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AMO 2024 – Primary 5 (Grade 5)

Question 1

Jasmine’s number machine takes a whole number, adds 20, takes $\frac35$ of the result, and then divides by 5 and outputs the remainder. What is the output for input 100?

Question illustration
  1. 4
  2. 3
  3. 2
  4. 0

Question 2

A square grows using two symbols: 1 bear, then 3 dolphins, then 5 bears, then 7 dolphins, as shown. Continuing this pattern to a 10-by-10 square, what is the difference between the total numbers of dolphins and bears?

Question illustration
  1. 100
  2. 20
  3. 10
  4. 8

Question 3

Beth can choose apples, bananas, oranges, pears and peaches. How many choices does she have for a juice using four different types of fruit?

Question illustration
  1. 20
  2. 10
  3. 5
  4. 3

Question 4

Each desk has one flat surface and four legs; each stool has one flat surface and three legs. Altogether there are 18 flat surfaces and 60 legs. How many desks are there?

Question illustration
  1. 18
  2. 12
  3. 10
  4. 6

Question 5

The stem-and-leaf plot contains all the students’ weekly screen times, in hours. What is their average weekly screen time? The key 3|1 means 31 hours.

Question illustration
  1. 30
  2. 25
  3. 21
  4. 15

Question 6

A turtle walks horizontally or vertically from $(1,1)$ through $(1,4),(4,4),(4,6),(6,6),(6,3),(8,3),(8,1)$ and back to $(1,1)$. What is the total distance?

Question illustration
  1. 16
  2. 18
  3. 20
  4. 24

Question 7

The square pyramid shown is built from unit cubes, with no empty space inside. How many cubes are there?

Question illustration
  1. 120
  2. 84
  3. 72
  4. 65

Question 8

Find the value of $1+\frac12+\frac13+\frac17+\frac1{42}$.

Question illustration
  1. 4
  2. 3
  3. 2
  4. $1\frac16$

Question 9

$N$ is between 1 and 100. Dividing $N$ by 2 leaves remainder 1, and dividing it by 7 leaves remainder 4. What is the largest possible $N$?

Question illustration
  1. 98
  2. 97
  3. 96
  4. 95