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 | 10038 | 6eae84a23c684eb1899dd108e1b92c60 | [
"其它"
] | 1 | single_choice | There are only lilies and roses in Bud\textquotesingle s garden. One third of the flowers are roses. There are 12 roses in total. How many flowers are there in Buds\textquotesingle s garden? | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$24$$ "
}
],
[
{
"aoVal": "E",
"content": "$$36$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$12\\div\\frac13=36$$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10048 | f6ad7069dbd04cfa8649fcb5a22d0b61 | [] | 1 | single_choice | A shop purchased some tennis rackets at ＄$$150$$ each. It then sold them at ＄$$175$$ each. How much did the shopkeeper earn for $$10$$ rackets? | [
[
{
"aoVal": "A",
"content": "＄$$150$$ "
}
],
[
{
"aoVal": "B",
"content": "＄$$200$$ "
}
],
[
{
"aoVal": "C",
"content": "＄$$250$$ "
}
],
[
{
"aoVal": "D",
"content": "＄$$300$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"$$(175-150)\\times 10 = 250$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10051 | 852a084f79704329a3e7234f0df71006 | [] | 1 | single_choice | Little Pig is standing in a line. There are $$16$$ animals in the line and her position is the $$4$$\textsuperscript{th} counting from front to back. How many animals are behind her?~\uline{~~~~~~~~~~}~ | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$11$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$13$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"Ms. Pig is included in the \"$$4$$\" , so there are $$16 - 4 = 12$$ animals behind her. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10053 | ed6df277297d4a219498823b25d0efcb | [
"其它"
] | 1 | single_choice | There are $5$ people in Linda\textquotesingle s family with an average weight of $56$ kg. The weights of Linda, Linda\textquotesingle s mom, Linda\textquotesingle s sister, and Linda\textquotesingle s brother are $45$ kg, $55$ kg, $50$ kg, and $60$ kg, respectively. What is the weight of Harry\textquotesingle s dad? | [
[
{
"aoVal": "A",
"content": "$$65$$ "
}
],
[
{
"aoVal": "B",
"content": "$$66$$ "
}
],
[
{
"aoVal": "C",
"content": "$$68$$ "
}
],
[
{
"aoVal": "D",
"content": "$$70$$ "
}
],
[
{
"aoVal": "E",
"content": "$$75$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"$$56\\times5-45-55-50-60=70$$ kg "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10055 | bae717935691490dbaedd190eb428cd5 | [] | 1 | single_choice | Della decides to buy some stationaries for her students. The price of two schoolbags is equal to the price of six notebooks, and the price of six pencilcases is equal to nine notebooks. Given that one schoolbag can be exchanged for four pens, how many pens can be exchanged for one pencilcase? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$3$$ "
}
],
[
{
"aoVal": "E",
"content": "$$2$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"$$1$$ schoolbag$$=3$$ notebooks$$=4$$ pens, and $$6$$ pencilcases$$=9$$ notebooks, Then, $$2$$ pencilcases$$=3$$ notebooks$$=4$$ pens. So, $$1$$ pencilcase$$=2$$ pens. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10059 | 9f8f6bcb5ad141dc80e1c9eff1a82697 | [
"其它"
] | 2 | single_choice | Suppose $20 \textbackslash\%$ of $x$ equals $40\textbackslash\%$ of $y$. What percentage of $y$ is $x$ ? (adapted from 2020 AMC 8, Question 15) | [
[
{
"aoVal": "A",
"content": "$$35$$ "
}
],
[
{
"aoVal": "B",
"content": "$$50$$ "
}
],
[
{
"aoVal": "C",
"content": "$$75$$ "
}
],
[
{
"aoVal": "D",
"content": "$150$ "
}
],
[
{
"aoVal": "E",
"content": "$$200$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$20 \\textbackslash\\% \\cdot x = 40\\textbackslash\\% \\cdot y$ $ x = 2 \\cdot y$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10061 | 6a5292165b2341409836a18a62d96c49 | [] | 1 | single_choice | Iate half an apple pie on Saturday and two thirds of the remainder on Sunday. What fraction of the pie was left for Monday? | [
[
{
"aoVal": "A",
"content": "None "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{1}{2}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{1}{3}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{2}{3}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$\\frac{1}{6}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Understanding the Base"
] | [
"After I eat one half, half of the apple pie is left. Eating two thirds of this half leaves one third of one half of the pie, which is one sixth, for Monday. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10062 | 6ec85a1e2fbd4a2c99595d27711fb80d | [] | 1 | single_choice | If $$1000\textbackslash\%$$ of a certain number is $$100$$, the certain number is． | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$100$$ "
}
],
[
{
"aoVal": "D",
"content": "$$1000$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"If $$1000\\textbackslash\\%$$ is $$100$$, then $$\\left(\\frac{1}{10}\\right)\\text{th}$$ of that, $$10$$, is $$100\\textbackslash\\%$$ of the number. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10064 | 91eea44d205446b0a65e7aaac998e481 | [] | 2 | single_choice | Jin loves carrots! Yesterday she ate $$\frac{7}{9}$$ of her carrots, and today she ate $$\frac{2}{7}$$ of the number of carrots she ate yesterday. She ate 14 carrots today. Yesterday she had started with carrots. | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$49$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
],
[
{
"aoVal": "E",
"content": "$$63$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"$14\\div\\dfrac{2}{7}\\div\\dfrac{7}{9}=63$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10065 | 734262e9f24a4d71922b342d645c8800 | [] | 1 | single_choice | A total of $$20$$ chickens and rabbits are caged together. If there are $$56$$ legs in total, how many chickens are there in the cage? | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$15$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"
] | [
"Suppose the number of chickens is $x$, so the number of rabbits is $(20-x)$. $2x+(20-x)\\times4=56$, $x=12$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10066 | 65ebe75f96b943eaab206cf5336b9351 | [] | 1 | single_choice | Ellie and Gloria have to interview a total of $$400$$ people. Ellie can interview $$60$$ people every week. If Gloria and Ellie work together, they can finish all the work in $$4$$ weeks. How many weeks will it take to finish interviewing everyone by Gloria herself? | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14$$ "
}
],
[
{
"aoVal": "E",
"content": "$$16$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems->Collaborative Work Word Problems"
] | [
"Working together: $$400\\div4=100$$ people every week Gloria: $$100-60=40$$ people every week $$400\\div40=10$$ weeks $\\textasciitilde$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10072 | 85401eee5cf84a30b1d10993cbb79b5f | [] | 1 | single_choice | $50$ balloons are distributed to Ariel and seven other children. Each of them can get at least one balloon, and no two of them get the same number of balloons. For Ariel, what is the largest possible number of balloons she can get? | [
[
{
"aoVal": "A",
"content": "$$22$$ "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14$$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Problems Involving Extreme Value"
] | [
"The largest number of balloons Ariel can get is: $$50 -- (1 + 2 + 3 + 4 + 5+6+7) = 22$$, that is, $$22$$ balloons at most. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10074 | ad45ededfc2341bf9fd3109431ab96ef | [
"其它"
] | 2 | single_choice | $$29$$ students came into the classroom in turn. The number of students that came in before Mike was $$5$$ more than the number of students who came in after him. Which place did Mike come in? (Adapted from 2015 Math Kangaroo Problem, Level 3 - 4, Question \#13) | [
[
{
"aoVal": "A",
"content": "$$11$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ "
}
],
[
{
"aoVal": "D",
"content": "$$17$$ "
}
],
[
{
"aoVal": "E",
"content": "$$18$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Order of one Character"
] | [
"The sum of the number of students that came in before Tom and the number of students that came in after him is $29 - 1 = 28$. The number of students that came in before Mike was $(28 + 6) \\div 2 = 17$, so Mike was the eighteenth. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10075 | 6a628a3a16d54dd5bdd0196dc359c4f5 | [] | 1 | single_choice | A $$15\textbackslash\%$$ sugar solution contains $$18$$ ounces of pure sugar. How many ounces of solution are there? | [
[
{
"aoVal": "A",
"content": "$$90$$ ounces "
}
],
[
{
"aoVal": "B",
"content": "$$100$$ ounces "
}
],
[
{
"aoVal": "C",
"content": "$$120$$ ounces "
}
],
[
{
"aoVal": "D",
"content": "$$150$$ ounces "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Basic Concentration Problems"
] | [
"$$18\\div15\\textbackslash\\% = 120$$ ounces. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10076 | 9b0d3498866e42d6accf73ee3833b32a | [] | 1 | single_choice | My first day of vacation is May $$10$$. My last day of vacation is May $$20$$ of the same year. How many days of vacation do I have? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$ 10 $$ "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"$20-10+1=11$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10079 | e8dd747172404febbdf716e450fcc095 | [] | 1 | single_choice | The sum of two numbers is $$71$$. The difference of the two numbers is $$9$$. Find the bigger number. | [
[
{
"aoVal": "A",
"content": "$$31$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$62$$ "
}
],
[
{
"aoVal": "D",
"content": "$$80$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"
] | [
"71 + 9 = 80 80 $\\div $ 2 = 40 "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10097 | 9fa8a0cd4c08480391f0e024baaf3cd7 | [] | 1 | single_choice | For a quarter ($$25$$￠), Pat can play a video game for $$5$$ minutes. How many quarters does Pat need to play for an hour? | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$55$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division"
] | [
"For a quarter ($$25$$￠), Pat can play a video game for $$5$$ minutes. The number of $$5$$-minute intervals in $$1$$ hour is $$60 \\div 5 = 12$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10098 | d1ebe824fc414485b7edffbd1ba0cd53 | [
"其它"
] | 1 | single_choice | The teacher has $$14$$ sweets. She wants to give eight students the same number of sweets. How many more sweets should she prepare? (adapted from $$2020$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$16$$) | [
[
{
"aoVal": "A",
"content": "$$0$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2$$ "
}
],
[
{
"aoVal": "D",
"content": "$$3$$ "
}
],
[
{
"aoVal": "E",
"content": "$$4$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$14=8+6$$, ~In this equation, $$8$$ means everyone can get $$1$$ sweet. There are $$6$$ sweets left, the teacher also needs $$8-6=2$$ sweets. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10099 | 661500241d7e46cea4ca7d8284f6e719 | [] | 1 | single_choice | Given that May $$16$$ of a certain year is a Monday, what day of the week will July $$8$$ fall on in the same year? | [
[
{
"aoVal": "A",
"content": "Monday "
}
],
[
{
"aoVal": "B",
"content": "Tuesday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Thursday "
}
],
[
{
"aoVal": "E",
"content": "Friday "
}
],
[
{
"aoVal": "F",
"content": "Saturday "
}
],
[
{
"aoVal": "G",
"content": "Sunday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"May: $31-16+1=16$ June: $30$ July: $8$ $16+30+8=54$ $54\\div7=7$ R $5$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10101 | 7c5b3d9c23894d118f57006c2f05574b | [] | 1 | single_choice | $$\frac{1}{4}$$ of the beads in a box are blue. $$\frac{1}{3}$$ of the blue beads are small. lf there are $$700$$ small blue beads, how many beads are there altogether in the box? | [
[
{
"aoVal": "A",
"content": "$$1200$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2100$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2450$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4900$$ "
}
],
[
{
"aoVal": "E",
"content": "$$8400$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"$\\frac{1}{4}\\times\\frac{1}{3}=\\frac{1}{12}$ of the total beads are small blue beads. $700\\times12=8400$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10105 | 89e28de887504979bbd887f81e75e37f | [
"其它"
] | 0 | single_choice | Nick bought $20$ apples from the supermarket. $40$\% of them were red and $60$\% of them were green. How many red apples did he buy? | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$20 \\times 40$\\%=$8$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10106 | f6bfde07413443039d5107b3d22eeec8 | [] | 1 | single_choice | Famer $$A$$ had $$1233$$ ducks. He had three times as many ducks as Farmer $$B$$. Farmer $$B$$ had $$199$$ more ducks than Farmer $$C$$. How many ducks did Farmer $$C$$ have? | [
[
{
"aoVal": "A",
"content": "$$212$$ "
}
],
[
{
"aoVal": "B",
"content": "$$411$$ "
}
],
[
{
"aoVal": "C",
"content": "$$610$$ "
}
],
[
{
"aoVal": "D",
"content": "$$3898$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Word Problems Involving Comparing and Ordering"
] | [
"Farmer B\\textquotesingle s duck: $$1233 \\div3 = 411$$ Farmer C\\textquotesingle s duck: $$411-199=212$$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10107 | ed7fecacb49e46d996afa582a543ed7e | [] | 1 | single_choice | Given that June $$14$$, $$2012$$ was Thursday, what day was June $$14$$, $$2014$$? | [
[
{
"aoVal": "A",
"content": "Monday "
}
],
[
{
"aoVal": "B",
"content": "Tuesday "
}
],
[
{
"aoVal": "C",
"content": "Friday "
}
],
[
{
"aoVal": "D",
"content": "Saturday "
}
],
[
{
"aoVal": "E",
"content": "Sunday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"It would pass $365+365=730$ days, which means June $$14$$, $$2014$$ was two days after Thursday. It was Saturday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10109 | 6a86817df9734b3b8851d9d795a672a9 | [
"其它"
] | 3 | single_choice | There are some apples and $8$ pears in a basket, each of them are green or yellow. There are three more apples than the total number of green fruit. There are $6$ yellow pears. How many yellow apples are there in the basket? | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
],
[
{
"aoVal": "E",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"NA "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10115 | 85626f0234f545929198e86c5d19efdf | [] | 1 | single_choice | Starting with some gold coins and some empty treasure chests, I tried to put $$9$$ gold coins in each treasure chest, but that left $$2$$ treasure chests empty. So instead I put $$6$$ gold coins in each treasure chest, but then I had $$3$$ gold coins left over. How many gold coins did I have? ． | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$27$$ "
}
],
[
{
"aoVal": "C",
"content": "$$45$$ "
}
],
[
{
"aoVal": "D",
"content": "$$63$$ "
}
],
[
{
"aoVal": "E",
"content": "$$81$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"
] | [
"Suppose $x$ is the number of treasure chests. Thus the number of gold coins can be represented as $$9(x-2)$$ or $$6x + 3$$. So, $$9(x-2)=6x+3$$, $$x=7$$. There are $$9\\times (7-2)=45$$ gold coins. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10116 | ed8225458c1f4b24b0010c9bec5761e9 | [] | 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 | 10121 | b6793c50885f45c88b71601d954f0487 | [] | 2 | single_choice | On a map $4\text{cm}$ represents $50\text{km}$. The distance between town A and town B is $14\text{cm}$. A car leaves town A and travels towards town B at $35$km per hour. How long does it take the car to travel to town B? | [
[
{
"aoVal": "A",
"content": "$4\\text{hours}$ "
}
],
[
{
"aoVal": "B",
"content": "$5\\text{hours}$ "
}
],
[
{
"aoVal": "C",
"content": "$10\\text{hours}$ "
}
],
[
{
"aoVal": "D",
"content": "$14\\text{hours}$ "
}
],
[
{
"aoVal": "E",
"content": "$18\\text{hours}$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Basic Units"
] | [
"If $$4\\textasciitilde\\text{cm}$$ represents $$50\\textasciitilde\\text{km}$$, $$2\\textasciitilde\\text{cm}$$ represents $$25\\textasciitilde\\text{km}$$. So, their actual distance apart is $$14\\div2\\times 25=175\\textasciitilde\\text{km}$$. $175\\div35=5$ hours. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10123 | 969ee083a420427f9c66a505aaf596b9 | [] | 1 | single_choice | Students guess that Norb\textquotesingle s age is $$24$$, $$28$$, $$30$$, $$32$$, $$36$$, $$38$$, $$41$$, $$44$$, $$47$$, and $$49$$. Norb says, "At least half of you guessed too low, two of you are off by one, and my age is a prime number." How old is Norb? ($$2011$$ AMC $$8$$ problem, Question \#$$21$$) | [
[
{
"aoVal": "A",
"content": "$$29$$ "
}
],
[
{
"aoVal": "B",
"content": "$$31$$ "
}
],
[
{
"aoVal": "C",
"content": "$$37$$ "
}
],
[
{
"aoVal": "D",
"content": "$$43$$ "
}
],
[
{
"aoVal": "E",
"content": "$$48$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"
] | [
"If at least half the guesses are too low, then Norb\\textquotesingle s age must be greater than $$36$$. If two of the guesses are off by one, then his age is in between two guesses whose difference is $$2$$. It could be $$31$$, $$37$$, or $$48$$, but because his age is greater than $$36$$, it can only be $$37$$ or $$48$$. Lastly, Norb\\textquotesingle s age is a prime number so the answer must be $$37$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10128 | 80ef214ca0944e1f99b6c093c269d362 | [] | 1 | single_choice | Joan needs $$250$$ pounds of metal with $$27\textbackslash\%$$ silver. If Joan combines one metal with $$23\textbackslash\%$$ silver, and another with $$43\textbackslash\%$$ silver,how much of each metal does Joan need respectively? | [
[
{
"aoVal": "A",
"content": "$$200$$;$$50$$ "
}
],
[
{
"aoVal": "B",
"content": "$$150$$;$$100$$ "
}
],
[
{
"aoVal": "C",
"content": "$$100$$;$$150$$ "
}
],
[
{
"aoVal": "D",
"content": "$$50$$;$$200$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"
] | [
"$$\\dfrac{43\\textbackslash\\%-27\\textbackslash\\%}{27\\textbackslash\\%-23\\textbackslash\\%}=\\dfrac{16}{4}=\\dfrac{4}{1}$$, $$23\\textbackslash\\%$$ silver:$$250\\times\\dfrac{4}{4+1}=200$$, $$43\\textbackslash\\%$$ silver:$$250\\times\\dfrac{4}{4+1}=50$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10133 | 921e1c9d500f4fb6908ed5ae5bf69f4b | [] | 1 | single_choice | Ten years ago, the sum of the ages of my mother and father was $$71$$. What is the sum of their ages today? | [
[
{
"aoVal": "A",
"content": "$$51$$ "
}
],
[
{
"aoVal": "B",
"content": "$$61$$ "
}
],
[
{
"aoVal": "C",
"content": "$$81$$ "
}
],
[
{
"aoVal": "D",
"content": "$$91$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"
] | [
"Ten years ago, the sum of the ages of my mother and father was $$71$$. Each has aged $$10$$ years, so the sum of their ages is now $$91$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10135 | c8ce363c75704746b22d6a22dab82be1 | [] | 1 | single_choice | If I start with $2$, and begin to count in $$3$$s, my $50^{}\text{th}$ number will be~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "$$148$$ "
}
],
[
{
"aoVal": "B",
"content": "$$149$$ "
}
],
[
{
"aoVal": "C",
"content": "$$150$$ "
}
],
[
{
"aoVal": "D",
"content": "$$151$$ "
}
],
[
{
"aoVal": "E",
"content": "$$152$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression"
] | [
"$2+(50-1)\\times3=149$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10142 | bb0f7f7359024a30b9c03e2c78a9fcf9 | [] | 1 | single_choice | In the yard there is an equal number of pigs, ducks and chickens. Together, they have $$144$$ legs. How many ducks are there in the yard? | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$21$$ "
}
],
[
{
"aoVal": "C",
"content": "$$35$$ "
}
],
[
{
"aoVal": "D",
"content": "$$42$$ "
}
],
[
{
"aoVal": "E",
"content": "$$43$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Word Problems for Linear Equations with One Variable"
] | [
"Suppose there are $$x$$ ducks in the yard. Since there is an equal number of pigs, ducks and chickens, $$2x+4x+2x=144$$, $$x=18$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10145 | 9b376731e4384b4eb5c84d621ed8ae70 | [
"其它"
] | 1 | single_choice | Emma is $9$ years old. Anna is $12$ years old. Peter is older than Emma but younger than Anna. How old is Peter? | [
[
{
"aoVal": "A",
"content": "$$13$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
],
[
{
"aoVal": "E",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"NA "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10146 | 9b377bb4559645a791fbd510ce8e4e95 | [
"其它"
] | 1 | single_choice | Some kangaroos are lining at bakery. Tom is the third kangaroo from the back, and the fifth from the front. How many kangaroos are there lining up in total? | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$3+5-1=7$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10157 | dfb9468e2d084f5e92efce40a53865cc | [
"其它"
] | 1 | single_choice | Henderson has $$9$$ sweets more than Flora. After teacher Johnny gave each of them $$7$$ more sweets, they have a total of $$43$$ sweets. How many sweets does Flora has at first? | [
[
{
"aoVal": "A",
"content": "$$16$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$17$$ "
}
],
[
{
"aoVal": "E",
"content": "$$19$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$43-14-9=20$$ $$20\\div2=10$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10161 | 6ab7c9dc4c474cc1bb6bd67284c2eb66 | [] | 1 | single_choice | If today is a Tuesday, then $$15$$ days ago was a. | [
[
{
"aoVal": "A",
"content": "Saturday "
}
],
[
{
"aoVal": "B",
"content": "Sunday "
}
],
[
{
"aoVal": "C",
"content": "Monday "
}
],
[
{
"aoVal": "D",
"content": "Wednesday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"Today is Tues. $$14$$ days ago was Tues. $$15$$ days ago was Mon. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10167 | 8dae3c7d2b1b4cc7afc61009c5a9b46a | [] | 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": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"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: $$2x+2y+2z=18$$, $$x+y+z=9$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10173 | 781df94552ff4868aecf85113a21c431 | [] | 1 | single_choice | In a jar of red, green, and blue marbles, all but $$16$$ are red marbles, all but $$18$$ are green, and all but $$14$$ are blue. How many marbles are in the jar? ． | [
[
{
"aoVal": "A",
"content": "$$16$$ "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$24$$ "
}
],
[
{
"aoVal": "E",
"content": "$$36$$ "
}
]
] | [
"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 $$\\begin{cases} x+y=14① \\textbackslash\\textbackslash{} y+z=16②\\textbackslash\\x+z=18③\\end{cases}$$, ①$$+$$②$$+$$③: $$2x+2y+2z=48$$, $$x+y+z=24$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10179 | 96c534b4d3dc4f0eb5c95e67274ed430 | [] | 1 | single_choice | Sanjay let me finish his box of mints. He had eaten $$\frac{5}{8}$$ of them. If $$36$$ mints were left for me, how many mints were there in the box at the start? | [
[
{
"aoVal": "A",
"content": "$$96$$ "
}
],
[
{
"aoVal": "B",
"content": "$$58$$ "
}
],
[
{
"aoVal": "C",
"content": "$$68$$ "
}
],
[
{
"aoVal": "D",
"content": "$$36$$ "
}
],
[
{
"aoVal": "E",
"content": "$$56$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"$36\\div(1-\\dfrac{5}{8})=96$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10190 | ad82efc65ea146d6be5abb18ad5c5487 | [] | 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 | 10191 | ad83a6be67494553a9b4b6808dbf8b25 | [
"其它"
] | 2 | single_choice | Calculate: $\frac{1}{1\times 7}+\frac{1}{7\times 13}+\frac{1}{13\times 19} + \cdots +\frac{1}{1207\times 1213}$ | [
[
{
"aoVal": "A",
"content": "$\\frac{1212}{1213}$ "
}
],
[
{
"aoVal": "B",
"content": "$\\frac{303}{1213}$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac{202}{1213}$ "
}
],
[
{
"aoVal": "D",
"content": "$\\frac{1212}{6065}$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples"
] | [
"C "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10194 | 6f543e755cdc4aca9d32c108d1d6b737 | [
"其它"
] | 1 | single_choice | There are $$300$$ students in Think Primary School. Three-tenths of the students are in year $$5$$ and three-fifths of the year $$5$$ students are girls. How many year $$5$$ girls are there in Think Primary School? | [
[
{
"aoVal": "A",
"content": "$$36$$ "
}
],
[
{
"aoVal": "B",
"content": "$$48$$ "
}
],
[
{
"aoVal": "C",
"content": "$$54$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
],
[
{
"aoVal": "E",
"content": "$$90$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages"
] | [
"$$300\\times\\frac{3}{10}\\times\\frac{3}{5}=54$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10199 | d6a3d5d087e74610849ebbfb78ccf315 | [
"其它"
] | 1 | single_choice | The five-digit number $411A2$ is a multiple of $9$. What digit does A represent? | [
[
{
"aoVal": "A",
"content": "$$0$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2$$ "
}
],
[
{
"aoVal": "D",
"content": "$$3$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division"
] | [
"From the Divisibility Rule of $9$, the sum of the digit of 411A2 must be divisible by $9$. $4 + 1 + 1+ 4 + 2 = 8 + A$ Hence A = $1$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10200 | 85a50c31d5664a38bac85dcbaf8c7ee1 | [] | 1 | single_choice | Iron Man\textquotesingle s flying speed is $$12,250$$km/h, which is $$25$$ times the speed of a regular airplane. What is the speed of the airplane? | [
[
{
"aoVal": "A",
"content": "$$490$$km/h "
}
],
[
{
"aoVal": "B",
"content": "$$500$$km/h "
}
],
[
{
"aoVal": "C",
"content": "$$4900$$km/h "
}
],
[
{
"aoVal": "D",
"content": "$$5000$$km/h "
}
],
[
{
"aoVal": "E",
"content": "$$245$$km/h "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"
] | [
"The speed of the airplane is~$12250\\div25=490$km/h. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10204 | 73c802dc558f4bcbab09a12d4d82909f | [] | 1 | single_choice | I am threading blue and purple beads onto a necklace in the ratio $$2 : 5$$. I use $$98$$ beads in total. How many more purple beads than blue do I use? | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$35$$ "
}
],
[
{
"aoVal": "C",
"content": "$$42$$ "
}
],
[
{
"aoVal": "D",
"content": "$$14$$ "
}
],
[
{
"aoVal": "E",
"content": "$$49$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Dividing Quantities Based on Ratio"
] | [
"The ratio $$2 : 5$$ means that $$2$$ in $$7$$ beads are blue and $$5$$ in $$7$$ purple. Since $$98 \\div 7 = 14$$, there are $$28$$ blue and $$70$$ purple beads, hence $$70 - 28 = 42$$ more purple than blue. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10205 | 813383f185f649208136f6697834391b | [
"其它"
] | 1 | single_choice | If Pip was 10 years old 5 years ago, how old will he be 7 years from now? | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$14$$ "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ "
}
],
[
{
"aoVal": "D",
"content": "$$22$$ "
}
],
[
{
"aoVal": "E",
"content": "$$18$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"$$10+5+7=22$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10206 | 8a2e5395b9eb47f481dc5b4f8b2d0466 | [
"其它"
] | 1 | single_choice | Harry planted some trees around a $20$m by $20$m square garden. If there are trees planted at each of the $4$ corners, and the distance between every $2$ trees is $5$m, at least how many trees did Harry plant? | [
[
{
"aoVal": "A",
"content": "$$16$$ "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$22$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Circular Paths->Planting Trees (circular path)"
] | [
"$20 \\div 5 = 4$ intervals on each side $4+1=5$ trees on each side $4\\times5-4=16$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10207 | 6aebd95af8944cebbc8801aa2e4d8bd2 | [
"其它"
] | 1 | single_choice | There is a basket of peaches. Three students take turns to take peaches. Sana takes $2$ less than the half of peaches. Joann takes $2$ more than half of the remaining peaches. Now, there are $5$ peaches in the basket. How many peaches are there in the basket at beginning? | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$22$$ "
}
],
[
{
"aoVal": "C",
"content": "$$24$$ "
}
],
[
{
"aoVal": "D",
"content": "$$28$$ "
}
],
[
{
"aoVal": "E",
"content": "$$18$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"$$5+2=7$$ $7+7=14$ $14-2=12$ $12+12=24$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10209 | 7cb6d56eaf41498887b277546ad90a04 | [] | 2 | single_choice | Mother\textquotesingle s Day in $$2020$$ was May $$10$$th, which was Sunday. Father\textquotesingle s Day in $$2020$$ was June $$21$$st. On what day did Father\textquotesingle s Day fall? | [
[
{
"aoVal": "A",
"content": "Thursday "
}
],
[
{
"aoVal": "B",
"content": "Saturday "
}
],
[
{
"aoVal": "C",
"content": "Sunday "
}
],
[
{
"aoVal": "D",
"content": "Tuesday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"It passed $$31-10 + 21 = 42$$ days in total. Since $$42 \\div 7 = 6$$, which means the Father\\textquotesingle s Day fell on Sunday as well. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10218 | 9fee5f2c8743488e8e60e6b37f3c2f9c | [] | 1 | single_choice | Andy has $$6$$ candies. Bob has twice as many candies as Andy. Chloe has $$4$$ times as many candies as Andy. How many candies do they have altogether? | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$35$$ "
}
],
[
{
"aoVal": "C",
"content": "$$42$$ "
}
],
[
{
"aoVal": "D",
"content": "$$48$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"
] | [
"omitted "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10220 | 813d58533c104684987e10cc5a3ddd80 | [
"其它"
] | 1 | single_choice | James wants to make $5$ cakes. Each day he makes one cake. He made the first cake on Tuesday. What day of the week will it be when he makes the last cake? (Adapted from 2011 Math Kangaroo Problem, Level 3-4, Question \#2) | [
[
{
"aoVal": "A",
"content": "Wednesday "
}
],
[
{
"aoVal": "B",
"content": "Thursday "
}
],
[
{
"aoVal": "C",
"content": "Friday "
}
],
[
{
"aoVal": "D",
"content": "Saturday "
}
],
[
{
"aoVal": "E",
"content": "Sunday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"Count day by day directly. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10228 | e908b28c0b1145519f961769146a5acb | [] | 1 | single_choice | Half a loaf of bread costs $$6$$ pence more than one-fourth of a loaf of bread. How many pence does a whole loaf of bread cost? ($$1998$$ Math Kangaroo Problem, Level $$3-4$$, Question \#$$14$$) | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$12$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$24$$ "
}
],
[
{
"aoVal": "E",
"content": "$$30$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"One-fourth of a loaf of bread is \"$$1$$ unit\". Half a loaf of bread is \"$$2$$ units\". One-fourth of a loaf of bread: $$6 \\div (2-1) =6$$. A whole loaf of bread: $$6 \\times 4 =24$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10232 | b6ac93d6d6744587b2fc2b72a7215a82 | [] | 1 | single_choice | Many years ago, $$1^{\text{st}}$$ of May was a Friday. Which day of the week was $$23^{\text{rd}}$$ of May in that year? | [
[
{
"aoVal": "A",
"content": "Thursday "
}
],
[
{
"aoVal": "B",
"content": "Friday "
}
],
[
{
"aoVal": "C",
"content": "Saturday "
}
],
[
{
"aoVal": "D",
"content": "Sunday "
}
],
[
{
"aoVal": "E",
"content": "Monday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"First Friday: $$1^{\\text{st}}$$ of May Second Friday: $$8^{\\text{th}}$$ of May Third Friday: $$15^{\\text{th}}$$ of May Fourth Friday: $$22^{\\text{nd}}$$ of May $$23^{\\text{rd}}$$ of May was a \\textbf{Saturday} in that year. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10233 | dfd29d6b2ca9419dbe3a49c5e20ac5c0 | [] | 0 | single_choice | There are stools and chairs in the room. Each stool has $$3$$ legs, and each chair has $$4$$ legs. Altogether there are $$17$$ legs. How many chairs are there in the room? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2$$ "
}
],
[
{
"aoVal": "E",
"content": "$$1$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"
] | [
"If there are five stools, the chairs have $17-3\\times5=2$ legs, which is not applicable. If there are four stools, the chairs have $17-3\\times4=5$~ legs, which is also not applicable. If there are three stools, the chairs have $17-3\\times3=8$ legs, which implies that there are $8\\div4=2$ chairs and is applicable according to the question. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10236 | a48449112fd6460783b4b789b3befa9d | [] | 1 | single_choice | The cost of my algebra book is $$200\textbackslash\%$$ of that of my geometry book. The cost of my geometry book is $$\frac{4}{3}$$ that of my calculus book. If my calculus book costs ＄$$21$$, how much do all $$3$$ books cost together? | [
[
{
"aoVal": "A",
"content": "＄$$28$$ "
}
],
[
{
"aoVal": "B",
"content": "＄$$56$$ "
}
],
[
{
"aoVal": "C",
"content": "＄$$84$$ "
}
],
[
{
"aoVal": "D",
"content": "＄$$105$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"
] | [
"The cost of the calculus book is ＄$$21$$. The cost of my geometry book is ＄$$21\\times \\left(\\frac{4}{3}\\right)=$$＄$$28$$. My algebra book costs ＄$$28 \\times2 =$$＄$$56$$. All $$3$$ books cost ＄$$21+$$＄$$28 +$$＄$$56 =$$＄$$105$$ in total. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10239 | ad9a6562f6074361b85ec39ec692ce41 | [] | 1 | single_choice | There are $$18$$ chocolates in Swee Tuth\textquotesingle s box, $$2$$ each of $$9$$ flavours. She likes only $$6$$ of the flavours. If she picks a chocolate at random, what is the probability of her getting one she doesn\textquotesingle t like? | [
[
{
"aoVal": "A",
"content": "$$\\frac{2}{9}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{1}{3}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{4}{9}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{1}{2}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$\\frac{2}{3}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"
] | [
"Out of $$18$$ chocolates there are $$6\\times2=12$$ of the flavours that she likes. So the probability of Swee Tuth getting one she doesn\\textquotesingle t like is $$\\frac{6}{18} =\\frac{1}{3}$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10243 | 7cd91dbcecf7462cb5f41be7b7cb341b | [] | 1 | single_choice | Maddie is $$2$$ years older than Lola, and Lola is $$6$$ years younger than Ellie. How much older is Ellie than Maddie? | [
[
{
"aoVal": "A",
"content": "$$2$$ years "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ years "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ years "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ years "
}
],
[
{
"aoVal": "E",
"content": "$$6$$ years "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems"
] | [
"Ellie is $$6$$ years older than Lola, and Maddie is $$2$$ years older than Lola. Therefore Ellie is $$4$$ years older than Maddie. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10247 | 85ca1cfe946447d49bd78a4fce6c5a9a | [] | 1 | single_choice | Some students are going to an amusement park. If each student carries $9$ bottles of water in his or her backpack, there will be $2$ students carrying nothing; if one of the students carries $2$ bottles of water and the rest students carry $8$ bottles each, all the bottles of water can be carried to the park. There are~\uline{~~~~~~~~~~}~bottles of water in total that need to be carried. | [
[
{
"aoVal": "A",
"content": "$$80$$ "
}
],
[
{
"aoVal": "B",
"content": "$$90$$ "
}
],
[
{
"aoVal": "C",
"content": "$$92$$ "
}
],
[
{
"aoVal": "D",
"content": "$$102$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Distribution Conversion Problems"
] | [
"Solve the problem as a problem of surplus and shortage. If each student carries $9$ bottles, there will be a shortage of $9\\times2=18$ bottles; if each student carries $8$ bottles, there will be a shortage of $8-2=6$ bottles. Therefore, there are $(18-6)\\div(9-8)=12$ students and $12\\times9-18=90$ bottles of water. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10252 | a004c47a001949c3835adb68300e6dda | [] | 3 | single_choice | In a certain calendar year, there are more Mondays than Fridays, and more Sundays than Wednesdays. Which day of the week is $$1^{}\text{st}$$ March in that year? | [
[
{
"aoVal": "A",
"content": "Monday "
}
],
[
{
"aoVal": "B",
"content": "Tuesday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Thursday "
}
],
[
{
"aoVal": "E",
"content": "Friday "
}
],
[
{
"aoVal": "F",
"content": "Saturday "
}
],
[
{
"aoVal": "G",
"content": "Sunday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"Nil "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10255 | 73f7fbc7b1274949a281c5cb4e6b3934 | [] | 2 | single_choice | A worm is staying at the bottom of a well with a depth of $$13$$ metres. If it climbs up $$4$$ metres in the daytime and slips down $$1$$ metres at night, which day will it climb up to the ground? | [
[
{
"aoVal": "A",
"content": "The $$4$$th day "
}
],
[
{
"aoVal": "B",
"content": "The $$5$$th day "
}
],
[
{
"aoVal": "C",
"content": "The $$6$$th day "
}
],
[
{
"aoVal": "D",
"content": "The $$7$$th day "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Snail Climbing out of Well Problems"
] | [
"It climbs up $$4$$ metres in the day time and slips down $$1$$ metre at night, so it climbs up $$3$$ metres in a whole day. For the first $$3$$ days, it climbs $$9$$ metres. During the day time of the forth day, it climbs $$4$$ metres and reaches the ground. Then it needs four days to climb up to the ground. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10262 | a9228105cf794b369bd1fa87cc69dcae | [] | 1 | single_choice | A jacket was on sale. The original price was ＄$$180$$, and Peter bought it at ＄$$135$$. What was the discount rate? | [
[
{
"aoVal": "A",
"content": "$$135\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$$180\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "C",
"content": "$$75\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$25\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"$$1-135\\div180=25\\textbackslash\\%$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10263 | dfdf9d79237e408ea69cf29acfeca74f | [
"其它"
] | 1 | single_choice | Justin said to his mom, "If I had planted three times as many flowers as I planted, I would have planted $48$ more flowers than I have planted now." How many flowers did Justin plant? | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$23$$ "
}
],
[
{
"aoVal": "C",
"content": "$$24$$ "
}
],
[
{
"aoVal": "D",
"content": "$$22$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems of Sum and Multiple"
] | [
"$48\\div(3-1)=24$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10271 | b237b1c024784dc4bb6d372384aa878b | [] | 1 | single_choice | Ella and George are lining up for dinner. Ella is sitting in the fifth from the front of the line, and George is sitting at the sixth from the end of the line. George and Ella are standing together. How many people are there in total?~(adapted from 2001 Math Kangaroo Problem, Level 3-4, Question \#13) | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$11$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
],
[
{
"aoVal": "E",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Problems Involving Queuing->Finding the Total Number According to the Position of Two Characters in a Line"
] | [
"$5 + 6 - 1 = 10$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10285 | b6c73b737eb04e8d8e77d4b402484383 | [
"其它"
] | 1 | single_choice | There are $20$ children lining up outside a theme park. John is the $14$\textsuperscript{th}~ person counting from the front of the line and Mary is the $2$\textsuperscript{th}~person counting from the back of the line. How many children are standing in line between John and Mary? | [
[
{
"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"
] | [
"Mary is the $$20-2+1=19$$\\textsuperscript{th} person in the line, so there are $$19-14-1=4$$ children are between them. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10290 | 85ed71b7a86c4f869899fd18e6142b0d | [
"其它"
] | 2 | single_choice | A mixture of $80$ liters of paint is $20 \textbackslash\%$ red tint, $30 \textbackslash\%$ yellow tint and $50 \textbackslash\%$ water. $20$ liters of yellow tint are added to the original mixture. What is the percent of yellow tint in the new mixture? (adapted from 2007 AMC 8, Question \#17 ) | [
[
{
"aoVal": "A",
"content": "$$33$$ "
}
],
[
{
"aoVal": "B",
"content": "$$36$$ "
}
],
[
{
"aoVal": "C",
"content": "$$39$$ "
}
],
[
{
"aoVal": "D",
"content": "$$42$$ "
}
],
[
{
"aoVal": "E",
"content": "$$44$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"The original mixture contains $80 \\times 30\\textbackslash\\% = 24$ liters of yellow tint. $$20$$ liters of yellow tint is added to the mixture, the new mixture now has $24+20=44$ liters of yellow tint. New percent of yellow =$\\frac{44}{80+20} =44\\textbackslash\\% $ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10292 | 92924af626904744a53a4aa24edfbaad | [
"其它"
] | 2 | single_choice | Calculate: $1^{3}+2^{3}+3^{3}+\cdots +17^{3}+18^{3}$ | [
[
{
"aoVal": "A",
"content": "$$4447881$$ "
}
],
[
{
"aoVal": "B",
"content": "$$23409$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12654$$ "
}
],
[
{
"aoVal": "D",
"content": "$$29241$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples"
] | [
"D "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10294 | edb7ac291f5541629c62d7dd3c0a710f | [] | 1 | single_choice | A $30\textbackslash\%$ sugar solution contains $12$ g of pure sugar. How many g of solution are there? | [
[
{
"aoVal": "A",
"content": "$30$ g "
}
],
[
{
"aoVal": "B",
"content": "$40$ g "
}
],
[
{
"aoVal": "C",
"content": "$50$ g "
}
],
[
{
"aoVal": "D",
"content": "$60$ g "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems"
] | [
"$$12\\div30\\textbackslash\\%=40$$ g. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10295 | 8a7454b816c54407afc302112d073b2e | [] | 1 | single_choice | Felix and Marmalade are two cats. Together they weigh $$10\text{kg}$$. Felix weighs $$4\text{kg}$$ less than Marmalade. How much does Marmalade weigh? | [
[
{
"aoVal": "A",
"content": "$$3\\text{kg}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6\\text{kg}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7 \\text{kg}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9\\text{kg}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14 \\text{kg}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Problems Involving Sum and Difference"
] | [
"$$F=M-4$$ $$m-4+M=10$$ $$M=7$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10296 | 9b98aaf8a68f48298d0f2f61414a5981 | [
"其它"
] | 0 | single_choice | $9$ more than $43$ is~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "$$42$$ "
}
],
[
{
"aoVal": "B",
"content": "$$52$$ "
}
],
[
{
"aoVal": "C",
"content": "$$62$$ "
}
],
[
{
"aoVal": "D",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction"
] | [
"$$43+9=52$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10297 | a4ab5599226441c289096e41918bfaf5 | [] | 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 | 10301 | 8e18a97bfaa642b9b466b1b99ca05f2b | [] | 1 | single_choice | Sammy\textquotesingle s mom is $$6$$ years older than his dad. Right now, his dad is $$27$$ years old. How old was his mother $$10$$ years ago? | [
[
{
"aoVal": "A",
"content": "$$32$$ "
}
],
[
{
"aoVal": "B",
"content": "$$21$$ "
}
],
[
{
"aoVal": "C",
"content": "$$15$$ "
}
],
[
{
"aoVal": "D",
"content": "$$23$$ "
}
],
[
{
"aoVal": "E",
"content": "$$22$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages"
] | [
"Now, his dad is $27$ years old, his mom is $$6$$ years older than his dad, so his mom is $33$ years old. $10$ years ago, his mom was $33-10=23$ years old. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10302 | 85fc7c11b2ce4b34bd5b08bb03ea86ef | [] | 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"
] | [
"The minute hand rotates $6^{\\circ}$ per minute. The hour hand rotates $\\dfrac{1}{60}\\times30^{\\circ}=\\left (\\dfrac{1}{2}\\right )^{\\circ}$ per mimte. Starting at $3$ O\\textquotesingle clock, the minute hand rotates $\\left (6t\\right )^{\\circ}$ and the hour hand rotates ~$$(90+ \\frac{1}{2}t)^{ \\circ }$$. When the minute and hour hands are next perpendicular: $$6t-\\left (90+ \\frac{1}{2}t\\right )=90$$, $$\\frac{11}{2}t=180$$, $$t= \\frac{360}{11}=32 \\frac{8}{11}$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10303 | a0292144be1847b2ae0cee828747fff1 | [] | 1 | single_choice | Given that October $$10$$th, $$2018$$ was Wednesday, on what day will October $$10$$th, $$2022$$ fall? | [
[
{
"aoVal": "A",
"content": "Monday "
}
],
[
{
"aoVal": "B",
"content": "Tuesday "
}
],
[
{
"aoVal": "C",
"content": "Wednesday "
}
],
[
{
"aoVal": "D",
"content": "Thursday "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Time"
] | [
"During this period, $$2020$$ is a leap years. Therefore, October $$10$$, $$2022$$ is $$1+2+1+1=5$$ days after Wednesday, which is Monday. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10306 | 971c58dc99e649feb3965cee42547cc9 | [
"其它"
] | 1 | single_choice | The average cost of a long-distance call in the USA in 1985 was 56 cents per minute, and the average cost of a long-distance call in the USA in 2018 was 2 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": "$$90$$ "
}
],
[
{
"aoVal": "B",
"content": "$$95$$ "
}
],
[
{
"aoVal": "C",
"content": "$$96$$ "
}
],
[
{
"aoVal": "D",
"content": "$$97$$ "
}
],
[
{
"aoVal": "E",
"content": "$$98$$ "
}
]
] | [
"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 $56-2=54$ so the percent decrease is $\\frac{54}{56}$ which is about $ 96 \\textbackslash\\%$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10308 | bff860a27e694aeaae9264611d50bd66 | [] | 1 | single_choice | At which of these times is the angle between the minute hand and the hour hand of a clock equal to $$150^{}\circ$$? | [
[
{
"aoVal": "A",
"content": "$$9\\text{pm}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8\\text{pm}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6\\text{pm}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5\\text{pm}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$4\\text{pm}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"At all the times given, the minute hand is pointing to $$12$$. When the minute hand is pointing to $$12$$ and the angle between the hands is $$150^{}\\circ$$, the hour hand has turned $$\\frac{150}{360}= \\frac{5}{12}$$ of a complete turn. Therefore the hour hand will point at $$5$$ and the time will be $$5\\text{pm}$$. (There are other times when the angle between the hands is $$150^{}\\circ$$ but, of these, only at $$7\\text{pm}$$ does the minute hand point to $$12$$ and $$7\\text{pm}$$ is not one of the times given.) "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10311 | 7435815422fe4896b89802601c19ee9f | [] | 1 | single_choice | In $$4$$ hours Rob drove $$120 \text{km}$$. He drove at an average rate of $$\text{m/min}$$. | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$105$$ "
}
],
[
{
"aoVal": "C",
"content": "$$120$$ "
}
],
[
{
"aoVal": "D",
"content": "$$500$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"NA "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10314 | bb665ae6d1b546d0af92bbd2e58fae33 | [
"其它"
] | 1 | single_choice | SASMO 2015 P2 Q10 John is 5 years old this year. His sister is 2 years old. What is the sum of their age after 3 years? | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$14$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems"
] | [
"$$5+3=8$$ $$7+3=10$$ $$10+8=18$$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10325 | 972ca3145ba84fb9a281b8dc7e4529b6 | [
"其它"
] | 0 | single_choice | Jack was able to sell $30$\% of his vegetables before noon. If he had 200 pounds of vegetables in the morning, how many pounds of vegetables was he able to sell by noon? | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$50$$ "
}
],
[
{
"aoVal": "C",
"content": "$$60$$ "
}
],
[
{
"aoVal": "D",
"content": "$$140$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] | [
"$200 \\times 30$\\%=$60$, He was able to sell $60$ pounds of vegetables by noon. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10326 | 8614723849fb462f8a8292cb13335ae9 | [] | 1 | single_choice | I am going to travel $$200\text{km}$$ at a rate of $$60\text{km}$$ per hour. How many minutes will my trip take? | [
[
{
"aoVal": "A",
"content": "$$60$$ "
}
],
[
{
"aoVal": "B",
"content": "$$200$$ "
}
],
[
{
"aoVal": "C",
"content": "$$260$$ "
}
],
[
{
"aoVal": "D",
"content": "$$320$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"
] | [
"I am going to travel $$200\\text{km}$$ at $$60\\text{km}$$ per hour. Since $$60\\text{km}$$ per hour is the same as $$1\\text{km}$$ per minute, my trip will take $$200$$ minutes. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10329 | 9bb3e04c6e9e4cfea30b76ef236f8eca | [] | 1 | single_choice | Last year, at the school where Gill teaches Mathematics, $$315$$ out of the $$600$$ pupils were girls. This year, the number of pupils in the school has increased to $$640$$. The proportion of girls is the same as it was last year. How many girls are there at the school this year? | [
[
{
"aoVal": "A",
"content": "$$339$$ "
}
],
[
{
"aoVal": "B",
"content": "$$338$$ "
}
],
[
{
"aoVal": "C",
"content": "$$337$$ "
}
],
[
{
"aoVal": "D",
"content": "$$336$$ "
}
],
[
{
"aoVal": "E",
"content": "$$335$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Knowing the Base"
] | [
"Last year, the fraction of girls at the school was $$\\frac{{315}}{{600}}=\\frac{{63}}{{120}}=\\frac{{21}}{{40}}$$. This year, there are $$40$$ more pupils at the school, but the proportion of girls has remained the same. So there are $$21$$ more girls at the school this year, making a total of $$315+21=336$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10330 | 92b44d441d4c445b9e410bc21076d1a6 | [
"其它"
] | 1 | single_choice | Chloe is buying candies at a grocery store. She can either spend $8$ dollars on a $15$ ounce bag or $12$ dollars on a $20$ ounce bag. Which is a better buy? | [
[
{
"aoVal": "A",
"content": "$15$ ounce bag "
}
],
[
{
"aoVal": "B",
"content": "$20$ ounce bag "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"
] | [
"$\\frac{8\\text{dollars}}{15\\text{ounces}}$ $\\frac{12\\text{dollars}}{20\\text{ounces}}$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10331 | 92b46c93d38c45eb96cc67581778d0dd | [] | 2 | single_choice | Jin loves carrots! Yesterday she ate $$\frac{1}{4}$$ of her carrots, and today she ate $$\frac{2}{7}$$ of the number of she ate yesterday. She ate 10 carrots today. Yesterday she have started with carrots. | [
[
{
"aoVal": "A",
"content": "$$36$$ "
}
],
[
{
"aoVal": "B",
"content": "$$48$$ "
}
],
[
{
"aoVal": "C",
"content": "$$60$$ "
}
],
[
{
"aoVal": "D",
"content": "$$72$$ "
}
],
[
{
"aoVal": "E",
"content": "$$140$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] | [
"$10\\div\\dfrac{2}{7}\\div\\dfrac{1}{4}=140$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10333 | ff8a75f4dedf4cfd864199b80fd8c9de | [] | 1 | single_choice | Tom scored a basket at the end of the third quarter of a basketball game between the Lakers and the Warriors. At that point, what fraction of the whole game remained to be played? | [
[
{
"aoVal": "A",
"content": "$$\\frac{1}{4}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{1}{3}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{1}{2}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{3}{4}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$\\frac{2}{3}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Rate"
] | [
"Basketball games consist of four quarters. Tom\\textquotesingle s scoring at the end of the third quarter implies that there is one quarter left, which is equivalent to 1/4 of the entire game. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10335 | 81b2dbbd3c284454a1b3ad659351ca29 | [
"其它"
] | 1 | single_choice | Five positive integers (not necessarily all different) are written on five cards. Boris calculates the sum of the numbers on every pair of cards. He obtains only three different totals: 57, 70 and 83. What is the largest integer on any card? | [
[
{
"aoVal": "A",
"content": "$$35$$ "
}
],
[
{
"aoVal": "B",
"content": "$$42$$ "
}
],
[
{
"aoVal": "C",
"content": "$$48$$ "
}
],
[
{
"aoVal": "D",
"content": "$$53$$ "
}
],
[
{
"aoVal": "E",
"content": "$$82$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] | [
"Let the five integers be a, b, c, d and e with a ≤ b ≤ c ≤ d ≤ e. The smallest total is 57, which is an odd number so b ≠ a. Similarly, the largest total is 83, which is also an odd number so d ≠ e. Hence we now have a \\textless{} b ≤ c ≤ d \\textless{} e and a + b = 57 and d + e = 83. Only one possible total remains and so b = c = d with c + d = 70. This gives c = d (= b) = 35 and therefore e, the largest integer, is 83 − 35 = 48 (whilst a = 22). "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10339 | 7d4469feaad24219b5be00619ac5bff8 | [
"其它"
] | 1 | single_choice | The average cost of a long-distance call in the USA in 1985 was 44 cents per minute, and the average cost of a long-distance call in the USA in 2005 was 11 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": "$$25$$ "
}
],
[
{
"aoVal": "B",
"content": "$$50$$ "
}
],
[
{
"aoVal": "C",
"content": "$$75$$ "
}
],
[
{
"aoVal": "D",
"content": "$$100$$ "
}
],
[
{
"aoVal": "E",
"content": "$$125$$ "
}
]
] | [
"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 $44-11=33$ so the percent decrease is $\\frac{33}{44}$ which is about $(\\mathbf{c}) 75 \\textbackslash\\%$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10346 | d6df55b356eb476284fbc5f21a128585 | [] | 1 | single_choice | James lives on the second floor, and Paul lives in the same building but has to walk up five times as many stairs as James. There are no stairs to the entrance of the building. On which floor does Paul live? (Adapted from 2000 Math Kangaroo Problem, Level 3-4, Question \#4) | [
[
{
"aoVal": "A",
"content": "On the $$2^{\\rm nd}$$ floor "
}
],
[
{
"aoVal": "B",
"content": "On the $$3^{\\rm rd}$$ floor "
}
],
[
{
"aoVal": "C",
"content": "On the $$4^{\\rm th}$$ floor "
}
],
[
{
"aoVal": "D",
"content": "On the $$5^{\\rm th}$$ floor "
}
],
[
{
"aoVal": "E",
"content": "On the $$6^{\\rm th}$$ floor "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Straight Line Type with Objects on Both Sides->Taking the Stairs"
] | [
"$5+1=6$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10347 | e9366a0a02754888b6aba42b509353d3 | [] | 1 | single_choice | Amy mixes $$10$$ grams of a $$20\textbackslash\%$$ sugar solution and $$40$$ grams of a $$25\textbackslash\%$$ sugar solution together. After~\uline{~~~~~~~~~~}~of water evaporates, the percent concentration of solution is $40\textbackslash\%$. | [
[
{
"aoVal": "A",
"content": "$$15$$ grams "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ grams "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ grams "
}
],
[
{
"aoVal": "D",
"content": "$$25$$ grams "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Concentration Problems->Finding and Making Use of Invariants"
] | [
"$$10\\times20\\textbackslash\\%+40\\times 25\\textbackslash\\%=12$$ grams. $$(10+40)-12\\div40\\textbackslash\\%=20$$ grams. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10353 | 9bccf96246cd42408eb735f1e887d559 | [] | 1 | single_choice | Greta was $$110\text{cm}$$ tall $$2$$ years ago, when she was $$10\text{cm}$$ taller than her brother. They both have grown, but now Greta is $$10\text{cm}$$ shorter than her brother. If her brother grew $$40\text{cm}$$ in those two years, Greta is now$$\text{cm}$$ tall. | [
[
{
"aoVal": "A",
"content": "$$120$$ "
}
],
[
{
"aoVal": "B",
"content": "$$130$$ "
}
],
[
{
"aoVal": "C",
"content": "$$140$$ "
}
],
[
{
"aoVal": "D",
"content": "$$150$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] | [
"Greta was $$110\\text{cm}$$ tall $$2$$ years ago, when she was $$10\\text{cm}$$ taller than her brother. Her brother was $$100\\text{cm}$$ then. Now Greta is $$10\\text{cm}$$ shorter than her brother. If her brother grew $$40\\text{cm}$$, he is now $$140\\text{cm}$$. Greta is now $$130\\text{cm}$$ tall. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10354 | 78eae92279bd483e83ae096cf8a151f2 | [
"其它"
] | 1 | single_choice | The average weight of $4$ students in Class $A$ is $37$ kilograms. The average weight of $11$ students in Class $B$ is $41$ kilograms. The total weight of $5$ students in Class $C$ is $161$ kilograms. What is the average weight of the students in the $3$ classes? | [
[
{
"aoVal": "A",
"content": "$36$ kilograms "
}
],
[
{
"aoVal": "B",
"content": "$38$ kilograms "
}
],
[
{
"aoVal": "C",
"content": "$40$ kilograms "
}
],
[
{
"aoVal": "D",
"content": "$43$ kilograms "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] | [
"$4 \\times 37 + 11 \\times 41+ 161 = 760$ kilograms in total. $760 \\div (4 + 11 + 5) = 38$ kg. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10355 | a969dfbf48ed4e0481eb5e9073bc9760 | [] | 1 | single_choice | Cici and Kiki took the same quiz. They agreed on the following rules: a person got $10$ points for a correct answer and lost $5$ points otherwise (getting a wrong answer or skipping a question). They each answered $10$ questions and together got $95$ points. If Cici got $15$ more points than Kiki, how many questions did Kiki answer correctly? | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems->Solving Chicken-Rabbit Problems by Using Hypothesis"
] | [
"Kiki got $(95-15)\\div2=40$ points. If she answered all the questions correctly, she would have gotten $100$ points. Hence, she skipped or got $(100-40)\\div(10+5)=4$ wrong answers and she answered $10-4=6$ questions correctly. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10363 | a0663162452d4fcf870abc0afe742479 | [] | 1 | single_choice | Amy and Bella bought some cookies in the ratio of $$3:4$$. Bella gave $$9$$ cookies to Amy. Then the ratio of the number of cookies Amy had to that of Bella was $$1:1$$. How many cookies did they have at first? | [
[
{
"aoVal": "A",
"content": "$$54$$ "
}
],
[
{
"aoVal": "B",
"content": "$$63$$ "
}
],
[
{
"aoVal": "C",
"content": "$$72$$ "
}
],
[
{
"aoVal": "D",
"content": "$$126$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Ratio Word Problems with Invariant Sums"
] | [
"Total number of cookies both of them had did not change. Make total the same number of units by finding LCM. Before $\\to$ $A:B:Total$ $\\to$ $3:4:7$ $\\to$ $6:8:14$ After $\\to$ $A:B:Total$ $\\to$ $1:1:2$ $\\to$ $7:7:14$ $1u=9$ $14u=14\\times9=126$ cookies at first (and also in the end) in total. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10364 | fbb4e8b2f7ec45c29bdeca6e8e6bec93 | [
"其它"
] | 1 | single_choice | Alex, John and Sam went to buy oranges. Alex paid $\textbackslash$20$, John paid $\textbackslash$15$, and Sam only paid $\textbackslash$5$. They bought $120$ oranges altogether. They divided them in proportion to the amount of money each of them had paid. How many oranges did John get? | [
[
{
"aoVal": "A",
"content": "$$15$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$45$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying of Multiplication and Division"
] | [
"A: J: S 20:15:5 = 40 120/40 = 3 oranges per person 3*15= 45 oranges "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10367 | c4acf0f4e7b14517b5dfe27326f25955 | [] | 1 | single_choice | If $$3^{}\text{th}$$February is Monday, what day of the week is $$27$$\textsuperscript{th~}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 $$22$$\\textsuperscript{nd} February is a Monday. Then count a few days back to find that $$24$$\\textsuperscript{th~}February is a Wednesday. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10370 | a4f110be05004094821c0604421bfa0a | [] | 1 | single_choice | The speed of high-speed train is approximately $$350$$ kilometres per hour, while the walking speed of a person is approximately $$5$$ metres per second. Approximately, how many times is the speed of a high-speed train faster than the walking speed of a person?． | [
[
{
"aoVal": "A",
"content": "$$2 $$ "
}
],
[
{
"aoVal": "B",
"content": "$$20 $$ "
}
],
[
{
"aoVal": "C",
"content": "$$70 $$ "
}
],
[
{
"aoVal": "D",
"content": "$$200 $$ "
}
],
[
{
"aoVal": "E",
"content": "$$700$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Basic Computation of the Multiples"
] | [
"The speed of high-speed train is approximately $$350$$ kilometres per hour, which is approximately $$100$$ metres per second. So its speed is roughly $$20$$ times faster than $$5$$ metres per second. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10371 | 865cc26bcee2402f8c00658139e33207 | [] | 1 | single_choice | Martha had ＄$$1.50$$. She bought $$12$$ caramels at $$5$$￠ each. How many chocolate mints at $$10$$￠ each can she buy with the money she has left? | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$11$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] | [
"Martha had ＄$$1.50$$. She bought $$12$$ caramels at $$5$$￠ each, spengding $$60$$￠ and leaving her with $$90$$￠. With $$90$$￠, she can buy $$90 \\div 10 =9$$ mints at $$10$$￠ each. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10383 | 81ff9ff9922c4c8b8e847d921e861c90 | [
"其它"
] | 1 | single_choice | Balloons are sold in packets of $$5$$, $$10$$, and $$25$$. Marius buys exactly $$70$$ balloons. What is the smallest number of packets he can buy? (2017 Math Kangaroo Problem, Level 3 - 4, Question \#11) | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Applying Multiplication and Division->Simple Multiplication Applications"
] | [
"$70 = 25 + 25 + 10 + 10$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10386 | db8fbe8dac32412b80a8b220b31b59f5 | [] | 1 | single_choice | Three hens and four rabbits are in a cage. How many legs do they have?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$4$$) | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$15$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$22$$ "
}
],
[
{
"aoVal": "E",
"content": "$$24$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Total Value using Unitary Method"
] | [
"A hen has two legs and a rabbit has four legs, so three hens have six legs and four chickens have sixteen legs. $6+16=22$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10390 | c036eb50c7e84ad8bd09f12d6d245f28 | [] | 1 | single_choice | A police spots a burglar from $$480$$ m apart. The burglar immdiately runs away at a speed of $$8$$ m/s and the police starts chasing him at $$12$$ m/s at the same time. At this rate, how long will it take the police to catch the burglar? | [
[
{
"aoVal": "A",
"content": "$$24$$ seconds "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ seconds "
}
],
[
{
"aoVal": "C",
"content": "$$1$$ minutes "
}
],
[
{
"aoVal": "D",
"content": "$$2$$ minutes "
}
]
] | [
"Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road"
] | [
"The distance between them is $$480$$ m, and the difference between their speeds is $$12-8=4$$ m/s. It takes $$480\\div4=120$$ seconds to catch the burglar, which is $$2$$ minutes "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10392 | d6fec6acf2974b90945455911c477aa9 | [
"其它"
] | 2 | single_choice | At the 2013 Winnebago County Fair a vendor is offering a "fair special" on sandals. If you buy one pair of sandals at the regular price of $\textbackslash$ 50$, you get a second pair at a $40 \textbackslash\%$ discount, and a third pair at half the regular price. Javier took advantage of the "fair special" to buy three pairs of sandals. What percentage of the $\textbackslash$ 150$ regular price did he save? (2013 AMC 8, Question \#12) | [
[
{
"aoVal": "A",
"content": "$$25$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$33$$ "
}
],
[
{
"aoVal": "D",
"content": "$$40$$ "
}
],
[
{
"aoVal": "E",
"content": "$$45$$ "
}
]
] | [
"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 sandals without the discount. We have $\\textbackslash$ 50 \\times 3$ sandals $=\\textbackslash$ 150$. Then, find the amount of money using the discount: $50+0.6 \\times 50+\\frac{1}{2} \\times 50=\\textbackslash$ 105$. Finding the percentage yields $\\frac{105}{150}=70 \\textbackslash\\%$ To find the percent saved, we have $100 \\textbackslash\\%-70 \\textbackslash\\%=(\\text{B}) 30$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 10394 | d701217906454a91b8a534738a6acf95 | [] | 1 | single_choice | There was a $15$-meter long corridor in the school. The teacher asked Jack to put a flowerpot on the corridor every three meters. How many flowerpots did Mike put?~(adapted from $$2008$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$7$$) | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Interval Problems->Planting no Trees on either Side (straight line type)->Cutting the Ropes"
] | [
"The corridor is divided into $15\\div3=5$ segments. The number of flowerpots is one more than that of the segments, so $5+1=6$. "
] | D |