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Question bank AMO 2023

Exam papers

250 questions

Question 1

Carter has some small cubes. He arranged all of them into a big cube, a square, a stick, and one by itself. There is no empty space in the big cube. How many little cubes does Carter have in total?

Question illustration
  1. 12
  2. 15
  3. 18
  4. 20

Question 2

The two-digit whole number $\overline{EF}$ satisfies $\overline{EF}+8=\overline{AB5}$. The digits $A,B,E,F$ are in $\{0,1,2,3,4,5,6,7,8,9\}$, and $A$ is not zero. What is $A+B+E+F$?

Question illustration
  1. 12
  2. 14
  3. 17
  4. 21

Question 3

On the number line below, a few numbers are shown. There is a number hidden that is the midpoint between 5 and 33. What is the value of that number?

Question illustration
  1. 15
  2. 19
  3. 22
  4. 23

Question 4

Carrie has three markers: blue, gray, and yellow. She is coloring a small organizer of three boxes. Each box will have a different color than the others. How many ways can Carrie color the organizer?

Question illustration
  1. 3
  2. 4
  3. 6
  4. 10

Question 5

In the following figure, a big square is divided into nine small squares of the same size. A pattern is colored within the big square. How many small squares does it take to cover the shaded pattern?

Question illustration
  1. 4
  2. 5
  3. 6
  4. 8

Question 6

A pencil and an eraser cost three dollars. An eraser and a notebook cost five dollars. A notebook and a pencil cost four dollars. What is the cost of a pencil, an eraser, and a notebook?

Question illustration
  1. 9 dollars
  2. 8 dollars
  3. 7 dollars
  4. 6 dollars

Question 7

Bob’s ruler with centimeter marks broke. Bob said he could still use it to measure his pencil. He placed his pencil next to his ruler at 12 centimeters. The pencil reached all the way to 31 centimeters, as shown in the picture below. What is the length of his pencil in centimeters?

Question illustration
  1. 10 cm
  2. 19 cm
  3. 20 cm
  4. 27 cm

Question 8

If the following pattern goes on, how many balls are there at the 7-th step?

Question illustration
  1. 24
  2. 28
  3. 30
  4. 32

Question 9

Nancy has a collection of colorful star stickers. She made a rectangular shape of 8 rows and 10 columns. After that, she has 11 stickers left. She wants to make a rectangular shape using all of her stickers. How should she arrange her stickers?

Question illustration
  1. In 5 rows and 12 columns.
  2. In 14 rows and 7 columns.
  3. In 9 rows and 15 columns.
  4. In 13 rows and 7 columns.