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english_AAAI_Math

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9ee836eb0a204a248346cf0a5a814237

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short_answer

The first term of an arithmetic progression is $$8$$ and the $$12^{}\text{th}$$ term is $$140$$. What is the common difference of the arithmetic progression?

3c267ac100df422598b3c04374b84cda

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short_answer

Amongst the children in a family each boy has as many sisters as brothers, but each girl has only half as many sisters as brothers. How many children are there in the family?

fffededa84664c688f626145cc4d0859

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short_answer

Andy drove $70$ miles in $90$ minutes. His average speed during the first $30$ minutes was $x$ miles per hour, and his average speed during the scond $30$ minutes was $(x-20)$ mph. His average speed during the last $30$ minutes was $(x+10)$ miles per hour. What is the value of $x$?

98507f7a1ab04ff5987283dcfdf7b586

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short_answer

Belinda ate $\frac35$ of a bar of chocolate. $60$ grams of chocolate remained. What was the original mass of the chocolate bar?

645e2eb6b0834d9c99a6e7716f19be7a

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short_answer

$$$$Calculate.$$$$ $$29+6\times(40-28)\div(34-22) $$ $\textasciitilde\textasciitilde$ $\textasciitilde\textasciitilde$ $\textasciitilde\textasciitilde$ $\textasciitilde\textasciitilde$

c7ffcb7a1eca4535a488e6da6a9364f7

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short_answer

Daniel spent three weeks preparing and writing a presentation on whales. He began work on the project on the $$15$$\textsuperscript{th} May. What date did he finish the project?

2c96bab18bda4f58822aca3d954a2306

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short_answer

Justin gave some pencils to all his students who took the exams. The $1$\textsuperscript{st}~student got $5$ pencils, the $2$\textsuperscript{nd}~student got $11$ pencils, the $3$\textsuperscript{rd}~student got $17$ pencils, the $4$\textsuperscript{th}~student got $23$ pencils, and so on. Given that the numbers of pencils received by the students formed an arithmetic sequence and the last student got $131$ pencils, find the total number of students who took the exams in Justin\textquotesingle s class.

db4d028578d9467fa3efdfc0289ceb82

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short_answer

Kelvin has $$$12$$ more than Sally. Ivan has twice as much as Kelvin. If Sally has $$$8$$, how much does Ivan have?

c92aa76e3e324a49ad94e03580521716

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short_answer

Express $$96$$ (base $$10$$) in the base $$6$$ number system.

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short_answer

$$27$$ apples are distributed to $$5$$ children and each of them can get at least one apple. The number of apple(s) for each child \uline{are different}. For the kid who gets the most apples, what is the least possible number of apples he can get?

ae40978145f94c6f9996c9e966b8c97d

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short_answer

Six people pay £$$5.50$$ each for a meal in a restaurant. They leave a $$10 \%$$ tip for the waiter. How much change do they receive from a £$$50$$ note?

f8ccc3d1db7a464b831820a4451322ff

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short_answer

\textbf{How\hspace{0pt} \hspace{0pt}many\hspace{0pt} \hspace{0pt}seconds\hspace{0pt} \hspace{0pt}are\hspace{0pt} \hspace{0pt}there\hspace{0pt} \hspace{0pt}in\hspace{0pt} \hspace{0pt}a\hspace{0pt} \hspace{0pt}minute?\hspace{0pt}}

a64f47165f93431bb686e430ed75deeb

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short_answer

One snail climbed from the bottom of a well that was 10m deep. It climbed up 4m during the day, and slid down 2m during the night. Which day could the snail climb out of the well? $4-2=2$ $10\div2=5$ The 5th day.

0588ff4a3789420685f1bed8b5f2e9be

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short_answer

Jason and Belinda play a game. Here are the rules: 1. There are $$26$$ marbles. 2. They take turns taking out marbles. In each turn, each player must take out $$1$$ to $$3$$ marbles, and cannot choose not to take any marbles out. 3. The one who takes out the last marble loses the game. If Jason takes some marbles out first, how many marbles should he take in the first turn so that he can make sure he will win the game?

29a8a89ddd5447e8affdeb65b7d6869b

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short_answer

If $$n$$ is a positive integer such that $$5+10+15\cdots+5n$$ is divisible by $$2013$$. Find the smallest possible value of $$n$$.

54efb1f9d0924e1d8fa4596005959b2a

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short_answer

Work out $$\frac{6}{7}$$ of $$42$$. ~\uline{~~~~~~~~~~}~

caf23672c0554b8295549b932bf0889a

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short_answer

Work out $953+1065$

cd9ad5be90634b298514a198bfb61625

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short_answer

If we want to rewrite $25$ as the sum of $7$ different natural numbers, how many different ways are there? Please list them all.

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short_answer

A certain alcoholic drinks 90\% of the day and goes to three fixed bars at random. One day, people find that the alcoholic is not at two of the bars. What is the probability of the alcoholic staying in the third bar?

8e243ca0416749c4ab65f908ade8388d

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short_answer

If $$\frac{3}{7}$$ of a number is $$18$$, what is $$\frac{5}{6}$$ of the \textbf{\uline{same}} number?

efa05afe196f4afa960648690f074c1f

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short_answer

A piece of pasture grows at a constant rate every week. $$120$$ cows will eat up the grass in $$12$$ weeks. $$150$$ cows will eat up the grass in $$8$$ weeks. How many cows can the pasture sustain for $$6$$ weeks?

32f18491c74041d8817a310362816c55

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short_answer

Daniel spent three weeks preparing and writing a presentation on whales. He began work on the project on the $$15\text{th}$$ May. What date did he finish the project?

e86fd8332fe14c18baddfef75e03ff27

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short_answer

The cost of $3$ pencils and $2$ markers is $$$13$$. The cost of $2$ pencils and $3$ markers is $$$12$$. What is the total cost of $$7$$ pencils and $7$ markers?

09a3a1d022104884aa725a719c560f60

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short_answer

If each volunteer in a tree-planting project plants $$4$$ trees, $$5$$ trees will be left. If each of them plants $$7$$ trees, one volunteer will have nothing to plant. How many volunteers are there in the tree-planting project? How many trees do they plant?

b3dcd19bf9ef49f6abe5c02758449b1a

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short_answer

What is $$6$$ more than $$98$$?

aa2c433bd04243828094f4f0da449459

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short_answer

Students from Think Primary School are arranged in a square array with equal row spacing and column spacing on a playground. The outermost layer of the array is full of boys, and its adjacent inner layer is full of girls, then boys, then girls, and so on until the innermost layer is reached. If there are $55$ more boys than girls in total, please find the total number of students.

662004bd60264ac5b02db70eebf6c2af

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short_answer

Subtract $$1476$$ from $$3200$$

aecd8ddb67d4485295695f4d5b6f8788

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short_answer

There were a total of $$270$$ stickers in Bag $$A$$ and Bag $$B$$. After $$56$$ stickers from Bag $$A$$ were moved to Bag $$B$$, the ratio of number of stickers in Bag $$B$$ to the number of stickers in Bag $$A$$ is $$3:2$$. How many stickers were there in Bag $$A$$ at first?

6681c9a39b3645079a46a6daf29a4854

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short_answer

What is the missing number?~\uline{~~~~~~~~~~}~ $$10:\boxed{\textasciitilde?\textasciitilde}=14:21$$

5b97b704f01a431fbcd061cfe8853201

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short_answer

Write down the next number in this sequence: $$5$$,$$11$$,$$17$$,$$23$$,$$29$$,$$35$$,$$41$$,$$\cdots \cdots$$ ~\uline{~~~~~~~~~~}~

54e546b3285e46baa909a946531986b5

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short_answer

Tony needs to buy chocolate bars for all the children in Year $$7$$. Each of the $$74$$ children get one chocolate bar. There are $$8$$ chocolate bars in each packet. Work out the least number of packets of chocolate bars that Tony needs to buy.

7d4469e90d7e44938c44082c04573041

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short_answer

Find $$5 \%$$ of $$180$$.

517f83e2071941a890e20a4e3126cc19

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short_answer

A perfect number is a positive integer that is equal to the sum of its positive factors, excluding the integer itself. For example, $28$ has factors $1, 2, 4, 7, 14$ and itself. Since $1 + 2 + 4 + 7 + 14 = 28$, we say that $28$ is a perfect number. Find the smallest perfect number.

2d6942e7e2a049b0875a5daaa2d8662f

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short_answer

Calculate: $$30-28+26-24+22-20+18-16+14=$$

31d560632aeb4f189ed15394a994b8ea

1

short_answer

Part of a number sequence is shown. $25, 28, 31$ If the last figure shown is the $10^{th}$~term in the sequence, what was the first?

6fa5dd836ec04fd1867acfcafb149b3b

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short_answer

Christopher makes $$80$$ cakes. They need to be put into boxes. Each box holds five cakes. How many boxes will Christopher need?

09f6f0f9df4e4407bb6d0d93d12f86f3

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short_answer

Lucy brought 30 sweets to school. She decided to keep 6 sweets to her sister. She give away the rest of the sweets equally to 6 of her friends. How many sweets will each of the friends get?

d0aafdcf41bd41af9f7703e35d618f89

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short_answer

Lovelle and Makayla had $$3998$$ muffins altogether. After Lovelle sold $$462$$ muffins and Makayla sold $\frac{2}{5}$ of her muffins, Lovelle and Makayla had an equal number of muffins left. How many muffins did Lovelle have at first?~\uline{~~~~~~~~~~}~

61cacff2e135446188147ef9331416bf

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short_answer

Irene had some money. She spent $$\frac{1}{4}$$ of it on a book and $$\frac{2}{7}$$ of it on a bag. The book and the bag cost $$225$$ dollars altogether. How much money did she have at first?

199f98404707430a8c113444383853f4

1

short_answer

In one equation, how many different positive integers at most can add up to $$30$$?

48c4af399af1492c8496fdcbe4b79ce4

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short_answer

A set of $$40$$ playing cards have $4$ different colours. The number of cards of the $$4$$ different colours are $$4$$, $$8$$, $$12$$ and $$16$$ respectively. A card dealer then selects some cards with his eyes closed. At least how many cards must he select such that there will definitely be $$10$$ cards of the same colour?

7334697b756d4565a7eb61beac61cfb8

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short_answer

Grace plants a row of daffodils. There is a gap of $$1.1$$ metres between each daffodil, and the row begins and ends with a daffodil. She has $$8$$ daffodils. How long is the row of daffodils when she has finished? ANSWER~\uline{~~~~~~~~~~}~$$\text{m}$$

e2768d76048543a996b33863b0237436

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short_answer

A ribbon of length $$87$$ $$\text{cm}$$ is cut into $$30$$ equal pieces. How long is each piece? ~\uline{~~~~~~~~~~}~$$\text{cm}$$

e139050ca60c4fb8ae683ddbe39fd88c

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short_answer

There is 1450 boxes in the storerooms and each box contains 258 books. Find the total number of books.

e79fe3bad58843cb9ba29a747eecfe37

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short_answer

Clara wants to distribute $9$ stickers into $$3$$ identical boxes. How many ways can she do so if each box cannot contain the same number of stickers?

e9d1fadd4f7340399f406e12d58bc690

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short_answer

A bottle contains $150$ ml of juice. Alex drink $50 \%$ more than Jane and these two friends finish the bottle between them. Calculate how much Alex drinks.

f3c45f5f9fe141138b4274ad08514257

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short_answer

The wet market is $48 \rm m$ from Auntie Lina\textquotesingle s house. Auntie Lina can walk $8 \rm m$ in one minute. How many minutes does it take her to reach the wet market? Aunt Lina thinks that she just needs~\textbf{$$5$$} minutes. Her working is done below: Minutes took===\textgreater$$48\div 8 = 5$$ Is she correct? If she is wrong, write the correct answer.

5d2b6883175743eda687b1bb058d4c89

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short_answer

There are $$5$$ girls and $$7$$ boys in a class. How many ways are there to form a group of $$4$$ if there must be at least $$1$$ boy in the group?

81ab24eed7cd4f2296d627d76b1e2ec2

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short_answer

Write the missing number to make this correct. $\frac{1}{4}$ of $16$ $=\frac{1}{2}$ of~\uline{~~~~~~~~~~}~

d349a45227c5469c8d98a746d07c5555

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short_answer

CC prepares $18$ pears, $30$ strawberries, and $18$ boxes of chocolate for her friends. She divides all of them equally among her $6$ friends. How many fruits does each of her friends get?

0116cb5ffe3f43828ce4925528badb2e

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short_answer

Bud had some money. She spent $$\frac{1}{4}$$ of it on a book and $$\frac{2}{5}$$ of remaining money on a bag. The bag cost £$$60$$. How much money did she have at first?

b50f8ca3f787492f9f27c716da3258de

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short_answer

Solve the equation. $3x\div5=15$

30aa83b2ee3f4ead83de91a226189785

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short_answer

There are two positive integers, $$x$$ and $$y$$. $$x$$ equals to $$5^{2}$$, and $$y$$ is the base of $$6^{3}$$. What is the product of $$x$$ and $$y$$?

3ef9ddcfb78d4c79b8835fcd29559ed7

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short_answer

Given that a book uses $157$ digits to print out all its page numbers, how many pages does the book have?

ef48001475784ca48f23a6a14697b062

0

short_answer

Find an odd number between $200$ and $241$ which can be divided by both $3$ and $7$.

6cc6f9f62af04d3f8eb7d700d44ac715

1

short_answer

$$\left( 70\div 7-7 \right)\times 13$$

41e25daefa484ddabc8596daad89dee5

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short_answer

$$41$$ peach trees are planted along a stretch of road with trees planted at both ends of the road. The distance between each tree is $$3\text{m}$$. On the opposite side of the road, lamp posts are placed at regular intervals of $$8\text{m}$$, with lamp posts placed at opposite ends of the road. How many lamp posts are there on this side of the road?

b1362edc59474e289cdb2ea885cdd477

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short_answer

Think Lab buys $$72$$ experimental apparatus. But two digits of the total price on the invoice are not clear, which only show $$\overline{\square 679\square }$$ dollars. Given that the unit price of this kind of apparatus is an integer, how much is it?

1ddfd41822fc4ff5909fb0c086a9e1cc

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short_answer

Miss Jenny is separating some candies for class A and class B. If each student in class A get $4$ candies, $20$ more candies are needed. If each student in class B can get $6$ candies, there will be $16$ candies left. It is known that the number of students in class A is twice of class B. How many candies does Miss Jenny havve?

501bce5f0d5c41eb96c1a803d85678b4

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short_answer

A $$360$$-$$\text{m}$$-long train passes a pole at a constant speed of $40\text{m/s}$. How long does the train take to totally pass the pole？

65c1681a1cc943ca8fed37eafd2809bd

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short_answer

If you add up the digits of $$14$$ you get $$5$$ ie.$$1+ 4=5$$. \textbf{How many} $$2$$-digit numbers are there altogether (including $$14$$) which add up to a multiple of $$5$$?

79002f093bcc4697a0f9a3929ef1d7a5

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short_answer

Work out $208 \div 8$.

600b0d1413ee4c7f9c8323852cd824de

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short_answer

There are some potted plants along the pavement. Between every $2$ potted plants, there is an empty space, also known as intervals. If there are $21$ intervals, how many potted plants are there?

44295cc103b24b67af16130f5db0f090

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short_answer

Liana has £$$24$$ of pocket money saved. She spends one third of her savings on a $$\text{DVD}$$ and $$25 \%$$ of the remainder on a book. How much does she have left? £~\uline{~~~~~~~~~~}~

a22a990372e6459ab93701b27bbe1333

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short_answer

On a vast grassland, lives a pack of wolves and $32$ rabbits. Rabbits eat grass and give birth to baby rabbits. Each year, there are $3$ times as many rabbits as last year. On the other hand, wolves eat half the rabbits\textquotesingle{} total population every year. How many rabbits will there be after $3$ years?

eb83c6f6832f41feaed4f34edd98a1ca

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short_answer

I travel $$1$$ mile at $$60\text{m.p.h.}$$ and then $$1$$ mile at $$30\text{m.p.h.}$$ What is my average speed in miles per hour?

a3995edc2a1a43daa636491bd11f901f

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short_answer

Every time Erica washes the car her mother gives her $£1.40$. How many times must she wash the car to make more than $£12$?

2450c7184dc1494db29badfda3df6350

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short_answer

How many numbers are there between $$0 \sim 40$$ that consist digit \textquotesingle$$2$$\textquotesingle?

64dfb01da35643c0b9de911c9ea05789

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short_answer

Emily got a lot of candies at Think Academy\textquotesingle s Halloween activities. On the first day, Emily ate two candies. On each day after that, she ate $$2$$ times the number of candies that she ate on the previous day. On the fourth day, how many candies did Emily eat?

34416f7c5b99456f877168a0fd62da99

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short_answer

John is thinking of a $$3-$$ digit number. When this number is divided by $$4$$ or $$6$$, there would be no remainder. The number is in between $$121$$ and $$135$$. What is the number John is thinking of?

875569394f454c87ba59b92ec3568007

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short_answer

The remainder when a natural number greater than $$1$$ divides $$290$$, $$235$$, and $$200$$ are $$a$$, $$a+2$$, and $$a+5$$, respectively. What is this natural number?

01a700f22d8440ff98528ae95438b080

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short_answer

Subtract $582$ from $901$

7a629088064049ac9991a8c0a6a39bc2

1

short_answer

A cleaner earns an average of $$£70$$ a day. Find the total amount he earns in a week if he works from Monday to Saturday.

05067bad937e48738bea7614f9cc4676

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short_answer

One of the angles in a triangle is a right angle. Two unknown angles are left and one of them is two times larger than the the other angle. What is the size of the largest angle betwen the two?

2a9c4ac0af274c21b3b543fdc562d57c

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short_answer

In the following, all the different letters stand for different digits. What is the value of $\overline{PI}$? $4\times \overline{IS}= \overline{PI}$

d93d643e886d4754abfa2f90328da9f1

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short_answer

On Memorial Day, the community center hosted a special event for nine elderly members. Their ages are nine consecutive natural numbers, and the sum of their ages is $$765$$. If their seats are arranged from the youngest to the eldest, what will be the age of the elderly member who sits in the middle?

5e8d313c1541406a95c53bcb9f149496

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short_answer

The total cost of $$9$$ similar necklaces and $$5$$ similar earrings was ＄$$1440$$. The total cost of $$3$$ such necklaces and $$1$$ such earring was ＄$$438$$. Find the total cost of $$1$$ necklace and $$1$$ earring.

91a598b887f6483a86d977ea27f5c731

0

short_answer

Last week, at a seaside resort, there was an average of $3$ hours of sunshine per day for the six days Monday to Saturday.~ On the Sunday, there were $10$ hours of sunshine. What was the average amount of sunshine per day for the whole week?

1edc3edaab9048beaf044a5eee61b184

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short_answer

Shawn\textquotesingle s walking speed is $$75$$ $$\text{m/min}$$. His running speed is $$2$$ times his walking speed. He takes $$24$$ minutes to walk to school. How long does it take him, if he covers half the journey by walking and the other half by running?~\uline{~~~~~~~~~~}~min.

13d1dc22063b44a6bfd3c253184381b8

1

short_answer

The road leading from Betty\textquotesingle s house to the school is planted with $$79$$ trees at regular intervals. There are no trees in front of the school or her house. If the road is $$320\text{m}$$ long, what is the distance between each tree?

d02e694f3a564aafaf5019cd2b7a9a4d

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short_answer

There are $$120$$ boys and $$80$$ girls at a small primary school. During the holidays, $$50 \%$$ of the boys and $$60 \%$$ of the girls saw the latest Harry Potter movie. How many pupils in total from the primary school saw the movie? Answer~\uline{~~~~~~~~~~}~

f1b82ff9340a4655b4cf7000c847b825

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short_answer

Kim gave $$\dfrac{1}{3}$$ of her savings to her mother. She then bought some dresses for ＄$$177$$ and spent ＄$$129$$ on a pair of earrings. After that, she found that the amount of money left was $$\dfrac{1}{2}$$ of what she gave her mother. How much was her savings?

3f5d80aa10384e98a458b98fad0305a2

1

short_answer

How many possible ways are there to keep $$6$$ apples into $$3$$ identical basket (the basket can be empty)?

909e9ffd178a4a82a7e2ba972d438c99

1

short_answer

A $$385$$ $$\text{cm}$$ length of string is cut into $$15$$ $$\text{cm}$$ lengths. If the maximum number of length are made, how much string is left over? Length left over~\uline{~~~~~~~~~~}~$$\text{cm}$$

4af0a33072c147caa27c6f6519d84e3f

1

short_answer

Write~$1\dfrac{3}{100}$ as a \textbf{decimal}.

3676c87ead1a489f9e921d0d75aa36ef

1

short_answer

Eight football teams play each other once. How many matches will need to be played?

fcb6d1b5111d48d9a3ae25817b7ba302

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short_answer

When $$2018$$ is divided by a positive integer $$N$$, the remainder is $$11$$. Find the sum of all possible values of $$N$$.

1a428efca7154d45b9f95d2f7093cbe7

1

short_answer

In a clothing factory, each worker could make $6$ skirts each day. The factory only had one worker on the first day, and another worker joined on the second day. Each day thereafter, a new worker would join. How many skirts did they make in total for nine days?

494681f041b745a591be1d725abc3a02

0

short_answer

There are $$8$$ cows and chickens altogether in a barn. The total number of legs of all the cows and chickens is $$26$$. How many chickens are there in the barn?

715019fd42ea4f559b0924cbe53893bc

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short_answer

Calculate: $$77.5\times 52 \%+5.2\times 2.25.$$

0a9deb608fe24aa6b6430859835ac8d7

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short_answer

Here are the first six terms of a number sequence: $$11$$, $$14$$, $$17$$, $$20$$, $$23$$, $$26$$ Which of the following numbers will also be in this sequence? $$30\textasciitilde\textasciitilde\textasciitilde\textasciitilde40\textasciitilde\textasciitilde\textasciitilde\textasciitilde50\textasciitilde\textasciitilde\textasciitilde\textasciitilde60$$

9e5271cce46840fc8756f7236f3fd9b2

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short_answer

A meal in a restaurant costs the same for each person. For $11$ people the total cost is £$253$. What is the total cost for $12$ people?

f1c6e0272fae419183c3fb080070f9ad

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short_answer

Find the $$2023^{\text{th}}$$ digit in the number $$12345678910111213\cdots 998999$$.

6885b2a6b6b54f2d8315a175fa94e91a

1

short_answer

A teacher distributes $$138$$ sweets evenly to her class. How big is the class size if at least one student gets $$5$$ sweets?

13dd71975a16405c87357c875ed6c03c

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short_answer

3 apples and 2 bananas costs £1.25 1 apple and 1 banana costs £0.48 Work out how much it would cost to buy 5 bananas.

c098a360c7f6486099fd66b709ca7e5a

1

short_answer

A programmer has an annual income of ＄$$150,000$$. The income tax is $$8 \%$$ of the first ＄$$50,000$$, and any amount above ＄$$50,000$$ is taxed at a rate of $$(8+ T) \%$$. The programmer noticed that the income tax he paid was ＄$$15,000$$. Find $$T$$.

6d1e50acecb5443699ff1409bbab9ab1

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short_answer

Woody participated in a math skills competition. There are $25$ questions in total. For each correct answer he gained $4$ points. For each incorrect answer he lost $2$ points. For each question he did not attempt, he scores $0$ point. Woody answered all but one of the questions and got a score of $66$ points. How many correct answers did he have?

ae271ee454574a6f9c07ffcb062507f5

0

short_answer

\textbf{$$n$$}~is the number where. $$3\times n\times11=66$$ \textbf{$$n=$$}~\uline{~~~~~~~~~~}~

eaa36f2338ce478c9ef3805f3e5db384

1

short_answer

Rachel and Alice have some pieces of candy. If Rachel gives Alice $10$ pieces of candy, then they would have the same number of pieces. However, if they both eat $8$ pieces of candy, Rachel has $3$ times as many pieces of candy left over as Alice. How many pieces of candy did they have in total originally?

a024f762eee54f819b5a5c703275d15c

1

short_answer

There are $432$ boys in a football club born in January. At least how many boys were born on the day of January with the most births?