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Question bank AIMO

Exam papers

160 questions

Question 1

How many line segments are there in the figure below?

Question illustration
  1. 7
  2. 10
  3. 12
  4. 15

Question 2

In the figure, the area of each equilateral triangle formed by three neighboring points is 1cm². Find the area of the figure.

Question illustration
  1. 12 cm²
  2. 15 cm²
  3. 18 cm²
  4. 21 cm²

Question 3

Find the value of 71 +57 +62 +38 +43 +29
  1. 100
  2. 200
  3. 300
  4. 400

Question 4

Find the value of 45 - (79 − 85) +74 .
  1. 126
  2. 45
  3. 74
  4. 125

Question 5

It is known that 1 feet equal 12 inches. A 18-feet long rope is cut into segments 2 feet 3 inches long. How many segments are cut in this way?
  1. 7
  2. 8
  3. 9
  4. 10

Question 6

A group of children form 3 queues. The first queue has 34 children, the second queue has 17 students, the third queue has 63 children. How many children, at least, are needed to move from the third queue to other queues to make the number of children in each queue equal?
  1. 25
  2. 29
  3. 46
  4. 17

Question 7

It is known that a right prism has 12 vertices, how many edges does that prism has?
  1. 14
  2. 16
  3. 18
  4. 20

Question 8

Charles wishes to buy a \$3 pen without changes. How many ways can he pay for the product if he has a lot of each \$1, 50 cents and 20 cents coin?
  1. 3
  2. 7
  3. 9
  4. 10

Question 9

Find the value of 18 + 27 – 36 – 45 – 54 – 63 + 72 + 81.
  1. 0
  2. 99
  3. 198
  4. 396

Question 10

Find the value of (32 + 33 + 34 + … +46) − (26 + 27 + 28 + … + 40).
  1. 84
  2. 90
  3. 96
  4. 261

Question 11

William and David has a total of 74 bananas. David has 26 more bananas than William. How many bananas does David have?
  1. 26
  2. 74
  3. 50
  4. 100

Question 12

A pyramid is formed by using 15 clay balls and 28 bamboo sticks. If the base of the pyramid is a polygon. How many sides does the polygon have? (Clay balls cannot be broken down as several balls, and the sticks cannot be bent)
  1. 14
  2. 15
  3. 25
  4. 28

Question 13

A group contains 8 students and each student needs to take a photo with the others. If there are only 2 people in each photo, how many photos in total will be taken in this way?
  1. 27
  2. 28
  3. 36
  4. 56

Question 14

In the attached cryptarithm, each of A, B, C each represents a one-digit integer. Find the value of A + B + C.

Editorial clarification: different letters may represent the same digit; the source imposes no distinct-digit condition.

Question illustration
  1. 8
  2. 11
  3. 14
  4. 17

Question 15

Starting from 2p.m., Johnny watches three movies each 100 minute long. If Johnny takes a 40-minute break after watching each movie, what is the time after he finished all the movie.
  1. 7:00pm.
  2. 7:40pm.
  3. 8:20pm.
  4. 8:40pm

Question 16

Find the value of (2020 × 1+ 1906× 2 +2720× 3) ÷ (680× 12 + 3812 +2020) .
  1. 0
  2. 1
  3. 2
  4. 3

Question 17

In the figure, the area of the each smallest square is 1 unit square. Find the area of the shaded region.

Answer: _____________________ unit square

Question illustration

Question 18

Christy has some \$5, \$2 and \$1 coin. She has 4 coins of each type. How many different face values can she form using those coins?

Answer: ____________________ face.

Editorial convention: use at least one coin and count positive amounts.

Question 19

In the attached cryptarithm, each of A, B, C, and D each represents a one-digit integer. Find the value of the 4-digit number ABCD.

Answer: ________________________

Editorial clarification: different letters may represent the same digit; the source imposes no distinct-digit condition.

Question illustration

Question 20

There are 216 balls. One of the balls is lighter than the others and the others carry equal weights. By using only a balance, at least how many times are needed to find the lighter ball?

Answer: __________________

Editorial clarification: find the minimum number of weighings that guarantees success in the worst case.