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english_AAAI_Math

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0d3f4384ce58444a89f0b0451c47a86a

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short_answer

Ashley, Ben and Charlie are running on a circular track. They take $56$ seconds, $80$ seconds and $105$ seconds to complete a lap respectively. They begin together at the starting point at $10.00$ a.m. At what time do they next meet together at the starting point of the track?

ec2f787ddc4f496c8e1670044fcde021

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short_answer

Peter exercises for an hour every day. $$\frac{1}{3}$$ of the time is spent cycling and the rest of the time is spent jogging. How many minutes does he spend jogging?

67374cb1f2b44b8594ce58b7c2757c30

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short_answer

Justin is asked how old he is. In reply, he answers~"In $$18$$ years\textquotesingle~time I will be $$4$$ times as old as I was $$6$$ years ago." How old is Justin now?

af56a6fc059e429192ef55675e57c67c

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short_answer

\textbf{$$n$$}~is the next number in the sequence. $$22$$~~~~~~$$18$$~~~~~~$$14$$~~~~~~$$10$$~~~~~~$$6$$~ ~ ~ ~ ~ $$2$$ \textbf{$$n=$$~\uline{~~~~~~~~~~}~}

340b86ff5e0b464289776aeb6627ceff

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short_answer

$$30$$ apples are distributed among $$6$$ children and each of them can get at least one apple. The number of apple(s) for each child is different. For the kid who gets the most apples, what\textquotesingle s the largest possible number of apples he can get?

f2faa17dbd4546fe9f05e0ca1b14be52

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short_answer

Sam and Tom are desperate for Mint Cake. Sam\textquotesingle s eco-friendly car takes him from London to Kendal, a distance of $$273$$ miles, while consuming petrol at an average rate of $$72.8$$ miles to the gallon. Tom\textquotesingle s gas-guzzler uses $$6 \frac{3}{4}$$ gallons more petrol to cover the same distance. At what average rate does Tom\textquotesingle s car consume petrol?

a4af03b27daa4f28856b42ba428afc2d

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short_answer

Bart has an M\&M\textquotesingle s chocolate pack with 3 red M\&M\textquotesingle s chips, 4 yellow M\&M\textquotesingle s chips and 5 brown M\&M\textquotesingle s chips. Bart wants to get 2 M\&M\textquotesingle s chips of different colours without looking. What is the smallest number of M\&M\textquotesingle s chips he needs to take out to make sure that he gets what he wants?

e24a897f0dea4a47950e3faa1cdaf6d1

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short_answer

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

f475cb94110941b287259508a63a9ff8

1

short_answer

Find the sum of $$3017$$ and $$4962$$.

333aed92d083437e97962341c0e3e05c

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short_answer

A six-digit number $$\overline{24572\square }$$ is divisible by $7$. What is this six-digit number?

a11a7f4df40f40c8820fc6e6e0c78560

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short_answer

$9039 + 93$

9ed706ba39e2411fba6e6de96d5ecfd7

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short_answer

Calculate: $${{1}^{2}}+{{3}^{2}}+{{5}^{2}}+\cdot \cdot \cdot +{{19}^{2}}$$

41fb6eaf263648dd86dc9ac6a43a72f3

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short_answer

There are two shirts and two skirts in Linda\textquotesingle s closet. How many different ways for Linda to match her outfit today?

b4ccb4b4d7b14da0aad36bfe517a8484

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short_answer

How many digit $$6$$ are used in the the first $$100$$ pages of a book?

f297a90915044281a14d6377f0457a4f

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short_answer

Find the patterns and fill in the blanks. 1, 3,~\uline{~~~~~~~~~~}~, 27, 81

b768e69a54ce422c9bdc0bc62ce7f112

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short_answer

Part of a number sequence is shown. $\cdots \cdots, 105, 120, 135,\cdots \cdots $ If these are the $7^{th}$, $8^{th}$~and $9^{th}$~values in the sequence, what is the $100^{th}$?

5b6e52b88b774ca78d70e6c94d7bdc3f

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short_answer

Calculate $$45+66$$ in a base $$7$$ number system.

dd9b6244a4c4445bb632f0876b616353

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short_answer

Mike and Sara are looking for a place to eat lunch. They know that nearby, there are $$9$$ Chinese restaurants, $$3$$ Mexican restaurants, and $$2$$ fast food restaurants. How many different choices do they have to eat one meal?

e94db5c96fbd44048da7eae72591635d

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short_answer

$$12-(3x-4)=x$$. $x=$．

601ad6e41047493c8d8f3dea2a05469a

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short_answer

The ratio of the number of oranges to the number of lemons in a basket was $$3:5$$. After $$48$$ oranges were sold, the ratio of the number of oranges to the number of lemons became $$1:2$$. How many lemons were there in the basket at first?

940e042aba2b4f56a60da84000fece0e

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short_answer

A rabbit eats $$4$$ carrots in a day. If it takes $$8$$ rabbits $$5$$ days to eat all the carrots in a barn, how many carrots was there in the barn originally?

a50a55a4409a4341b2950b27e6d39826

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short_answer

A bale of hay can be eaten by a horse in 2 days, by a cow in 3 days and by a sheep in 12 days. A farmer has 22 bales of hay and one horse, one cow and one sheep to feed. How many days will his bales last?

c41373fcf732485caf9d92171e911149

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short_answer

Calculate $\dfrac{5}{8}$~of $ $160$.

7ed96bead1224f409f2317f83bd45b09

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short_answer

The mother told her daughter, "When you reach my age, I will be $$75$$ years old". While the daughter told her mother, "When you were at my age, I was only $$3$$ years old." How old is the mother now?

996413eb0e084c8fad4262d2e563cbe1

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short_answer

Work out $$146\times37$$.

025a48e3ac854ca98f6c3b39cdf5562f

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short_answer

\textbf{$$n$$~}is the number for which $$3\times n\times6=72$$. \textbf{$$n=$$~\uline{~~~~~~~~~~}~}

a62c00fc50db459e9f0fdc6cdac1102e

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short_answer

Dates can be writen as an $$8$$-digit number in the form $$y$$ $$y$$ $$y$$ $$y$$ $$m$$ $$m$$ $$d$$ $$d$$. For example, $$20140125$$ stands for January $$25^{}\text{th}$$ $$2014$$. How many days are there in the year $$2014$$ such that its $$8$$-digit representation contains equal numbers of digit $$0$$, $$1$$ and $$2$$?

c5d002031015489ba21101105aaa559a

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short_answer

There are $$11$$ green, $$5$$ red and $$7$$ yellow apples in a basket. Isabella wants to take $$3$$ red apples from the basket without looking. What is the smallest number of apples she needs to take out to make sure that she get $$3$$ red apples?

c350a05252414b3db3a1131ee3b9e465

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short_answer

Solve the equations below : $$7(x+2)=51+2(x-1)$$．

27762b79cb644368b2a5457a17f92ee7

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short_answer

Calculate the following percentage change an increase from $200$ to $204$.

597ad4cf18ea4c63bf6c95cd675bf196

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short_answer

A Year $$6$$ class has $$30$$ pupils. There are $$21$$ who are right-handed. There are $$16$$ girls in the class. Not all the girls are right-handed. What is the smallest number of girls who are right-handed?

3509ed6613a44f60bb123d2ebb9a5094

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short_answer

Calculate: $$20 -- 19 + 18 -- 17 + 16 -- 15 + 14 - 13=$$.

7a09b099857143ed8e06a64d34c8813c

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short_answer

Everything at the store is 80\% off, Tiffany spent $$6400$$ dollars on a fridge and a washing machine, how much money did she save？

2f9ea1c8c72f424db4c1a4c24536bbb0

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short_answer

Six teams, $$A$$, $$B$$, $$C$$, $$D$$, $$E$$, and $$F$$, competed in a single round-robin soccer tournament. In each game, the winner got two points, the loser got none, and each team got one point for a tie. At the end of all games, what was the point total of all six teams?

892a76fc652846adbcd762365971437f

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short_answer

There are $$45$$ children going to the theatre. If each minibus can carry $$8$$ children how many minibuses are needed to get the children there?

3393c5c42ebe4894a4440ce64fee1a72

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short_answer

Calculate the following sums quickly. $$101+97+102+99+98+103-100 = $$~\uline{~~~~~~~~~~}~

c616f997861742469b08bfc319528f5b

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short_answer

There are $$4$$ red, $$7$$ green, $$6$$ blue and $$2$$ orange marbles in a bag. Jane is blindfolded. How many marbles must she draw from the bag so that there are $$4$$ different coloured marbles?

e594932553e149d89309f852797d5586

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short_answer

There are 90 more boys than girls in a school. The ratio of the number of girls who can swim to the number of girls who can not swim is 31:49. The number of boys who can swim is 120 less than the number of boys who can not swim. If there are 1690 pupils in the school, how many pupils can not swim?

8b599766a2704c0eb0e8c0f696e62f06

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short_answer

Find a whole number between $1$ and $100$ that has the following properties. When the number is divided by $2$, the remainder is $0$. When the number is divided by $3$, the remainder is $0$. When the number is divided by $5$, the remainder is $0$. When the number is divided by $7$, the remainder is $6$.

9f8109ce906145b3a3bb3b7938082e99

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short_answer

The product of $$n$$ whole numbers $$1\times2\times3\times4 \times5\times \cdots\times (n - 1)\times n$$ has twenty eight consecutive zeros. Find the largest value of $$n$$.

7af09b472cda4e49ba756b79f79625b3

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short_answer

Work out $$789 \times 6$$

ee58fa876fa247d58050d060bebe1078

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short_answer

$$a$$ and $$b$$ are prime numbers and $$3a+7b=41$$. Work out $$a+b$$.~\uline{~~~~~~~~~~}~

fd889752fd27457fbe03dc85570eec17

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short_answer

$4\text{pc}$ of chicken tenders costs $7$ dollars and $6\text{pc}$ of chicken tenders costs $8.5$. Which one is a better buy?

ac6b5f6822aa44afb8423aeef1df7f92

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short_answer

In a dice game, two dice are thrown together and the results added. A player with a £$$1$$ bet receives £$$10$$ if the total of two dice is greater than $$10$$. If this game is played $$60$$ times, how much will this player expect to lose?

e49cf16bbb284f1fbfb9c440134d58be

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short_answer

What is $$1.83 +0.2$$?

e3aa5800105743d5b2435db12b158401

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short_answer

Kiera spent $$ $740$$ of her monthly salary on a new phone and $75 \%$ of the remaining money on her rent. If she had~$\dfrac{1}{5}$~of her salary left, how much was her salary for the month?

d13312f8d069494cab8f69737daed0b0

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short_answer

A basket with 5 apples weighs 580 grams. If 3 of the apples were taken out, the remaining weight would be 280 grams. What is the weight (in grams) of the basket?

02a402ada62746cca4a7c0600dfc8a9b

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short_answer

How many different natural numbers can be formed using the numbers $$2$$，$$3$$，$$4$$?(without using the same number two times like $$22$$)

bdfc511086b14c2a828a8ce71b43f330

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short_answer

On my clock\textquotesingle s display, the time has just changed to $02:31$. How many minutes will it be until all the digits $0, 1, 2, 3$ next appear together again?

19fa00d48659426b9b8f9c7cc44133aa

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short_answer

Pip bought a bottle of water and drank half of it before class. Then after class, he drank 100ml and there was 150ml of water left in the bottle. Do you know how many milliliters of water were in the bottle originally?

6008ef744a284692b526a28fd0e8a695

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short_answer

Judy\textquotesingle s dad gathered $40$ mushrooms in total in two hours. The number of mushrooms that he gathered in the first hour is $26$ less than that in the second hour. How many mushrooms did Judy\textquotesingle s dad gather in the second hour?

66c31d7e12eb4ffb8ad1f1e8bb55f199

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short_answer

Lynn and Mary had the same amount of money at first. After Lynn spent ＄$$160$$ and Mary spent ＄$$58$$, Mary had thrice as much money left as Lynn. How much money did Lynn have left?

fa119130b0764e8fa4d0f0a2fa2f19fd

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short_answer

If $A$◆$B=A\times A-3B$ and $A$$\triangle$$B=5A-B\times B$, then $(4$◆$2)$$\triangle$$6$ $=$~\uline{~~~~~~~~~~}~.

e4bab25ee48f4b6185a11c389207eebf

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short_answer

Yasmin had $$210\rm kg$$ of grapes. She sold $$\frac37$$ of the grapes on Monday and $$\frac38$$ of the remainder on Tuesday.~ She packed the remaining into identical small bags each containing $$\frac34\rm kg$$ of grapes.~ How many small bags of grapes did Yasmin pack?

5a50e00932e34a2eae95e3e9228b6993

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short_answer

A concert hall has sold $$60 \%$$ of its tickets for a particular night. $$28$$ tickets remain unsold. How many people can the concert hall hold in total? Answer:~\uline{~~~~~~~~~~}~

1e1a13a0a844402da455fc7eb9d39755

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short_answer

There are $$6$$ classes in the fifth grade with $$36$$ students in each class, and $$3$$ classes in the sixth grade with $$38$$ students in each class. How many students are there in the fifth and the sixth grade in total?

a098761e7204471dbfd3c5f04017e952

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short_answer

A division gives a quotient of $$27$$ and a remainder of $$9$$. What is the minimum value of the dividend?

9e459979ca2e4f8e84e5da348f9dba5d

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short_answer

Deⅵ is $$8$$ years older than Jerry. In $$4$$ years\textquotesingle{} time, the ratio of their age will be $$5:7$$. What is the age of Jerry now?

36398085891449859c0c35083ebfdaad

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short_answer

Calculate: $$64-62+60-58+56-54+52-50+48-46+44=$$

41284b5312574903a6aad669cbd6ab65

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short_answer

Serene was working on a mathematic problem involving the subtraction of two $2$-digits number. When she is solving the question, she mistook the tens place in the subtrahend as $5$ instead of $3$ and the ones place as $3$ instead of $2$. Thus, she got a difference of $36$. What should be the correct difference?~\uline{~~~~~~~~~~}~

56303c0854a843e68eb523ba25963b8f

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short_answer

Phoebe thought of a number, multiplied it by five and then subtracted four. The answer she got was $41$. What was the number?

a9b59929e341406986d4962db964c9ec

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short_answer

Jane bought $7$ bottles of apple juice. Each bottle contained $195ml$ of apple juice. She poured all the apple juice into jugs. The capacity of each jug is $250ml$. Find the least number of jugs that was used.

3444a75f07964bfca7021f8d0f95217f

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short_answer

A bag contains $49$~red balls and $1$~blue ball. How many red balls should be removed for the bag to contain $$90 \%$$ red balls?

757e6ca91df84091a26bd18fc1b7fa2a

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short_answer

Calculate：$$\frac{100}{97}+\frac{100\times 99}{97\times 96}+\frac{100\times 99\times 98}{97\times 96\times 95}+\cdots +\frac{100\times 99\times 98\times \cdots \times 5\times 4}{97\times 96\times 95\times \cdots \times 2\times 1}$$

e9f7473a32874d5c820cadf0a1870a0b

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short_answer

A box contains $220$ matches and weighs $45$ grams. The empty box weighs $12$ grams. Calculate the weight of one match.

d6c3aebbe67749778e84875f4bfe6ebf

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short_answer

There were a total of $$1300$$ cows and birds in a large field. There were a total of $$3440$$ birds\textquotesingle{} and cows\textquotesingle{} legs. How many cows were there?

8a9992f6a3c04fea9afe2ab07209e489

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short_answer

How many factors does $$96$$ have？ Pip\textquotesingle s answer: $$96=1\times 96$$ $$=2\times 48$$ $$=3\times 32$$ $$=4\times 24$$ $$=6\times 16$$ So $$96$$ has $$10$$ factors.

f58f700fac024611a683956a1768c0ec

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short_answer

A 500 kg car travels 20 m/s due north. It hits a 500 kg car traveling due west at 30 m/s. The cars lock bumpers and stick together. What is the velocity the instant after impact?

20346fdc304242a383a7ac635afbb0e0

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short_answer

Fatimah thought of a $$3$$-digit odd number. The number was divisible by $$9$$. The digit in its tens place was divisible by $$4$$. What was the greatest possible $$3$$-digit odd number?

0f159b78762443838fac481eb0a7bed3

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short_answer

$18 - 17 + 16 - 15 + 14 - 13$

00e7cd11eefb4db19a4650a5e8cf1454

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short_answer

Jenny has $83$ pens. If Jenny gives Ben $28$ pens, the two of them will have the same number of pens. How many pens does Ben have at first?

4f45df48b0844cadb68195e413cce783

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short_answer

Bob reads $$6$$ books in $$3$$ weeks. How many books in total does he read in $$8$$ weeks?

237e4009b4c54725a1fe587507e1513b

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short_answer

There are $$21$$ trees planted along the road divider with trees planted at opposite ends. The trees are planted at regular intervals of $$2\text{m}$$. If some lamp posts are to be placed along the opposite side of the road at regular intervals of $$10\text{m}$$, how many lamp posts are required on the opposite side of the road if lamp posts are placed at opposite ends of the road?

4585a53e3fbb44e9b8554c9841fc9066

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short_answer

Calculate $15.05 - 14.84$

32f4232fd0304fc781fcf26ecbab7e3e

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short_answer

Mrs Kumar paid ＄$$14438$$ for $$5$$ similar laptops and $$4$$ similar $$DVD$$ players. If $$1$$ laptop and $$1$$ DVD player cost ＄$$2960$$ altogether, what was the cost of each $$DVD$$ player?

cb9e84648a164fd796bda214bd912eed

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short_answer

A brand launches handbags of three different sizes (S, M and L). Each size has 5 available colours (black, white, red, yellow and purple). How many different types of handbags are there?

e6aad1cc98b64cac96958775db869e00

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short_answer

The average weight of the people in a group was calculated. Aaron, who weighs $$45\text{kg}$$, joined the group and the average changed to $$61\text{kg}$$. Then Ben, who weighs $$71\text{kg}$$, joined the group after Aaron. The average changed to $$62\text{kg}$$. What was the average weight of the group before Aaron and Ben joined them?

0bd951281c1c44b48652968acdb95351

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short_answer

In the following, all the different letters stand for different digits. What is the value of one triangle? \hspace{0pt}

f743e1d8460a4eb08dd3685920fb9466

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short_answer

Two distinct numbers from $$1$$ to $$100$$ inclusive will form a pair if the sum of these two is a multiple of $$5$$. How many different pairs are there?

74f45194f12f4ae7be245fca2332fd63

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short_answer

The pattern $$123451234512345\ldots{} $$ is continued to form a $$2000$$-digit number. What is the sum of all $$2000$$ digits?

473e918a9fd74e4aaf831efa01b71026

0

short_answer

John paid a total of $£5.15$ for a jar of coffee, a carton of milk and a bag of sugar. The jar of coffee cost $£3.69$ and the carton of milk cost $89$p. How much did the bag of sugar cost?

702bd47461974ab69465dea85d588eab

0

short_answer

Marci looked at a clock and realized that the number of hours that had passed since midnight was twice the number of hours remaining until noon. What time did the clock shown?

a98ea86c6ab94572a37ea72e70fc26dd

1

short_answer

There are $$5$$ blue balls, $$4$$ orange balls and $$2$$ yellow balls in a bag. Sheila will be blindfolded before she takes the balls out, one at a time. How many balls must Sheila take out in order to get $$4$$ balls of the same colour?

639b8a35b20848139819ed0f716ed926

1

short_answer

Find pair of numbers to form whole numbers, then calculate. $2.3+9.7+5.2-2.2=$

b591b0d58af5497096019cf0b220ebb3

1

short_answer

$2+12\times (8-3)\div4$

5eab24fc6ea24611818fe89f4277708d

1

short_answer

Mike is shopping at the supermarket. Oranges are priced at $$1.5$$ dollars per kilogram and mangoes are priced at $$2.3$$ dollars per kilogram. He buys $$4.1$$ kilograms of oranges and $$2$$ kilograms of mangoes. How much did Mike spend in total?

bfd53c31223f4d469ed9eef0d582baeb

1

short_answer

$$\left(45\div 9\right)\times \left(100\div 10\right)+\left(23-19\right)$$ $\textasciitilde\textasciitilde\textasciitilde$ $\textasciitilde\textasciitilde\textasciitilde$ $\textasciitilde\textasciitilde\textasciitilde$

1e698072c71546a1a63ac8be1c0891fe

0

short_answer

The \textbf{mean} of these numbers is $$5$$. What is the value of $$a$$? $$2$$~ ~ ~ $$3$$~ ~ ~ $$8$$~ ~ ~ $$4$$~ ~ ~ $$a$$~ ~ ~ $$7$$~ ~ ~ $$6$$

230b8cfda67a440eb974960188adca8c

1

short_answer

Work out $$4825+1754$$ Answer:~\uline{~~~~~~~~~~}~

6ac549d7fd244d5c97410534859cd40b

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short_answer

$$A$$ can do a job in $$15$$ days while $$B$$ can do it in $$10$$ days. They work on it together for $$4$$ days and then worker $$A$$ has to take off to deal with a family emergency. In how many days can $$B$$ finish the remaining job?

292095048e3e4e1983e4b66c7cd45d35

1

short_answer

Calculate using the Golden Pyramid Method: $$1+2+3+4+5+\cdots +12+13+13+12\cdots +5+4+3+2+1$$．

45ba73cc1b1e4ca6b099a7a996e9c3b4

1

short_answer

A freezer normally costs £$650$ but it is due to be replaced by an updated model. A store manager decides to reduce the price to £$455$. What is the percentage reduction in the price?

2e1b20f5fdfd4bc595117f252b7bcea6

2

short_answer

Students from Sunshine Primary School are arranged in a square array with equal row spacing and column spacing on the playground. The outermost layer of the array is full of boys, and the adjacent inner layer is full of girls, then boys, then girls and so on until the innermost layer is reached. If there are $52$ more boys than girls in total, find the total number of students.

f380084cf36b45bbbda0a1c8d0634812

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short_answer

Tom boughts $$1000$$ bottles for his science laboratory. Among them, one bottle had poison in it. When mixed with chemical $$X$$, this poisonous water will change its colour while the bottles without poison will not have its colour changed. Every mixture takes $$6$$ hours for the result to be observed as every mixture requires one test tube. What is the least number of test tubes that is required so as to find out which bottle contains poison in them?

28c2da8de504408d83cd9b973e4a5df2

1

short_answer

Find the smallest three-digit number and leaves a remainder of $$1$$ when divided by $$5$$ or $$6$$ or $$7$$.

3c35813541b2403abf942fa5547821b4

1

short_answer

In the animal school,$$4$$ ducklings, $$2$$ baby geese and several lambs are taking lessons. The teacher owl found out that all of her pupils have $$36$$ legs altogether. How many lambs are there among them?

d5bc2d04c57440d0a114ebf980abe4d0

0

short_answer

$$n$$ is the number of mililitres in $$2.5$$ litres. $$n=$$?

754c4e4720274d728d76669caba145eb

1

short_answer

A huge bowl contains many sweets. On the first day, Kenneth ate $$\frac 17$$ of the number of sweets. On the second day, he ate $$\frac{1}{6}$$ of the remaining number of sweets. On the third day, he ate $$\frac 15$$ of the remaining number of sweets. On the fourth day, he ate $$\frac 14$$ of the remaining number of sweets. How many sweets were there in the bowl initially if there are $$6$$ sweets remaining after the fourth day?

40435e2c684944fdbc3ffece625e8a3a

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short_answer

Charlene baked some cookies. She kept $\frac{1}{2}$ of the cookies plus $$8$$ cookies. She gave the remaining cookies to Emerald. Emerald ate $$\frac{1}{3}$$ of the cookies plus $$4$$ cookies. Then Emerald gave the remaining cookies to Hebe. Hebe ate $$\frac{1}{4}$$ of the cookies and had $$42$$ cookies left. How many cookies did Charlene have at first?~\uline{~~~~~~~~~~}~

3aad0d27a09d4acabf6d7f99f57fe23b

1

short_answer

A group of children is trick-or-treating at Mr. Johnson's house for Halloween. Ivy is the first kid to show up and she gets $$17$$ chocolates. Eddie is the last kid to show up and he gets $$150$$ chocolates. If the difference in chocolates between two consecutive kids is $$7$$, how many kids show up in total?