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english_AAAI_Math

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b7e31907e86c496e848fa4239fbfcc8e

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short_answer

Ali and Kumar share some country erasers at the ratio of $$7:5$$. After Ali gave Kumar $$10$$ country erasers, the ratio of the number of their country erasers become $1:5$. How many country erasers do they have altogether?

c5a32fbb6fcb46b48f3e67ce27fcc7b2

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short_answer

Some students were solving math problems together. The $1$\textsuperscript{st} student solved $4$ problems, the $2$\textsuperscript{nd} student solved $7$ problems, the $3$\textsuperscript{rd} student solved $10$ problems, the $4$\textsuperscript{th} student solved $13$ problems and so on. Find the number of math problems solved by the $23$\textsuperscript{rd} student.

f015194282af429a8af72aaa964f578e

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short_answer

Tina started her trip from city $$A$$. She went east for $$15\text{km}$$, then went north for $$3 \text{km}$$. After that she went west for $$9\text{km}$$. Finally, she went north for $$5 \text{km}$$ to end her trip at city $$B$$. What is the shortest distance, in $$\text{km}$$, from city $$A$$ to city $$B$$?

7866c751419b4d9097fee74972b01d9d

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short_answer

A shop sells bananas and pears. Max bought $1$ banana and $3$ pears. He paid $84$p. Emily bought $1$ banana and $1$ pear. She paid $48$p. How much does $1$ banana cost?

30f09344ca4a4013b33fc28adc31ff05

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short_answer

Eureka Primary School is having their Sports Day. Each activity is $$45$$-minute long, and there is a $$20$$-minute break between each activity. The entire duration of Sports Day, from the start of the first activity to the end of the last activity, is $$8$$ hours and $$20$$ minutes. How many activities are there in Sports Day?

69bc4bec9bee483683d61a26cbefa4ac

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short_answer

Adam, Ben and Carl are weighing themselves. Together, Adam and Ben weigh $$102\text{kg}$$ Ben and Carl weigh $$97\text{kg}$$ Adam and Carl weigh $$92\text{kg}$$ What is their total weight in $$\text{kg}$$? Answer~\uline{~~~~~~~~~~}~

b5e98b7ca17e48e9aceb47ddcd12fb5e

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short_answer

There are four cards as shown below. $$\boxed{0}$$~ ~ $$\boxed{3}$$~ ~ $$\boxed{5}$$~ ~ $$\boxed{8}$$ Using each card only once, how many different $$4-$$digit numbers which are greater than $$5000$$ can be formed using the four cards?

999d1345ce434bc0b7648892d297c82e

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short_answer

Find $$x$$． $$2+3\left( x-26 \right)=52-\left( x-40 \right)$$．

46cd8c8fc22a4192a04253ceaca842cf

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short_answer

$$A$$\textquotesingle s efficiency is twice $$B$$\textquotesingle s and $A$ is able to finish a job in $$5$$ days less than $$B$$. In how many days can $$B$$ finish the work by himself?

5993b277c13b4ff38cb800c6c4a33a65

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short_answer

Sujatha's marks in $$4$$ tests were $$16$$, $$15$$, $$16$$ and $$10$$. What was her mean score? Answer:~\uline{~~~~~~~~~~}~

ec93c9b0e33b4132b916d18ebb789c94

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short_answer

What is~$\dfrac{3}{5}$ of $35$?

899bd98193b34e558ea4353df664f200

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short_answer

Mr Tan posted a question to the class. "Is $$123456$$ divisible by $$11$$?" After thinking for a few seconds, George answered "No, $123456$ is not divisible by $11$. There will be a remainder of $1$". Is George correct? If not, explain how George is able to get the answer without doing any calculations and find the correct answer.

2fe30b6237e0498f8b46e088fbbc4301

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short_answer

Claire buys $$40$$ bulbs. $$25 \%$$ are crocus bulbs,~$\dfrac{1}{5}$ are tulip bulbs and the rest are daffodil bulbs. How many daffodil bulbs does she buy?

9f293803776049bca507bf11f748846b

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short_answer

An icicle measured $2.06\text{m}$~at the start of a sunny day, but only $78\text{cm}$~at theend of the day. What length of icicle had melted?

66c27502b84244db8f72fb311fd7f115

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short_answer

What is $$40 \%$$ of $$650$$ grams?

aa84ae289f2b4586bef8164084d18865

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short_answer

Pip is climbing up a staircase with $$9$$ steps. If Pip is climbing either $$1$$ or $$4$$ steps up per move, how many different ways can he climb the staircase?

ee942986e3444be99926258561b6aba7

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short_answer

Calculate the following answer using long division: $3549\div7=$~\uline{~~~~~~~~~~}~

b417154f43274315bf9c280cf406e937

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short_answer

Pip can fold 17 paper planes in 12 minutes. How many paper planes did Pip fold in 36 minutes?

f50bfa91cfc94371b13058e0e79935a3

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short_answer

A bus has $35$ passengers on board. At the first stop two-fifths get off and then $7$ people get on. At the next stop a quarter of the people remaining on the bus get off and then $13$ get on. How many passengers are there on the bus now?

96f6824d7c5c43528d8840695801e0fa

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short_answer

Calculate: $$0.5^{3}+1^{3}+1.5^{3}+\cdots+10^{3}$$.

2d139d10c0eb4247b231356fa4fdf082

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short_answer

Mr Jones is shopping at a supermarket. He estimates that the price of the contents of his shopping trolley is £$35$ to the nearest £$5$. Assuming that he is correct, what is the least amount his shopping bill could actually be?

40a2c5266dff4ef9b884738049f2b326

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short_answer

The sum of Geoff\textquotesingle s age and his sister\textquotesingle s age is $$22$$. In how many years will the sum of their ages be $$40$$?

7f37d7d7b9fc4673a77900f514ce7751

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short_answer

Three schools ordered a total of $$300$$ magazines. Each school ordered $$98$$ magazines at least and $$102$$ magazines at most. How many different combinations are there for the number of each school\textquotesingle s magazine orders?

985600d1f0d24b41a9d3607140bd9878

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short_answer

There are 40 toys in a row. The elephant is at the $$10^{\rm th}$$ position counting from left to right. There are $$5$$ toys counting from the rabbit to the elephant. If the elephant is on the right side of the rabbit, what is the rabbit\textquotesingle s position counting from right to left?

ff86d855c39d4764a5ffb262848abdd0

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short_answer

Nancy and Tim write a book together. Nancy can complete writing the book alone in $6$ days. If Tim helps, they can complete writing the book in $4$ days. How long will it take Tim to complete writing the book by himself?

7a500b5489884af9ad95dc1143f1643a

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short_answer

Alison has a large number of coloured pencils. When the pencils are divided between two of her friends there is one pencil left over. If they are divided between three friends there are two left over. Between four friends there would be three left over. Between five friends there would be four left over. What is the smallest number of coloured pencils that Alison could have?

bb41ee852bed4cf5adccccc9b1c77534

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short_answer

Ewan shares $12$ biscuits equally between him and his $3$ sisters. How many biscuits do they get each? ~\uline{~~~~~~~~~~}~

111b0f86493b40b19e61144527ced67f

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short_answer

What is $$\dfrac{3}{7}$$ of $$385$$?

c694691621a9431ea4bca6bc4ce553d4

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short_answer

Chef Ken used three special ingredients, $P$, $Q$ and $R$ to make a sauce. Each packet of Ingredient $P$ had a mass of $300\textasciitilde g$. Each packet of ingredients Q and R had a mass of $400\textasciitilde g$ and $500\textasciitilde g$ respectively. The ratio of the number of packets of ingredients $P$, $Q$ and $R$ used was $7 : 3 : 2$. Given that the total mass of the sauce was $172\textasciitilde kg$, how many packets of ingredients were used altogether?

f3c6461dee114615a71a938306942695

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short_answer

The \textbf{mean} of these numbers is $$12$$. What is the value of $$a$$? $$8$$~ ~ ~ $$14$$~ ~ ~ $$6$$~ ~ ~ $$9$$~ ~ ~ $$a$$~ ~ ~ $$13$$~ ~ ~ $$12$$

e78f15baf14349d3a74406de623335fc

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short_answer

The Road Authority decided to use a new system on traffic lights. The traffic lights are arranged such that $3$ traffic lights turn green at the same time every $9$ minutes. The first traffic light changes lights every minute and the second traffic light changes lights every $1.5$ minutes. Determine the shortest possible time the third traffic light takes to change lights, considering that it should be at least $30$ seconds or longer.

c9a78261a27b44b1bdd0c3d2ee5a8794

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short_answer

There are three pieces of ribbon. The pink ribbon is $2.5$ metres long, the blue ribbon is $220$ centimetres long and the orange ribbon is $30.5$ centimetres long. Which ribbon is the longest? ~\uline{~~~~~~~~~~}~

dab2cf7eb1d44c0eba4e7832b4ff92e8

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short_answer

Sara is preparing a dish. It costs $10$ minutes for preparing ingredients, $15$ minutes for baking the dish, $5$ minutes for washing the plate, and $15$ minutes for eating. At least, it will take~\uline{~~~~~~~~~~}~minutes for Sara to finish the dish.

4c802ea687a8492b9acb91c335e6d58b

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short_answer

You paid $75$ dollars for a cup on sale for $50 \%$ off. What was the original price of the cup?

758c762d7161444799a78a19de32398f

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short_answer

There are 3 red cars, 12 blue cars and 15 green cars in the car park. Each red car can carry 10 people, each blue car can carry 15 people and each green car can carry 20 people. Find the average amount of people that each car can carry.

3ac7118d01c14ab5a18f0c5846d9e605

2

short_answer

Eleanor was travelling from City F to City G at a uniform speed. She drove past Rachel who was travelling at a uniform speed of $84 \text{km/h}$ in the opposite direction. One and a half hours later, Eleanor reached City G while Rachel was still $39 \text{km}$ away from City F. If Eleanor took $4$ hours to travel from City F to City G, what was the distance between the two cities?

c4b23a034eb54649b787eefdf2846d0a

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short_answer

The symbol "$⊙$" defines a new operation as shown below: $$1\odot 4=1+11+111+1111=1234$$ $$2\odot 3=2+22+222=246$$ $$3\odot 2=3+33=36$$ George tries to find the value of $$4\odot 3$$ using the following working: $$4\odot 3=3+33+333+3333$$ $$\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde\textasciitilde=3702$$ Is he correct? If not, show the correct working and answer.

75592f9b267643f6ad1600fe6fa8b090

0

short_answer

A class consists of $25$ students. If only $5$ of them are boys, what percent is that?

c6530b57d5304a398df4e406019afc9f

1

short_answer

Suppose that $1$ U.S. dollar is worth $1.25$ Canadian dollars. Sherry is traveling in Canada, and she wants to buy a book, which costs $64$ Canadian dollars. How many U.S. dollars does the book cost?

1f5b327371834bc891e8992a355a3c02

1

short_answer

Sara is looking for a book in the library. The librarian tells her, "all the shelves in our library are arranged in one row. The book you are looking for is located on the $$8$$\textsuperscript{th} shelf if you count from front to back, and the $$10$$\textsuperscript{th} if you count from back to front. " How many shelves are there in the library?

eb710dc184384ed3b2e9731301601159

1

short_answer

A test is with a full score of $100$ points. Five students in a group wants to reach an average of $90$ points. If everyone scores a different whole number, the lowest score among them could be~\uline{~~~~~~~~~~}~.

4b26a9102a274ba0b8e309640745063b

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short_answer

Ribbon A is $3$ times as long as Rope B. Rope C is $56$ cm longer than Rope B. If Rope A is $1$ m $30$ cm longer than Rope C, find the total length of the three ropes.~\uline{~~~~~~~~~~}~cm.

8af91674f16f411fb99260d559566771

1

short_answer

Subtract three times the smallest number from twice the largest number in this list: $$4$$, $$11$$, $$8$$, $$2$$, $$7$$, $$13$$ Answer~\uline{~~~~~~~~~~}~

ce900c6f009e458cad1bdac095599872

0

short_answer

$4.6 - 3.55$

07ed7dd4a7c04b8aaf4b1c03f590920c

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short_answer

A string of $3$ different letters is to be chosen from a group of letters: A, B, C, D ,E. What is the probability A and B will both be in the string?

4287149f96d446cfa12f1fd21889e61b

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short_answer

A youth club has $50$ male and $70$ female members. $16 \%$ of the male members and $10 \%$ of the female members are students. What percentage of the members are students?

b2b5b4f81d8448afaba3be6d10769542

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short_answer

200 litres ($$\text{L}$$) of a punch bowl that contains $$35 \%$$ fruit juice is mixed with $$300$$ litres of another punch bowl that contains $$50 \%$$ fruit juice. Find the percentage concentration of the new mixture.

3c6c375d11374de1b3101dfbfc2c9524

1

short_answer

The ratio $$x:48$$ is equivalent to the ratio $$3:4$$. What is $$x$$?

5c67d22d929c48579cb3027189617400

1

short_answer

Work out $$1212\div6$$

c18565e80cc44b0cb72b59076a383b6d

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short_answer

Amy has $$37$$ apples and John has $$15$$ apples. How many apples does Amy have to give John such that she has exactly $$4$$ more apples than John?

ae4e6b1dfa8a49a5b3241156334f3bed

1

short_answer

Betty, Veron, Eliza sold a total of $$855$$ cookies on National Girl Scout Cookie Day. Eliza sold twice as many cookies as Veron. Betty sold $$185$$ fewer cookies than Eliza. How many cookies did Betty sell?

bc597e322c194058a175f92bfbfd92e3

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short_answer

A teacher is marking the papers of the whole class. She plans to finish the work in $5$ hours. After working for one hour, she finds that if she wants to finish the work as planned, she needs to mark $6$ more papers per hour. But if she can mark $10$ more papers per hour, she can even finish marking all the papers $1$ hour earlier. How many papers does she need to mark in total?

ff63e777962f41f4899b17ad9e14deeb

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short_answer

Work out: $1 + 3 + 5 + \ldots.. + 155 + 157 + 159$.

70deaa04761b4956a63e868e9ffc6d99

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short_answer

Bud\textquotesingle s mother baked three types of pies. 40 of them were chicken pies, 20 were vegetable pies, and， 30 of them were fruit pies. (1) What fraction of the chicken pies more than vegetable pies? (2) What fraction of the vegetablw pies less than fruit pies?

622956fd3ac44f62a123456124a4a8b9

1

short_answer

Sally bought $$32$$ markers. She gave away $$7$$ markers. After that, she packed the markers left into bags of $$5$$. How many bags of markers did she pack? She packed~\uline{~~~~~~~~~~}~bags of markers.

dd320540af104d229ba61a14357af45a

1

short_answer

$$4$$ identical jugs and $$5$$ identical cups cost £$$85$$. $$2$$ identical jugs and $$2$$ identical cups cost £$$40$$. What is the cost of a cup?

939e258bc3ae4686add9892e1a88d211

1

short_answer

If $$ab$$ is a $$2$$-digit number such that $$8\times ab=3\times ba$$, find the value of the $2$-digit number $$ab$$.

b75379f387c44ded9da89ecef088d85d

1

short_answer

Ken went to a restaurant. The bill for the meal was $55$ dollars, and he left a $20 \%$ tip (The tip is only based on the food bill here). There was also a sales tax which is $10 \%$ of the bill. What was the total cost of Ken\textquotesingle s meal?

52eea861c20540a8873541169102d6b1

1

short_answer

Find the sum of the greatest $$1$$-digit even number and the smallest $$2$$-digit odd number.

85d27affc1b445c88f9b4a5e100c1bd9

2

short_answer

A textbook has $$207$$ pages, numbering from $1$ to $207$. What is the sum of all the digits numbering this book?

433eb146729b4478bbfd89939dc13d1d

1

short_answer

Patrick has made~$\dfrac{3}{4}$ of the designs in his origami book. If he has made $$24$$ designs, how many are there altogether in his book?

9d40cceb3a7043b58f824a777d1db3e8

1

short_answer

How many three-digit numbers are there that have the sum of their digits equal to 4?

9b15cde54f244f2688f75ecf97188c89

2

short_answer

The digit sum of $1024$ is $$1+0+2+4=7$$. How many three-digit numbers have a digit sum of $7$?

0e7224d495f743d994a3285524f8f2a5

2

short_answer

Caleb spent $$\frac{2}{5}$$ of his money on $$4$$ caps and $$6$$ wristbands. The cost of each cap is $$3$$ times the cost of each wristband. He bought some more caps with $$\frac{1}{3}$$ of his remaining money. How many caps did Caleb buy altogether?~\uline{~~~~~~~~~~}~caps

b9a7c7092370400a8a6b8c58ae2510c9

1

short_answer

$$5.4 + 3.7 =$$

8a063eb7bf3f4613bbd55a6c63048295

2

short_answer

A skydiver jumps from a hovering helicopter that\textquotesingle s 3,000 meters above the ground. If air resistance can be ignored, how fast will he be falling when his altitude is 2,000 m?

bacdd0107009480e90e10957f1ab6f1c

2

short_answer

A deck of $$52$$ cards have four different patterns: hearts, spades, diamonds and clubs. Each has $$13$$ numbers (From $$1$$ to $$13$$) At least how many cards do I need to draw to ensure that I can get $$4$$ cards with consecutive numbers?~\uline{~~~~~~~~~~}~

a43767a35548410b91388a97d31bf269

1

short_answer

A ten-digit number, $ABCDEFGHIJ$, is formed using the digit from $0$ to $9$, every digit being used exactly once. Its first digit can be divided by $1$, the number formed by the first two digits can be divided by $2$, and the number formed by the first three digits can be divided by $3\dots$, the whole number can be divided by $10$. If $$A=3$$, $$C=1$$, $$G=7$$, what digits does other letters represent?

aa716df8b445405ab6cdebdb3ae4adf9

1

short_answer

Ashley is $$10$$ years old. Three years ago, she was $$2$$ years older than her brother. How old is Ashley\textquotesingle s brother?

9c2c49e5d3134ddeb8fb6b3c0c42f5cd

3

short_answer

A book has $89$ pages, but the page numbers are printed incorrectly. Every third page number has been omitted, so that the pages are numbered $1,2,4,5,7,8,\cdots $ and so on. What is the number on the last printed page?

6e9234dea3b64376a232e45d14effce4

1

short_answer

The tickets for a charity show were ＄$$5$$ for each adult and ＄$$3$$ for each child. $$19$$ tickets were sold. The total amount for the sale of tickets was＄$$75$$. How many adult tickets were sold?~\uline{~~~~~~~~~~}~．

5cb5ef0814c74ded81cb8b6ce6f1bbb5

1

short_answer

Solve the equation. $3x-(2x+3)=5$

8a66caf6aaba494f95bca104943cb7c4

1

short_answer

$$459+3762$$

0bced7bb4af84506acecdc385274abfd

1

short_answer

Among the natural numbers from $1$ to $600$, how many numbers are multiples of $3$ or $5$?

f8495fe245f34edeb912b66b7ea8ce5c

1

short_answer

Calculate $123 + 468$

66edf568e9a74a2aa97d9e92b05d94e2

1

short_answer

Tom is 10 years old now. Grandma says :" when you are 20 years old, I will be 60 years old." How old is Grandma now?

94bb6ae56dbd4a98a0fbeaa59c7d8691

3

short_answer

Miss Jenny is separating some candies for class A and class B. If each student in class A gets $4$ 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 have?

9bfff3c25a624f939fbe758d02cada7b

2

short_answer

A file in the school bookshop costs $$70$$ pence. Jeremy has $$5$$ ten-pence, $$3$$ twenty-pence and $$1$$ fifty-pence coins in his wallet. In how many ways can he make up $$70$$ pence to pay for the file?

ecaddfdc1ad84d24a6e9ae0e8904ebc2

1

short_answer

There are $$3$$ red stickers and $$3$$ green stickers in a bag. Without looking into the bag, at least how many stickers must you take from the bag to be sure you get $$2$$ stickers of the same colour?

24f3b610c11745edb5ef8e3bb5e6b77b

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 without questions?

9435fd70b9e341539b05792950bee0ca

1

short_answer

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

dd8d8a23d4864feb861a8645d06813fa

1

short_answer

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

0dbb0cc68b7945019907f84cebf4487e

2

short_answer

There were three times as many boys as girls in a party. Each boy received $$2$$ sweets and each girl received $$4$$ sweets. There was a total of $$570$$ sweets. Find the number of boys who were present.~\uline{~~~~~~~~~~}~

7f4c057f9edc486381868b2cb62f8eb3

1

short_answer

The digits $3$, $1$, $9$ and $2$ can be arranged in any order to make four digit numbers. What is the difference between the largest and smallest numbers that you can make?

5395374ab911412c892a95bcb1538a6c

1

short_answer

SASMO 2015 P2 Q13 A fruit seller makes a solid pyramid out of identical fruit boxes. The top three layers are shown. What is the total number of fruit boxes in these top three layers?

9882354a7f8745e7818f5641ce7c7354

1

short_answer

$8.7 \times 3.4$

6c31ab9c5c724ce1b5dd8e18d56c817d

1

short_answer

Pavan bought a sandwich for £$2.35$, a drink for $78$ pence and a packet of crisps for $65$ pence. How much change will he have from a £$5$ note?

dfc1f111c9384999a8ce3a20bc2cffc5

1

short_answer

Neither of the two photocopiers in our office works very well. Photocopier $$\text{A}$$ produces $$1$$ \textquotesingle bad\textquotesingle{} copy for every $$4$$ \textquotesingle good\textquotesingle{} ones. Photocopier $$\text{B}$$ produces $$1$$ \textquotesingle bad\textquotesingle{} copy for every $$5$$ \textquotesingle good\textquotesingle{} ones. We need to produce $$600$$ \textquotesingle good\textquotesingle{} copies of a poster. $$\frac{3}{5}$$ of the \textquotesingle good\textquotesingle{} copies will be produced by Photocopier $$\text{A}$$. $$\frac{2}{5}$$ of the \textquotesingle good\textquotesingle{} copies will be produced by Photocopier $$\text{B}$$. How many copies in total (including the \textquotesingle bad\textquotesingle{} ones) will be needed?

a53c706f0348463594c82aefd860177b

2

short_answer

Calculate: $$(1.2+1.23+1)\times (1.2+1.23+1)-(1.2+1.23+1)\times (1.2+1.23)=$$~\uline{~~~~~~~~~~}~

ffae2b155c6e4e12a0dd3224c209353d

1

short_answer

A palindromic number is the same when written backwards as forwards, e.g.$$454$$ is a palindromic number. How many palindromic numbers are there between $$100$$ and $$200$$?

b7345c517ee645059ca6864ac5589ef4

2

short_answer

A farmer needs a total of $$24$$ hours to harvest his crops. If his son helps out by working for $$6$$ hours, they will finish the harvesting in $$16$$ hours. How many hours will the farmer\textquotesingle s son take to harvest the crops all by himself?

53c10c1a3da34ac99c165981e9123c15

1

short_answer

In Norton Juster\textquotesingle s book \emph{The Phantom Tollbooth} we learn that the hero, Milo,smiles warmly on average $$47$$ times a day. How often would you expect him to smile warmly in January?(There are $$31$$ days in January)

765a3cf2104c412c90dfa3e660a67e11

1

short_answer

A group of $40$ students were supposed to form the shape of a square. How many students were there along one side of the square?

0fca214bb995431dbbfd8125bbcbb3a8

1

short_answer

Annie has $300$ grams of a solution with a sugar concentration of $15 \%$, Becky has $400$ grams of a solution with a sugar concentration of $25 \%$ and Carol has $300$ grams of a solution with a sugar concentration of $35 \%$. They mixed the solutions together. What is the concentration of the resulting sugar solution?

8ce469dd3f78455bbe361dfbac65ec35

1

short_answer

A ball is dropped from a height of $10{\rm{m}}$. It bounces off the floor to half its original height. How far, in total, will the ball have travelled when it reaches the floor for a second time?

61c631f4351c4f37b2e5a67ac813bbb5

1

short_answer

Dorothy has $$96$$ stickers. She has 3 less than $$9$$ times as many stickers as Timmy. Kevin has $$45$$ more stickers than Timmy. How many stickers does Kevin have?

5d35989e2b284f488fb943b1ec405028

1

short_answer

Rehema rolls a fair dice $$30$$ times. How many times should she expect to get a $$5$$?

2b60051b00824874b4fa3beaf2110c81

1

short_answer

What is the largest three-digit number that is divisible by $36$?

3a2ed089aaaf41639e7c8cf3a2c8a734

3

short_answer

I have five children and want to place them in a line for a photograph. However, Hugh refuses to stand anywhere in between Louise and Richard. How many ways are there to place the children in a line and still keep Hugh happy?

98777c411fcc4cb6af9079ff424408ba

0

short_answer

How many numbers are there from $1$ to $10$?