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timestamp[s] | queId
stringlengths 32
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stringclasses 5
values | qtype
stringclasses 1
value | problem
stringlengths 6
2.89k
| knowledge_point_routes
sequence |
|---|---|---|---|---|---|
2023-07-07T00:00:00 | fbf9b992307b444eb938a67abf0f79d0 | 1 | short_answer | $\dfrac{2}{3}$~of £$$729 =$$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions->Multiplication of Fractions"
] |
2023-07-07T00:00:00 | 8f5505c28f074abd9d90140697874060 | 1 | short_answer | There are $$12$$ people in a room. If each of them shakes hands with the other, find the total number of times they shake hands. | [
"Overseas Competition->Knowledge Point->Counting Modules"
] |
2023-07-07T00:00:00 | 3b9a5ab85be34057a1a3e3b571572c35 | 2 | short_answer | A drawer contains $9$ yellow socks, $7$ identical green socks, $4$ identical white socks, $2$ red socks and $1$ black sock. Daniel picks socks from the drawer without observing. What is the smallest number of socks he must pick to be sure that he has two pairs of matching socks with the same colour? | [
"Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems",
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] |
2023-07-07T00:00:00 | 43bd21f970c34177be1554432de294ca | 1 | short_answer | Lucy buys five bottles of lemonade at £$1.09$ each and $6$ chocolate bars at $55\rm p$. How much change should she receive from a ten-pound note? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Money Calculation"
] |
2023-07-07T00:00:00 | e45422d20b09414ca93da798ae6e4103 | 1 | short_answer | In four years time, Sam will be twice as old as he was four years ago. Calculate Sam\textquotesingle s current age. | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Age Problems->Basic Relationships in Age Problems->Difference of Ages"
] |
2023-07-07T00:00:00 | 1b74b0ce31ca43179e9aa5db9f92ec32 | 1 | short_answer | How many ways are there to rearrange the letters in the word \textbf{RAINBOW} if the vowels are never together? Bud: We can arrange all the vowels in between the consonants so that they can not be together! Pip: There are 5 total places in which vowels can be placed. _ R _ N _ B _ W _ | [
"Overseas Competition->Knowledge Point->Counting Modules"
] |
2023-07-07T00:00:00 | 11a8c054bda64d72bdfd6571d70646f1 | 0 | short_answer | \textbf{$$n$$}~is the smallest odd number which can be made using all the digits $$3$$, $$7$$, $$2$$, $$8$$ once. \textbf{$$n=$$}~\uline{~~~~~~~~~~}~ | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value in Enumeration Problems"
] |
2023-07-07T00:00:00 | ed6e120cf0bc499d8e4a9bf4a9c4fd73 | 2 | short_answer | In an arithmetic progression, the sum of first $10$ terms is $20$, and the sum of first $30$ terms is $90$. What is the common difference of this arithmetic progression? | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"
] |
2023-07-07T00:00:00 | de33ae344c7942fbb4e480c5ae79a90e | 1 | short_answer | Work out $492.9 + 73.521 + 32.12$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Decimals",
"Overseas In-curriculum->Knowledge Point->Operations of Numbers ->Addition and Subtraction of Decimals->Addition of Decimals"
] |
2023-07-07T00:00:00 | 0143483f1edf4af3a803bb1221bcb8e1 | 1 | short_answer | A given number is between $$10$$ and $$20$$. It is a multiple of $$4$$ and a factor of $$36$$. What is the number? | [
"Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"
] |
2023-07-07T00:00:00 | 43d937a1a1ef47ef8b56b4494d1b2a22 | 1 | short_answer | $3.462 \div ~0.3$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals->Division of Decimals"
] |
2023-07-07T00:00:00 | 3fb10b4abb524d58afc63043c1689553 | 2 | short_answer | Solve the equation. $$15 \%x-25 \%\left( 1000-x \right)=-50$$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Percentage Calculation"
] |
2023-07-07T00:00:00 | dab22ef1b9474ab2b0ebf64fe8f912d5 | 2 | short_answer | I am thinking of a number. When my number is divided by $3$. it gives remainder $2$. When my number is divided by $5$, it gives remainder $3$. When my number is divided by $7$, it gives remainder $4$. What is the smallest possible value of my number? | [
"Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem->Chinese Remainder Theorem with Constant Remainder"
] |
2023-07-07T00:00:00 | 104a46795ca64208939686b66fb9a82e | 2 | short_answer | Ronald McDonald, a farmer, has chickens, goats and cows in his farm. He has $$40$$ chickens and goats combined. He notices that $$3$$ times the number of his chickens is $$5$$ times the number of his cows. On the other hand, $$2$$ times the number of goats is $$10$$ times the number of his cows. Help Ronald McDonald determine the total number of animal feet in his farm. | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Chicken-Rabbit Problems"
] |
2023-07-07T00:00:00 | c0f56c7d52444d1a9b65ef7a1513a044 | 1 | short_answer | Subtract $128 - 54$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Subtraction of Whole Numbers->Subtraction in Horizontal Form"
] |
2023-07-07T00:00:00 | 1b32f8e585fc46068085a2478636e072 | 1 | short_answer | (UK St Paul's Girls School Sample Paper Section $A$ Question $$10$$) Mary, Jess and Jo run a race. Jess's time is $18$ seconds. Jo finishes $6$ seconds before Jess. Mary finishes $4$ seconds after Jo. What is Mary's time in seconds? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] |
2023-07-07T00:00:00 | d900be8e099f4d49838cded0aec8d0e8 | 1 | short_answer | The ratio of the number of stickers Amy has to the number of stickers Penny has is $$5:4$$. Both girls have a total of $$117$$ stickers. How many stickers does Penny have?~\uline{~~~~~~~~~~}~ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions->Proportions"
] |
2023-07-07T00:00:00 | 35c1ed41867c49dfb5f6c880fb136ac2 | 1 | short_answer | How many times does the digit \textquotesingle$$2$$\textquotesingle{} appear in a book that is $$150$$ pages thick? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Page Number Problem->Questions Involving Page Number"
] |
2023-07-07T00:00:00 | 36e844fd0400420f989f1166d3df56c7 | 0 | short_answer | Bud can type 125 words per minute. How many words does Bud type in 9 minutes? If Bud practises typing for 9 minutes a day, how many words will be typed in 6 days? | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] |
2023-07-07T00:00:00 | 921b2f01420749da85075867e970dacb | 1 | short_answer | Lucy can walk at a constant speed of $3.6$ kilometers per hour. How many meters can she walk in $300$ seconds? | [
"Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"
] |
2023-07-07T00:00:00 | b370814add5e431bb51f7d7dac8d3ba5 | 1 | short_answer | Jack sold $$40$$ apples yesterday, which is make up $$\frac 47$$ of the number of apples he brought. Yesterday he brought $$\frac 12$$ of all apples he has. How many apples does he have altogether? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Finding the Base"
] |
2023-07-07T00:00:00 | 44d68779a7c0423eb6e762338b582fca | 2 | short_answer | Four numbers are written in a row. The average of the first $$2$$ numbers is $$10$$. The average of the last two numbers is $$22$$ and the average of the first and Iast numbers is $$14$$. Find the average of the two middle numbers. | [
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability",
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)"
] |
2023-07-07T00:00:00 | 6028933632e54b1a828b0f6d3598c001 | 1 | short_answer | $$200+202+204+206+208$$ | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] |
2023-07-07T00:00:00 | a754f6b5ebcb4917afb374104733b09e | 0 | short_answer | Use all the digits $$9$$, $$0$$, $$2$$ and $$3$$ to form a number that is closest to $$2978$$. | [
"Overseas Competition->Knowledge Point->Counting Modules->Questions Involving Enumeration->Enumeration"
] |
2023-07-07T00:00:00 | 653842c3dbaa4a70846409866d45815a | 1 | short_answer | There are \textbf{ten} lines in the plane, and at most, how many different parts can you divide the plane into? | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations",
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Inductive Recursion"
] |
2023-07-07T00:00:00 | 5ecddfaa220c43cf8e47b0f83763a84d | 1 | short_answer | The front row of a theatre has $$48$$ seats and every other row has four more seats than the row in front. There are $$80$$ seats in the last row. How many seats are there \textbf{altogether} in the theatre? | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences->Sum of Terms in Arithmetic Sequences"
] |
2023-07-07T00:00:00 | 8da4fb1e422544f0a8b82f886050843b | 2 | short_answer | How many whole numbers between $200$ and $500$ contain the digit $3$? (2022AMC 27) | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Calculation of Multi-digit Numbers"
] |
2023-07-07T00:00:00 | 668003c3b4ee4430939bf7445ffe574b | 1 | short_answer | Two $$2$$-digit multiples of $$7$$ have a product of $$7007$$. What is their sum? | [
"Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Applying Prime Factorization"
] |
2023-07-07T00:00:00 | 40a9e9bead5546a4a0e08b6e1af8f008 | 1 | short_answer | Freya thinks of a number. She multiplies the number by $2$ and then subtracts $10$ The result is $50$ What number did Freya think of ? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Inverse Operation Problems->Inverse Operations"
] |
2023-07-07T00:00:00 | fbd5c2b741d540409dda4ac6ae1eefe3 | 1 | short_answer | The average of $$A$$ and $$B$$ is $$22$$. $$C$$ is $$19$$. Find the average of $$A$$, $$B$$ and $$C$$. | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems "
] |
2023-07-07T00:00:00 | 6d5b83fe42184fb9bc959fdc4861c9b3 | 2 | short_answer | The average age for Chinese and English teachers is $$34$$. The average age for English and Mathematics teachers is $$36$$. The average age for Chinese and Mathematics is $$44$$. What is the average age of these $$3$$ subject teachers? | [
"Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle"
] |
2023-07-07T00:00:00 | 28594ee0096c4c27b6982e846d9415e3 | 1 | short_answer | Queen Elizabeth l was bom on $$7$$ September $$1533$$ and died on $$24$$ March $$1603$$. What was her age when she died? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Applying Addition and Subtraction->Simple Addition and Subtraction"
] |
2023-07-07T00:00:00 | 6b5f28a0da7644bf91c51262467f22af | 1 | short_answer | 37 coins are shared equally among 5 children. How many coins are left？ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division with Remainders"
] |
2023-07-07T00:00:00 | 5532a59da23d4cbea467c1a0cabeb494 | 1 | short_answer | A baker puts cakes in the display case in her bakery every day. One day, she wants to put $$50$$ cakes on $$9$$ layers in the case. At least how many cakes are there in the layer with the most cakes? | [
"Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle",
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] |
2023-07-07T00:00:00 | f83aeb54a6454c92abe4a6bb1cd131df | 1 | short_answer | SASMO 2014 Jane has a rope of length 23 cm. She wants to cut the rope so that she can form the biggest possible square, where the length of each side, in cm, is a whole number. What is the length of the rope that she must cut to form the square? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Squares"
] |
2023-07-07T00:00:00 | 830b4822d207437b89a3a6ce5de16c84 | 1 | short_answer | Subtract $20 + {\rm{(1}} \times {\rm{7)}}$ from ${\rm{(21 + 1)}} \times 7$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Mixed Operations"
] |
2023-07-07T00:00:00 | 3fa5ea265a5d4c0297ecf03b1cb17e9d | 2 | short_answer | $$[x]$$ is defined as the largest integer less than or equal to $$x$$, and $$ {x }=x-[x]$$. For example, $$[4.3]=4$$, $$ {4.3 }=4.3-[4.3]=0.3$$. $$[5]=5$$, $$ {5 }=5-[5]=0$$. Find the value of $$\left { \frac{2018+1}{5} \right } + \left { \frac{2018+2}{5} \right } + \cdots \cdots + \left { \frac{2018+2017}{5} \right } + \left { \frac{2018+2018}{5} \right }$$. | [
"Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operating Directly"
] |
2023-07-07T00:00:00 | 01afb46f9dd94497ab3c9968556ca7a1 | 3 | short_answer | There are ten boxes labelled from $1$ to $10$,~ with a total of $425$ cookies in them. Box $1$ has $11$ cookies, and the number of cookies in each box increases by the same amount. What is the difference between the number of cookies in two adjacent boxes? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Practical Application of Arithmetic Progression"
] |
2023-07-07T00:00:00 | f2e7d75d544640ef95f39ae11d58e429 | 3 | short_answer | $\tfrac{3}{4}$~of Chelsia\textquotesingle s money is the same as~$\tfrac{2}{3}$~of Benson\textquotesingle s money. If Chelsia had $$$18$$ less than Benson, what is Chelsia and Benson\textquotesingle s total sum of money? | [
"Overseas Competition->Knowledge Point->Word Problem Modules"
] |
2023-07-07T00:00:00 | a38e073e5c4f4c3f94fc8c0ac26838a1 | 1 | short_answer | The sum of seven consecutive odd numbers is $357$. What is the smallest of these seven numbers? | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"
] |
2023-07-07T00:00:00 | 7de9bf80e9294c29a99d27418f478a8e | 0 | short_answer | How many different five-digit numbers can be formed using the numbers $$1$$, $$1$$, $$2$$, $$3$$ and $$4$$? | [
"Overseas Competition->Knowledge Point->Counting Modules"
] |
2023-07-07T00:00:00 | 53f7ab0a979c47e9875a6745078c1158 | 1 | short_answer | 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? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages"
] |
2023-07-07T00:00:00 | 65457d2cc6de489f9eda50d81a2a99cd | 0 | short_answer | Work out: $$12\times1.99$$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals"
] |
2023-07-07T00:00:00 | 854a818f3b564ec2936328e1204553fa | 2 | short_answer | Given that $$A=\dfrac{1}{\dfrac{1}{1995}+ \dfrac{1}{1996}+ \cdots + \dfrac{1}{2008}}$$, what is the integer part for $$A$$? | [
"Overseas Competition->Knowledge Point->Calculation Modules->Comparing, Ordering and Estimating->Scaling"
] |
2023-07-07T00:00:00 | 3c4de249075d4f07b0fc0c817ff3c58b | 1 | short_answer | $$5$$ similar tables and $$12$$ similar chairs cost ＄$$720$$. Each table costs ＄$$25$$ more than each chair. What is the cost of a table? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems->Equivalent Substitution in Equation Word Problems"
] |
2023-07-07T00:00:00 | d5fb71d8282e4dad9d6f8b784f5145e7 | 0 | short_answer | Find a whole number between $$200$$ and $$400$$ that has the following properties. When the number is divided by $$3$$ the remainder is $$2$$. When the number is divided by $$4$$ the remainder is $$2$$. When the number is divided by $$5$$ the remainder is $$2$$. When the number is divided by $$7$$ the remainder is $$5$$. What is the number? | [
"Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems"
] |
2023-07-07T00:00:00 | a6f219bbae8a4dde8e0a10e161120049 | 1 | short_answer | The ratio of time taken by Martin and Carter to complete a race of the same length is $9:13$. Martin\textquotesingle s speed is $20$ metres per minute faster than Carter\textquotesingle s speed. What is the speed of Carter? | [
"Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"
] |
2023-07-07T00:00:00 | 4b3d2f8a295c449eb0b933dd026b4cf9 | 1 | short_answer | How many possible ways are there to get a sum of $$13$$ by adding $$3$$ numbers (excluding $$0$$)? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"
] |
2023-07-07T00:00:00 | eb64f29a539744afa20fabe47cf4247f | 1 | short_answer | Find the smallest number which leaves a remainder $$1$$ when divided by $$5$$ or $$6$$ or $$7$$. | [
"Overseas Competition->Knowledge Point->Number Theory Modules->Remainder Problems->Chinese Remainder Theorem->Step-by-step Calculation"
] |
2023-07-07T00:00:00 | 985a10206885415abe07e67ad7c806da | 1 | short_answer | Write down one number that is \textbf{both~}Even \textbf{and} prime. | [
"Overseas Competition->Knowledge Point->Number Theory Modules->Perfect Square Numbers->Basic Applications of Square Numbers",
"Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Common Factors and the Greatest Common Factors->The Greatest Common Factor of Two Numbers",
"Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers->Determining Prime and Composite Numbers->Knowing Prime and Composite Numbers"
] |
2023-07-07T00:00:00 | 033e1d824bce41289651265703300be3 | 0 | short_answer | Work out $$12636\div54$$. | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division in Vertical Form"
] |
2023-07-07T00:00:00 | e7dc5d1f98e34b2b9e1ae130e2a988c0 | 1 | short_answer | Fred and George can paint a room in $6$ hours. Fred would take $9$ hours on his own. How long would George take on his own? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Work Word Problems"
] |
2023-07-07T00:00:00 | 39314ee04d5249c699fbe6a90a08ea57 | 1 | short_answer | Lucy has $18$ metres of cloth. She uses $x$ metres of cloth to make a dress. How much cloth has Lucy left？ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Finding Unknowns Using the Given Operations"
] |
2023-07-07T00:00:00 | 5b0fce7f22474da9ace32b857c116492 | 0 | short_answer | Calculate the following and give your answer as a fraction in its lowest terms or a whole number. $3\div\dfrac{1}{3}$. | [
"Overseas Competition->Knowledge Point->Calculation Modules->Fractions->Operations of Fractions->Division of Fractions"
] |
2023-07-07T00:00:00 | 281326e2a0e3497ca68a17bd591efba8 | 1 | short_answer | $543+284$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Addition and Subtraction ->Addition of Whole Numbers->Addition in Horizontal Form"
] |
2023-07-07T00:00:00 | c0b11362a9114743b4f269d706e86245 | 1 | short_answer | There are $$14$$ red apples in a bag, and $$20$$ yellow apples. We need to take out at least~\uline{~~~~~~~~~~}~apples to ensure that there are two apples of the same colour. | [
"Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems"
] |
2023-07-07T00:00:00 | d7922e5e4a59420081b76bfba68dfc63 | 1 | short_answer | The ratio of the number of red pens to the number of black pens in a bookstore was $$3 : 7$$. An equal number of red pens and black pens were sold. In the end, the ratio of the number of red pens left to the number of black pens left was $$5 : 13$$. There were $$20$$ red pens in the end. How many red pens were sold? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"
] |
2023-07-07T00:00:00 | 0c22c9cf700b49a797234271b1f29ce6 | 0 | short_answer | $$$$Calculate.$$$$ $$(132+68)\times (520-506)$$ $\textasciitilde\textasciitilde$ $\textasciitilde\textasciitilde$ $\textasciitilde\textasciitilde$ $\textasciitilde\textasciitilde$ | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] |
2023-07-07T00:00:00 | 8af761818c504f10a3169d69baf02a4b | 2 | short_answer | Tina, a pet lover, has 2 cats, 2 dogs, 1 rabbit and some birds. If the total number of legs of all her pets is 28, how many birds does Tina have? | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication"
] |
2023-07-07T00:00:00 | 90366a7b3e114b0782979eb7a1e2fcf7 | 2 | short_answer | There are 5 entrances to a zoo. Tina, Joe, Mike, and Black are going to visit the zoo. They can choose the same entrance, or different ones. The order in which the four people enter the zoo is uncertain. How many different ways are there for them to enter the zoo? | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"
] |
2023-07-07T00:00:00 | 75543c0d8a344cd8a2e2dae02cbf92b8 | 1 | short_answer | $$2.42 \times 1.6=$$~\uline{~~~~~~~~~~}~. | [
"Overseas Competition->Knowledge Point->Calculation Modules->Decimals->Multiplication and Division of Decimals->Multiplication of Decimals"
] |
2023-07-07T00:00:00 | 30f6b3c01a03478b9d6e70cbb8b7a3d4 | 3 | short_answer | A rich man bought a house two years ago. The houseing market is buoyant, and after a year the house had increased in value by 5\%, so the value was £10,500 in the last year. In this year, the housing market slumps. The house loses 5\% of its value. Comparing with the original price, calculate the amount of profit or loss in this year. | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Fractions and Percentages->Percentages Word Problems"
] |
2023-07-07T00:00:00 | 2bbb1e71338f41f6b5859b75e2be3aa2 | 2 | short_answer | How many numbers between $$1$$ and $$200$$ can be divided exactly by $$5$$ or $$7$$, or both? | [
"Overseas Competition->Knowledge Point->Counting Modules->Inclusion-Exclusion Principle->Inclusion-Exclusion Principle for Two Sets",
"Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"
] |
2023-07-07T00:00:00 | b3c36c7c2db9474583eeb898917fa090 | 1 | short_answer | A third of a certain number is $$27$$. What is the number? | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Multiplication and Division of Whole Numbers->Multiplication out of the Multiplication Table"
] |
2023-07-07T00:00:00 | 3eeca15404314eae896ffb6e5ded37b1 | 1 | short_answer | Justin wrote a number and says, "The number is a factor of $$42$$. It is more than $$10$$ and less than $$20$$." What is the number? | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] |
2023-07-07T00:00:00 | 8abbe2b1899a4c2e80f9586a6a4dca94 | 1 | short_answer | The four numbers $$8$$, $$3$$, $$9$$ and $$\square$$ have an average of $$6$$. What number goes in the box? Answer:~\uline{~~~~~~~~~~}~ | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)"
] |
2023-07-07T00:00:00 | 465d94564aeb464d90ec7faaf9940c3d | 1 | short_answer | Chuck bought $$2$$ rulers and $$9$$ pens for $$$21.60$$. A ruler costs $ $0.90$ more than a pen. How much is each ruler? $ $$~\uline{~~~~~~~~~~}~ | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Basic Profit and Loss Concepts"
] |
2023-07-07T00:00:00 | 3e5011dfff4a4b9b81f4caef853a49dc | 0 | short_answer | When I lay a new patio in my back garden, I will need $300\text{kg}$~of gravel. How many$12\text{kg}$~bags do I need to buy? | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers"
] |
2023-07-07T00:00:00 | 52bf46560c164e7bb42b6bd92f0f48a8 | 3 | short_answer | In a magic show, after giving Leon, one of the audience, a calculator, the magician asks Leon to write his birthday and calculate according to the following steps: ($1$) Leon inputs his month of birth. ($2$) Multiply it by $$4$$. ($3$) Add $$6$$ to the results. ($4$) Multiply it by $$5$$. ($5$) Subtract $$20$$ from the results. ($6$) Multiply it by $$5$$. ($7$) Add the number to his day of birth. ($8$) Subtract $$50$$ from the results. In the end, Leon gets $1126$. Do you know his birthday? | [
"Overseas Competition->Knowledge Point->Combinatorics->Strategies and Operations->Operational Problem"
] |
2023-07-07T00:00:00 | e85ba3fcd99f4dd3a67b9b4bdac33f3c | 1 | short_answer | Eve is thinking of a two-digit number and gives the following clues: My number is: • two less than a multiple of $$3$$ • a prime number • two more than a multiple of $$5$$ • less than $$50$$ What is Eve\textquotesingle s number? | [
"Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples",
"Overseas Competition->Knowledge Point->Number Theory Modules->Prime Factorization->Prime Factorization (Equations)"
] |
2023-07-07T00:00:00 | f5b4975343a544e0a0162174eaf7d4af | 2 | short_answer | （AMC 2020 Question \#26） Janine thinks of three numbers. Between them, they use the digits 1, 3, 5, 6, 7, 8 and 9, with each digit being used exactly once. The second number is 2 times the first number. The third number is 4 times the first number. What is the third number? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Questions Involving Sum, Difference and Multiples->Questions Involving Varying Multiples"
] |
2023-07-07T00:00:00 | cab2106c28234f39ae49d4baa681fd8d | 2 | short_answer | Determine the sum of the following equation: 4+8+12+\ldots+396+400+396+\ldots+12+8+4 | [
"Overseas Competition->Knowledge Point->Calculation Modules->Sequences and Number Tables->Arithmetic Sequences"
] |
2023-07-07T00:00:00 | f9135cf12fe94650a246bc80d424cf81 | 1 | short_answer | Multiply $$24 \times 7$$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Multiplication and Division of Whole Numbers->Multiplication out of the Multiplication Table"
] |
2023-07-07T00:00:00 | 8c8c3f8464b24d8c81c07c35b9ea6792 | 1 | short_answer | Think Soda shop is selling coke at the price of $5$ dollars each cup with a refill price of $1$ dollar everytime. Richard has $10$ dollars, how many cups of coke can he afford? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"
] |
2023-07-07T00:00:00 | ee339de70e1e49448ce55adaeae5eaa7 | 2 | short_answer | $3$ monkeys eat $$96$$ peaches in $$2$$ days. Every monkey eats the same amount of peaches each day. $$5$$ monkeys eat~\uline{~~~~~~~~~~}~peaches in $$4$$ days. | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Unitary Method Problems->Finding the Unit Rate and then the Total Value"
] |
2023-07-07T00:00:00 | 3f1a8e5b057c47568af8eaa8c8a7ce10 | 1 | short_answer | $$729 \div 9 =$$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division out of the Multiplication Table"
] |
2023-07-07T00:00:00 | 9e46398b6b5e425abaa591db8be0c422 | 1 | short_answer | There are $$2$$ different story books, $$3$$ different comic books, and $$4$$ different science books on the bookshelf. If books of the same kind need to be put together, how many different ways are there to arrange these books? | [
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations"
] |
2023-07-07T00:00:00 | 14c24a868f9148719c30a1b91c427e21 | 1 | short_answer | A doctor has an annual income of ＄$$120,000$$. The income tax is $$6 \%$$ of the first ＄$$50,000$$ and any amount above ＄$$50,000$$ is taxed at a rate of $$\left( 6+T \right) \%$$. The doctor noticed that the income tax he paid was＄$$10, 000$$. Find $$T$$. | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Tax Problems"
] |
2023-07-07T00:00:00 | 3681f2592b314f8ab3a72fc47b8f90bb | 2 | short_answer | How many ways are there to distribute $$5$$ identical ice-cream to three friends: Zyan, Xuan Ying and SiCheng by ensuring each of them will get at least $$1$$ ice-cream? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Equation Word Problems"
] |
2023-07-07T00:00:00 | 8b8ec14b7a8644c29978ed2f26e00750 | 1 | short_answer | Work out $$345 \times 5$$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Multiplication and Division of Whole Numbers->Multiplication out of the Multiplication Table"
] |
2023-07-07T00:00:00 | e01c74553e6347a3b1a064b18bd7140d | 2 | short_answer | Mason spent an average of $450$ dollars per month from January to March, $350$ dollars per month from April to July, $1,250$ dollars in total from August to October, and $400$ dollars per month from November to December. How much did he spend on average per month from January to December? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)",
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] |
2023-07-07T00:00:00 | 27b3555bfced4c3fa57ebd84801ad9e9 | 1 | short_answer | Sam walks to the library at a speed of $40 \text{m}/\min $. He returns from the library at a cycling speed of $60 \text{m}/\min $. What was his average speed for the whole trip? | [
"Overseas Competition->Knowledge Point->Distance Word Problems->Distance Word Problems on Straight Road",
"Overseas Competition->Knowledge Point->Word Problem Modules"
] |
2023-07-07T00:00:00 | 462088e1598d4df6ad551447b191e0c2 | 1 | short_answer | Sophie\textquotesingle s mother gave her some money to buy ice cream. Sophie wanted to buy $$5$$ servings of ice cream, but she was short of $$$2.30$$. So, she bought $$3$$ servings of ice cream and had $$30$$ cents left. How much money did Sophie\textquotesingle s mother give her? $$$$$~\uline{~~~~~~~~~~}~ | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Distribution Problems->Basic Distribution Problems"
] |
2023-07-07T00:00:00 | 8b91281c082e4e1e8991287413079e54 | 1 | short_answer | Solve the following equation. $\frac{3.5}{3x+2}+\frac{2}{1.5x+1}=\frac{4.5}{5-6x}-\frac{3}{2.5-3x}$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Equivalent Substitution->Algebraic Expressions"
] |
2023-07-07T00:00:00 | bcade51c8974433b902c06454320d2d6 | 0 | short_answer | Pamela has $$25$$ bags of sweets. Each bag has the same number of sweets. There are $$\overline{127 M}$$ sweets altogether. How many sweets are there in each bag? | [
"Overseas Competition->Knowledge Point->Number Theory Modules->Division without Remainders->Applying the Properties of Dividing without Remainders->Maximum/Minimum Problems of Division without Remainders ",
"Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Basic Concepts of Factors and Multiples"
] |
2023-07-07T00:00:00 | e9b595c255074a5b964141db77e7289a | 1 | short_answer | Given that $$9:x=y:2$$, the relationship between $$x$$ and $$y$$ is~\uline{~~~~~~~~~~}~proportional relationship. $y=$~\uline{~~~~~~~~~~}~when $x=3$. | [
"Overseas Competition->Knowledge Point->Calculation Modules->Ratios and Proportions"
] |
2023-07-07T00:00:00 | 51ad76377c2d44b9bc497caa5e86cd99 | 0 | short_answer | \textbf{$$n$$}~is the smallest odd number that uses all the digits $$2$$, $$3$$, $$5$$ and $$6$$ only once. \textbf{$$n=$$}~\uline{~~~~~~~~~~}~ | [
"Overseas Competition->Knowledge Point->Combinatorics->Combinatorics Involving Extreme Values->Extreme Value in Enumeration Problems",
"Overseas Competition->Knowledge Point->Number Theory Modules->Place Value and Number Bases->Numbers->Understanding Numbers and Digits"
] |
2023-07-07T00:00:00 | 1d0c88113962459d9a867535f00b7776 | 1 | short_answer | Calculate $391$ divided by seventeen. | [
"Overseas Competition->Knowledge Point->Calculation Modules->Whole Numbers->Whole Numbers Multiplication and Division->Division of Whole Numbers->Division out of the Multiplication Table"
] |
2023-07-07T00:00:00 | 54499dc98e4442c5aaa04120c1769fbe | 1 | short_answer | There are 7 green balls and 8 blue balls in a bag. How many would you need to take out of the bag without looking to make sure that you have removed at least two of the same colour? （⭐⭐⭐） | [
"Overseas Competition->Knowledge Point->Combinatorics"
] |
2023-07-07T00:00:00 | 09b871767fd046788bf00397a1526767 | 1 | short_answer | Think of a number Add $3$ Multiply by $2$ Take away $2$ Add $10$ Divide by $2$ Take away the number you started with Write down the number that is left? | [
"Overseas Competition->Knowledge Point->Calculation Modules->Operations with New Definition->Operations with New Definition in Flow Charts"
] |
2023-07-07T00:00:00 | a9e6ee1f892d4e91b4af844be4862a94 | 1 | short_answer | Felicia and Janice had some bracelets. Felicia sold $$\frac{{3}}{{5}}$$ of her bracelets. Janice bought $$\frac{{2}}{{5}}$$ of the bracelets that Felicia sold. Then, the ratio of the number of Felicia\textquotesingle s bracelets to the number of Janice\textquotesingle s bracelets became $$5:7$$. If Janice had $$96$$ bracelets at first, how many bracelets did Janice buy from Felicia? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Solving Problems Involving Proportions->Complex Ratio Problems"
] |
2023-07-07T00:00:00 | 931e1d2a335c4a7daca31b92b6d6c0ee | 1 | short_answer | Using a calculator, evaluate the following and round off to the nearest $3$ decimal places: $\frac{-6.94-\sqrt[3]{9.604}}{\sqrt{\frac{44.541}{67}}-\left(-\frac{377}{6}\times 1\frac{2}{3}\right)}$ | [
"Overseas Competition->Knowledge Point->Calculation Modules->Negative Numbers"
] |
2023-07-07T00:00:00 | a58850681f6c454b93664a02ebcf4745 | 1 | short_answer | Calculate: $$299+199+99+5=$$~\uline{~~~~~~~~~~}~ | [
"Overseas Competition->Knowledge Point->Counting Modules"
] |
2023-07-07T00:00:00 | 618cd3abae4a408c89cdfe804dd7861f | 1 | short_answer | A bookstore sells science fictions for $4$ dollars per book, comic books for $5$ dollars per book, and novels for $6$ dollars per book. During the winter vacation, the bookstore decides to donate $50$ books to a nearby kindergarten, including $20$ science fictions, $10$ comic books and $20$ novels. If the amount of book remains unchanged, how much does each book cost on average? | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Average Problems ->Questions Involving Average->Questions Involving Average (ordinary type)",
"Overseas Competition->Knowledge Point->Counting Modules->Statistics and Probability"
] |
2023-07-07T00:00:00 | 7025bfa134974b12917661070ac0ccfc | 1 | short_answer | How many prime numbers are there between $50$ and $100$? | [
"Overseas Competition->Knowledge Point->Number Theory Modules->Prime and Composite Numbers"
] |
2023-07-07T00:00:00 | 0015db147ca4414ca1e9736f722c0a81 | 1 | short_answer | How many three-digit numbers contain at least two sevens? | [
"Overseas Competition->Knowledge Point->Counting Modules->Law of Addition and Multiplication->Complex Forming Numbers->Complex Forming Numbers (with special requirements)"
] |
2023-07-07T00:00:00 | 21b53a84fa7744b799aa83b063cea3d3 | 1 | short_answer | Jack had $$5$$ times as much money as Kyle. After Jack lost $$ $72$$, Kyle had $$\frac{2}{7}$$ as much money as Jack. How much money did Kyle have? | [
"Overseas Competition->Knowledge Point->Calculation Modules"
] |
2023-07-07T00:00:00 | f0b55e6d454f4ee0b6b7bab29ab5fcde | 1 | short_answer | There are $6$ orange, $10$ yellow, $4$ pink and $12$ brown shirts in the closet. At least how many shirts must Annabella take out the closet to get $$1$$ yellow shirt for sure? | [
"Overseas Competition->Knowledge Point->Combinatorics->Pigeonhole Principle->Worst Case in Pigeonhole Principle Problems",
"Overseas Competition->Knowledge Point->Counting Modules->Permutations and Combinations->Combinations"
] |
2023-07-07T00:00:00 | 81c24559e88e4ed8bcd27664fdc09676 | 1 | short_answer | Ms Lee has many students. They can be split into $$9$$ groups, $$10$$ groups or $$15$$ groups equally. What is the least number of students she might have?~\uline{~~~~~~~~~~}~ | [
"Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples->Word Problems Involving Factors and Multiples->Multiples Word Problems"
] |
2023-07-07T00:00:00 | 839a183a0d534ab08d061613682d208e | 1 | short_answer | A multipack of $15$ packets of crisps costs £$3.90$. A packet of crisps costs $35$ pence if they are bought individually. Calculate how much cheaper it is to buy a multipack of $15$ packets of crisps than to buy $15$ packets individually. | [
"Overseas Competition->Knowledge Point->Word Problem Modules->Word Problems in Economics->Money Calculation"
] |
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