $30$ minutes due to heavy rain during his trip. When did Joshua arrive in Town $$Y$$? (2009 Math kangaroo Problems, Level 3-4 , Question \#8) | [
[
{
"aoVal": "A",
"content": "$11:15$ "
}
],
[
{
"aoVal": "B",
"content": "$10:45$ "
}
],
[
{
"aoVal": "C",
"content": "$10:55$ "
}
],
[
{
"aoVal": "D",
"content": "$11:45$ "
}
],
[
{
"aoVal": "E",
"conte... | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$7:55+ 3$ hours $$20$$ minutes=$11:15$ $11:15$+$30$ minutes=$11:45$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1659 | 5e1ca765d89240a3bd326cca23dc8d84 | [
"其它"
] | 1 | single_choice | A whole number has two digits. The product of the digits of this number is 15. The sum of digits of this number is: | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
],
[
{
"aoVal": "E",
"content": "$$... | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"
] | [
"3 + 5 = 8 "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1663 | 39cd74a1141f4ee3b8f79370143e4479 | [] | 1 | single_choice | Abe holds $1$ green and $1$ red jelly bean in his hand. Bob holds $1$ green, $1$ yellow, and $2$ red jelly beans in his hand. Each randomly picks a jelly bean to show the other. What is the probability that the colors match? ($2013$ AMC $8$ Problem, Question \# $14$) | [
[
{
"aoVal": "A",
"content": "$\\dfrac{1}{4}$ "
}
],
[
{
"aoVal": "B",
"content": "$\\dfrac{1}{3}$ "
}
],
[
{
"aoVal": "C",
"content": "$\\dfrac{3}{8}$ "
}
],
[
{
"aoVal": "D",
"content": "$\\dfrac{1}{2}$ "
}
],
[
{
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"
] | [
"The probability of both show a green bean is $\\dfrac{1}{2}\\times \\dfrac{1}{4}=\\dfrac{1}{8}$. The probability of both show a red bean is $\\dfrac{1}{2}\\times \\dfrac{2}{4}=\\dfrac{1}{4}$. Therefore, the probability is $\\dfrac{1}{4}+\\dfrac{1}{8}=\\boxed {\\left (\\text{C}\\right )\\dfrac{3}{8}}$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1667 | 23f9ae16f74c4a4fbbaf7a92242a10c0 | [] | 1 | single_choice | Calculate: $$230\times9 =$$． | [
[
{
"aoVal": "A",
"content": "$$2070$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1980$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2130$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2240$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Principle of Multiplication"
] | [
"$$230$$x(10-1) =230x10-230x1 =2300-230 =2070 "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1668 | 283df565a5014b5a88c62e62616d38ce | [] | 1 | single_choice | How many whole numbers between $$5000$$ and $$6000$$ consist of four different digits that decrease from left to right? | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$69$$ "
}
],
[
{
"aoVal": "D",
"content": "$$120$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Finding the Shortest Path by Number Notation->Finding the Shortest Path by Number Notation (with specific points or areas)"
] | [
"The only such numbers are $$5432$$, $$5431$$, $$5430$$, $$5421$$, $$5420$$, $$5410$$, $$5321$$, $$5320$$, $$5310$$, and $$5210$$. In all, there are $$10$$ such numbers. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1671 | 82fc23b75f2946c692af29fa152cc7b8 | [] | 1 | single_choice | $$151$$ traffic ambassadors lined up neatly in a straight line (at equal distances from each other) on a highway to promote traffic laws. After completing their task, at which position of the highway should they assemble in order to minimise their total walking distance from their respective positions to the assembly a... | [
[
{
"aoVal": "A",
"content": "$$75^{}\\text{th}$$ traffic ambassador\\textquotesingle s position "
}
],
[
{
"aoVal": "B",
"content": "$$76^{}\\text{th}$$ traffic ambassador\\textquotesingle s position "
}
],
[
{
"aoVal": "C",
"content": "Between the $$... | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"There are an odd number of positions, the assembly area should be in the mid-point, $$\\left( 151+1 \\right)\\div 2=76$$, that is, the $$76^{}\\text{th}$$ traffic ambassador\\textquotesingle s position "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1672 | f12c124690ca46559a23667e9e0a469b | [] | 1 | single_choice | One morning, a rabbit, a dog, a cat, and a duck went looking for food outside. The rabbit says: "If I get food, the dog will also get food." The dog says: "If I get food, the cat will also get food." The cat says: "If I get food, the duck will also get food." In the evening, they find that all of them tell the trut... | [
[
{
"aoVal": "A",
"content": "The rabbit; the dog "
}
],
[
{
"aoVal": "B",
"content": "The dog; the cat "
}
],
[
{
"aoVal": "C",
"content": "The cat; the duck "
}
],
[
{
"aoVal": "D",
"content": "The cat; the rabbit "
}
]
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"We can infer that if the rabbit gets food, then all of the other three would get food; if the dog gets food, then both of the cat and duck would get food. Therefore, only when the rabbit and the dog don\\textquotesingle t get food, the cat and the duck would get food. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1676 | 62c81205c9d94e5a910a7e889508aa0e | [] | 1 | single_choice | Sam\textquotesingle s exam was meant to begin at $$13:45$$ but started $$17$$ minutes late. At what time did it begin? | [
[
{
"aoVal": "A",
"content": "$$13:28$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13:38$$ "
}
],
[
{
"aoVal": "C",
"content": "$$13:56$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14:02$$ "
}
],
[
{
"aoVal": "E",
... | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"Seventeen minutes after $$13:45$$ is $$14:02$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1679 | 357e06dfd883445ea9c7707e1d9d3c6c | [] | 1 | single_choice | There are $$24$$ four-digit numbers which is formed using each of the digits $$3$$, $$4$$, $$5$$ and $$6$$ once only. When all of these $$24$$ four-digit numbers are put in order from smallest to largest, which one is in the seventh position? | [
[
{
"aoVal": "A",
"content": "$$3546$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3645$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4356$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4536$$ "
}
],
[
{
"aoVal": "E",
"c... | [
"Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"
] | [
"$3456, 3465, 3546, 3564, 3546, 3564$ $\\underline{4356}, 4365, 4536, 4563, 4635, 4653$ $5346, 5364, 5436, 5463, 5634, 5643$ $6345, 6354, 6435, 6453, 6534, 6543$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1680 | be4176ea62284e0f8c306760f0f6fd4f | [] | 1 | single_choice | Jack enters the classroom and sees all the $6$ classmates in the classroom. How many students are there in the classroom now? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
],
[
{
"aoVal": "E",
"content": "It... | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"$$6+1=7$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1681 | 39fa9ae6649a44578070833ab7ef9d48 | [] | 1 | single_choice | In how many different ways can six identical coins be distributed among Al, Bo, and Carl so that each gets at least $$1$$ oin? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$9$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"The only possible distributions (Al, Bo, Carl) are these ten: $$(1,1,4)$$, $$(1,2,3)$$, $$(1,3,2)$$, $$(1,4,1)$$, $$(2,1,3)$$, $$(2,2,2)$$, $$(2,3,1)$$, $$(3,1,2)$$, $$(3,2,1)$$, and $$(4,1,1)$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1683 | 2433f1ce1d74454a83f1d7d9c13ff39e | [] | 2 | single_choice | If $$a⊕b= \frac{1}{ \dfrac{1}{a}+ \dfrac{1}{b}}$$, then what is the value of $$ (1\times2)⊕(2\times3)⊕(3 \times4)⊕\ldots⊕(2013\times2014)$$? | [
[
{
"aoVal": "A",
"content": "$$\\frac {2013}{2014}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{2014}{2013}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{2014}{2015}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{2015}{20... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"Notice that $$x\\_{1}⊕x\\_{2}⊕\\ldots⊕x\\_{n}={{(\\sum\\nolimits\\_{i=1}^{n}{x\\_{i}^{-1}})}^{-1}}$$, $$\\sum\\nolimits\\_{i=1}^{n}{\\frac{1}{i(i+1)}}=\\sum\\nolimits\\_{i=1}^{n}{(\\frac{1}{1}}-\\frac{1}{i+1})=1-\\frac{1}{n+1}=\\frac{1}{n+1}$$ and so $$(1\\times 2)\\oplus (2\\times 3)\\oplus (3\\times 4)\\oplus ... | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1684 | 39fbf643f5bb4f00822616bd37e2438b | [] | 1 | single_choice | What is the angle between the hour hand and the minute hand at seven o\textquotesingle clock?~ ~ ．(Only consider angles less than 180^{}\circ) | [
[
{
"aoVal": "A",
"content": "$50^{}\\circ $ "
}
],
[
{
"aoVal": "B",
"content": "$120^{}\\circ $ "
}
],
[
{
"aoVal": "C",
"content": "$135^{}\\circ $ "
}
],
[
{
"aoVal": "D",
"content": "$150^{}\\circ $ "
}
],
[
{
... | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Reading the Clock"
] | [
"The smaller angle is $\\frac 5{12}$ of a full circle. A full circle has $360$ degrees, so the angle is $\\frac 5{12}\\times 360^{}\\circ =150^{}\\circ $. So, the answer is $\\rm D$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1685 | 87aa3bb8e7d34e189e17dcdd165316c7 | [] | 1 | single_choice | If we throw two $6-$sided dice of the same shape and size, which statements among the following options is an impossible event? | [
[
{
"aoVal": "A",
"content": "The sum of dots is $$12$$. "
}
],
[
{
"aoVal": "B",
"content": "The product is a prime number. "
}
],
[
{
"aoVal": "C",
"content": "The sum of dots is larger than $$1$$ but smaller than $$3$$. "
}
],
[
{
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"So $$\\text{D}$$ is the answer. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1692 | 3a06acae6d3e47d6b367cc69d386d382 | [] | 0 | single_choice | The time twelve thousand and twelve hours after $$7$$ A.M. is． | [
[
{
"aoVal": "A",
"content": "$$1$$ A.M. "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ P.M. "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ A.M. "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ P.M. "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"Divide $$12012\\div24$$ to get remainder $$12$$. $$12$$ hours after $$7$$ A.M. is $$7$$ P.M. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1699 | 245bf38d9b6a4d2fb44c0db8201e5aa5 | [] | 1 | single_choice | There are $$18$$ boys in Pat\textquotesingle s math class. If there are twice as many girls as boys in the class, how many girls are there in the class? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ "
}
],
[
{
"aoVal": "C",
"content": "$$36$$ "
}
],
[
{
"aoVal": "D",
"content": "$$54$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"
] | [
"girls = $18\\times2=36$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1702 | 35a60dfffc8c4d21bb3ee59cee37d7e9 | [
"其它"
] | 1 | single_choice | Kevin has 3 regular dice. Each dice has numbers from 1 to 6. Which of the following could not be the sum of the numbers on top of the 3 dice? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13$$ "
}
],
[
{
"aoVal": "C",
"content": "$$17$$ "
}
],
[
{
"aoVal": "D",
"content": "$$22$$ "
}
],
[
{
"aoVal": "E",
"content": ... | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"
] | [
"maximum is 6+6+6 = 18. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1703 | 87b6269e455443ecac4605226e3c0771 | [] | 1 | single_choice | Veronica rolls three six-sided dice. The product of the three numbers is $$90$$. What is the sum of the three numbers? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$14$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$90$$ "
}
],
[
{
"aoVal": "E",
"content":... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"Given that the numbers on a die are $$1$$, $$2$$, $$3$$, $$4$$, $$5$$ and $$6$$, to achieve a product of $$90$$, one of the numbers must be $$5$$ and the other two must have a product of $$18$$. Thus the numbers can only be $$3$$, $$5$$ and $$6$$ , whose sum is $$14$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1706 | 3a1e941c19a746a98feed2461f1a0cd6 | [] | 1 | single_choice | Mike and Sara are looking for a place to eat lunch. They know there are nine Chinese restaurants, three Mexican restaurants, and two fast food restaurants nearby. How many different choices do they have in total to eat one meal? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$54$$ "
}
],
[
{
"aoVal": "C",
"content": "$$27$$ "
}
],
[
{
"aoVal": "D",
"content": "$$18$$ "
}
],
[
{
"aoVal": "E",
"content": ... | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"
] | [
"They can only choose one place, so it can only be Chinese, Mexican, or fast food. Therefore, we can add each one up to get $$9+3+2 = 14$$. ~ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1707 | 6c14b8de695c48ae90a0617802524347 | [
"其它"
] | 1 | single_choice | Mary had equal number of green, yellow and red tokens. She used some of those tokens to make a pile. You can see all used tokens in the figure. She still has five tokens which are not on the pile. How many yellow tokens did she have have at the beginning? insert pic | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
],
[
{
"aoVal": "E",
"content": "$... | [
"Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures->Counting Solid Figures"
] | [
"The used tokens are 5 red tokens at the bottom, 4 green tokens and 4 yellow tokens. Now we distribute the unused 5 tokens to the 3 colors such that each color has the same number of tokens. Firstly, we need 1 more green token and 1 more yellow token to make all colors equal in number of tokens. We are left with ... | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1708 | 4318c317eda64578a34f69e6355509d7 | [
"其它"
] | 2 | single_choice | Josip has 4 toys - a car, a doll, a ball and a ship. He wants to put them on a line on a shelf. The ship has to be next to the car and the doll has to be next to the car. In how many ways can he arrange them so all the conditions would be fulfilled? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "$$... | [
"Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"
] | [
"The car is in the middle of the ship and the doll. There are 2 ways to arrange the three toys, i.e. door-call-ship and ship-car-doll. The last toy, the ball, can be placed on either of the 2 ends. Therefore, there are 2 x 2 = 4 ways to arrange the toys. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1710 | c78c3c59ee61497bbda755ce2fd68dd3 | [
"其它"
] | 1 | single_choice | In a toy store, cars are available in 5 different colours: blue, white, yellow, black and red. A car has either 2 or 4 doors. How many different version of the car are available? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
],
[
{
"aoVal": "E",
"content": "... | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"
] | [
"5 * 2 = 10 "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1712 | 6c1720a33e2e4554bbd467c0594fb8d7 | [] | 3 | single_choice | A box contains $5$ red balls and $3$ white balls that are identical in all aspects except color. One ball is drawn at random from the box and then replaced. The box is then thoroughly shaken so that the balls are arranged at random again and a second ball is drawn randomly from the box. What is the probability of drawi... | [
[
{
"aoVal": "A",
"content": "$$\\frac{5}{8}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{3}{8}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{25}{64}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{9}{64}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"$$D$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1721 | b070c18da2bd43158736190bd4e7702e | [] | 1 | single_choice | There are $6$ stairs, and you can walk for one or three staris each time. There are~\uline{~~~~~~~~~~}~different ways to walk the $6$ stairs. | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$... | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"$$\\left( 1,1,1,1,1,1 \\right)$$；$$\\left( 3,1,1,1 \\right)$$；$$\\left( 1,3,1,1 \\right)$$；$$\\left( 1,1,3,1 \\right)$$；$$\\left( 1,1,1,3 \\right)$$；$$\\left( 3,3 \\right)$$． "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1722 | 31679dc093494643b6e794adbadac9dc | [] | 1 | single_choice | There are $$17$$ balls in a bag. Each ball has a number from $$1$$ to $$17$$ on it. We randomly pick a ball from the bag. What is the smallest number of balls we have to pick in order to be sure that we have at least one pair of balls with a sum equal to $$18$$? | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$11$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"Among these numbers, there are $$8$$ pairs of numbers can get the sum of $$18$$($$1+17=2+16=3+15=4+14=5+13=6+12=7+11=$$$$8+10$$), and $$9$$ is useless. So in the worst case, after we choose $$9$$, we need $$8+1=9$$ more numbers to make sure a pair appears. Thus, the answer is $$1+8+1=10$$. Copyrighted material u... | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1727 | 94bf0d44b07d4a5da9f148d4a28a50d5 | [
"其它"
] | 2 | single_choice | The faces of each of two fair dice are numbered $1$, $2$, $3$, $5$, $7$, and $8$. When the two dice are tossed, what is the probability that their sum will be an even number? (2019 AMC 8 Problems, Question \#18) | [
[
{
"aoVal": "A",
"content": "$\\dfrac{4}{9}$ "
}
],
[
{
"aoVal": "B",
"content": "$\\dfrac{1}{2}$ "
}
],
[
{
"aoVal": "C",
"content": "$\\dfrac{5}{9}$ "
}
],
[
{
"aoVal": "D",
"content": "$\\dfrac{3}{5}$ "
}
],
[
{
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"
] | [
"We have a 2 dice with 2 evens and 4 odds on both dice. For the sum to be even, the 2 rolls can be 2 odds or 2 evens. Ways to roll 2 odds (Case 1 ): The total number of ways to obtain 2 odds on 2 rolls is $4 * 4=16$, as there are 4 possible odds on the first roll and 4 possible odds on the second roll. Ways to ro... | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1728 | 433c38c0d5df4ef3aeea022889e4d797 | [] | 1 | single_choice | Three kids line up to play games. In how many different ways can they form the line? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Queuing Problems"
] | [
"There are $3\\times 2\\times 1=6$ different ways for three kids to line up. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1729 | 94c020c6757e4b91946b6f6f46d75188 | [] | 1 | single_choice | The numbers $$1$$, $$2$$, $$3$$, $$4$$, $$5$$, $$6$$, $$7$$, $$8$$, $$9$$, $$10$$, $$11$$, and $$12$$ are arranged in $3$ columns of $4$ numbers each so that the sum of the numbers in each column is the same. The sum of the numbers in each column is． | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$21$$ "
}
],
[
{
"aoVal": "C",
"content": "$$26$$ "
}
],
[
{
"aoVal": "D",
"content": "$$32$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Using Formulas"
] | [
"It\\textquotesingle s just like a magic square! The sum of all $$12$$ numbers is $$78$$. Hence, the answer is $$78\\div3 = 26$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1733 | 94c1c4d5f9814db0ab7ef45d30059df0 | [
"其它"
] | 1 | single_choice | Mother has $$12$$ identical peaches. She wants to place them into $$3$$ identical baskets. How many ways can she place the peaches if the number of peaches in each basket cannot be zero and must be different from one other? | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"
] | [
"Order does not matter as peaches and baskets are identical. But we need to have different number of peaches in each basket and none of the baskets can be empty. $$12=1+2+9$$ $$12=1+3+8$$ $$12=1+4+7$$ $$12=1+5+6$$ $$12=2+3+7$$ $$12=2+4+6$$ $$12=3+4+5$$ There are $$7$$ ways she can place the peaches. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1734 | 28f00d1d506146e1897a8e14e321820b | [
"其它"
] | 1 | single_choice | Fill in the blank:~\uline{~~~~~~~~~~}~is $2$ tens $8$ ones less than $5$ tens $5$ ones. | [
[
{
"aoVal": "A",
"content": "$$27$$ "
}
],
[
{
"aoVal": "B",
"content": "$$37$$ "
}
],
[
{
"aoVal": "C",
"content": "$$73$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content":... | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Law of Addition"
] | [
"$55 - 28 = 27$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1736 | 35f1b35f04b14e8c9f52a608da0d0982 | [
"其它"
] | 1 | single_choice | Una rolls 6 standard 6 -sided dice simultaneously and calculates the product of the 6 numbers obtained. What is the probability that the product is divisible by 4 ? | [
[
{
"aoVal": "A",
"content": "$\\frac{3}{4}$ "
}
],
[
{
"aoVal": "B",
"content": "$\\frac{57}{64}$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac{59}{64}$ "
}
],
[
{
"aoVal": "D",
"content": "$\\frac{187}{192}$ "
}
],
[
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"We will use complementary counting to find the probability that the product is not divisible by 4 . Then, we can find the probability that we want by subtracting this from 1 . We split this into 2 cases. Case 1: The product is not divisible by 2. We need every number to be odd, and since the chance we roll an odd ... | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1737 | 318d3edaa35e404cbab437bb3c94d092 | [
"其它"
] | 1 | single_choice | A data set consists of~~(not distinct) positive integers: 1,7,5,2,5 and x. The average (arithmetic mean) of the~~numbers equals a value in the data set. What is the sum of all positive values of x? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$26$$ "
}
],
[
{
"aoVal": "C",
"content": "$$32$$ "
}
],
[
{
"aoVal": "D",
"content": "$$36$$ "
}
],
[
{
"aoVal": "E",
"content":... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"$$10+22+4=36$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1739 | 2903d72e734d4f0e9e62c5a5d63d3bbc | [] | 1 | single_choice | If the average of two numbers is $$7$$, the numbers could be． | [
[
{
"aoVal": "A",
"content": "$$3$$ and $$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1$$ and $$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2$$ and $$14$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ and $$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"If the average of two numbers is $$7$$, their sum is $$2\\times7 = 14$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1742 | 2911b7803f38479387146347299c7015 | [
"其它"
] | 2 | single_choice | Five balls are arranged around a circle. Chris chooses two adjacent balls at random and interchanges them. Then Silva does the same, with her choice of adjacent balls to interchange being independent of Chris\textquotesingle s. What is the expected number of balls that occupy their original positions after these two su... | [
[
{
"aoVal": "A",
"content": "$$1.6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1.8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2.0$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2.2$$ "
}
],
[
{
"aoVal": "E",
"conte... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"After the first swap, we do casework on the next swap. Case 1: Silva swaps the two balls that were just swapped There is only one way for Silva to do this, and it leaves $5$ balls occupying their original position. Case 2: Silva swaps one ball that has just been swapped with one that hasn\\textquotesingle t swap... | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1745 | 70d7ac798f4f41389bd5c17998c880b4 | [] | 1 | single_choice | The average mass of $$2$$ bags of flour is $$1.72 \text{kg}$$. The mass of one of the bag of flour is $$1.68 \text{kg}$$. What is the mass of the other bag of flour? | [
[
{
"aoVal": "A",
"content": "$$1.76kg$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3.44kg$$ "
}
],
[
{
"aoVal": "C",
"content": "$$1.68kg$$ "
}
],
[
{
"aoVal": "D",
"content": "$$1.72kg$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"$$1.72\\times2=3.44$$ $$3.44 -1.68 = 1.76$$ The mass of the other bag of flour is $$1.76\\text{kg}$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1746 | 55688aaa8c5f420ea67ba8fc384dc356 | [
"其它"
] | 1 | single_choice | Two different numbers are randomly selected from the set $-5, -3, -1, 3, 5$~and multiplied together. What is the probability that the product is a negative number?~ | [
[
{
"aoVal": "A",
"content": "$\\frac{5}{6}$ "
}
],
[
{
"aoVal": "B",
"content": "$\\frac{2}{5}$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac{3}{4}$ "
}
],
[
{
"aoVal": "D",
"content": "$\\frac{1}{2}$ "
}
],
[
{
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"$\\frac25\\times\\frac34+\\frac35\\times\\frac24=\\frac{3}{5}$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1748 | 436055da612d46c0b1618ec271daea71 | [
"其它"
] | 1 | single_choice | Jack built a cube using 27 small cubes which are colored either black or white (see figure). No two of the small cubes which are colored in the same color have a common face. How many white cubes did Jack use? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ "
}
],
[
{
"aoVal": "C",
"content": "$$13$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14$$ "
}
],
[
{
"aoVal": "E",
"content":... | [
"Overseas Competition->Knowledge Point->Counting Modules->Counting the Number of Figures->Counting Solid Figures"
] | [
"14 grey cubes and 13 white cubes. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1750 | be5f463b40014193af975ac5d1bbdd12 | [] | 1 | single_choice | I donate a ＄$$100$$ bill, $$2$$＄$$50$$ bills, $$3$$＄$$20$$ bills, $$4$$＄$$10$$ bills, and $$5$$＄$$5$$ bills. If $$5$$ people divide my money equally, each person receives． | [
[
{
"aoVal": "A",
"content": "＄$$37$$ "
}
],
[
{
"aoVal": "B",
"content": "＄$$65$$ "
}
],
[
{
"aoVal": "C",
"content": "＄$$70$$ "
}
],
[
{
"aoVal": "D",
"content": "＄$$75$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"I donate a total of ＄$$100+2\\times $$＄$$50+3\\times $$＄$$20+4\\times $$＄$$10+5\\times $$＄$$5=$$＄$$325$$. Each person receives ＄$$325 \\div5 =$$＄$$65$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1751 | 67ac8ca30a5f4a5e8b15e0efc265972c | [
"其它"
] | 1 | single_choice | Find the number of two-digit positive integers whose digits total $7$. (2004 AMC 8 Problem, Question \#8) | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
],
[
{
"aoVal": "E",
"content": "$$... | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"The numbers are $16,25,34,43,52,61,70$ which gives us a total of $(\\text{B}) 7$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1752 | 9e09133b4ff0440291ebe9f67bbd206b | [
"其它"
] | 2 | single_choice | Rabbit Borya likes cabbages and carrots very much. In a day he eats either 9 carrots, or 2 cabbages, or 1 cabbage and 4 carrots. During one week Borya has eaten 30 carrots. How mnay cabbages has he eaten during this week? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
],
[
{
"aoVal": "E",
"content": "$$... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"Borya ate 30 carrots in a week, which is a number divisible by 3. On the days that he ate 9 carrots, the total number of carrots is also divisible by 3. Hence, the total number of carrots he ate on days that he ate 4 carrots must also be divisible by 3, meaning the number of days he ate 4 carrots is divisible by... | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1753 | 3612e2e1b770400ebd328622a8ff2c2e | [] | 2 | single_choice | What is the average (mean) of all $$5-$$digit numbers that can be formed by using each of the digits $$1$$, $$3$$, $$5$$, $$7$$, and $$8$$ exactly once? ($$2005$$ AMC $$10B$$ Problem, Question \#$$20$$) | [
[
{
"aoVal": "A",
"content": "$$48000$$ "
}
],
[
{
"aoVal": "B",
"content": "$$49999.5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$53332.8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$55555$$ "
}
],
[
{
"aoVal": "E",
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"Method $$1$$: We first look at how many times each number will appear in each slot. If we fix a number in a slot, then there are $$4!=24$$ ways to arrange the other numbers, so each number appears in each spot $$24$$ times. Therefore, the sum of all such numbers is $$24\\times (1+3+5+7+8)\\times (11111)=24\\times2... | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1755 | b9bd53e0d7154a31963c1d8e20dba6c4 | [
"其它"
] | 2 | single_choice | Timi has $8$ paintings: $3$ of them are drawing landscape, and $5$ of them are drawing figure. Among the $5$ figure paintings, there are $3$ drawing the whole family of Timi, and the other $2$ are drawing himself. Now, Timi wants to put those painting in a line. The $3$ landscape paintings cannot be adjacent. How many ... | [
[
{
"aoVal": "A",
"content": "$$288$$ "
}
],
[
{
"aoVal": "B",
"content": "$$72$$ "
}
],
[
{
"aoVal": "C",
"content": "$$144$$ "
}
],
[
{
"aoVal": "D",
"content": "$$96$$ "
}
],
[
{
"aoVal": "E",
"content... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"
] | [
"$\\_2P\\_2\\times \\_3P\\_3 \\times \\_2P\\_2 \\times \\_3P\\_3=144$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1756 | 59fbc19381244b308666096671fabb30 | [
"其它"
] | 1 | single_choice | How many digits are there from $8$ to $78$? | [
[
{
"aoVal": "A",
"content": "$$70$$ "
}
],
[
{
"aoVal": "B",
"content": "$$71$$ "
}
],
[
{
"aoVal": "C",
"content": "$$138$$ "
}
],
[
{
"aoVal": "D",
"content": "$$140$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"$8$ to $9 = 2$ digits $10$ to $78: 78 - 10 + 1 = 69$ numbers, $69 \\times 2 = 138$ digits $138 + 2 = 140$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1760 | b5250d41a03e44538b083c7bc79626ae | [] | 1 | single_choice | There are $$124$$ teams participating in a volleyball match held in the Boston. Using the single elimination method, how many games will be played in total? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$62$$ "
}
],
[
{
"aoVal": "C",
"content": "$$124$$ "
}
],
[
{
"aoVal": "D",
"content": "$$248$$ "
}
],
[
{
"aoVal": "E",
"content"... | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Sports Competition"
] | [
"Single elimination tournament: $$124-1=123$$ games "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1761 | 2525995aace248febca9bbcf8181eed7 | [
"其它"
] | 1 | single_choice | SASMO 2016 P2 Q6 Uncle John has a farm. His wife and his two sons are staying with him in the farm. They raise 10 cows and 20 chickens. How many total legs are there in the farm? | [
[
{
"aoVal": "A",
"content": "$$60$$ "
}
],
[
{
"aoVal": "B",
"content": "$$80$$ "
}
],
[
{
"aoVal": "C",
"content": "$$86$$ "
}
],
[
{
"aoVal": "D",
"content": "$$88$$ "
}
],
[
{
"aoVal": "E",
"content":... | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"
] | [
"10 x 4 + 20 x 2 + 2 + 2 + 4 = 88. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1762 | 70e6cf4eaab940eab0ae38b0668ca08d | [] | 1 | single_choice | Abby, Bret, Carl, and Dana are seated in a row of four seats numbered $$1$$ to $$4$$. Joe looks at them and says: ``Bret is next to Carl." "Abby is between Bret and Carl." However, all of Joe\textquotesingle s statements are false. Bret is actually sitting in seat $$3$$. Who is sitting in seat $$2$$? | [
[
{
"aoVal": "A",
"content": "Abby "
}
],
[
{
"aoVal": "B",
"content": "Bret "
}
],
[
{
"aoVal": "C",
"content": "Carl "
}
],
[
{
"aoVal": "D",
"content": "Dana "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing"
] | [
"We know that Carl does not sit next to Bret, so he must sit in seat $$1$$. Since Abby is not between Bret and Carl, she must sit in seat $$4$$. Finally, Dana has to take the last seat available, which is $$2$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1763 | 43798c9abe88493c9e310873429ea390 | [
"其它"
] | 1 | single_choice | Determine how many two-digit numbers satisfy the following property: when the number is added to the number obtained by reversing its digits, the sum is $132$ . (2016 AMC 8 Problem, Question \#11) | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$11$$ "
}
],
[
{
"aoVal": "E",
"content": "$... | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"We can write the two digit number in the form of $10 a+b$; reverse of $10 a+b$ is $10 b+a$. The sum of those numbers is: $$ \\begin{gathered} (10 a+b)+(10 b+a)=132 \\textbackslash\\textbackslash{} 11 a+11 b=132 \\textbackslash\\textbackslash{} a+b=12 \\end{gathered} $$ We can use brute force to find order pairs $(... | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1765 | 8b9bd294693f4de888ec98e0ad2fed12 | [] | 1 | single_choice | Ms. Osborne asks each student in her class to draw a rectangle with integral side lengths and a perimeter of $$50$$ units. All of her students calculate the area of the rectangle they draw. What is the difference between the largest and smallest possible areas of the rectangles? | [
[
{
"aoVal": "A",
"content": "$$76$$ "
}
],
[
{
"aoVal": "B",
"content": "$$120$$ "
}
],
[
{
"aoVal": "C",
"content": "$$128$$ "
}
],
[
{
"aoVal": "D",
"content": "$$132$$ "
}
],
[
{
"aoVal": "E",
"conten... | [
"Overseas Competition->Knowledge Point->Geometry Modules->Objects with Straight Sides->Knowing Graphs"
] | [
"As we know, the sum of the length and width is $$25$$. The largest area is $$13\\times12=156$$ and the smallest area is $$24\\times1=24$$, so the difference is $$156-24=132$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1767 | 2d891671aff94c0ba31d6d85250c68c4 | [] | 2 | single_choice | A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won $$4$$ games, Ines won $$3$$ games, Janet won $$2$$ games, Kendra won $$2$$ games and Lara won $2$ games, how many games did Monica (the sixth player) win? ($$2006 \text{ AMC } 8$$ Problem, Question \#$$20$$... | [
[
{
"aoVal": "A",
"content": "$$0$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2$$ "
}
],
[
{
"aoVal": "D",
"content": "$$3$$ "
}
],
[
{
"aoVal": "E",
"content": "$$... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"There are $$6$$ players, so there are $$6\\times5\\div2=15$$ games in total. By now, $$4+3+2+2+2=13$$ games have been finished (there is one winner in each game), so Monica needs to win $$15-13=2$$ games. Therefore, the answer is $$\\rm C$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1768 | 2d8bf1c480d74fa19cf9b15144874312 | [] | 1 | single_choice | Each of $$300$$ students belongs to exactly $$2$$ of the $$5$$ school clubs. What is the average number of students in each club? | [
[
{
"aoVal": "A",
"content": "$$50$$ "
}
],
[
{
"aoVal": "B",
"content": "$$60$$ "
}
],
[
{
"aoVal": "C",
"content": "$$120$$ "
}
],
[
{
"aoVal": "D",
"content": "$$150$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] | [
"Since $$300$$ students belong to $$2$$ clubs each, there are $$600$$ club memberships. The average membership of the $$5$$ clubs is $$600\\div 5 = 120$$ students. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1770 | e36587c6c7b040799bc2e3c5fc7c5d12 | [
"其它"
] | 1 | single_choice | How many terms are there in the arithmetic sequence~$2,\textbackslash{} 5,\textbackslash{} 8,\textbackslash{} 11,\textbackslash{} 14\cdots \textbackslash{} 95,\textbackslash{} 98$$?$terms. | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$31$$ "
}
],
[
{
"aoVal": "C",
"content": "$$32$$ "
}
],
[
{
"aoVal": "D",
"content": "$$33$$ "
}
],
[
{
"aoVal": "E",
"content":... | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"$(98-2)\\div3+1=33$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1771 | abf1b845320044be82c69848e0b93524 | [] | 1 | single_choice | Three friends, Ms Raja, Ms Omar and Ms Beatty all live in the same street. They are a doctor, an engineer and a musician in some order. The youngest one, the doctor, does not have a brother. Ms Beatty is older than the engineer and is married to Ms Omar\textquotesingle s brother. What are the names, in order, of the do... | [
[
{
"aoVal": "A",
"content": "Raja and Omar "
}
],
[
{
"aoVal": "B",
"content": "Omar and Beatty "
}
],
[
{
"aoVal": "C",
"content": "Beatty and Omar "
}
],
[
{
"aoVal": "D",
"content": "Raja and Beatty "
}
],
[
{
... | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning->Reasoning by Comparing"
] | [
"The doctor is the youngest and does not have a brother. Since Ms Omar has a brother and Ms Beatty is older than the engineer, the doctor is Ms Raja. Also, since Ms Beatty is older than the engineer she cannot be the engineer. Hence the engineer is Ms Omar. Therefore the doctor and the engineer in order are Raja an... | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1773 | 903ded1863604801aeb335109b598651 | [
"其它"
] | 1 | single_choice | There were $20$ ducks, pigs, and sheep in total in Sam\textquotesingle s farm. After Sam bought some new sheep, the number of sheep has doubled. There are $27$ ducks, pigs, and sheep in total. Originally, how many ducks and pigs were there? | [
[
{
"aoVal": "A",
"content": "$$13$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14$$ "
}
],
[
{
"aoVal": "E",
"content": ... | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"$27-20=7$ $7+7=14$ $27-14=13$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1775 | ecaa01c33c7a4e54a9c62bbaeca39a71 | [
"其它"
] | 1 | single_choice | A fair $6$-sided die is rolled twice. What is the probability that the first number that comes up is greater than or equal to the second number? | [
[
{
"aoVal": "A",
"content": "$\\dfrac{1}{6}$ "
}
],
[
{
"aoVal": "B",
"content": "$\\dfrac{5}{12}$ "
}
],
[
{
"aoVal": "C",
"content": "$\\dfrac{1}{2}$ "
}
],
[
{
"aoVal": "D",
"content": "$\\dfrac{7}{12}$ "
}
],
[
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability->Questions Involving Probability->Basic Concepts of Probability"
] | [
"There are $6\\cdot 6=36$ ways to roll the two dice, and $6$ of them result in two of the same number. Out of the remaining $36-6=30$ ways, the number of rolls where the first dice is greater than the second should be the same as the number of rolls where the second dice is greater than the first. In other words, t... | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1777 | 9e19e5df8abc4b57ba8d85a90910de5c | [] | 1 | single_choice | What is the angle between the hour hand and the minute hand at seven o\textquotesingle clock?． | [
[
{
"aoVal": "A",
"content": "$50^{}\\circ $ "
}
],
[
{
"aoVal": "B",
"content": "$120^{}\\circ $ "
}
],
[
{
"aoVal": "C",
"content": "$135^{}\\circ $ "
}
],
[
{
"aoVal": "D",
"content": "$150^{}\\circ $ "
}
],
[
{
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"The smaller angle is $\\frac 5{12}$ of a full circle. A full circle has $360$ degrees, so the angle is $\\frac 5{12}\\times 360^{}\\circ =150^{}\\circ $. So, the answer is $\\rm D$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1778 | 5a182ddaf3584def8a28471480816fb3 | [] | 1 | single_choice | How many whole numbers between $$5000$$ and $$6000$$ consist of four different digits that decrease from left to right? | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$69$$ "
}
],
[
{
"aoVal": "D",
"content": "$$120$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"The only such numbers are $$5432$$, $$5431$$, $$5430$$, $$5421$$, $$5420$$, $$5410$$, $$5321$$, $$5320$$, $$5310$$, and $$5210$$. In all, there are $$10$$ such numbers. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1779 | 5ea921c71b6843c9926a5855741695a3 | [
"其它"
] | 2 | single_choice | Frieda the frog begins a sequence of hops on a $3 \times 3$ grid of squares, moving one square on each hop and choosing at random the direction of each hop-up, down, left, or right. She does not hop diagonally. When the direction of a hop would take Frieda off the grid, she "wraps around" and jumps to the opposite edge... | [
[
{
"aoVal": "A",
"content": "$\\frac{9}{16}$ "
}
],
[
{
"aoVal": "B",
"content": "$\\frac{5}{8}$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac{3}{4}$ "
}
],
[
{
"aoVal": "D",
"content": "$\\frac{25}{32}$ "
}
],
[
{
... | [
"Overseas Competition->Knowledge Point->Counting Modules"
] | [
"We will use complementary counting. First, the frog can go left with probability $\\frac{1}{4}$. We observe symmetry, so our final answer will be multiplied by 4 for the 4 directions, and since $4 \\cdot \\frac{1}{4}=1$, we will ignore the leading probability. From the left, she either goes left to another edge $\... | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1784 | 559db01df85746308c15885b6063e3c3 | [] | 1 | single_choice | Sam\textquotesingle s exam was meant to begin at $$13:45$$ but started $$17$$ minutes late. At what time did it begin? | [
[
{
"aoVal": "A",
"content": "$$13:38$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13:56$$ "
}
],
[
{
"aoVal": "C",
"content": "$$14:02$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14:06$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"Seventeen minutes after $$13:45$$ is $$14:02$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1785 | e80d5adfd7834fe0831120d9364615c2 | [
"其它"
] | 1 | single_choice | SASMO 2014 P2 Q6 A shop sells sweets where every 3 sweet wrappers can be excanged for one more sweet. Ali has enough money to buy only 7 sweets. What is the biggest number of sweets that he can get from the shop? | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
],
[
{
"aoVal": "E",
"content": "$... | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"
] | [
"7 = 3 + 3 + 1 + (1) + (1) + (1) = 10 "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1786 | 3f2debe2bbf84634999aabf6179615de | [] | 1 | single_choice | One day, Pip asks his parents: "What day is it today?" His mother says: "Today is Monday." His father says: "Today is Tuesday." Which of the following is true? | [
[
{
"aoVal": "A",
"content": "One of these two sentences is definitely wrong and the other one is correct. "
}
],
[
{
"aoVal": "B",
"content": "It is possible that both of Pip\\textquotesingle s parents are wrong. "
}
],
[
{
"aoVal": "C",
"content": "I... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"\"Today is Monday\" is not the opposite of \"Today is Tuesday\".i.e. they can both be false. \"Today is Monday\" is the direct opposite of \"Today is not Monday\". One must be true and the other must be false. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1787 | 904d2efadea04dafbbf833c3346904a9 | [] | 1 | single_choice | Five students are lining up to take a picture. If Jessica is standing in the middle, and Ian is standing on either end, how many ways can the students line up? ． | [
[
{
"aoVal": "A",
"content": "$6$ "
}
],
[
{
"aoVal": "B",
"content": "$8$ "
}
],
[
{
"aoVal": "C",
"content": "$10$ "
}
],
[
{
"aoVal": "D",
"content": "$12$ "
}
],
[
{
"aoVal": "E",
"content": "$14$ "
... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"$$2\\times3\\times2\\times1=12$$ ways. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1788 | 3211a6e1de4f43da89d9b02db1e1983a | [] | 1 | single_choice | A sergeant stands too long in the sun and gets confused. His troops are lined up facing north. Then he gives the order to "Right Turn $90^{}\circ$" $$70$$ times, and his troops do so. In which direction are the troops facing at the end? | [
[
{
"aoVal": "A",
"content": "$$$$north "
}
],
[
{
"aoVal": "B",
"content": "$$$$east "
}
],
[
{
"aoVal": "C",
"content": "$$$$south "
}
],
[
{
"aoVal": "D",
"content": "$$$$west "
}
],
[
{
"aoVal": "E",
... | [
"Overseas Competition->Knowledge Point->Combinatorics->Directions and Coordinates->Directions"
] | [
"After every $$4$$ \"Right turns\" the troops will be facing north again; so after $$68$$ turns they are facing north, after $$69$$ turns east, and after $$70$$ turns south. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1791 | 6c6d443982e749b6b231f6357043c04a | [
"其它"
] | 2 | single_choice | Hansel wants to buy 2 dice of different colours. If the available colours in a store are red, blue, green, yellow, pink and white, how many different combinations of 2 dice are there in the store? (Example: 1 combination is yellow and white) | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$15$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": ... | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] | [
"RB, RG, RY, RP, RW BG, BY, BP, BW GY, GP, GW, YP, YW, PW "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1792 | e36f6864cf5b45538f5271f3ee2ae513 | [
"其它"
] | 2 | single_choice | There is a cuboid with a dimension of $3\times4\times5$. Now paint all the surfaces red and cut it into many $1\times1\times1$ cubes. How many cubes that have two faces painted red are there? | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$11$$ "
}
],
[
{
"aoVal": "E",
"content": "... | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Coloring Problems"
] | [
"Remove the two cubes in both ends, and then we can get: $[(3-2)+(4-2)+(5-2)]\\times4=24$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 1796 | 29add6104d624851b8f8dc4e36b4b25a | [] | 1 | single_choice | Sophia's average score on six tests is $$82$$. Her average scores on the $$7^{}\text{th}$$ and $$8^{}\text{th}$$ tests is $$98$$. What is her average score on all eight tests? ． | [
[
{
"aoVal": "A",
"content": "$$86$$ "
}
],
[
{
"aoVal": "B",
"content": "$$88$$ "
}
],
[
{
"aoVal": "C",
"content": "$$90$$ "
}
],
[
{
"aoVal": "D",
"content": "$$94$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)"
] | [
"Sophia\\textquotesingle s total score on the first six tests is $$6\\times82=492$$. Her total score on all eight tests is $$492+2\\times98=688$$, and her average score is $$688\\div8=86$$. "
] | A |
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