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 | 2994 | 091acec720664c15b3c2da44698978c6 | [
"其它"
] | 1 | single_choice | Mariam had ＄$$4y$$. After buying some cloth at ＄$$7$$ per metre, she had ＄$$y$$ left. How many metres of cloth did she buy? | [
[
{
"aoVal": "A",
"content": "$$\\frac{3y}{7}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{5y}{7}$$ "
}
],
[
{
"aoVal": "C",
"content": "$21y$ "
}
],
[
{
"aoVal": "D",
"content": "$$35y$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions"
] | [
"Amount of money she spent to buy the cloth $$\\rightarrow$$＄$$4y-$$＄$$y$$ $$=$$＄$$3y$$, Length of cloth she bought $$\\rightarrow$$＄$$3y\\div $$＄$$7/\\text{m}$$ $$= \\frac{3y}{7}\\text{m}$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 2995 | 0f931b5bb90746c8bcbbe42900113c52 | [
"其它"
] | 1 | single_choice | The mid points of the four sides of a rectangle are $(−3,0)$, $(2,0)$, $(5,4)$, and $(0, 4)$. What is the area of the rectangle? | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$25$$ "
}
],
[
{
"aoVal": "C",
"content": "$$40$$ "
}
],
[
{
"aoVal": "D",
"content": "$$50$$ "
}
],
[
{
"aoVal": "E",
"content": "$$80$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"NA "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3004 | 3837cbbd0ce24bc3a9672bdce2914a8b | [] | 1 | single_choice | Pick two consecutive positive integers whose sum is less than $$100$$. Square both of those integers and then find the difference of the square numbers. Which of the following could be the difference? ($2007$ AMC $8$ Problem, Question \#$19$) | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$64$$ "
}
],
[
{
"aoVal": "C",
"content": "$$79$$ "
}
],
[
{
"aoVal": "D",
"content": "$$96$$ "
}
],
[
{
"aoVal": "E",
"content": "$$131$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Operations through Formulas-> Difference of Two Squares Formula"
] | [
"Let\\textquotesingle s say that $x$ is the smaller of the two numbers. So the question is $$(x+1)+x\\textless100(x+1)^{2}-x^{2}=x^{2}+2x+1-x^{2}=2x+1$$. ~$$2x+1$$ is obviously odd, so the answer could be $$\\text{C}$$ or $$\\text{E}$$. $$2x+1=131$$ doesn\\textquotesingle t match with $$2x+1\\textless100$$, so the answer is $$79$$. Therefore, the answer is $$\\text{C}$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3006 | 339d23c6d10d423696ef81cebc0ee787 | [
"其它"
] | 3 | single_choice | Two integers are inserted into the list $3,3,8,11,28$ to double its range. The mode and median remain unchanged. What is the maximum possible sum of the two additional numbers? | [
[
{
"aoVal": "A",
"content": "$$56$$ "
}
],
[
{
"aoVal": "B",
"content": "$$57$$ "
}
],
[
{
"aoVal": "C",
"content": "$$58$$ "
}
],
[
{
"aoVal": "D",
"content": "$$60$$ "
}
],
[
{
"aoVal": "E",
"content": "$$61$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"D "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3010 | ab4a2fac752e41dda61332f79fdfc6ff | [] | 1 | single_choice | The $1986^{}\text{th}$ digit at the right of the decimal point in the decimal expression of $\dfrac{1}{7}$ is~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Basic Permutation"
] | [
"$$\\frac{1}{7}=0.\\overline{142857}$$, it is a decimal which repeats in cycles of $6$. Every $6$\\textsuperscript{th}~digit is $7$. The $1986$\\textsuperscript{th} digit is $7$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3014 | 1cbf29a1824f450f8d5a03ab34502b3d | [
"其它"
] | 1 | single_choice | There are four more girls than boys in Mr. Tse\textquotesingle s class of 28 students. What is the ratio of number of girls to the number of boys in her class? | [
[
{
"aoVal": "A",
"content": "$4:3$ "
}
],
[
{
"aoVal": "B",
"content": "$3:2$ "
}
],
[
{
"aoVal": "C",
"content": "$7:4$ "
}
],
[
{
"aoVal": "D",
"content": "$2:1$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"
] | [
"We can set up an equation with $x$ being the number of girls in the class. The number of boys in the class is equal to $x-4$. Since the total number of students is equal to 28 , we get $x+x-4=28$. Solving this equation, we get $x=16$. There are $16-4=12$ boys in our class, and our answer is $16: 12=$ (B) $4: 3$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3022 | e79a938986014ae0b8681a678f3871c1 | [
"其它"
] | 0 | single_choice | Cassandra is helping her mother to pack $$75$$ cupcakes. The boxes that her mother prepares can only fit $$7$$ cupcakes. She must ensure the box is full before she can use the next box. How many boxes she can fill up? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10$$ "
}
],
[
{
"aoVal": "D",
"content": "$$68$$ "
}
],
[
{
"aoVal": "E",
"content": "$$70$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers"
] | [
"$$75\\div7=10R5$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3025 | 825baef83b3e42d9afae2f1ee4e3100f | [] | 1 | single_choice | If $*abcd*=a\times d+b\times c$, then $*2543*=$~\uline{~~~~~~~~~~}~. ($2004$ Math League.com contest problem, $8$\textsuperscript{th} Grade, Question \#$33$) | [
[
{
"aoVal": "A",
"content": "$$14$$ "
}
],
[
{
"aoVal": "B",
"content": "$$22$$ "
}
],
[
{
"aoVal": "C",
"content": "$$26$$ "
}
],
[
{
"aoVal": "D",
"content": "$$120$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"
] | [
"$*2543*=2\\times3+5\\times4=6+20=26$. So the answer is $\\rm C$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3029 | b92f825aa14a463c884b78ba09d73857 | [
"其它"
] | 1 | single_choice | Louis had $8$ sticks. He broke three of them into two pieces. How many sticks does he have now? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$11$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
],
[
{
"aoVal": "E",
"content": "$$13$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"$8 + 3 = 11$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3034 | 33aa4abc98b3494aae488e50a499574b | [
"其它"
] | 2 | single_choice | If $3^{}p+3^{4}=90$, $2^{}r+44=76$, and $5^{3}+6^{}s=1421$, what is the product of $p$, $r$, and $s$? (2013 AMC 8 Problem, Question \#15) | [
[
{
"aoVal": "A",
"content": "$$27$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50$$ "
}
],
[
{
"aoVal": "D",
"content": "$$70$$ "
}
],
[
{
"aoVal": "E",
"content": "$$90$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers"
] | [
"Start with $3^{}p+3^{4}=90$. Then, change $3^{4}$ to $81$. Subtract from $81$ from both sides to get $3^{}p=9$ and see that $p$ is $2$. Now, solve for $r$. Since $2^{}r+44=76$, $2^{}r$ must equal $32$, so $r=5$. Now, solve for $s$. $5^{3}+6^{}s=1421$ can be simplified to $125+6^{}s=1421$, which simplifies further to $6^{}s=1296$. Therefore, $s=4$. $prs$ equals $2\\times5\\times4$ which equals $40$. So, the answer is $40$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3039 | c7222249cad54e39affd54dd8fc0ed22 | [
"其它"
] | 1 | single_choice | Hannah bought $$5$$ whole pizzas: $$1$$ for herself and $$1$$ for each of her $$4$$ students. Hannah sliced her pizza into $$5$$ equal parts and ate only $$3$$ slices. Student $$A$$ sliced his pizza into $$4$$ equal parts, but ate only $$3$$ slices. Student $$B$$ sliced his pizza into $$8$$ equal parts, but ate only $$7$$ slices. Student $$C$$ sliced her pizza into $$3$$ equal parts, but ate only $$2$$ slices. Student $$D$$ sliced her pizza into $$6$$ equal parts, but ate only $$3$$ slices. Who ate less pizza than Hannah? | [
[
{
"aoVal": "A",
"content": "Student $$A$$ "
}
],
[
{
"aoVal": "B",
"content": "Student $$B$$ "
}
],
[
{
"aoVal": "C",
"content": "Student $$C$$ "
}
],
[
{
"aoVal": "D",
"content": "Student $$D$$ "
}
],
[
{
"aoVal": "E",
"content": "Nobody "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions"
] | [
"All of them eat more than $$\\frac{1}{2}$$, except student $$D$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3042 | 0fe9ea5733434bb3999766d2af02150f | [
"其它"
] | 1 | single_choice | When Koko the Koala is awake, he eats $84$ grams of leaves per hour. He was awake for $2$ hours yesterday and $10$ hours today. How many grams of leaves did he eat in total in the two days? (adapted from 2014 Math Kangaroo Problem, Level 3-4, Question \#4) | [
[
{
"aoVal": "A",
"content": "$$840$$ "
}
],
[
{
"aoVal": "B",
"content": "$$168$$ "
}
],
[
{
"aoVal": "C",
"content": "$$672$$ "
}
],
[
{
"aoVal": "D",
"content": "$$1008$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"
] | [
"$84 \\times (10 + 2) = 84 \\times 10 + 84 \\times 2 = 840 + 168 = 1008$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3047 | 9d5b54d3ca0d4dfe980eac13b829b188 | [] | 1 | single_choice | Which of the following is not an equivalent ratio of $$4:12$$? | [
[
{
"aoVal": "A",
"content": "$$1:3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2:6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8:36$$ "
}
],
[
{
"aoVal": "D",
"content": "$$32:96$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions"
] | [
"Option A: $$1:3$$ $\\to$ $4:12$ Option B: $2:6$ $\\to$ $$1:3$$ $\\to$ $4:12$ Option C: $8:36$ $\\to$ $4:18$ Option D: $32:96$ $\\to$ $$1:3$$ $\\to$ $4:12$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3051 | 0c521e91f13a48f9b0b8207028cee9b7 | [
"其它"
] | 1 | single_choice | In a math competition, each participant has a unique $5$-digit registration number of the form $\overline{BBCAC}$, where $0 \leq A \textless{} B\textless{} C \leq 9$ and $B$ is the average of $A$ and $C$. What is the maximum number of participant that can join this competition? | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$18$$ "
}
],
[
{
"aoVal": "D",
"content": "$$20$$ "
}
],
[
{
"aoVal": "E",
"content": "$$25$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"D "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3059 | 384db7f8e417484398459f2da518902f | [
"其它"
] | 2 | single_choice | For $\triangle ABC$, all its side lengths are integers. The primeter of $\triangle ABC$ with a side of length $14$ and a side length of $8$ is at least ． | [
[
{
"aoVal": "A",
"content": "$$25$$ "
}
],
[
{
"aoVal": "B",
"content": "$$26$$ "
}
],
[
{
"aoVal": "C",
"content": "$$27$$ "
}
],
[
{
"aoVal": "D",
"content": "$$28$$ "
}
],
[
{
"aoVal": "E",
"content": "$$29$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"
] | [
"We know from the triangle inequality that the last side, $s$, fulfills $s+8\\textgreater14$. Therefore, $P\\textgreater14+14$. The least integer value of $P$ is $29$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3060 | 2f1912f582c94b3cb9fdf661a69a062b | [
"其它"
] | 1 | single_choice | There are two positive integers, $$x$$ and $$y$$. $$x$$ equals to $$3^{2}$$, and $$y$$ is the base of $$5^{3}$$. What is the product of $$x$$ and $$y$$? | [
[
{
"aoVal": "A",
"content": "$15$ "
}
],
[
{
"aoVal": "B",
"content": "$45$ "
}
],
[
{
"aoVal": "C",
"content": "$90$ "
}
],
[
{
"aoVal": "D",
"content": "$1125$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers"
] | [
"$$x=3^{2}=9$$ $$5$$ cubed is $$5^{3}$$. And the base is $$5$$. So, $$x\\cdot y=9\\times 5=45$$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3061 | 0c5c6aa8452b43919bde5a93ed8675f6 | [
"其它"
] | 1 | single_choice | SASMO 2016 P2 Q5 What number does () stands for? | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns->Encryption and Decryption"
] | [
"banana = 32-24= 8 A + 8 = 12 A = 4 "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3063 | 41857e581e2a46869b29dafc95600556 | [
"其它"
] | 2 | single_choice | For $\triangle ABC$, all its side lengths are integers. The perimeter of $\triangle ABC$ with a side of length $14$ and a side length of $8$ is at least ． | [
[
{
"aoVal": "A",
"content": "$$25$$ "
}
],
[
{
"aoVal": "B",
"content": "$$26$$ "
}
],
[
{
"aoVal": "C",
"content": "$$27$$ "
}
],
[
{
"aoVal": "D",
"content": "$$28$$ "
}
],
[
{
"aoVal": "E",
"content": "$$29$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"
] | [
"We know from the triangle inequality that the last side, $s$, fulfills $s+8\\textgreater14$. Therefore, $P\\textgreater14+14$. The least integer value of $P$ is $29$ "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3065 | 1ce6aa2cc04e4ae0a78ef22986778c89 | [
"其它"
] | 1 | single_choice | $2018$ is an interesting number. This is because when we add the first digit and the last digit, we will get the reverse of the middle two digits. Which of the options below is also an interesting number? | [
[
{
"aoVal": "A",
"content": "$$3014$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3129$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4319$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2017$$ "
}
],
[
{
"aoVal": "E",
"content": "$$4913$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"
] | [
"NA "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3073 | 187d23b145854fc3af538ceafbb56d10 | [
"其它"
] | 0 | single_choice | Given: $a-b\textgreater a$ and $a+b\textless b$. Which of the following must be true?~\uline{~~~~~~~~~~}~ $I$. $a b$ is negative $II$. $a+b$ is negative $III$. $a-b$ is negative | [
[
{
"aoVal": "A",
"content": "$I$ only "
}
],
[
{
"aoVal": "B",
"content": "$I$ and $III$ only "
}
],
[
{
"aoVal": "C",
"content": "$II$ only "
}
],
[
{
"aoVal": "D",
"content": "$I$, $II$, $III$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"
] | [
"$a-b\\textgreater a$ then $b\\textless0$ $a+b\\textless b$ then $a\\textless0$. So both $a$ and $b$ are negative. $I$ is false, since the product will be positive. $II$ is true since the sum of two negative numbers is negative. $III$ is false because if $a=-1$ and $b=-2$ then $a-b$ is positive. Only $II$ is true. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3082 | 0c99a520a2684252805a3492987c0a25 | [
"其它"
] | 3 | single_choice | What is the remainder when $2^{2023}+2023$ is divided by $2^{20}+1$? (Adapted From 2020 AMC 10B Problems, Question \#22) | [
[
{
"aoVal": "A",
"content": "$$2015$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2^{5}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$2023$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2048$$ "
}
],
[
{
"aoVal": "E",
"content": "$$20$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"Let $x=2^{20}$. We are now looking for the remainder of $\\frac{8x^{101}+2023}{x+1}$. By Polynomial Remainder Theorem, the remainder is $8\\times (-1)^{101} + 2023 = 2015$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3084 | 7dc26cf49b234cd4995ea03f3dcb57c7 | [] | 1 | single_choice | The last four digits in Andy\textquotesingle s ID card are $2025$. What is the the difference between the largest and the smallest digit in $2025$?~(adapted from $$2011$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$7$$) | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$0$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"
] | [
"The largest digit is $5$, and the smallest digit is $0$. $5-0=5$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3085 | 1cfbee250a164e71b742fb4b4f7dd1d0 | [
"其它"
] | 1 | single_choice | Let $a$ and $b$ be relatively prime positive integers with $a\textgreater b\textgreater0$ and $\frac{a^{3}-b^{3}}{(a-b)^{3}}=\frac{73}{3}$. What is $a-b$? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
],
[
{
"aoVal": "E",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions"
] | [
"Slightly expanding, we have that $\\frac{(a-b)\\left(a^{2}+a b+b^{2}\\right)}{(a-b)(a-b)(a-b)}=\\frac{73}{3}$. Canceling the $(a-b)$, cross multiplying, and simplifying, we obtain that $0=70 a^{2}-149 a b+70 b^{2}$. Dividing everything by $b^{2}$, we get that $$ 0=70\\left(\\frac{a}{b}\\right)^{2}-149\\left(\\frac{a}{b}\\right)+70 \\text {. } $$ Applying the quadratic formula and following the restriction that $a\\textgreater b\\textgreater0$ $$ \\frac{a}{b}=\\frac{10}{7} \\text {. } $$ Hence, $7 a=10 b$. Since they are relatively prime, $a=10, b=7$. $$ 10-7= 3 \\text {. } $$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3086 | 0ca2c393bd9448e08058dc264eb35c99 | [
"其它"
] | 1 | single_choice | Which number has to be subtracted from $17$ in order to obtain $-33$? (Adapted from 2017 Math Kangaroo Problem, Level 7-8, Question \#3) | [
[
{
"aoVal": "A",
"content": "$$-50$$ "
}
],
[
{
"aoVal": "B",
"content": "$$-16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ "
}
],
[
{
"aoVal": "D",
"content": "$$40$$ "
}
],
[
{
"aoVal": "E",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"
] | [
"$17-50=-33$, so the answer is $E$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3090 | 462dbfeddd304192b5a0729c40eec657 | [
"其它"
] | 0 | single_choice | Fill in the blank:~\uline{~~~~~~~~~~}~is $$3$$ tens $$7$$ ones less than $$4$$ tens $$6$$ ones. | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$19$$ "
}
],
[
{
"aoVal": "C",
"content": "$$73$$ "
}
],
[
{
"aoVal": "D",
"content": "$$83$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"$$3$$ tens $$7$$ ones: $$37$$ $$4$$ tens $$6$$ ones: $$46$$ less than: $$46-37=9$$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3093 | 3cf571d3965345a4bc833ed99c9cec48 | [
"其它"
] | 1 | single_choice | There were $$16$$ monkeys in total in the animal school. After the whistle, they arranged themselves into $$8$$ rows. How many monkeys were there in each row after the whistle? (Adapted from 2005 Math Kangaroo Problem, Level 3-4, Question \#4) | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
],
[
{
"aoVal": "E",
"content": "$$5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"
] | [
"There were $$16 \\div 8 = 2$$ monkeys in each row. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3097 | 462ffa8d8796404ab3306171f72c5899 | [
"其它"
] | 2 | single_choice | Find all values of $x$ such that $\textbar3 x+12\textbar\textless9$ and $\textbar x+2\textbar\textless\textbar-3 x-6\textbar$.~\uline{~~~~~~~~~~}~ | [
[
{
"aoVal": "A",
"content": "$x\\textless-2$ "
}
],
[
{
"aoVal": "B",
"content": "$-7\\textless x\\textless-1$ "
}
],
[
{
"aoVal": "C",
"content": "$-7\\textless x\\textless-2$ "
}
],
[
{
"aoVal": "D",
"content": "$-7\\textless x\\textless-1 ; x \\neq-2$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"
] | [
"Based on the first inequality, we know that $-9\\textless3 x+12\\textless9$ because $3 x+2$ must be less than 9 units away from zero. We can subtract 12 from all three parts of the inequality to arrive at $-21\\textless3 x\\textless-3 \\rightarrow-7\\textless x\\textless-1$. From the second inequality we can rewrite $\\textbar-3 x-6\\textbar$ as $\\textbar3 x+6\\textbar=3\\textbar x+2\\textbar$ because they must be equal. The second inequality must be true for all numbers except for when $\\textbar x+2\\textbar=0$, or when $x=-2$. Thus the answer includes all numbers from $-7$ to $-1$ with the exception of $-2$. The answer is $\\mathbf{D}$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3099 | 104cb24c29ac4e95a5906515857ad9c5 | [
"其它"
] | 2 | single_choice | For $\triangle ABC$, all its side lengths are integers. The perimeter of $\triangle ABC$ with a side of length $3$ and a side length of $4$ is at least ． | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"
] | [
"We know from the triangle inequality that the last side, $s$, fulfills $s+3\\textgreater4$. Therefore, $P\\textgreater4+4$. The least integer value of $P$ is $9$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3101 | 1050c8cd59ef4048b090596ce767379b | [
"其它"
] | 1 | single_choice | Suppose that $x$ and $y$ are nonzero real numbers such that $\frac{3 x+y}{x-3 y}=-2$. What is the value of $\frac{x+3 y}{3 x-y}$? | [
[
{
"aoVal": "A",
"content": "$$-3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$-1$$ "
}
],
[
{
"aoVal": "C",
"content": "$$1$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2$$ "
}
],
[
{
"aoVal": "E",
"content": "$$3$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Proportional Equations"
] | [
"Rearranging, we find $3 x+y=-2 x+6 y$, or $5 x=5 y \\Longrightarrow x=y$. Substituting, we can convert the second equation into $\\frac{x+3 x}{3 x-x}=\\frac{4 x}{2 x}= 2$ More step-by-step explanation: $$ \\begin{aligned} \\&\\frac{3 x+y}{x-3 y}=-2 \\textbackslash\\textbackslash{} \\&3 x+y=-2(x-3 y) \\textbackslash\\textbackslash{} \\&3 x+y=-2 x+6 y \\textbackslash\\textbackslash{} \\&5 x=5 y \\textbackslash\\textbackslash{} \\&x=y \\textbackslash\\textbackslash{} \\&\\frac{x+3 y}{3 x-y}=\\frac{1+3(1)}{3(1)-1}=\\frac{4}{2}=2 \\end{aligned} $$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3105 | 0cd694cef6ec494b8071562f50e7d515 | [] | 1 | single_choice | Compare these fractions. $$\frac{8}{31}$$~\uline{~~~~~~~~~~}~$$\frac{4}{15}$$, ~$$\frac{9}{61}$$~\uline{~~~~~~~~~~}~$$\frac{3}{22}$$ | [
[
{
"aoVal": "A",
"content": "$$\\textgreater$$, $$\\textgreater$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\textgreater$$, $$\\textless$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\textless$$, $$\\textgreater$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\textless$$, $$\\textless$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"
] | [
"$$\\frac{8}{31}\\textless\\frac{8}{30}$$;~$$\\frac{9}{61}\\textgreater\\frac{9}{66}$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3109 | 2a9f364dcd2c4697a2002751ad9c9a06 | [] | 1 | single_choice | Compare these fractions. $$\frac{3}{7}$$~\uline{~~~~~~~~~~}~$$\frac{5}{9}$$, $$\frac{5}{8}$$~\uline{~~~~~~~~~~}~$$\frac{7}{11}$$ | [
[
{
"aoVal": "A",
"content": "$$\\textgreater$$, $$\\textgreater$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\textgreater$$, $$\\textless$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\textless$$, $$\\textgreater$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\textless$$, $$\\textless$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Comparing and Ordering"
] | [
"$$\\frac{27}{63}\\textless\\frac{35}{63}$$;~$$\\frac{55}{88}\\textless\\frac{56}{88}$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3120 | 2aa671beb13e4c0e987bf38779f6f986 | [] | 1 | single_choice | If $ a◆b$ means $(a\times b)+b$ , then $（2◆3）◆4$ has the value． | [
[
{
"aoVal": "A",
"content": "$$45$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$16$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
],
[
{
"aoVal": "E",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"
] | [
"If $a◆b$~ represents $(a\\times b)+b$ , $2◆3=(2\\times3)+3=9,9◆4=(9\\times4)+4=40$ . "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3125 | 2aa8627cef2b444dbb189c1d669cf4dd | [
"其它"
] | 3 | single_choice | (2) Eddie had 120 dollars as his pocket money, and spent $$ \frac{3}{4} $$of it. How much money is left? | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$60$$ "
}
],
[
{
"aoVal": "C",
"content": "$$90$$ "
}
],
[
{
"aoVal": "D",
"content": "$$120$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions"
] | [
"left！！！not spent! So you need to calculate the fraction of left money. Then use T*F=C "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3129 | 107bd421b05c488a8b8c4edbe9555001 | [] | 1 | single_choice | Divide $$2$$、$$3$$、$$24$$、$$33$$、$$55$$ and $$60$$ into two groups with 3 numbers in each group to make the product of numbers in each group the same, so the product is． | [
[
{
"aoVal": "A",
"content": "$$3630$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1584$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3960$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2880$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Power of Products"
] | [
"$$2=2$$， $$3=3$$， $$24=2\\times 2\\times 2\\times 3$$， $$33=11\\times 3$$， $$55=11\\times 5$$， $$60=2\\times 2\\times 3\\times 5$$， $$2\\times 60\\times 33=24\\times 55\\times 3$$， $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde2\\times 60\\times 33$$ $$=(2\\times 33)\\times 60$$ $$=66\\times 60$$ $$=3960$$． $$\\text{C}$$． "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3130 | 2aaab2c7197449e39c7d48d630f9ad82 | [
"其它"
] | 1 | single_choice | Which of the following integers cannot be written as the sum of four consecutive odd integers? (2015 AMC 8 Problems, Question \#14) | [
[
{
"aoVal": "A",
"content": "$$16$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$72$$ "
}
],
[
{
"aoVal": "D",
"content": "$$100$$ "
}
],
[
{
"aoVal": "E",
"content": "$$200$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables"
] | [
"Let our $4$ numbers be $n, n+2, n+4, n+6$, where $n$ is odd. Then our sum is $4 n+12$. The only answer choice that cannot be written as $4 n+12$, where $n$ is odd, is (D) 100 . "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3133 | 4f79338751d14373824ad19253db5cda | [] | 1 | single_choice | $$100-99+98-97+96-95+\cdots +4-3+2-1$$. | [
[
{
"aoVal": "A",
"content": "$$20$$ "
}
],
[
{
"aoVal": "B",
"content": "$$40$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50$$ "
}
],
[
{
"aoVal": "D",
"content": "$$80$$ "
}
],
[
{
"aoVal": "E",
"content": "$$100$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "
] | [
"$$\\begin{eqnarray}\\&\\&\\left( 100-99 \\right)+\\left( 98-97 \\right)\\cdots +\\left( 4-3 \\right)+\\left( 2-1 \\right)\\textbackslash\\textbackslash{} \\&=\\&50\\times 1\\textbackslash\\textbackslash{} \\&=\\&50．\\end{eqnarray}$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3135 | 2f45ea48881c49ce935b004458a4e070 | [] | 1 | single_choice | Of the following, which has a value different from the others? | [
[
{
"aoVal": "A",
"content": "$$40\\times 50$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4\\times 5000$$ "
}
],
[
{
"aoVal": "C",
"content": "$$50\\times 400$$ "
}
],
[
{
"aoVal": "D",
"content": "$$40\\times 500$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"
] | [
"To see which value is different, count the total number of $$0$$\\textquotesingle s in each product. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3148 | 18d151cf57304f1faabe74ceb029b2d3 | [] | 1 | single_choice | $$12 \times \left( \frac{1}{2} \times \frac{1}{3} \times \frac{1}{4}\right)=$$． | [
[
{
"aoVal": "A",
"content": "$$72$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{4}{3}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{1}{2}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"
] | [
"$$12 \\times \\left( \\frac{1}{2} \\times \\frac{1}{3} \\times \\frac{1}{4}\\right)$$ $$=\\left(12 \\times \\frac{1}{2}\\right) \\times \\frac{1}{3} \\times \\frac{1}{4}$$ $$=6 \\times \\frac{1}{3} \\times \\frac{1}{4}$$ $$=2 \\times \\frac{1}{4}$$ $$= \\frac{2}{4}$$ $$=\\frac{1}{2}$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3157 | 149f548c79214e2e96d267efa3cd3e51 | [
"其它"
] | 2 | single_choice | For $\triangle ABC$, all its side lengths are integers. The primeter of $\triangle ABC$ with a side of length $3$ and a side length of $4$ is at least ． | [
[
{
"aoVal": "A",
"content": "$$7$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$12$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"
] | [
"We know from the triangle inequality that the last side, $s$, fulfills $s+3\\textgreater4$. Therefore, $P\\textgreater4+4$. The least integer value of $P$ is $9$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3158 | 1d3939fc360b4acf9bb5f701720ee8d3 | [] | 1 | single_choice | $$(60 \div 5)\times4 =$$. | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$16$$ "
}
],
[
{
"aoVal": "C",
"content": "$$48$$ "
}
],
[
{
"aoVal": "D",
"content": "$$96$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"
] | [
"$$(60\\div5)\\times4 = 12 \\times4 =48$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3170 | 10bab04c693d45a682c2dd25c9be35be | [] | 1 | single_choice | The fraction $$\dfrac{214}{263}$$ keeps the same value when both its numerator and denominator are~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "multiplied by $$2~ $$ "
}
],
[
{
"aoVal": "B",
"content": "increased by $$2$$ "
}
],
[
{
"aoVal": "C",
"content": "decreased by $$2$$ "
}
],
[
{
"aoVal": "D",
"content": "$$ $$squared$$ $$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions"
] | [
"The problem is about the basic property of fractions, namely, multiplying or dividing the numerator and denominator by the same number (except $$0$$), the value of the fraction is unchanged. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3174 | 871a91f435174c6d874964fe2a512898 | [
"其它"
] | 2 | single_choice | For $\triangle ABC$, all its side lengths are integer. The primeter of $\triangle ABC$ with a side of length $12$ and a side length of $7$ is at least ． | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$25$$ "
}
],
[
{
"aoVal": "C",
"content": "$$26$$ "
}
],
[
{
"aoVal": "D",
"content": "$$27$$ "
}
],
[
{
"aoVal": "E",
"content": "$$28$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"
] | [
"We know from the triangle inequality that the last side, $s$, fulfills $s+7\\textgreater12$. $P=s+7+12\\textgreater12+12$. Therefore, $P\\textgreater24+1=25$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3176 | 10c410e94f714a968414b9fe9b49ddfd | [] | 1 | single_choice | $$10\times20\times30\times40=24\times$$． | [
[
{
"aoVal": "A",
"content": "$$10^{3}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10^{4}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$10^{5}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$10^{6}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"
] | [
"$$10\\times20\\times30\\times40=(1\\times2\\times3\\times4)\\times10^{4}=24\\times10^{4}$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3178 | 14b9a6231ea34a369555235854cd782b | [
"其它"
] | 2 | single_choice | What is the correct ordering of the three answers from $\frac5{19}\div \frac{25}{38}$, $1\frac12 \div \frac{15}8$, and $\frac74 \div \frac{35}{12}$, in increasing order? (adapted from 2012 AMC 8 Problems, Question \#20) | [
[
{
"aoVal": "A",
"content": "$\\frac5{19}\\div \\frac{25}{38}$ \\textless~$1\\frac12 \\div \\frac{15}8$ \\textless{} $\\frac74 \\div \\frac{35}{12}$ "
}
],
[
{
"aoVal": "B",
"content": "$\\frac74 \\div \\frac{35}{12}$ \\textless~$1\\frac12 \\div \\frac{15}8$ \\textless~$\\frac5{19}\\div \\frac{25}{38}$ "
}
],
[
{
"aoVal": "C",
"content": "$1\\frac12 \\div \\frac{15}8$ \\textless{} $\\frac74 \\div \\frac{35}{12}$ \\textless~$\\frac5{19}\\div \\frac{25}{38}$ "
}
],
[
{
"aoVal": "D",
"content": "$\\frac5{19}\\div \\frac{25}{38}$ \\textless{} $\\frac74 \\div \\frac{35}{12}$ \\textless~$1\\frac12 \\div \\frac{15}8$ "
}
],
[
{
"aoVal": "E",
"content": "$\\frac74 \\div \\frac{35}{12}$ \\textless~$\\frac5{19}\\div \\frac{25}{38}$ \\textless~$1\\frac12 \\div \\frac{15}8$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions->Division of Fractions"
] | [
"$\\frac5{19}\\div \\frac{25}{38}=\\frac25$ ~ $\\frac74 \\div \\frac{35}{12}=\\frac35$ $1\\frac12 \\div \\frac{15}8=\\frac45$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3184 | 0d8645b641864aaf89ccbabd1766f528 | [] | 0 | single_choice | Choose the answer in the simplest form. $$\frac{9}{4}\times \frac{8}{27}=$$． | [
[
{
"aoVal": "A",
"content": "$$\\frac{72}{108}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{18}{27}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{8}{12}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{2}{3}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions"
] | [
"$$\\frac{9}{4}\\times \\frac{8}{27}=\\frac{2}{3}$$． "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3188 | 8adb1db084c44752a477a8050b885e20 | [] | 1 | single_choice | In the arithmetic sequence $3$, $7$, $11$, $15$, $\cdots$ , the $26$\textsuperscript{th} number is． | [
[
{
"aoVal": "A",
"content": "$$103$$ "
}
],
[
{
"aoVal": "B",
"content": "$$107$$ "
}
],
[
{
"aoVal": "C",
"content": "$$111$$ "
}
],
[
{
"aoVal": "D",
"content": "$$115$$ "
}
],
[
{
"aoVal": "E",
"content": "$$119$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"
] | [
"$3+4\\times(26-1)=103$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3190 | e7a739171d584f8286b66dae9c61810d | [] | 1 | single_choice | If a whole number is multiplied by itself, the ones\textquotesingle{} digit of the product \emph{cannot} be． | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$7$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"
] | [
"If a whole number is multiplied by itself, the ones\\textquotesingle{} digit of the product could be $$1 (1\\times1)$$ or $$5 (5\\times5)$$ or $$9 (3\\times3)$$, but not $$7$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3207 | 1910c45a41094f67a6aefa7c4f2d8ab9 | [
"其它"
] | 1 | single_choice | Bob: " Hi, Stanley. What is the coefficient of the variable in this algebraic expression $3x^{2}-4$?" Stanley:" I can give you a hint. The value of the coefficient is $7$ more than the constant." Stanley\textquotesingle s hint is~\uline{~~~~~~~~~~}~and the coefficient of the variable is~\uline{~~~~~~~~~~}~. | [
[
{
"aoVal": "A",
"content": "correct, $3$ "
}
],
[
{
"aoVal": "B",
"content": "correct, $-4$ "
}
],
[
{
"aoVal": "C",
"content": "incorrect, $3$ "
}
],
[
{
"aoVal": "D",
"content": "incorrect, $4$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"
] | [
"Constant: $-4$ Coefficient of the variable: $3$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3208 | 3892760088974be3809057c4a34f9ea5 | [
"其它"
] | 1 | single_choice | Gilda has a bag of marbles. She gives $20 \textbackslash\%$ of them to her friend Pedro. Then Gilda gives $25 \textbackslash\%$ of what is left to another friend, Ebony. Finally, Gilda gives $5 \textbackslash\%$ of what is now left in the bag to her brother Jimmy. What percentage of her original bag of marbles does Gilda have left for herself? (adapted 2019 AMC 8, Question \#8) | [
[
{
"aoVal": "A",
"content": "$$95\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "B",
"content": "$33\\textbackslash\\%$ "
}
],
[
{
"aoVal": "C",
"content": "$$45\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "D",
"content": "$$57\\textbackslash\\%$$ "
}
],
[
{
"aoVal": "E",
"content": "$$63\\textbackslash\\%$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"
] | [
"After Gilda gives $20 \\textbackslash\\%$ of the marbles to Pedro, she has $80 \\textbackslash\\%$ of the marbles left. If she then gives $25 \\textbackslash\\%$ of what\\textquotesingle s left to Ebony, she has $(0.75 * 0.8)=60 \\textbackslash\\%$ of what she had at the beginning. Finally, she gives $5 \\textbackslash\\%$ of what\\textquotesingle s left to her brother, so she has $(0.6 * 0.95)$ (D) $57\\textbackslash\\%$~ of what she had in the beginning left. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3210 | 10fd6979282b4979b9957a12921a5454 | [] | 1 | single_choice | Given that $$x\otimes y=6\times x-5\times y$$, find $$7\otimes 6$$. | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$13$$ "
}
],
[
{
"aoVal": "C",
"content": "$$42$$ "
}
],
[
{
"aoVal": "D",
"content": "$$30$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"
] | [
"$$7\\otimes 6=6\\times 7-5\\times 6=12$$, so $$\\text{A}$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3212 | 389341fb19f24bb9854c00120b1497dd | [
"其它"
] | 2 | single_choice | For $\triangle ABC$, all its side lengths are integer. The primeter of $\triangle ABC$ with a side of length $12$ and a side length of $7$ is at least ． | [
[
{
"aoVal": "A",
"content": "$$24$$ "
}
],
[
{
"aoVal": "B",
"content": "$$25$$ "
}
],
[
{
"aoVal": "C",
"content": "$$26$$ "
}
],
[
{
"aoVal": "D",
"content": "$$27$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"
] | [
"We know from the triangle inequality that the last side, $s$, fulfills $s+7\\textgreater12$. $P=s+7+12\\textgreater12+12$. Therefore, $P\\textgreater24+1=25$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3213 | 1913a1ef9a3f4a85b785d99103fe3aec | [
"其它"
] | 1 | single_choice | A slug called Glug eats $$2$$ tomatoes for every $$3$$ strawberries. Yesterday it had eaten $$35$$ tomatoes and strawberries altogether. How many tomatoes did it eat? | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$14$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
],
[
{
"aoVal": "E",
"content": "$$21$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"
] | [
"$$35\\times \\frac {2} {2+3} = 14$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3223 | 2661bd89429e4781b774bf3f04b5ee94 | [
"其它"
] | 4 | single_choice | How many perfect cubes lie between $2^{2}+1$ and $2^{8}+1$, inclusive? (Adapted from 2018 AMC 8 Problem, Question \#25) | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$6$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers->Exponentiation of Powers"
] | [
"$2^{2}+1=5$, $2^{8}+1=257$. $2^{3}=8$, $3^{3}=27$, $4^{3}=64$, $5^{3}=125$, $6^{3}=216$. Thus, the answer is $5$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3228 | 1922af64ee39418faf2982a09de961a8 | [] | 1 | single_choice | Steven subtracts the units digit from the tens digit for each two-digit number. He then finds the sum of all his answers. What is the value of Steven\textquotesingle s sum? | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$45$$ "
}
],
[
{
"aoVal": "C",
"content": "$$55$$ "
}
],
[
{
"aoVal": "D",
"content": "$$90$$ "
}
],
[
{
"aoVal": "E",
"content": "$$100$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"
] | [
"The sum of all the tens digits is $$\\left(1+2+3+4+5 +6 +7+8+9\\right)\\times10$$. The sum of all the units digits is $$\\left(0 + 1+2+3 +4+5 +6 +7+8+9\\right)\\times9$$. Therefore Steven\\textquotesingle s sum is $$\\left(1+2+3 +4+5+6+7+8+9\\right)\\times1=45$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3229 | a6bbd2266dd14466b6278a5aa480f07a | [] | 0 | single_choice | The product of two different nonzero integers cannot be． | [
[
{
"aoVal": "A",
"content": "prime "
}
],
[
{
"aoVal": "B",
"content": "zero "
}
],
[
{
"aoVal": "C",
"content": "even "
}
],
[
{
"aoVal": "D",
"content": "composite "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"
] | [
"The product of two different nonzero integers can never be $$0$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3237 | 112339a3eed14f7a92441f199fdbd2ba | [
"其它"
] | 1 | single_choice | Bob bought three kinds of meat: pork, beef and chicken with the total cost of $152. The ratio of the weight of pork, beef and chicken is~$2:4:3$. The ratio of the price per pound of pork, beef and chicken is~$6:5:2$. What is the sum of the last digits of the cost of each kind in dollars? | [
[
{
"aoVal": "A",
"content": "$$8$$ "
}
],
[
{
"aoVal": "B",
"content": "$$10$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$15$$ "
}
],
[
{
"aoVal": "E",
"content": "$$16$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"
] | [
"Let~$x,\\textbackslash{} y\\textbackslash{} and\\textbackslash{} z$~be the weight of pork, beef and chicken, respectively. ~$\\textbackslash{} x:y:z=2:4:3$~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ (1) The ratio of the price will be~$\\left( 6x\\right):\\left( 5y\\right):\\left( 2z\\right).$ The costs of pork, beef and chicken are~$A,B\\textbackslash{} and\\textbackslash{} C,$~respectively. ~$A=\\dfrac{6x}{6x+5y+2z}\\times152$~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~(2) From (1), we get: ~$y=2x,\\textbackslash{} and\\textbackslash{} z=\\dfrac{3}{2}x$~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~(3) (2) becomes:~$A=\\dfrac{6x}{6x+5\\left( 2x\\right)+2\\times\\dfrac{3}{2}x}\\times152=\\dfrac{6x}{19x}\\times152=48$ Similarly,~$B=\\dfrac{5y}{6x+5y+2z}\\times152=\\dfrac{5y}{19x}\\times152=\\dfrac{10x}{19x}\\times152=80.$ And~$C=\\dfrac{2z}{6x+5y+2z}\\times152=\\dfrac{2z}{19x}\\times152=\\dfrac{3x}{19x}\\times152=24.$ Pork costs $48 per pound, beef costs $80, and chicken costs $24. The sum of the last digits of the costs is 8+0+4=12. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3239 | 8ae1f9550be84771a09fb8060f539cde | [] | 0 | single_choice | $$1000\text{m}$$ per second $$=$$$$\text{km}$$ per hour. | [
[
{
"aoVal": "A",
"content": "$$60$$ "
}
],
[
{
"aoVal": "B",
"content": "$$360$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3600$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6000$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Unit Conversion->Converting between Compound Units"
] | [
"$$1000\\text{m/s}=1\\text{km/s}=3600\\text{km/hr}$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3241 | 266d6bbe3d344f59ba5f1e69b7aa9406 | [] | 1 | single_choice | Solve the equation: $$16\times 25-13\left( 3x+2 \right)=179$$． | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"
] | [
"$$39x=400-26-179$$ $$\\textasciitilde\\textasciitilde\\textasciitilde\\textasciitilde x=5$$． "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3252 | 15123010499b4516bea8a0dda21162d9 | [
"其它"
] | 0 | single_choice | Find the missing term in the following sequence: $$1, 2, 4, 7,~\uline{~~~~~~~~~~}~, 16$$. | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$11$$ "
}
],
[
{
"aoVal": "C",
"content": "$$12$$ "
}
],
[
{
"aoVal": "D",
"content": "$$13$$ "
}
],
[
{
"aoVal": "E",
"content": "$$14$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"
] | [
"The number sequence are in the pattern of $$+1, +2, +3, +4, +5, \\cdots $$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3254 | 1d8b25027f93406ab007abfe91add3c8 | [
"其它"
] | 2 | single_choice | On Kangaroo planet each kangyear has 20 kangmonths and each kangmonth has 6 kangweeks, How many kangweeks are there in one quarter of a kangyear? | [
[
{
"aoVal": "A",
"content": "$$9$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$60$$ "
}
],
[
{
"aoVal": "D",
"content": "$$90$$ "
}
],
[
{
"aoVal": "E",
"content": "$$120$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions"
] | [
"$\\dfrac{1}{4}$kangyear x~$\\dfrac{20\\textbackslash{} kangmonths}{1\\textbackslash{} kangyear}$~x~$\\dfrac{6\\textbackslash{} kangweeks}{1\\textbackslash{} kangmonth}$~= 30 kangweeks. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3256 | 2f8118d645384ada90ffe775e12e9d20 | [
"其它"
] | 1 | single_choice | A vase was being sold at the price of $250$ dollars. The store decides to sell it with a $40\textbackslash\%$ discount. If you buy the vase now, how much will you save? | [
[
{
"aoVal": "A",
"content": "$$150$$ "
}
],
[
{
"aoVal": "B",
"content": "$$100$$ "
}
],
[
{
"aoVal": "C",
"content": "$$80$$ "
}
],
[
{
"aoVal": "D",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"
] | [
"$250\\times 40\\textbackslash\\%$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3262 | 58d3c74b24664a3cb0fc82356cb97f24 | [
"其它"
] | 1 | single_choice | Calculate: $$2.7\times0.2\div3=$$． | [
[
{
"aoVal": "A",
"content": "$0.16$ "
}
],
[
{
"aoVal": "B",
"content": "$1.6$ "
}
],
[
{
"aoVal": "C",
"content": "$0.18$ "
}
],
[
{
"aoVal": "D",
"content": "$1.8$ "
}
],
[
{
"aoVal": "E",
"content": "$0.14$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals"
] | [
"$$2.7\\times0.2\\div3$$ $$=0.54\\div3$$ $$=0.18$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3264 | 21fded3a3d774d508f7ba65bcfc03795 | [
"其它"
] | 1 | single_choice | Mary wanted to buy $12$ lemons. The lemons were sold either for $90$ cents each or at $3$ dollars for a bag of $4$ lemons. How much money would Mary save if she buys three bags of lemons instead of buying $12$ lemons separately? | [
[
{
"aoVal": "A",
"content": "$1.2$ dollars "
}
],
[
{
"aoVal": "B",
"content": "$1.5$ dollars "
}
],
[
{
"aoVal": "C",
"content": "$1.6$ dollars "
}
],
[
{
"aoVal": "D",
"content": "$1.8$ dollars "
}
],
[
{
"aoVal": "E",
"content": "$2.1$ dollars "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"$0.9 \\times 12 - 3 \\times 3 = 1.8$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3269 | 4b057a81ece5453cbc863a9390e2a87d | [
"其它"
] | 1 | single_choice | The following are the weights (in pounds) of ten people: $100,115, 135, 140, 180, 197, 203, 230, x, y$ (not necessarily in increasing order). It is also given that the average weight of these ten people is $157$ pounds, and there is a unique mode of $135$. Find the $56$-th percentile. | [
[
{
"aoVal": "A",
"content": "$$100$$ "
}
],
[
{
"aoVal": "B",
"content": "$$115$$ "
}
],
[
{
"aoVal": "C",
"content": "$$125$$ "
}
],
[
{
"aoVal": "D",
"content": "$$135$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"First of all, we find the values of $x$ and $y$. Since the average is $157$, we have $(100+115+135+140+ 180+197+203+230+x+y = 157 \\times 10 = 1570$ $1300+x+y =1570$ $x+y = 270$. There is a unique mode, $135$, then $135$ must appear at least twice. Therefore, one of $x, y$ is $135$. It is easy to deduce that both $x$ and $y$ are $135$. List the weights in increasing order: $100,115, 135, 135, 135, 140, 180, 197, 203, 230$. $np=10(0.56)=5.6 \\uparrow 6$. The $56$-th percentile is $140$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3270 | 19497aea1f704de08090350deae1c33b | [
"其它"
] | 1 | single_choice | Which of the following equations are NOT equivalent to $x+5=13$? | [
[
{
"aoVal": "A",
"content": "$x+5-5=13-5$ "
}
],
[
{
"aoVal": "B",
"content": "$2(x+5)=26$ "
}
],
[
{
"aoVal": "C",
"content": "$x+5-13=0$ "
}
],
[
{
"aoVal": "D",
"content": "$x+5+13=0$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation"
] | [
"Equations are equivalent when you can obtain one by subtracting, adding, dividing, or multiplying the same number on the other. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3274 | 341a7691f2514dbc8fc63d2f3460b378 | [] | 1 | single_choice | $$\frac{1}{9}+ \frac{3}{9}+ \frac{5}{9}=$$． | [
[
{
"aoVal": "A",
"content": "$$\\frac{1}{3}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{10}{9}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{5}{243}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"
] | [
"$$\\frac{1}{9}+ \\frac{3}{9}+ \\frac{5}{9}= \\frac{9}{9}=1$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3277 | 194ee6d931274284a25e5690ee08b9ce | [
"其它"
] | 0 | single_choice | What is $$9762 + 7 \times 8 \times 9 \times 4 \times 99 \times 0$$ | [
[
{
"aoVal": "A",
"content": "$$9762$$ "
}
],
[
{
"aoVal": "B",
"content": "$$9818$$ "
}
],
[
{
"aoVal": "C",
"content": "$$9889$$ "
}
],
[
{
"aoVal": "D",
"content": "$$209346$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"Anything times $$0$$ equal $$0$$. $$9762 + 0 = 9762$$ "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3278 | 38ae263839cd4d3eba1db18b241ce7c9 | [
"其它"
] | 2 | single_choice | In a triangle with integer side lengths, one side is three times as long as a second side, and the length of the third side is $15$. What is the greatest possible perimeter of the triangle? （2006 AMC10B, Question 10) | [
[
{
"aoVal": "A",
"content": "$$43$$ "
}
],
[
{
"aoVal": "B",
"content": "$$44$$ "
}
],
[
{
"aoVal": "C",
"content": "$$45$$ "
}
],
[
{
"aoVal": "D",
"content": "$$46$$ "
}
],
[
{
"aoVal": "E",
"content": "$$47$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"
] | [
"Let $x$ be the length of the first side. The lengths of the sides are: $x, 3 x$, and 15 . By the Triangle Inequality, $$ \\begin{aligned} \\&3 x\\textless x+15 \\textbackslash\\textbackslash{} \\&2 x\\textless15 \\textbackslash\\textbackslash{} \\&x\\textless\\frac{15}{2} \\end{aligned} $$ The greatest integer satisfying this inequality is 7 . So the greatest possible perimeter is $7+3 \\cdot 7+15=$ (A) 43 "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3281 | 794303f54c514be1ada033886d8e62ee | [] | 1 | single_choice | $$1 + 10 + 100 + 1000 =$$． | [
[
{
"aoVal": "A",
"content": "$$4$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1111$$ "
}
],
[
{
"aoVal": "C",
"content": "$$1234$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4000$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "
] | [
"$$1 + 10 + 100 + 1000 =11+11$$ hundred $$=1111$$. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3282 | 98d26ede6f794ef48df034f32c552962 | [] | 1 | single_choice | The $$2022$$th digit to the right of the decimal point in the decimal representation of $$\frac 1{54}$$ is． | [
[
{
"aoVal": "A",
"content": "$$0$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$8$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Periodic Problems->Periodic Problems of Sequence Operations"
] | [
"The decimal is $$0.0185185\\cdots $$. An \"$$8$$\" appears in the $$3$$rd, $$6$$th, $$9$$th, $$\\cdots $$, $$2022$$th decimal place. So a \"$$8$$\" is in the $$2022$$th place. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3283 | 41dda41f37a54ceeade78881ad9a241f | [] | 1 | single_choice | According to the regulation of the pyramid series, the formula $$1+2+3+4+5+6+5+4+3+2+1=$$． | [
[
{
"aoVal": "A",
"content": "$$6\\times6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$6\\times7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6\\times5$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables"
] | [
"``Pyramid series''$$1+2+3+4+\\cdots +\\left( n-1 \\right)+n+\\left( n-1 \\right)+\\cdots +3+2+1$$ $$={{n}^{2}}$$． So the answer is $$\\text{A}$$． "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3286 | 268bea9cb73a4149a8d99051ca743043 | [] | 0 | single_choice | Which of the following has a result of $183$? | [
[
{
"aoVal": "A",
"content": "$$103+86$$ "
}
],
[
{
"aoVal": "B",
"content": "$$117+76$$ "
}
],
[
{
"aoVal": "C",
"content": "$$90+83$$ "
}
],
[
{
"aoVal": "D",
"content": "$$82+101$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction "
] | [
"$$103+86=189$$ $$117+76=193$$ $$90+83=173$$ $$82+101=183$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3287 | 268cdc9de32f4468b6c377df36dc9679 | [] | 1 | single_choice | Calculate: $$\frac{1}{4}\times \frac{5}{6}+\frac{3}{7}\times \frac{7}{8}=$$． | [
[
{
"aoVal": "A",
"content": "$$\\frac{5}{12}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$\\frac{5}{16}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$\\frac{5}{17}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$\\frac{7}{12}$$ "
}
],
[
{
"aoVal": "E",
"content": "$$\\frac{11}{12}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions"
] | [
"$$\\frac{1}{4}\\times \\frac{5}{6}+\\frac{3}{7}\\times \\frac{7}{8}$$=$$\\frac{5}{24}+\\frac{3}{8}$$=$$\\frac{5}{24}+\\frac{9}{24}$$=$$\\frac{14}{24}$$=$$\\frac{7}{12}$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3294 | 1184c85e9c074d8d964671f585e4cc72 | [] | 1 | single_choice | Simplify the following expression: $$a^{2}\times a+b^{2}\times b^{3}$$. | [
[
{
"aoVal": "A",
"content": "$$a^{3}+b^{5}$$ "
}
],
[
{
"aoVal": "B",
"content": "$$a^{3}b^{5}$$ "
}
],
[
{
"aoVal": "C",
"content": "$$a^{2}+b^{5}$$ "
}
],
[
{
"aoVal": "D",
"content": "$$a^{2}+b^{6}$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Power->Computing Powers"
] | [
"$$a^{2}\\times a+b^{2}\\times b^{3}=$$$$a^{3}+b^{5}$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3297 | 2b0d61123980438fa2a96e1bcae6c2af | [] | 1 | single_choice | What is the next number in this sequence? $$1$$, $$2$$, $$3$$, $$6$$, $$11$$, $$20$$, $$37$$,~\uline{~~~~~~~~~~}~? ． | [
[
{
"aoVal": "A",
"content": "$$47$$ "
}
],
[
{
"aoVal": "B",
"content": "$$54$$ "
}
],
[
{
"aoVal": "C",
"content": "$$57$$ "
}
],
[
{
"aoVal": "D",
"content": "$$68$$ "
}
],
[
{
"aoVal": "E",
"content": "$$74$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"
] | [
"After the first three numbers, each number is the sum of the previous three numbers. So the next number is $$11 + 20 + 37 = 68$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3302 | 1db905558a66450a8a1e6b387136a2f6 | [
"其它"
] | 2 | single_choice | \textbf{Sean and Evan are college roommates who have part-time jobs as servers in restaurants. The distribution of Sean's weekly income is approximately normal with mean $\textbackslash$225$ and standard deviation $\textbackslash$25$. The distribution of Evan's weekly income is approximately normal with mean $\textbackslash$240$ and standard deviation $15. Assuming their weekly incomes are independent of each other, which of the following is closest to the probability that Sean will have a greater income than Evan in a randomly selected week?} | [
[
{
"aoVal": "A",
"content": "\\textbf{0.067} "
}
],
[
{
"aoVal": "B",
"content": "\\textbf{0.159} "
}
],
[
{
"aoVal": "C",
"content": "\\textbf{0.227} "
}
],
[
{
"aoVal": "D",
"content": "\\textbf{0.303} "
}
],
[
{
"aoVal": "E",
"content": "\\textbf{0.354} "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"\\textbf{Sean \\textasciitilde{} N(225, 25)} \\textbf{Evan \\textasciitilde{} N(240, 15)} \\textbf{→} \\textbf{Sean - Evan \\textasciitilde{} N(-15, 29.155)} \\textbf{P(Sean-Evan \\textgreater{} 0) = 1-P(X\\textless0) = 0.303} "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3304 | 221fbe122a08482c918036dd259c03af | [
"其它"
] | 1 | single_choice | An amusement park has a collection of scale models, with ratio $1: 40$, of buildings and other sights from around the country. The height of empire state building is 1250 feet. What is the height in feet of its replica to the nearest whole number? (adapted from 2018 AMC 8, Question 1) | [
[
{
"aoVal": "A",
"content": "$$30$$ "
}
],
[
{
"aoVal": "B",
"content": "$$31$$ "
}
],
[
{
"aoVal": "C",
"content": "$$32$$ "
}
],
[
{
"aoVal": "D",
"content": "$$33$$ "
}
],
[
{
"aoVal": "E",
"content": "$$34$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"
] | [
"You can see that since the ratio of real building\\textquotesingle s heights to the model building\\textquotesingle s height is $1: 40$. We also know that the Empire State Building is 1250 feet, so to find the height of the model, we divide by 40 . That gives us $31.25$ which rounds to 31 . Therefore, to the nearest whole number, the duplicate is (B) 31 feet. "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3308 | cbdfd117a28345e39ef4c31a6f120e4c | [
"其它"
] | 1 | single_choice | A basketball is on sale with 35\% off, the discounted price is $$52$$ dollars, the original price of the basketball wasdollars． | [
[
{
"aoVal": "A",
"content": "$$18.2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$33.8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$80$$ "
}
],
[
{
"aoVal": "D",
"content": "$$148$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"$$x \\times 65\\textbackslash\\% = 52$$ $$x = 80$$ "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3312 | 544b34950e3f413d94bfff58e2a2d61c | [] | 1 | single_choice | Which of these is equal to $$(0.3+0.4 + 0.5 -0.9)\div0.6$$? | [
[
{
"aoVal": "A",
"content": "$$0.02 $$ "
}
],
[
{
"aoVal": "B",
"content": "$$0.05 $$ "
}
],
[
{
"aoVal": "C",
"content": "$$0.2 $$ "
}
],
[
{
"aoVal": "D",
"content": "$$0.5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$1$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Four Operations of Decimals"
] | [
"Note that $$(0.3+0.4+0.5 -0.9)\\div0.6 =(1.2 -0.9)\\div0.6 =0.3\\div0.6 = 3\\div6$$ $$=0.5$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3318 | 38c53be9572f4affbdbb72551ff8c50b | [
"其它"
] | 0 | single_choice | The ratio of $w$ to $x$ is $4: 3$, the ratio of $y$ to $z$ is $3: 2$, and the ratio of $z$ to $x$ is $1: 6$. What is the ratio of $w$ to $y$? (2020 AMC 10B Problems, Question \#3) | [
[
{
"aoVal": "A",
"content": "$4: 3$ "
}
],
[
{
"aoVal": "B",
"content": "$3: 2$ "
}
],
[
{
"aoVal": "C",
"content": "$8: 3$ "
}
],
[
{
"aoVal": "D",
"content": "$4: 1$ "
}
],
[
{
"aoVal": "E",
"content": "$16: 3$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"We need to somehow link all three of the ratios together. We can start by connecting the last two ratios together by multiplying the last ratio by two. $z: x=1: 6=2: 12$, and since $y: z=3: 2$, we can link them together to get $y: z: x=3: 2: 12$. Finally, since $x: w=3: 4=12: 16$, we can link this again to get: $y: z: x: w=3: 2: 12: 16$, so $w: y=(\\mathbf{E}) 16: 3$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3323 | 11bf02814ab34c17909f045cd43a5820 | [
"其它"
] | 0 | single_choice | The digit $9$ in what number represents a value of $0.09$? | [
[
{
"aoVal": "A",
"content": "$$9.012$$ "
}
],
[
{
"aoVal": "B",
"content": "$$0.469$$ "
}
],
[
{
"aoVal": "C",
"content": "$$51.9$$ "
}
],
[
{
"aoVal": "D",
"content": "$$26.49$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Basic Understanding of Decimals"
] | [
"If the digit $$9$$ represents a value of $$0.09$$, it means the digit $$9$$ is located on the hundredth place on that number, which is the second digit after the decimal point. Check Lesson 4 Concept 1 on textbook "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3334 | 8f9727d2e34943bbb7756e11519a210b | [
"其它"
] | 2 | single_choice | What is the smallest whole number larger than the perimeter of any triangle with a side of length $9$ and a side of length $1$? (adapted from 2015 AMC8, Question 8) | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$19$$ "
}
],
[
{
"aoVal": "C",
"content": "$$20$$ "
}
],
[
{
"aoVal": "D",
"content": "$$21$$ "
}
],
[
{
"aoVal": "E",
"content": "$$22$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Inequalities"
] | [
"We know from the triangle inequality that the last side, $s$, fulfills $s\\textless9+1=10$. Adding $9+1$ to both sides of the inequality, we get $s+9+1\\textless20$, and because $s+9+1$ is the perimeter of our triangle, (C) 20 is our answer. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3340 | 4fb752545a624cc9b34f7ad4d607355c | [
"其它"
] | 1 | single_choice | The sum of three numbers is $20$. The first is four times the sum of the other two. The second is seven times the third. What is the product of all three numbers? | [
[
{
"aoVal": "A",
"content": "$$18$$ "
}
],
[
{
"aoVal": "B",
"content": "$$28$$ "
}
],
[
{
"aoVal": "C",
"content": "$$32$$ "
}
],
[
{
"aoVal": "D",
"content": "$$40$$ "
}
],
[
{
"aoVal": "E",
"content": "$$294$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"B "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3345 | 11daa872b99c46b4831afd0b857a18ec | [] | 1 | single_choice | $$4\times4\times20\times20=80\times$$? | [
[
{
"aoVal": "A",
"content": "$$80$$ "
}
],
[
{
"aoVal": "B",
"content": "$$20$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"
] | [
"$$(4\\times20)\\times (4\\times20)=80\\times80$$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3349 | 19a2c6e824074bf4a232d87d48cff7ef | [
"其它"
] | 1 | single_choice | The number $-11+(-7)$ is equal to: | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$-3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$-25$$ "
}
],
[
{
"aoVal": "D",
"content": "$$25$$ "
}
],
[
{
"aoVal": "E",
"content": "$$-18$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"
] | [
"$-11+(-7)=-18$. "
] | E |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3360 | 94426feb080e432c82996da41b2b1b95 | [] | 1 | single_choice | If $$2x-3=y+5$$ and $$3y-1=5$$, then $$x=$$． | [
[
{
"aoVal": "A",
"content": "$$3$$ "
}
],
[
{
"aoVal": "B",
"content": "$$4$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$7$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"
] | [
"From $$3y -1=5$$, then we can get $$y=2$$. Therefore from $$2x-3=2+5$$, we obtain $$x=5$$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3363 | 224d543d02ad48dfa35f1086aaa2c7ea | [
"其它"
] | 2 | single_choice | Write each of the numbers 0,1,2,3,4,5,6 in the sqaures to make the addition correct. What digit will be in the grey square? pic | [
[
{
"aoVal": "A",
"content": "$$2$$ "
}
],
[
{
"aoVal": "B",
"content": "$$3$$ "
}
],
[
{
"aoVal": "C",
"content": "$$4$$ "
}
],
[
{
"aoVal": "D",
"content": "$$5$$ "
}
],
[
{
"aoVal": "E",
"content": "$$6$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Patterns->Encryption and Decryption"
] | [
"work backwards "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3370 | 344e2d2e73d348daaee93e69c4cce343 | [] | 1 | single_choice | What is the product of $125$ and $6$? | [
[
{
"aoVal": "A",
"content": "$$420$$ "
}
],
[
{
"aoVal": "B",
"content": "$$1230$$ "
}
],
[
{
"aoVal": "C",
"content": "$$750$$ "
}
],
[
{
"aoVal": "D",
"content": "$$720$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division"
] | [
"omitted "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3372 | 12030463e2a04760912a8fbfc9d07f67 | [
"其它"
] | 1 | single_choice | If 5 plates weigh as much as 9 mugs, then 99 mugs weigh as much as~\uline{~~~~~~~~~~}~plates. | [
[
{
"aoVal": "A",
"content": "$$10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$18$$ "
}
],
[
{
"aoVal": "C",
"content": "$$55$$ "
}
],
[
{
"aoVal": "D",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution"
] | [
"omitted "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3391 | 6b74c4d6297543859672b09a9aea3b98 | [
"其它"
] | 2 | single_choice | On the first day of a $7-$day holiday, Judy reads $9$ pages of a book. On the second day, she reads $12$. Then each day later, she reads $3$ pages more than the day before. On the last day of the holiday, she reads the corresponding number of pages and exactly finishes reading the book. How many pages does the book have? | [
[
{
"aoVal": "A",
"content": "$$27$$ "
}
],
[
{
"aoVal": "B",
"content": "$$30$$ "
}
],
[
{
"aoVal": "C",
"content": "$$120$$ "
}
],
[
{
"aoVal": "D",
"content": "$$126$$ "
}
],
[
{
"aoVal": "E",
"content": "$$128$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"
] | [
"Use the formula of arithmetic sequence to solve this problem. On the last day, she reads $9+6\\times3=27$ pages. The book has $(9+27)\\times7 \\div2=126$ pages. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3393 | 6b764442083a424f901b4e879b668396 | [] | 1 | single_choice | Linda, Alice, Joe, Lily, and Rachel lost their balloons. The numbers on their balloons were all smaller than $8$. The difference between the largest number and the smallest number was $5$. What are their balloon\textquotesingle s numbers? (adapted from $$2021$$ Math kangaroo Problems, Level $$1-2$$, Question \#$$8$$） | [
[
{
"aoVal": "A",
"content": "$7, 5, 4, 3,2$ "
}
],
[
{
"aoVal": "B",
"content": "$4, 1, 7,9,6$ "
}
],
[
{
"aoVal": "C",
"content": "$6,4,2,5,3$ "
}
],
[
{
"aoVal": "D",
"content": "$0,7,4,9,5$ "
}
],
[
{
"aoVal": "E",
"content": "$1,8,5,4,6$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Subtraction of Whole Numbers->Subtraction in Horizontal Form"
] | [
"In~ B, D, and E, the largest number more than $8$. In the C, the difference between the largest number and the smallest number is $4$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3394 | cbe7c5cf77d045cc877c080e41decd05 | [
"其它"
] | 1 | single_choice | $$8+9+12+17+23+31=$$？． | [
[
{
"aoVal": "A",
"content": "$$100$$ "
}
],
[
{
"aoVal": "B",
"content": "$$90$$ "
}
],
[
{
"aoVal": "C",
"content": "$$80$$ "
}
],
[
{
"aoVal": "D",
"content": "$$70$$ "
}
],
[
{
"aoVal": "E",
"content": "$$50$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers"
] | [
"$$=8+12+9+31+23+17$$ $$=20+40+40$$ $$=100$$． "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3402 | 4b33a4397d3e419db68d0ae52b802da2 | [] | 1 | single_choice | $$$$Calculate$$$$ $$\left (403 \frac{3}{5}+183 \frac{5}{11}+155 \frac{3}{13}+118 \frac{12}{17}\right ) \div$$$$ \left~~( \frac{1009}{15}+ \frac{1009}{33}+ \frac{1009}{39}+ \frac{1009}{51}\right )$$. | [
[
{
"aoVal": "A",
"content": "$$5$$ "
}
],
[
{
"aoVal": "B",
"content": "$$5.5$$ "
}
],
[
{
"aoVal": "C",
"content": "$$6$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6.5$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Fast Calculation in Fractions"
] | [
"$$\\left (403 \\frac{3}{5}+183 \\frac{5}{11}+155 \\frac{3}{13}+118 \\frac{12}{17}\\right ) \\div$$$$ \\left ( \\frac{1009}{15}+ \\frac{1009}{33}+ \\frac{10009}{39}+ \\frac{1009}{51}\\right )$$ $$=2018\\left ( \\frac{1}{5}+ \\frac{1}{11}+ \\frac{1}{13}+ \\frac{1}{17}\\right ) \\div \\frac{1000}{3}\\left ( \\frac{1}{5}+ \\frac{1}{11}+ \\frac{1}{13}+ \\frac{1}{17}\\right )$$ $=6$. "
] | C |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3405 | 3d76d99232d14dd2aee1be5b933e1c4b | [
"其它"
] | 0 | single_choice | What is the next number in the sequence below? $$47, 44, 38, 29, 17, \cdots $$ | [
[
{
"aoVal": "A",
"content": "$$12$$ "
}
],
[
{
"aoVal": "B",
"content": "$$8$$ "
}
],
[
{
"aoVal": "C",
"content": "$$5$$ "
}
],
[
{
"aoVal": "D",
"content": "$$2$$ "
}
],
[
{
"aoVal": "E",
"content": "None of the above "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Patterns in Number Sequences"
] | [
"The pattern is: $$-3, -6, -9, -12, -15, \\cdots $$ Thus, $$17-15=2$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3413 | 19ddc6e443b74cf08a1a69d4cbd68974 | [
"其它"
] | 1 | single_choice | $10000$ years ago, Owen the fisher traded $3$ fishes for $1$ rabbit from Oscar the hunter. Then, Oscar traded $2$ rabbits for $3$ packs of wheat from Dennis the farmer. How many fishes should Owen give Dennis for a pack of wheat? | [
[
{
"aoVal": "A",
"content": "$$1$$ "
}
],
[
{
"aoVal": "B",
"content": "$$2$$ "
}
],
[
{
"aoVal": "C",
"content": "$$3$$ "
}
],
[
{
"aoVal": "D",
"content": "$$4$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions->Simplifying Continued Ratios"
] | [
"fish:rabbit$=3:1$ wheat:rabbit$=3:2$ fish: wheat$=2:1$ "
] | B |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3416 | 1e1825c7a3b146368f107f216fb7bc8a | [
"其它"
] | 1 | single_choice | Harry and Terry are each told to calculate $8-(2+5)$.~Harry gets the correct answer. Terry ignores the parentheses and calculates $8-2+5$.~If Harry\textquotesingle s answer is $H$~and Terry\textquotesingle s answer is $T$, what is $H-T$? (2014 AMC $8$ Problem, Question \#1) | [
[
{
"aoVal": "A",
"content": "$$-10$$ "
}
],
[
{
"aoVal": "B",
"content": "$$-6$$ "
}
],
[
{
"aoVal": "C",
"content": "$$0$$ "
}
],
[
{
"aoVal": "D",
"content": "$$6$$ "
}
],
[
{
"aoVal": "E",
"content": "$$10$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"
] | [
"We have $H=8-7=1$ and $T=8-2+5=11$. Clearly $1-11=-10$, so our answer is $A$. "
] | A |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3418 | 58fcf59618bf4aa8ac9626033ac19e96 | [
"其它"
] | 1 | single_choice | Two non-zero real numbers, $x$ and $y$, satisfy $(x+y)^{2}=3xy$. Which of the following is a possible value of $$\frac{x+y}{y}-\frac{x-y}{x}$$? (Adapted From 2000 AMC 12 Problems, Question \#11) | [
[
{
"aoVal": "A",
"content": "$-1$ "
}
],
[
{
"aoVal": "B",
"content": "$-\\frac{1}{2}$ "
}
],
[
{
"aoVal": "C",
"content": "$\\frac{1}{2}$ "
}
],
[
{
"aoVal": "D",
"content": "$1$ "
}
],
[
{
"aoVal": "E",
"content": "$$2$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] | [
"Note that $(x+y)^{2} = x^{2}+y^{2}+2xy = 3xy \\Rightarrow x^{2}+y^{2} = xy$. Then, $$\\frac{x+y}{y}-\\frac{x-y}{x}=\\frac{x(x+y)-y(x-y)}{xy}=\\frac{{{x}^{2}}+xy-xy+{{y}^{2}}}{xy}=\\frac{{{x}^{2}}+{{y}^{2}}}{xy} = 1$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3419 | 123e1c6a9ce048e682373cdfdf18e259 | [
"其它"
] | 0 | single_choice | Eddie has a card. The number on the card is a neighbouring number of 8, but is not a neighbouring number of 6. What is the number on Eddie\textquotesingle s card?~\uline{~~~~~~~~~~}~ | [
[
{
"aoVal": "A",
"content": "$$6$$ "
}
],
[
{
"aoVal": "B",
"content": "$$7$$ "
}
],
[
{
"aoVal": "C",
"content": "$$8$$ "
}
],
[
{
"aoVal": "D",
"content": "$$9$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers"
] | [
"$$Omitted.$$ "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3420 | b4b7aa1d17ed41b78291b053e664475b | [] | 1 | single_choice | What percent of $$20$$ is $$50$$? | [
[
{
"aoVal": "A",
"content": "$$40$$ "
}
],
[
{
"aoVal": "B",
"content": "$$140$$ "
}
],
[
{
"aoVal": "C",
"content": "$$200$$ "
}
],
[
{
"aoVal": "D",
"content": "$$250$$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Basic Understanding of Fractions"
] | [
"$$\\frac{50}{20}=2.5=2.5\\times100\\textbackslash\\%=250\\textbackslash\\%$$. "
] | D |
prime_math_competition_en_single_choice_8K_dev | 2023-07-07T00:00:00 | 3423 | 46a1f7bb3e2d4fa0a5b14a723092a395 | [
"其它"
] | 1 | single_choice | If $A:B=3:5$, $B:C=3:2$, find $A:B:C$. | [
[
{
"aoVal": "A",
"content": "$3:5:4$ "
}
],
[
{
"aoVal": "B",
"content": "$9:15:10$ "
}
],
[
{
"aoVal": "C",
"content": "$9:3:10$ "
}
],
[
{
"aoVal": "D",
"content": "$8:15:10$ "
}
]
] | [
"Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"
] | [
"$A:B=3:5$ $B:C=3:2$ $A:B:C=9:15:10$ "
] | B |
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