dataset_name
stringclasses 4
values | dataset_version
timestamp[s] | qid
stringlengths 1
5
| queId
stringlengths 32
32
| competition_source_list
sequence | difficulty
stringclasses 5
values | qtype
stringclasses 1
value | problem
stringlengths 6
1.51k
| answer_option_list
list | knowledge_point_routes
sequence | answer_analysis
sequence | answer_value
stringclasses 7
values |
|---|---|---|---|---|---|---|---|---|---|---|---|
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7783 | ffe5dfecf5fa4c55a1dc51dcb5a20b4b | [
"其它"
] | 0 | single_choice | A school has three classes in the morning, and there is a $$15$$-minutes break between each two classes. Each class is of the same length. The first class starts at $$9:45 $$, and the third class ends at $$12:00 $$. How long is each class? | [
[
{
"aoVal": "A",
"content": "$$25$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$35$$ "
}
],
[
{
"aoVal": "D",
"content": "$$40$$ "
}
],
[
{
"aoVal": "E",
"content": "$$45$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"From $$9:45$$ to $$12:00$$ = $$2$$ h $$15$$m = $$135$$ min, two $$15$$-minute parts = $$30$$ min, and $$135 - 30 = 105$$ min. $$105\\div3=35$$min "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7791 | 982bfbf3b11d4e64b9aea0ddc80d49f2 | [
"其它"
] | 1 | single_choice | The weights of four boys are 45kg, 48kg, 52kg and 53kg. Mason\textquotesingle s weight is an even number. Joshua\textquotesingle s weight is a multiple of 5. Christopher is not the heaviest and Mateo is not the lightest. Who is the heaviest among the four boys? | [
[
{
"aoVal": "A",
"content": "Mason "
}
],
[
{
"aoVal": "B",
"content": "Joshua "
}
],
[
{
"aoVal": "C",
"content": "Christopher "
}
],
[
{
"aoVal": "D",
"content": "Mateo "
}
],
[
{
"aoVal": "E",
"content": "Impossible to determine "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"Mason\\textquotesingle s weight is an even number = 48kg / 52kg. Joshua\\textquotesingle s weight is a multiple of 5 = 45kg. Christopher is not the heaviest = x 53kg. Mateo is not the lightest = x 45kg Jason - \\textgreater{} either Mason or Christpoher is 28/52kg -\\textgreater{} Mateo. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7793 | 9ca7cf140328497b98122848bf76a11e | [
"其它"
] | 2 | single_choice | From $1$ to $45$, how many numbers must be chosen at least to ensure that there are two of chosen numbers sum to $30$? | [
[
{
"aoVal": "A",
"content": "$$25$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$31$$ "
}
],
[
{
"aoVal": "D",
"content": "$$32$$ "
}
],
[
{
"aoVal": "E",
"content": "$$22$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Constructing and Proving"
] | [
"$$16+1+14+1=32$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7796 | e517a849e66442fea50288d5d850b461 | [
"其它"
] | 1 | single_choice | Teacher James distributes $82$ apples to $12$ students. At least how many apples can the student with the most apples get? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
],
[
{
"aoVal": "E",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle"
] | [
"$82\\div12=6R10$, $6+1=7$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7803 | aebca65fe557477eac922bcb94429f7a | [
"其它"
] | 1 | single_choice | $A$ and $B$ play a game as follows. First $A$ says $1, 2$ or $3$. Then $B$ can add $1, 2$ or $3$ to the number the first player said. The game continues with the players playing alternately, in each turn adding $1, 2$ or $3$ to the previous number. For example, A can say $2$, then B can say $5$, then A could say $6$, and so on. The player who says $100$ wins. Who has the winning strategy? | [
[
{
"aoVal": "A",
"content": "A "
}
],
[
{
"aoVal": "B",
"content": "B "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations"
] | [
"Observe that B can always say a multiple of 4 in his turn. For example, consider the following sequence of moves: A-1; B-4; A-6; B-8 and so on. Regardless of what A says, B can always say a multiple of 4. Hence B will say 100 and will win "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7813 | dc1416d88f1643fca435b690b39ad738 | [
"其它"
] | 1 | single_choice | SASMO 2016 P2 Q7 It takes 5 mintues to boil an egg. What is the least amount of time it takes to boil 3 eggs? | [
[
{
"aoVal": "A",
"content": "$$8$$minutes "
}
],
[
{
"aoVal": "B",
"content": "$$12$$minutes "
}
],
[
{
"aoVal": "C",
"content": "$$15$$minutes "
}
],
[
{
"aoVal": "D",
"content": "$$18$$minutes "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"5 minutes, boil together. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7817 | dc1c33e698aa483792fa273b1c66f0ea | [] | 1 | single_choice | There are $9$ water glasses, all facing up. You need to turn exactly $2$ glasses over in each time. Is it possible to turn all $9$ of them upside down after several moves? | [
[
{
"aoVal": "A",
"content": "Yes, it is possible. "
}
],
[
{
"aoVal": "B",
"content": "No, it is impossible. "
}
],
[
{
"aoVal": "C",
"content": "I have no idea. "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Turning Mugs over"
] | [
"You have to flip a cup an odd number of times to turn it over. To make all the $9$ cups face down, you have to make an odd number of flips. Each time you flip exactly $2$ cups, the total number of flips is an even number of times. Hence it is impossible. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7819 | e53cd3db96b54eb1b9a196eca73619ee | [
"其它"
] | 1 | single_choice | David went to watch $Spider Man$ at the cinema on June $25$\textsuperscript{th}. The movie started at $6 : 32$ P.M. and finished at $7 : 54$ P.M.. On the same day, Mary needed to go abroad by plane. The plane took off at $11 : 40$ P.M., and the time she spent on plane was $2$ hours and $11$ minutes longer than that David spent at the cinema. When would Mary get off the plane? | [
[
{
"aoVal": "A",
"content": "$3 : 23$ P.M. on June $25$\\textsuperscript{th} "
}
],
[
{
"aoVal": "B",
"content": "$3 : 13$ A.M. on June $25$\\textsuperscript{th} "
}
],
[
{
"aoVal": "C",
"content": "$3 : 13$ P.M. on June $26$\\textsuperscript{th} "
}
],
[
{
"aoVal": "D",
"content": "$3 : 13$ A.M. on June $26$\\textsuperscript{th} "
}
],
[
{
"aoVal": "E",
"content": "$3 : 23$ A.M. on June $26$\\textsuperscript{th} "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"From $6 : 32$ P.M. to $7 : 54$ P.M., it lasted $1$ hour and $22$ minutes. The time Mary spent on plane: $1$ hour and $22$ minutes $+$ $2$ hours and $11$ minutes $=$ $3$ hours and $33$ minutes. Thus, Mary would get off the plane at $3 : 13$ A.M. on June 26\\textsuperscript{th}. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7824 | d311b61d546a40b780d83ca5753e68d4 | [
"其它"
] | 1 | single_choice | Cindy and Chloe are siblings. Each of them have $$2$$ brothers and $$2$$ sister in. How many children are there in the family? | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"Cindy is sister to Chloe and Chloe is sister to Cindy. Thus, they have one more common sister. There are a total of $$3$$ girls in the family. Their brother are the same, thus $$2$$ boys in the family. In total $$5$$ children. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7826 | aef6ddcbe2464c3681fafc4a14abf013 | [
"其它"
] | 1 | single_choice | Jacky wants to insert the digit 3 somehwere in the number 2014. Where should she insert digit 3 if she wants her five digit number to be as small as possible? | [
[
{
"aoVal": "A",
"content": "in front of 2014 "
}
],
[
{
"aoVal": "B",
"content": "between the 2 and the 0 "
}
],
[
{
"aoVal": "C",
"content": "between the 0 and the 1 "
}
],
[
{
"aoVal": "D",
"content": "between the 1 and the 4 "
}
],
[
{
"aoVal": "E",
"content": "behind 2014. "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Forming a Maximum/Minimum Multi-Digit Numbers with Fixed Sums"
] | [
"3 is a digit between 1 and 4. Try to put into and see which number is the smallest. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7828 | c577f21c39b6449c9c83f3cf13fe61d1 | [
"其它"
] | 0 | single_choice | Jack, Rebecca, Dustin and Steve write down one number, respectively, which are $44$, $85$, $72$ and $39$.Both Jack\textquotesingle s and Dustin\textquotesingle s numbers are odd. Both Jack\textquotesingle s and Steve\textquotesingle s numbers are more than $60$. What number is written by Rebecca? | [
[
{
"aoVal": "A",
"content": "$$44$$ "
}
],
[
{
"aoVal": "B",
"content": "$$85$$ "
}
],
[
{
"aoVal": "C",
"content": "$$72$$ "
}
],
[
{
"aoVal": "D",
"content": "$$39$$ "
}
],
[
{
"aoVal": "E",
"content": "Impossible to determine "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"Eliminate odd numbers and numbers more than $60$, so the only number left is $44$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7830 | b7f588e52ccd4fd985b6d78e3df0841e | [] | 1 | single_choice | In class, Anna, Bell, and Julie are doing math homework at school. Among them, Anna took $$18$$ minutes and $$25$$ seconds. Bell took $$19$$ minutes and $$36$$ seconds, and Julie took $$20$$ minutes and $$15$$ seconds. How long did the three take in total? (adapted from 2008 Math Kangaroo Problem, Level 3 - 4, Question \#15) | [
[
{
"aoVal": "A",
"content": "$$57$$ minutes $$16$$ seconds "
}
],
[
{
"aoVal": "B",
"content": "$$58$$ minutes $$16$$ seconds "
}
],
[
{
"aoVal": "C",
"content": "$$58$$ minutes $$26$$ seconds "
}
],
[
{
"aoVal": "D",
"content": "$$58$$ minutes $$6$$ seconds "
}
],
[
{
"aoVal": "E",
"content": "$$57$$ minutes $$26$$ seconds "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$18$ minutes + $19$ minutes + $20$ minutes + $25$ seconds $+$ $36$ seconds + $15$ seconds = $57$ minutes $76$ seconds = $58$ minutes $16$ seconds "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7831 | 9d1da5d5bdf24b01ae0600d065e7fbe1 | [] | 1 | single_choice | The time in Thornsburg is $$6$$ hours ahead of London. The time in London is $$8.27$$ pm. What is the time in Thornsburg? Choose the answer. | [
[
{
"aoVal": "A",
"content": "$$02.27$$ pm "
}
],
[
{
"aoVal": "B",
"content": "$$14.27$$ pm "
}
],
[
{
"aoVal": "C",
"content": "$$02.27$$ pm "
}
],
[
{
"aoVal": "D",
"content": "$$02.27$$ am "
}
],
[
{
"aoVal": "E",
"content": "$$14.27$$ am "
}
]
] | [
"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 | 7833 | c58278d1722a49f582032d973b65db1b | [
"其它"
] | 1 | single_choice | Suppose $a, b$, and $c$ are nonzero real numbers, and $a+b+c=0$. What are the possible value(s) for $\frac{a}{\textbar a\textbar}+\frac{b}{\textbar b\textbar}+\frac{c}{\textbar c\textbar}+\frac{a b c}{\textbar a b c\textbar} ?$ (2017 AMC 8 Problem, Question \#21) | [
[
{
"aoVal": "A",
"content": "$$0$$ "
}
],
[
{
"aoVal": "B",
"content": "$1$ and $-1$ "
}
],
[
{
"aoVal": "C",
"content": "$2$ and $-2$ "
}
],
[
{
"aoVal": "D",
"content": "$0,2$ and $-2$ "
}
],
[
{
"aoVal": "E",
"content": "$0,1$ and $-1$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Mathematical Thoughts->Absolute Value"
] | [
"There are 2 cases to consider: \\textbf{Case 1:} 2 of $a, b$, and $c$ are positive and the other is negative. WLOG, we can assume that $a$ and $b$ are positive and $c$ is negative. In this case, we have that $$ \\frac{a}{\\textbar a\\textbar}+\\frac{b}{\\textbar b\\textbar}+\\frac{c}{\\textbar c\\textbar}+\\frac{a b c}{\\textbar a b c\\textbar}=1+1-1-1=0 \\text {. } $$ \\textbf{Case 2}: 2 of $a, b$, and $c$ are negative and the other is positive. Without loss of generality, we can assume that $a$ and $b$ are negative and $c$ is positive. In this case, we have that $$ \\frac{a}{\\textbar a\\textbar}+\\frac{b}{\\textbar b\\textbar}+\\frac{c}{\\textbar c\\textbar}+\\frac{a b c}{\\textbar a b c\\textbar}=-1-1+1+1=0 \\text {. } $$ Note these are the only valid cases, for neither 3 negatives nor 3 positives would work, as they cannot sum up to 0 . In both cases, we get that the given expression equals $(\\mathbf{A}) 0$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7846 | a1b82e06aaae4bd794bea2357cfb6047 | [
"其它"
] | 1 | single_choice | The numbers $$2$$, $$4$$, $$6$$, $$8$$, $$9$$ and $$11$$ are divided into groups of one or more numbers. The sum of the numbers in each group is the same. Which number must be in the group with the number $$11$$? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
],
[
{
"aoVal": "E",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value with Fixed Sums"
] | [
"$2+4+6+8+9+11=40$ $2$ groups: sum of each group is $20$, $20=9+11=2+4+6+8$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7851 | d33adfc876df4f4b93bfbc5358322a96 | [] | 1 | single_choice | Joy writes a four-digit number on a piece of paper and let Sandy guess. $\textasciitilde$ Sandy asks: "Is it $$6031$$?" Joy says: "You guess $1$ digit correct and it\textquotesingle s in the correct place." Sandy asks: "Is it $$5672$$?" Joy says: "You guess $2$ digits correct and they\textquotesingle re in the wrong places." Sandy asks: "Is it $$4796$$?" Joy says: "You guess $4$ digits correct and they\textquotesingle re in the wrong places." $\textasciitilde$ According to the conversation above, what number does Joy write? | [
[
{
"aoVal": "A",
"content": "$$4967$$ "
}
],
[
{
"aoVal": "B",
"content": "$$9764$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9647$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6497$$ "
}
],
[
{
"aoVal": "E",
"content": "$$6947$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"The number is formed by $4,7,9,6$ according to last question. Thus, according to the first question, $6$ should be in the thousands place. From the second and last question, $7$ is in ones place, $4$ is in tens place, and $9$ is in hundreds place. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7864 | eea5f58127d04072a1e0f8dcad0c8ecb | [
"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 | 7867 | d36ea5f7c22442c58ab13b4e2ee01e6c | [] | 1 | single_choice | Let\textquotesingle s convert! $$1$$ hour $$45$$ minutes $$=$$~\uline{~~~~~~~~~~}~minutes | [
[
{
"aoVal": "A",
"content": "$$145$$ "
}
],
[
{
"aoVal": "B",
"content": "$$105$$ "
}
],
[
{
"aoVal": "C",
"content": "$$95$$ "
}
],
[
{
"aoVal": "D",
"content": "$$75$$ "
}
],
[
{
"aoVal": "E",
"content": "$$65$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"$60+45=105$ minutes. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7889 | cf4243d0f1cb4474bc033bc8118047c8 | [
"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 x~24~ "
}
],
[
{
"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，$$1$$ 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 | 7891 | ef11f5ae9d5f4934aedaabeb5d05d0a8 | [
"其它"
] | 1 | single_choice | For any two numbers $$x$$ and $$y$$, the special operation $$^{}\otimes$$ is defined as follow $$x^{}\otimes y=x+y-\frac {2012}{335}$$. Calculate $$\frac {2^{}\otimes 4^{}\otimes 6^{}\otimes \cdots ^{}\otimes 2010^{}\otimes 2012}{2012}$$. | [
[
{
"aoVal": "A",
"content": "$$1006$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1005$$ "
}
],
[
{
"aoVal": "C",
"content": "$$503$$ "
}
],
[
{
"aoVal": "D",
"content": "$$502$$ "
}
],
[
{
"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 | 7896 | d3dc8a20dc884659a4f2b2c1645c42ba | [] | 1 | single_choice | A train started from the starting station at 7:30, it takes 8 hours and 37 minutes to arrive at the terminal station. When will it arrive? | [
[
{
"aoVal": "A",
"content": "$$3:30$$ A.M. "
}
],
[
{
"aoVal": "B",
"content": "$$3:37$$ P.M. "
}
],
[
{
"aoVal": "C",
"content": "$$4:37$$ P.M. "
}
],
[
{
"aoVal": "D",
"content": "$$4:07$$ P.M. "
}
],
[
{
"aoVal": "E",
"content": "$$4:37$$ A.M. "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"$$7:30$$+$$8$$h$$37$$m=$$16:07$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7912 | ef3edca139b24b908536f5ce722676ce | [
"其它"
] | 1 | single_choice | The weights of four boys are $45\rm{kg}$, $48\rm{kg}$, $52\rm{kg}$ and $53\rm{kg}$. Mason\textquotesingle s weight is an even number. Joshua\textquotesingle s weight is a multiple of $5$. Christopher is not the heaviest and Mateo is not the lightest. Who is the heaviest among the four boys? | [
[
{
"aoVal": "A",
"content": "Mason "
}
],
[
{
"aoVal": "B",
"content": "Joshua "
}
],
[
{
"aoVal": "C",
"content": "Christopher "
}
],
[
{
"aoVal": "D",
"content": "Mateo "
}
],
[
{
"aoVal": "E",
"content": "Impossible to determine "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Logical Reasoning"
] | [
"Mason\\textquotesingle s weight is an even number = 48kg / 52kg. Joshua\\textquotesingle s weight is a multiple of 5 = 45kg. Christopher is not the heaviest = x 53kg. Mateo is not the lightest = x 45kg Jason - \\textgreater{} either Mason or Christpoher is 28/52kg -\\textgreater{} Mateo. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7923 | c6918d40841c418fabc414dbdb8fa0c8 | [
"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? (2010 Math Kangaroo Problem, Level 1--2, Question \#12) | [
[
{
"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 | 7927 | eaee82725b3447859c92e1e3077451c1 | [
"其它"
] | 1 | single_choice | Peter can draw a cartoon in $30$ minutes. How many hours does it take to paint four cartoons?~(adapted from 2011 Math kangaroo Problems, Level 1-2, Question \#4) | [
[
{
"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->Time Problem->Time Calculation"
] | [
"There are $60$ minutes in an hour. It will take $120$ minutes to draw $4$ cartoons.~ $120$ minutes=$2$ hours. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7928 | c6ac83fc0e1f43aa88b2e376d15fde98 | [] | 1 | single_choice | Bob and Linda went mountain climbing together. They climbed the mountain from $8$:$30$. Bob reached the top at $14$:$00$, and Linda was $1$ hour and $40$ minutes behind him. How long did it take Linda climb?~(adapted from 2003 Math Kangaroo Problem, Level 3 - 4, Question \#10) | [
[
{
"aoVal": "A",
"content": "$3$ hr $30$ min "
}
],
[
{
"aoVal": "B",
"content": "$4$ hr $30$ min "
}
],
[
{
"aoVal": "C",
"content": "$7$ hr $10$ min "
}
],
[
{
"aoVal": "D",
"content": "$6$ hr $20$ min "
}
],
[
{
"aoVal": "E",
"content": "$8$ hr $40$ min "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem->Time Calculation"
] | [
"It lasted $3$ hours and $30$ minutes from $8$:$30$ to $12$:$00$. It lasted $2$ hours from $12$:$00$ to $14$:$00$. So Bob took $5$ hours and $30$ minutes. Linda was $1$ hour and $40$ minutes behind Bob. Linda\\textquotesingle s time was $7$ hours and $10$ minutes. Bob: $3$h+$30$min+$2$h=$5$h$30$min Linda:$3$h+$30$min+$2$h+$1$h+$40$min=$7$h$10$min "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7936 | f425c85b93394731a1d7b6b7b063df1c | [
"其它"
] | 0 | single_choice | A certain play has three $30$-minute parts and two intermission among them. The play started at $8:30$ and ended at $10:15$. How many minutes long were the intermissions in total? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$25$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Time Problem"
] | [
"From $8:30$ 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 | 7950 | dd99e23150a54cf9b5d1d6e958ee1f87 | [] | 1 | single_choice | There are two piles of matches. Each pile has $$6$$ sticks. Cindy and Doris take turns to pick up matches from either pile. There is no limit to how many matches they can pick up, but they must pick up at least one match each turn. The person who picks up the last match will be the winner. If Cindy starts picking up matches first,~\uline{~~~~~~~~~~}~will be the winner (has a winning strategy). | [
[
{
"aoVal": "A",
"content": "Cindy "
}
],
[
{
"aoVal": "B",
"content": "Doris "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Game Strategy"
] | [
"Doris will be the winner, since she can simply mirror the number of matches Cindy picks up every turn. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7962 | f4aa7d6c44594caaac75e8b80c0511dd | [] | 1 | single_choice | Two cups with capacities of 9 liters and 3 liters, respectively, have different diameters at the top and bottom and are unmarked. If water can be taken arbitrarily, how many operations are required at least to pour out 6 liters of water? (Filling the cup is counted as one operation, pouring the water out is counted as another operation.) | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem->Pouring Water Problems"
] | [
"2 operations at least. 1. Fill the 9 liter cup to the top. 2. Pour water from the 9 liter cup into the 3 liter cup until the 3 liter cup is full, leaving 6 liters of water in the 9 liter cup. The answer is B "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7966 | f94e5095fed648a0af370b4e2e6c710d | [
"其它"
] | 0 | single_choice | From $1$ to $30$, how many integers can be chosen at most to ensure that no two of chosen numbers sum to $36$? | [
[
{
"aoVal": "A",
"content": "$$15$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$17$$ "
}
],
[
{
"aoVal": "D",
"content": "$$18$$ "
}
],
[
{
"aoVal": "E",
"content": "$$19$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Constructing and Proving"
] | [
"1, 2, 3, 4, 5, 18→ 6 $30-5-1=24$, $24\\div2=12$ $$6+12=18$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7969 | de07443fc5504a5f8a30d5c4e7d4cb80 | [
"其它"
] | 2 | single_choice | Out of 8 bottles of sugar, 1 bottle has a lighter mass than the other 7. How many times can the balance be used to ensure that the lighter one is found? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Combinatorics->Fun Problems in Math"
] | [
"omit "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 7989 | f57d1581f15740f5ad444a74793bbd89 | [] | 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 did\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 | 7994 | 00437161c674491894df0e1c19c954c8 | [] | 1 | single_choice | If the exam lasts for two days and ends on Wednesday, what day does the exam start?~(adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$4$$) | [
[
{
"aoVal": "A",
"content": "Monday "
}
],
[
{
"aoVal": "B",
"content": "Tuesday "
}
],
[
{
"aoVal": "C",
"content": "Friday "
}
],
[
{
"aoVal": "D",
"content": "Saturday "
}
],
[
{
"aoVal": "E",
"content": "Thursday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"
] | [
"Tuesday to Wednesday is exactly two days. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8001 | 00c41d59a843421c99cf0a9310b7997b | [] | 1 | single_choice | The number of apples in basket $$A$$ was $$\frac{13}{19}$$ of that in basket $$B$$. After $$10$$ apples were taken out from basket $$A$$ and were put in basket $$B$$, the number of apples in basket $$A$$ became $$\frac{1}{3}$$ of that in basket $$B$$. How many apples were there in basket $$A$$ and basket $$B$$, respectively, in the beginning? ． | [
[
{
"aoVal": "A",
"content": "$$13$$ apples in basket $$A$$; $$19$$ apples in basket $$B$$ "
}
],
[
{
"aoVal": "B",
"content": "$$26$$ apples in basket $$A$$; $$19$$ apples in basket $$B$$ "
}
],
[
{
"aoVal": "C",
"content": "$$26$$ apples in basket $$A$$;~$$38$$ apples in basket $$B$$ "
}
],
[
{
"aoVal": "D",
"content": "$$19$$ apples in basket $$A$$; $$13$$ apples in basket $$B$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"
] | [
"The total number of apples in basket $$A$$ and basket $$B$$ is constant. In the beginning, $$A: B=13:19$$; now, $$A: B=1:3=8:24$$ (the total number of portions is still $$32$$). By comparison, the number of portions in basket $$A$$ decreases by $$5$$, and the number of portions in basket $$B$$ increases by $$5$$, so each portion is $$10\\div5=2\\text{kg}$$. Formerly, there were $$13\\times2=26$$ apples in basket $$A$$ and $$19\\times2=38$$ apples in basket $$B$$. So, the answer is $$C$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8003 | 00dda9f02ca64cb292cd2a8564138558 | [
"其它"
] | 1 | single_choice | The average cost of a long-distance call in the USA in 1985 was 50 cents per minute, and the average cost of a long-distance call in the USA in 2008 was 5 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (adapted from 2007 AMC 8, Question \#6) | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50$$ "
}
],
[
{
"aoVal": "D",
"content": "$$80$$ "
}
],
[
{
"aoVal": "E",
"content": "$$90$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $50-5=45$ so the percent decrease is $\\frac{45}{50}$ which is ~$ 90 \\textbackslash\\%$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8004 | 097e549b99444475b22e74850de5ceba | [] | 1 | single_choice | My mom\textquotesingle s birthday is on Sunday, and my dad\textquotesingle s birthday is $$55$$ days later. On what day of the week will my dad\textquotesingle s birthday be? | [
[
{
"aoVal": "A",
"content": "$$ $$Sunday$$ $$ "
}
],
[
{
"aoVal": "B",
"content": "$$ $$Monday$$ $$ "
}
],
[
{
"aoVal": "C",
"content": "$$ $$Tuesday$$ $$ "
}
],
[
{
"aoVal": "D",
"content": "$$ $$Thursday$$ $$ "
}
],
[
{
"aoVal": "E",
"content": "$$ $$Saturday$$ $$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"After $$1$$ day, it is Monday; after $$2$$ days, it is Tuesday; after $$3$$ days, it is Wednesday $$\\cdots$$ After $$8$$ days, it is still Monday, and the period is $$7$$ days. $$55\\div 7=7$$(weeks) $$\\rm R$$ $$6$$ (days). The birthday is Saturday. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8006 | 12a44af54376463da580ed205dd44ec5 | [] | 1 | single_choice | If $$10$$ February $$2013$$ falls on Friday, which day of the week will $$10$$ February $2014$ fall on? | [
[
{
"aoVal": "A",
"content": "Sunday "
}
],
[
{
"aoVal": "B",
"content": "Monday "
}
],
[
{
"aoVal": "C",
"content": "Tuesday "
}
],
[
{
"aoVal": "D",
"content": "Wednesday "
}
],
[
{
"aoVal": "E",
"content": "Thursday "
}
],
[
{
"aoVal": "F",
"content": "Friday "
}
],
[
{
"aoVal": "G",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"No leap year, 365 days "
] | G |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8012 | 1bf06eab37644b91be0d58bc2c525830 | [] | 1 | single_choice | On a map of England and Wales the distance between St Ives in Cornwall and St Ives in Cambridgeshire measures $$18\text{cm}$$. In reality the distance between the two towns is about $$450\text{km}$$. Which of the options below is the scale of the map? | [
[
{
"aoVal": "A",
"content": "$$1:2500000$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1:1000000$$ "
}
],
[
{
"aoVal": "C",
"content": "$$1:750000$$ "
}
],
[
{
"aoVal": "D",
"content": "$$1:500000$$ "
}
],
[
{
"aoVal": "E",
"content": "$$1:250000$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"
] | [
"The scale of the map is $$18\\text{cm} : 450\\text{km}$$; converting the actual distance to centimetres, this is equivalent to $$18 : 450 \\times 1000 \\times 100 = 18 : 45 000 000$$. Simplifying gives a scale of $$1 : 2 500 000$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8013 | 0129abdaa0db4312ac58082b33476cce | [] | 1 | single_choice | A mixture of $$30$$ litres of paint is $$25\textbackslash\%$$ red tint, $$30\textbackslash\%$$ yellow tint and $$45\textbackslash\%$$ water. Five litres of yellow tint are added to the original mixture. What is the percentage of yellow tint in the new mixture? | [
[
{
"aoVal": "A",
"content": "$$25\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$35\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$40\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$45\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "E",
"content": "$$50\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"
] | [
"Since $$30\\textbackslash\\%$$ of the original $$30$$ liters of paint was yellow, and $$5$$ liters of yellow paint were added to make the new mixture, there are $$9+5=14$$ liters of yellow tint in the new mixture. Since only $$5$$ liters of paint were added to the original $$30$$, there are a total of $$35$$ liters of paint in the new mixture. This gives $$40\\textbackslash\\%$$ of yellow tint in the new mixture, which is $$40$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8015 | 013029d4f788492fa90c125bc4baf373 | [] | 1 | single_choice | Rick and Roy each stands at different ends of a straight road that is $$2021$$m long. They run toward each other. Rick\textquotesingle s speed is $$21\text{m/s}$$ and Roy\textquotesingle s speed is $$22\text{m/s}$$. They will meet in~\uline{~~~~~~~~~~}~seconds. ($$2016$$ Math League.com contest problem, $$5$$th Grade, Question \#$$26$$) | [
[
{
"aoVal": "A",
"content": "$$35$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$47$$ "
}
],
[
{
"aoVal": "D",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$2021\\div (21+22)=47$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8020 | 01513e9d25f246f9960e3d25c02db5af | [] | 1 | single_choice | If $$13^{}\text{th}$$February is Friday, what day of the week is $$1$$\textsuperscript{st~}February? | [
[
{
"aoVal": "A",
"content": "Sunday "
}
],
[
{
"aoVal": "B",
"content": "Monday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Thursday "
}
],
[
{
"aoVal": "E",
"content": "Saturday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"We can count backward by days or by weeks. Count a few weeks back to find that February $$6$$ is a Friday. Then count a few days back to find that February $$1$$ is a Sunday. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8021 | 2098f3c77dac4765aea3be75e95c88d7 | [
"其它"
] | 1 | single_choice | To defeat a dragon, Matthias has to cut off all the dragon\textquotesingle s heads. If he can cut off $$3$$ of the dragon\textquotesingle s heads, one new head immediately grows. Matthias defeats the dragon by cutting off $$17$$ heads in total. How many heads did the dragon have at the beginning? | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$9$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$11$$ "
}
],
[
{
"aoVal": "E",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Including and Excluding "
] | [
"$17\\div3=5R2$, so Matthias has $5$ groups of $3$ cuts, which means $5$ new heads grew. Thus, there are $17-5=12$ heads originally. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8023 | 1bf74c5b01e746029d25880f2313247c | [] | 1 | single_choice | Gabriel wrote his name $$100$$ times in the sand. What was the $$100\text{th}$$ letter he wrote? ． | [
[
{
"aoVal": "A",
"content": "$$a$$ "
}
],
[
{
"aoVal": "B",
"content": "$$b$$ "
}
],
[
{
"aoVal": "C",
"content": "$$r$$ "
}
],
[
{
"aoVal": "D",
"content": "$$i$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"
] | [
"The $$1\\text{st}$$ letter Gabriel wrote was $$G$$, and every $$7\\text{th}$$ letter after was $$G$$. The $$99\\text{th}$$ letter he wrote was $$G$$, and the $$100\\text{th}$$ was an\"$$a$$.\" "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8024 | 01783de305314dc7ba5d87cc1dc397db | [
"其它"
] | 2 | single_choice | At the $2018$ Tompkins County Fair a vendor is offering a "fair special" on hats. If you buy one hat at the regular price of $\textbackslash$ 30$, you get a second hat at a $40\textbackslash\%$ discount, and a third pair at half the regular price. James took advantage of the "fair special" to buy three hats. What percentage of the $\textbackslash$ 90$ regular price did he save? (adapted from 2013 AMC 8, Question \#12) | [
[
{
"aoVal": "A",
"content": "$$15$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$25$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30$$ "
}
],
[
{
"aoVal": "E",
"content": "$$40$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"First, the amount of money one will pay for three hats without the discount $=\\textbackslash$ 90$. Then, find the amount of money using the discount: $30+0.6 \\times 30+\\frac{1}{2} \\times 30=\\textbackslash$ 63$. Finding the percentage yields $\\frac{63}{90}=70\\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-70\\textbackslash\\%= 30\\textbackslash\\%$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8027 | 019224a476eb40419f76370b179c20f8 | [] | 1 | single_choice | The sales tax rate in Bergville is $$6\textbackslash\%$$. During a sale at the Bergville Coat Closet, the price of a coat is discounted $$20\textbackslash\%$$ from its ＄$$90.00$$ price. Two clerks, Jack and Jill, calculate the bill independently. Jack rings up ＄$$90.00$$ and adds $$6\textbackslash\%$$ sales tax, then subtracts $$20\textbackslash\%$$ from this total. Jill rings up ＄$$90.00$$, subtracts $$20\textbackslash\%$$ of the price, then adds $$6\textbackslash\%$$ of the discounted price for sales tax. What is Jack's total minus Jill's total? | [
[
{
"aoVal": "A",
"content": "＄$$-1.06$$ "
}
],
[
{
"aoVal": "B",
"content": "＄$$-0.53$$ "
}
],
[
{
"aoVal": "C",
"content": "＄$$0$$ "
}
],
[
{
"aoVal": "D",
"content": "＄$$0.53$$ "
}
],
[
{
"aoVal": "E",
"content": "＄$$1.06$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Complex Money Word Problems"
] | [
"The price Jacks rings up is $$(90.00)(1.06)(0.80)$$. The price Jill rings up is $$(90.00)(0.80)(1.06)$$. By the commutative property of multiplication, these quantities are the same, and the difference is $$(\\text{C})$$＄$$0$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8039 | 3c80e363215c4e2092e2d3873e641db4 | [] | 2 | single_choice | The distance between Exeter and London is $$175$$ miles. Sam left Exeter at $$10:00$$ on Tuesday for London. Morgan left Exeter~ for London at $$13:00$$ the same day. They travelled on the same road. Sam\textquotesingle s average speed was $$25$$ miles per hour, and Morgan\textquotesingle s average speed was $$50$$ miles an hour. At what time did Sam and Morgan meet? | [
[
{
"aoVal": "A",
"content": "$$16:00$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15:55$$ "
}
],
[
{
"aoVal": "C",
"content": "$$15:30$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15:00$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14:40$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$25\\times3=75$miles $75\\div (50-25)=3$h $13+3=16$ They meet at $16:00$. revise from ($$2017$$ Junior Mathematical Challenge Question \\#$$25$$) "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8041 | 3337a0520fa449f0ac9b992628ee44b1 | [] | 1 | single_choice | There were $$31$$ runners competing in a race. The number of runners who finished before John is four times smaller than the number of runners who finished later than John. At what place did John finish? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$21$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"
] | [
"Before is ``$$1$$'', so after is ``$$4$$'', Before: $$(31-1) \\div (4+1) = 6$$, and John: $$6+1=7$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8043 | 058a929170a4407cbbefa0e9be4c7f66 | [] | 1 | single_choice | Gary will be three times as old as Harry $$4$$ years from now. If Harry is $$5$$ years old now, how old will Gary be in $$4$$ years? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$23$$ "
}
],
[
{
"aoVal": "C",
"content": "$$27$$ "
}
],
[
{
"aoVal": "D",
"content": "$$31$$ "
}
],
[
{
"aoVal": "E",
"content": "$$36$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"
] | [
"Harry is $$5$$ years old now; he\\textquotesingle ll be $$9$$ in $$4$$ years. Gary is thus $$3\\times9=27$$ years old "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8044 | 058d22cc76eb4bff836858ecf11fa6ff | [] | 1 | single_choice | Bowen has $$40$$ grams of a $$25\textbackslash\%$$ sugar solution. After~\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of the solution is $$40\textbackslash\%$$. (Evaporate: the water turns from liquid into vapor and is no longer in the solution anymore.) | [
[
{
"aoVal": "A",
"content": "$$15$$ grams "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ grams "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ grams "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ grams "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"
] | [
"$$40-40\\times25\\textbackslash\\%\\div40\\textbackslash\\%=40-25=15$$ ounces. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8045 | 0205c319805f4938a574d5dd9f5c727d | [] | 1 | single_choice | Mike makes $5$ cakes every minute. He works for $16$ minutes. How many cakes does he make altogethe? | [
[
{
"aoVal": "A",
"content": "$$80$$ "
}
],
[
{
"aoVal": "B",
"content": "$$90$$ "
}
],
[
{
"aoVal": "C",
"content": "$$100$$ "
}
],
[
{
"aoVal": "D",
"content": "$$70$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"
] | [
"$$16\\times 5 = 80$$ ~ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8054 | 024d959f3f824a3ab90354b8e95efb48 | [
"其它"
] | 1 | single_choice | Luis has 7 apples and 2 bananas. He gives 2 apples to Yuri who, in return gives bananas to Luis. Then Luis has as many apples as bananas. How many bananas did Yuri give to Luis? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"
] | [
"$$7-2=5$$ $$5-2=3.$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8057 | 05b67ba0dfcb444fa1ae089f5f1e0f2b | [
"其它"
] | 1 | single_choice | Alice\textquotesingle s first day in Caterpillar Club was Tuesday. She wants to throw a party on her 40th day in the club. If Alice attends the club everyday, on which day of the week will the party be? | [
[
{
"aoVal": "A",
"content": "Friday "
}
],
[
{
"aoVal": "B",
"content": "Saturday "
}
],
[
{
"aoVal": "C",
"content": "Sunday "
}
],
[
{
"aoVal": "D",
"content": "Monday "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"40th day = 39th day after first day joining. 39 days/7 = 5 weeks R 4 days. 4 days after Tues is Saturday. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8058 | 025b8851af974508a90f60e2c9275f2a | [] | 1 | single_choice | A fifth-grade class has $8$ boys and $10$ girls. What is the ratio of boys to girls?. | [
[
{
"aoVal": "A",
"content": "$8:10$ "
}
],
[
{
"aoVal": "B",
"content": "$10:8$ "
}
],
[
{
"aoVal": "C",
"content": "$4:5$ "
}
],
[
{
"aoVal": "D",
"content": "$5:4$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"
] | [
"Simplify $8:10$ to $4:5$, or $\\text{C}$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8063 | 2e99a27703e94c19a675a14ed25fc891 | [] | 1 | single_choice | Emily was $$6$$ years old last year, and her sister was $$6$$ years old six years ago. What is the age difference between Emily and her sister today? | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$13$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages"
] | [
"Emily was $$6$$ years old last year , which means Emily is $7$ years old this year. Her sister was~ $$6$$ years old six years ago, which tells us her sister is~ $12$ years old this year, so the age difference is $5$ today. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8066 | 028868fac05b42c6802aa97c4ccf38bb | [
"其它"
] | 1 | single_choice | Gill is now 27 and has moved into a new flat. She has four pictures to hang in a horizontal row on a wall which is 4800 mm wide. The pictures are identical in size and are 420 mm wide. Gill hangs the first two pictures so that one is on the extreme left of the wall and one is on the extreme right of the wall. She wants to hang the remaining two pictures so that all four pictures are equally spaced. How far should Gill place the centre of each of the two remaining pictures from a vertical line down the centre of the wall? | [
[
{
"aoVal": "A",
"content": "$$210mm$$ "
}
],
[
{
"aoVal": "B",
"content": "$$520mm$$ "
}
],
[
{
"aoVal": "C",
"content": "$$730mm$$ "
}
],
[
{
"aoVal": "D",
"content": "$$840mm$$ "
}
],
[
{
"aoVal": "E",
"content": "$$1040mm$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"omitted "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8067 | 028967df4030433b910b34f63ed4bd61 | [] | 1 | single_choice | David and Billy are on the bus together. They sit in the same column. There are $5$ people in front of David, Billy is in the middle. There are $10$ people behind Billy, and David is in the middle. How many people in this column? (adapted from2004 Math Kangaroo Problem, Level 3 - 4, Question \#19) | [
[
{
"aoVal": "A",
"content": "$$14$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$11$$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line"
] | [
"$5 + 10 - 2 = 13$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8068 | 09e29390f8544d238200f3f59870f9ce | [
"其它"
] | 1 | single_choice | How many pieces can we get if we break a wooden stick in $8$ places? (Adapted from 1999 Math Kangaroo Problem, Level 3-4, Question \#3) | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
],
[
{
"aoVal": "E",
"content": "$$16$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Planting no Trees on either Side (straight line type)->Sawing Woods"
] | [
"$8+1=9$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8070 | c2663bc98b5846eea1da2771587378b3 | [] | 1 | single_choice | There were $$27$$ children in a class. There were twice as many boys as girls. How many boys were there? | [
[
{
"aoVal": "A",
"content": "$$21$$ boys "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ boys "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ boys "
}
],
[
{
"aoVal": "D",
"content": "$$14$$ boys "
}
],
[
{
"aoVal": "E",
"content": "$$9$$ boys "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"
] | [
"$$\\dfrac{27}{(2+1)}=9$$, $$9\\times2=18$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8072 | 02a4749306bd4a8b9cf07c36debaade2 | [] | 1 | single_choice | There are twice as many boys in a room as girls. If $$5$$ boys leave the room, there would be an equal number of boys and girls in the room. How many boys were in the room at first? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$15$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Difference and Multiple"
] | [
"The number of boys that leave the room must equal the number of boys that remain. Since $$5$$ boys leave, there are $$5$$ boys still in the room for a total of $$10$$ boys. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8073 | 0e4e05f173f54207ae66a4357a5f29d3 | [
"其它"
] | 1 | single_choice | There are twelve rooms in a building and each room has two windows and one light. Last evening, eighteen windows were lit. In how many rooms was the light off? (2016 Math Kangaroo Problem, Level 1-2, Question \#14) | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$6$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"$18\\div2=9$, $12-9=3$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8083 | 53bda166eaeb4de180072d3fadab501e | [] | 1 | single_choice | There were $$31$$ runners competing in a race. The number of runners who finished before John is $18$ less than the number of runners who finished later than John. At what place did John finish? (Adapted from 1998 Math Kangaroo Problem, Level 3 - 4, Question \#13) | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$21$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"
] | [
"Before: $$(31-1-18) \\div 2 = 6$$, and John: $$6+1=7$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8086 | 3c899876d4434a43ab94cea802694831 | [
"其它"
] | 0 | single_choice | A basket with $$5$$ watermelons weighs $$3250$$ grams. If $$3$$ of the watermelons were taken out, the remaining weight would be $$1510$$ grams. What is the weight (in grams) of the basket? | [
[
{
"aoVal": "A",
"content": "$$350$$ grams "
}
],
[
{
"aoVal": "B",
"content": "$$1160$$ grams "
}
],
[
{
"aoVal": "C",
"content": "$$1740$$ grams "
}
],
[
{
"aoVal": "D",
"content": "$$870$$ grams "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Equivalent Substitution in Equation Word Problems->Replacement of Equivalent Substitution"
] | [
"$$NA.$$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8088 | 031405a4a395494e8ec510a2d8c30626 | [
"其它"
] | 1 | single_choice | In a magic land, a monkey wants to climb a tree of $180$ m. The monkey can make one of the two kinds of climb each day: $6$ m up or $10$ m up. Beginning at the ground , at least how many days will the monkey need in order to rest on the branch of $108$ m high? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value"
] | [
"$10 \\times 9 + 6 \\times 3 = 108$ $9 + 3 = 12$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8093 | 03504ffde2d4458bb0a086c175b201ad | [
"其它"
] | 1 | single_choice | $4$ years gao, the sum of Cathy\textquotesingle s and Larry\textquotesingle s ages was $$20$$. What is the sum of their ages this years? | [
[
{
"aoVal": "A",
"content": "$$16$$ "
}
],
[
{
"aoVal": "B",
"content": "$$28$$ "
}
],
[
{
"aoVal": "C",
"content": "$$24$$ "
}
],
[
{
"aoVal": "D",
"content": "$$36$$ "
}
],
[
{
"aoVal": "E",
"content": "$$38$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$20 + 4 + 4 = 28$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8094 | 0a1465c41f524726bf1fcdd08b0d5106 | [] | 1 | single_choice | $$75$$ out of $$100$$ apples are \textbf{not} rotten. What percentage of the apples are rotten? | [
[
{
"aoVal": "A",
"content": "75\\% "
}
],
[
{
"aoVal": "B",
"content": "100\\% "
}
],
[
{
"aoVal": "C",
"content": "25\\% "
}
],
[
{
"aoVal": "D",
"content": "50\\% "
}
],
[
{
"aoVal": "E",
"content": "175\\% "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"
] | [
"$$\\frac{75}{100}=75 \\textbackslash\\%$$, $$100\\textbackslash\\%-75\\textbackslash\\%=25\\textbackslash\\%$$, $$25\\textbackslash\\%$$ of the apples are rotten. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8095 | 86e12cc4a2204e229c11663b0558beec | [] | 2 | single_choice | Find the exact number of minutes after $3.00 \text{pm}$ when the minute and hour hands are first at $90^{\circ}$ to each other. | [
[
{
"aoVal": "A",
"content": "$$31 \\frac{2}{11}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$31 \\frac{3}{11}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$32 \\frac{8}{11}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$33 \\frac{3}{11}$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Distance Word Problems->Clock Problems"
] | [
"NA "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8097 | 6fa3d07122024f82a3903e98aaf8ec6f | [
"其它"
] | 1 | single_choice | How many times does it take to cut a rope into $$5$$ pieces? The rope can\textquotesingle t be folded. | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "It depends on how long the rope is. "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"$$5 - 1 = 4$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8098 | 064fbdccba4a49ad854ca364681b3bf1 | [
"其它"
] | 1 | single_choice | Amy has $12$ candies and Nancy has $33$ candies. How many candies do they have in total? | [
[
{
"aoVal": "A",
"content": "$$21$$ "
}
],
[
{
"aoVal": "B",
"content": "$$33$$ "
}
],
[
{
"aoVal": "C",
"content": "$$44$$ "
}
],
[
{
"aoVal": "D",
"content": "$$45$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$12+33=45$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8100 | 29fda63f65c64ee58c40dffe55e85719 | [] | 1 | single_choice | Paul was going to buy $$4$$ servings of ice cream, but he was $$80$$ pence short. So, he bought $$3$$ servings and had $$30$$ pence left. What was the price of one serving of ice cream? | [
[
{
"aoVal": "A",
"content": "$$70$$ pence "
}
],
[
{
"aoVal": "B",
"content": "$$80$$ pence "
}
],
[
{
"aoVal": "C",
"content": "$$90$$ pence "
}
],
[
{
"aoVal": "D",
"content": "$$100$$ pence "
}
],
[
{
"aoVal": "E",
"content": "110 pence "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems"
] | [
"$$(80+30)\\div (4-3)=110$$ pence. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8104 | 06590ff09c274ceba9e8a7894fbf117d | [
"其它"
] | 0 | single_choice | Luke and Matthew ran a lemonade stand on Saturday. They agreed that Matthew would get $65$\% of the profit because the lemonade stand was his idea. They made a profit of $60$ dollars. How much money did Luke make? | [
[
{
"aoVal": "A",
"content": "$$21$$ "
}
],
[
{
"aoVal": "B",
"content": "$$24$$ "
}
],
[
{
"aoVal": "C",
"content": "$$36$$ "
}
],
[
{
"aoVal": "D",
"content": "$$39$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$60 \\times 65$\\%=$39$, $60-39=21$, Luke made $21$ dollars. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8106 | 03c6ab73b39e41dcb5c43c6429a9a46a | [] | 1 | single_choice | Alan is $5$ years old, his mother is $18$ years older than him, and his father is $2$ years older than his mother. How old is his father?~(adapted from $$2005$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$7$$) | [
[
{
"aoVal": "A",
"content": "$$21$$ "
}
],
[
{
"aoVal": "B",
"content": "$$25$$ "
}
],
[
{
"aoVal": "C",
"content": "$$27$$ "
}
],
[
{
"aoVal": "D",
"content": "$$28$$ "
}
],
[
{
"aoVal": "E",
"content": "$$30$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages"
] | [
"Alans\\textquotesingle{} mother is $18$ years older than him, his mother is $23$ years old. His father is two years older than his mother, so he is $25$ years old. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8116 | 04300e2d3c1646b8b230770b596978fa | [] | 1 | single_choice | On Monday morning, a snail fell down a well which is $$5$$ metres deep. During the day, it climbs up $$2$$ metres, and during the night it slides down $$1$$ metre. On what day of the week will the snail get out of the well? | [
[
{
"aoVal": "A",
"content": "$$$$Tuesday "
}
],
[
{
"aoVal": "B",
"content": "$$$$Wednesday "
}
],
[
{
"aoVal": "C",
"content": "$$$$Thursday "
}
],
[
{
"aoVal": "D",
"content": "$$$$Friday "
}
],
[
{
"aoVal": "E",
"content": "$$$$Monday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems->Snail Climbing out of Well (completed)"
] | [
"Nil "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8122 | 6afde6f03ce14fdb8799de8411707621 | [
"其它"
] | 1 | single_choice | $$37$$ sakura trees were planted along one side of the road. The trees were planted at $$4m$$ intervals. After drivers complained the road was too pink, pineapple trees were planted on the other side of the road at $$6m$$ intervals. If there were sakura and pineapple trees at both ends of the road, how many pineapple trees were planted? ． | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$25$$ "
}
],
[
{
"aoVal": "C",
"content": "$$144$$ "
}
],
[
{
"aoVal": "D",
"content": "$$18$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"Number of sakura intervals = $$37-1 = 36$$ Length of road = $$36 \\times 4 = 144m$$ Number of pineapple intervals = $$144m \\div 6m = 24$$ Number of pineapple trees = $$24 + 1 = 25$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8123 | 0a5475e16c9f416494e261766197a564 | [] | 1 | single_choice | Fatimah has $$3$$ bags of marbles. There are $$291$$ marbles in each bag. How many marbles does Fatimah have in all? | [
[
{
"aoVal": "A",
"content": "$$97$$ "
}
],
[
{
"aoVal": "B",
"content": "$$294$$ "
}
],
[
{
"aoVal": "C",
"content": "$$582$$ "
}
],
[
{
"aoVal": "D",
"content": "$$873$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"$$3\\times291=873$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8124 | 2eadd69c9425495ca68a939822878f57 | [] | 1 | single_choice | I ate lunch every day of my $$12$$-week summer break. I ate lunch out-doors only on every Saturday, Sunday, and Tuesday. I ate lunch in-doors ondays. | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$36$$ "
}
],
[
{
"aoVal": "C",
"content": "$$48$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"I ate lunch every day of my $$12$$-week summer break. I ate lunch out-doors only on every Saturday, Sunday, and Tuesday. I ate lunch in-doors $$4$$ days each week. In $$12$$ weeks, that\\textquotesingle s $$12\\times 4=48$$ days. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8127 | 53c6cb79db614be89558f79509c017c8 | [
"其它"
] | 0 | single_choice | Bella and her brother agreed to share a pizza which was cut into $15$ slices. Bella ate $40$\% of the pizza. How many slices did she eat? | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$11$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$15 \\times 40$\\%=$6$, She ate $6$ slices. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8130 | 0486b1fbf39e418c9804273217989ce9 | [] | 1 | single_choice | In a jar of red, green, and blue marbles, all but $$6$$ are red marbles, all but $$8$$ are green, and all but $$4$$ are blue. How many marbles are in the jar? ． | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
],
[
{
"aoVal": "E",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Multivariate Linear Equation Word Problems"
] | [
"Suppose there are $$x$$ red marbles, $$y$$ green marbles and $$z$$ blue marbles. Thus, we can get $$\\begin{cases} x+y=4① \\textbackslash\\textbackslash{} y+z=6②\\textbackslash\\x+z=8③\\end{cases}$$, ①$$+$$②$$+$$③: $$2x+2y+2z=18$$, $$x+y+z=9$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8132 | 048aba6a7bd14f23a83ceadf07f21bf6 | [] | 1 | single_choice | Cecilia and her dad are climbing stairs from the first floor. They start at the same time, and each of them keeps her or his speed of climbing unchanged. When Cecilia arrives at the third floor, her dad arrives at the fifth floor. When Cecilia arrives at the eighth floor, which floor does her dad arrive at? | [
[
{
"aoVal": "A",
"content": "$$14$$\\textsuperscript{th} "
}
],
[
{
"aoVal": "B",
"content": "$$15$$\\textsuperscript{th} "
}
],
[
{
"aoVal": "C",
"content": "$$10$$\\textsuperscript{th} "
}
],
[
{
"aoVal": "D",
"content": "$$13$$\\textsuperscript{th} "
}
],
[
{
"aoVal": "E",
"content": "$$16$$\\textsuperscript{th} "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"$(5-1) \\div(3-1)=2$. $(8-1) \\times 2+1=15$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8140 | 6b026e80bf1e487a8637003d3039ada4 | [
"其它"
] | 1 | single_choice | After Sally takes 20 shots, she has made $50 \textbackslash\%$ of her shots. After she takes 5 more shots, she raises her percentage to $60 \textbackslash\%$. How many of the last 5 shots did she make? (adapted from 2004 AMC 8, Question\#6) | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
],
[
{
"aoVal": "E",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"Sally made $0.5\\times 20=10$ shots originally. Letting $x$ be the number of shots she made, we have $\\frac{10+x}{25}=0.60$. Solving for $x$ gives us $x=$ $(E)5$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8143 | 072e63fc31c04c10a581a7f99d871ce8 | [] | 1 | single_choice | Irene mixes $$100$$ grams of dogfood that contains $$50\textbackslash\%$$ rice with $$400$$ grams of dogfood that contains $$80\textbackslash\%$$ rice. Find the percent concentration of the rice in the new mixture. | [
[
{
"aoVal": "A",
"content": "$$70\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$72\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$75\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$74\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"
] | [
"$$\\dfrac{100\\times50\\textbackslash\\%+400\\times80\\textbackslash\\%}{100+400}=74\\textbackslash\\%$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8148 | 3ca008279c6240388e135d83fccacd3d | [
"其它"
] | 1 | single_choice | The average cost of a long-distance call in the USA in 1985 was 41 cents per minute, and the average cost of a long-distance call in the USA in 2005 was 7 cents per minute. Find the approximate percent decrease in the cost per minute of a long- distance call. (2007 AMC 8, Question \#6) | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$17$$ "
}
],
[
{
"aoVal": "C",
"content": "$$34$$ "
}
],
[
{
"aoVal": "D",
"content": "$$41$$ "
}
],
[
{
"aoVal": "E",
"content": "$$80$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"The percent decrease is (the amount of decrease)/(original amount) the amount of decrease is $41-7=34$ so the percent decrease is $\\frac{34}{41}$ which is about $(\\mathbf{E}) 80 \\textbackslash\\%$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8155 | 744eb4d9cfd44941b4668c2f224a1207 | [] | 1 | single_choice | Mike has $$160$$ grams of a $$3\textbackslash\%$$ salt solution and Danni has an $$8\textbackslash\%$$ salt solution. If Danni gives $$200$$ grams of her solution to Mike, they will have the same amount of pure salt in their solutions. How many grams of solution did Danni have in the beginning? | [
[
{
"aoVal": "A",
"content": "$400$ "
}
],
[
{
"aoVal": "B",
"content": "$450$ "
}
],
[
{
"aoVal": "C",
"content": "$460$ "
}
],
[
{
"aoVal": "D",
"content": "$480$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"
] | [
"$$160\\times3\\textbackslash\\%+200\\times8\\textbackslash\\%=20.8$$ ounces. $$20.8\\div8\\textbackslash\\%+200=260+200=460$$ ounces. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8156 | 0761893e09464f8d9ba99347521683a9 | [
"其它"
] | 2 | single_choice | At the 2017 King County Fair a vendor is offering a "fair special" on hats. If you buy one hat at the regular price of $40$ dollars, you get a second hat at a $10 \textbackslash\%$ discount, and a third pair at half the regular price. James took advantage of the "fair special" to buy three hats. What percentage of the $120$ dollars regular price did he save? (adapted from 2013 AMC 8, Question \#12) | [
[
{
"aoVal": "A",
"content": "$$15$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$25$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30$$ "
}
],
[
{
"aoVal": "E",
"content": "$$40$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"First, find the amount of money one will pay for three hats without the discount. We have $\\textbackslash$ 40 \\times 3$ hats $=\\textbackslash$ 120$. Then, find the amount of money using the discount: $40+0.9 \\times 40+\\frac{1}{2} \\times 40=\\textbackslash$ 96$. Finding the percentage yields $\\frac{96}{120}=80 \\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-80 \\textbackslash\\%=(\\text{B}) 20$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8165 | 17bdd4b62c4d44b4ae0c7314e7eee864 | [] | 1 | single_choice | My aunt can fold $$16$$ paper cranes in $$4$$ minutes. My uncle can fold $$15$$ paper cranes in $$5$$ minutes. How long would it take them to fold $$42$$ cranes if they work together at those rates? | [
[
{
"aoVal": "A",
"content": "$$6$$ minutes "
}
],
[
{
"aoVal": "B",
"content": "$$9$$ minutes "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ minutes "
}
],
[
{
"aoVal": "D",
"content": "$$13$$ minutes "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"
] | [
"My aunt can fold $$4$$ paper cranes in $$1$$ minute. My uncle can fold 3 paper cranes in $$1$$ minute. Together they fold $$7$$ paper cranes in $$1$$ minute. It takes them $$42\\div7 = 6$$ minutes to fold $$42$$ paper cranes. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8172 | 3808f854e18248dcb53e5d5917034ff4 | [] | 1 | single_choice | On the farm, there are $$5$$ sheep, $$5$$ hens, $$2$$ dogs, $$2$$ cats, and the farmer. How many legs are there altogether? (2006 Math Kangaroo Problem, Level 1-2, Question \#15) | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$14$$ "
}
],
[
{
"aoVal": "C",
"content": "$$24$$ "
}
],
[
{
"aoVal": "D",
"content": "$$48$$ "
}
],
[
{
"aoVal": "E",
"content": "$$46$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"
] | [
"$5\\times4+5\\times2+2\\times4+2\\times4+2=48$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8175 | 58731479c7c9412db282d3d519e30879 | [
"其它"
] | 1 | single_choice | If $$11$$th November 2031 is a Tuesday, what day of the week will $$11$$th November 2032 be? | [
[
{
"aoVal": "A",
"content": "Tuesday "
}
],
[
{
"aoVal": "B",
"content": "Wednesday "
}
],
[
{
"aoVal": "C",
"content": "Thursday "
}
],
[
{
"aoVal": "D",
"content": "Friday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"
] | [
"$$1$$ leap year, so $$2$$ days shifted. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8187 | 07c5f4cf9e7545529e14a00ac089da46 | [] | 1 | single_choice | An average of $$40$$ campers sign up for each of the $$6$$ sports at camp. If each camper signs up for exactly $$3$$ sports, how many campers are there? | [
[
{
"aoVal": "A",
"content": "$$80$$ "
}
],
[
{
"aoVal": "B",
"content": "$$120$$ "
}
],
[
{
"aoVal": "C",
"content": "$$160$$ "
}
],
[
{
"aoVal": "D",
"content": "$$180$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"Since $$40\\times 6=240$$, $$240$$ campers have signed up for the $$6$$ sports, and each camper is counted $$3$$ times. There are $$240\\div 3=80$$ campers in all. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8191 | 0efb74891373421e8d0147802e56a726 | [] | 1 | single_choice | Al ran twice as far as Bob ran. They ran a total off $$18\rm km$$. How far did Al run? | [
[
{
"aoVal": "A",
"content": "$$3\\rm km$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6\\rm km$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9\\rm km$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12\\rm km$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"
] | [
"Al ran twice as far as Bob. Split $$18\\rm km$$ into two parts, one twice the other, to see that Bob ran $$6\\rm km$$ and Al ran twice as far, $$12\\rm km$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8200 | 17dc38aa5551484c95c8f281e7bd5404 | [] | 1 | single_choice | David has $$15$$ more candies than Andy at the beginning. David has $$3$$ candies more than Andy after giving some candies to Andy. How many candies does Debbic give to Aiden? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
],
[
{
"aoVal": "E",
"content": "$$2$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples"
] | [
"$$15-3=12$, $$8\\div 2=4$$. $$\\text{D}$$． "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8203 | 2a32777a3f294c3db19c96bcc6f40345 | [] | 1 | single_choice | Adam paid ＄$$6$$ for $$15$$ buns. How many dollars did Tom pay for the same kind of buns if he bought $$5$$ more of them? (2008 Math Kangaroo Problem, Level 1-2, Question \#13) | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"There are $$3$$ groups of $$5$$ buns in $$15$$ buns: $$15\\div 5=3$$, so $$5$$ buns cost $$6\\div 3=$$＄$$2$$. In total, Tom bought $$15 + 5 = 20$$ buns, which is $$4$$ groups of $$5$$ buns. So, Tom paid $$4\\times 2 =$$＄$$8$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8208 | 080fc4c0106943e99c5c7510e03e431e | [] | 1 | single_choice | If $$20$$ years ago Allen was half as old as he is today, how old was he $$10$$ years ago? | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$40$$ "
}
],
[
{
"aoVal": "D",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->When..., When... Type Age Problems"
] | [
"If $$20$$ years ago Allen was half as old as he is today, then today he is $$40$$. Thus, $$10$$ years ago he was $$30$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8209 | 1c6f60eea57d4b6b9420726a56c8f0a4 | [] | 1 | single_choice | A teacher distributes scorecards equally to students, and there is a surplus of $8$ cards. If $2$ more cards are given to each student, all the cards will be distributed. Then there arestudents in the class in total. | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"If $2$ more scorecards are given to each student, all the cards are distributed. Therefore, the class has $8\\div2=4$ students. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8211 | 53daf37c5f9c4d8bac1a46ec688117cb | [] | 1 | single_choice | Ryan buys a watch on sale for $$20\textbackslash\%$$ off in a shopping mall. He has an additional $$200-$$dollar coupon since he is a member of this shopping mall. The sales tax in his city is $$5\textbackslash\%$$, and he paid $$\textbackslash$2730$$ for this watch. What was the original price of the watch? | [
[
{
"aoVal": "A",
"content": "＄$$2600$$ "
}
],
[
{
"aoVal": "B",
"content": "＄$$2800$$ "
}
],
[
{
"aoVal": "C",
"content": "＄$$3200$$ "
}
],
[
{
"aoVal": "D",
"content": "＄$$3500$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Tax Problems"
] | [
"$$\\dfrac{2730}{1+5\\textbackslash\\%}=2600$$, $$\\dfrac{2600+200}{1-20\\textbackslash\\%}=3500$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8215 | 0f28a2ee525d4883921c8c7d065b5c21 | [
"其它"
] | 1 | single_choice | Workers want to plant some trees between houses. There are $17$ houses on one side of a road. Workers want to plant three trees between every two adjacent houses. How many trees do they need to plant? | [
[
{
"aoVal": "A",
"content": "$$45$$ "
}
],
[
{
"aoVal": "B",
"content": "$$48$$ "
}
],
[
{
"aoVal": "C",
"content": "$$51$$ "
}
],
[
{
"aoVal": "D",
"content": "$$54$$ "
}
],
[
{
"aoVal": "E",
"content": "$$57$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems"
] | [
"$(17 - 1）\\times 3 = 48$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8218 | 4158c9ed7cd1486abe8c31a7aabc6b3d | [] | 1 | single_choice | A sum of $$\textbackslash$459$$ was shared among $$5$$ boys and $$14$$ girls. Each girl received $$\textbackslash$16$$. How much did each boy get? | [
[
{
"aoVal": "A",
"content": "$$$38$$ "
}
],
[
{
"aoVal": "B",
"content": "$$$47$$ "
}
],
[
{
"aoVal": "C",
"content": "$$$52$$ "
}
],
[
{
"aoVal": "D",
"content": "$$$56$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Unitary Method with One Variable"
] | [
"Girls $=14\\times\\textbackslash$16=\\textbackslash$224$ Boys $=\\textbackslash$459-\\textbackslash$224=\\textbackslash$235$ Each boy $=\\textbackslash$235\\div5=\\textbackslash$47$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8225 | 824cc608e403425ab5229c62b26a91b9 | [] | 1 | single_choice | The radius of a coin is $$3\text{cm}$$. When $$4000$$ of these coins are placed side by side in a straight line, how long would this line be? | [
[
{
"aoVal": "A",
"content": "$$240\\text{cm}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12\\text{m}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$240\\text{m}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$1.2\\text{km}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$2.4\\text{km}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"The length of the line is $$4000\\times 2\\times 3\\text{cm=}24000\\text{cm=}240\\text{m}$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8226 | 25a71039e2d649ea95715815053dd12c | [
"其它"
] | 1 | single_choice | Alicia, Bryant, and Charles work for a software company and they want to write a particular computer program. Alicia and Bryant first write $\frac{1}{3}$ of the program in $6$ days. Then Bryant and Charles write $\frac{1}{4}$ of the remaining program in $2$ days. In the end three of them work together to finish the program in $5$ days. How many days will it take if Alicia works on the program by herself? | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$36$$ "
}
],
[
{
"aoVal": "C",
"content": "$$45$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
],
[
{
"aoVal": "E",
"content": "$$75$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"In the second part, Bryant and Charles can write $\\left( 1-\\frac{1}{3} \\right) \\times \\frac{1}{4}=\\frac{1}{6}$ of the program in 2 days. Therefore, they can write $\\frac{1}{6} \\div 2 =\\frac{1}{12}$ in one day. There is still $1-\\frac{1}{3}-\\frac{1}{6}=\\frac{1}{2}$ left. Now in the last part, they work together and finish in $5$ days. They can write $\\frac{1}{2} \\div 5=\\frac{1}{10}$ in one day. Therefore, Alicia can write $\\frac{1}{10}-\\frac{1}{12}=\\frac{1}{60}$ in one day, which means she needs $60$ days to complete. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8229 | 08668fdb94c74452ac365f111e2e8e33 | [
"其它"
] | 1 | single_choice | A gardener has a box of bulbs to plant in a garden. The garden has three sections. She plants 1/2~of the bulbs in the first section. She plants 3 /4~of the remaining bulbs in the second section. She has 6 bulbs left, which she plants in the third section. How many bulbs were in the box at the start? | [
[
{
"aoVal": "A",
"content": "$$16$$ "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ "
}
],
[
{
"aoVal": "C",
"content": "$$24$$ "
}
],
[
{
"aoVal": "D",
"content": "$$32$$ "
}
],
[
{
"aoVal": "E",
"content": "$$48$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"1- 1/2 - 1/2 x 3/4=1/8，1/8 means 6 bulbs, so in total there are 6~$\\div$~1/8=48 bulbs. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8236 | 139128ca94ae4d4bab6367b96fcccc3b | [
"其它"
] | 1 | single_choice | John is 8 years and 3 months old. Alice is 102 months old. Cindy has been alive for 4380 days. Who is the oldest? | [
[
{
"aoVal": "A",
"content": "John "
}
],
[
{
"aoVal": "B",
"content": "Alice "
}
],
[
{
"aoVal": "C",
"content": "Cindy "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time->Period of Dates"
] | [
"omitted "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8240 | 0b750c016aa84b1e98d018a58e707e55 | [
"其它"
] | 1 | single_choice | As a Grade 1 student, Jenny saw thirteen seats in a row in the class, and she didn\textquotesingle t know which one belonged to her. The teacher told her that there were seven students behind her seat. So which seat should she sit?(Adapted from 2015 Math Kangaroo Problem, Level 1-2, Question \#18) ~\hspace{0pt}\hspace{0pt}\hspace{0pt}\hspace{0pt} | [
[
{
"aoVal": "A",
"content": "$$5$$\\textsuperscript{th} "
}
],
[
{
"aoVal": "B",
"content": "$$6$$\\textsuperscript{th} "
}
],
[
{
"aoVal": "C",
"content": "$$7$$\\textsuperscript{th} "
}
],
[
{
"aoVal": "D",
"content": "$$8$$\\textsuperscript{th} "
}
],
[
{
"aoVal": "E",
"content": "$$9$$\\textsuperscript{th} "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$13-7=6$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 8245 | 53e3e22d97e4474ebe87536c3dd401b6 | [] | 1 | single_choice | A clothing store bought some shirts at＄$$96$$ each. It wants to earn＄$$24 $$ for each shirt after a discount of $$20 \textbackslash\% $$. What is the selling price before the discount for each shirt? | [
[
{
"aoVal": "A",
"content": "$$100$$ dollars "
}
],
[
{
"aoVal": "B",
"content": "$$120$$ dollars "
}
],
[
{
"aoVal": "C",
"content": "$$150$$ dollars "
}
],
[
{
"aoVal": "D",
"content": "$$180$$ dollars "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"$$\\left( 96+24 \\right)\\div \\left( 1-20 \\textbackslash\\% \\right)=150$$ dollars. "
] | C |
Subsets and Splits