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FMO 2026 - Grade 6 - International - Paper 05

Question 1

Each student in class 6A votes for exactly one of five candidates for class monitor. Six students vote for Wendy. Using the chart, how many students are in the class?

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  1. 50
  2. 24
  3. 36
  4. 30
  5. 25

Question 2

Sarah has ten coins of denominations 2, 1, 0.5, 0.2 and 0.1 dollars, with at least one coin of every denomination. What is the smallest possible total value?
  1. 1 dollar
  2. 3.8 dollars
  3. 4.3 dollars
  4. 4 dollars
  5. 4.8 dollars

Question 3

Use the pattern in the array to find the missing figure.

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Question 4

Brown eggs come in cartons of 12 and white eggs in cartons of 10. Henry buys the same positive number of eggs of each colour. What is the least total number of cartons he must buy?

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  1. 22
  2. 11
  3. 60
  4. 12
  5. 21

Question 5

Isabella writes a two-digit prime whose digit sum is the smallest two-digit prime. How many different numbers could she write?
  1. 2
  2. 4
  3. 3
  4. 6
  5. 5

Question 6

Jessi draws the shaded triangle inside a rectangle on a square grid. Each grid cell has side length 1 cm. Find the triangle’s area.

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  1. 10 cm²
  2. 9 cm²
  3. 6 cm²
  4. 8 cm²
  5. 7 cm²

Question 7

Ariana folds a square in half twice as shown, then cuts along both red segments. How many pieces result when the paper is unfolded?

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  1. 12
  2. 8
  3. 6
  4. 9
  5. 10

Question 8

How many even numbers occur among the first 2023 terms of the repeating sequence 2,0,2,3,2,0,2,3,…?
  1. 1030
  2. 518
  3. 1033
  4. 1515
  5. 1518

Question 9

Two squares of side 5 cm overlap as shown. Their overlap is a square of area 4 cm². Find the perimeter of the shaded union.

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  1. 38 cm
  2. 36 cm
  3. 20 cm
  4. 32 cm
  5. 46 cm

Question 10

The calculator follows the flowchart. Adrian inputs F, the smallest two-digit number divisible by 3. What final result does it give?

Question illustration
  1. 14
  2. 30
  3. 12
  4. 11
  5. 24

Question 11

Cubes of side 2 cm form the sequence shown. Find the total volume of the first fifteen figures.

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  1. 1560 cm³
  2. 3024 cm³
  3. 2744 cm³
  4. 3120 cm³
  5. 3520 cm³

Question 12

A motorbike starts at 09:40 at 36 km/h. Five minutes later, a car starts in the same direction at 54 km/h. When does the car catch the motorbike?

Editorial clarification of the intended catch-up model: both vehicles start at the same point and maintain the stated speeds.
  1. 09:50
  2. 09:45
  3. 09:55
  4. 09:51
  5. 10:01

Question 13

The seven-digit number shown is divisible by 45. Each letter is a missing digit. Find the largest possible value of F×M×O.

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  1. 25
  2. 45
  3. 360
  4. 280
  5. 450

Question 14

Oliver handles 900 cups. For each cup washed without breaking he earns 0.5 dollars. For a broken cup he receives no washing pay and pays the owner 2 dollars. His net earnings are 360 dollars. How many cups did he break?
  1. 45
  2. 60
  3. 36
  4. 90
  5. 40

Question 15

Adrian glues identical cubes into the letters F, M and O as shown, then paints every exposed surface blue. How many cubes have exactly four painted faces?

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  1. 23
  2. 24
  3. 22
  4. 21
  5. 25

Question 16

Miley scores only 5, 8 or 10 points when she hits a target. She scores 8 and 10 equally often, for a total of 81 points. Half of all her shots miss. How many shots does she take altogether?
  1. 16
  2. 20
  3. 13
  4. 22
  5. 26

Question 17

Cubes A, B and C have sides 10 cm, 5 cm and 3 cm. The whole left face of B is glued to the right face of A, and the whole bottom face of C is glued to the top face of B, as shown. Find the resulting solid’s surface area.

Question illustration
  1. 736 cm²
  2. 786 cm²
  3. 768 cm²
  4. 804 cm²
  5. None of the above

Question 18

The five different weights A, B, C, D and E weigh 12, 24, 36, 48 and 60 g in some order. Use the three scales to find C.

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  1. 12 g
  2. 24 g
  3. 36 g
  4. 48 g
  5. 60 g

Question 19

Find the value represented by a red crab.

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  1. 7
  2. 15
  3. 12
  4. 11
  5. None of the above

Question 20

Two years ago, Ali and his father’s ages summed to 32. Four years from now, the father will be three times Ali’s age. In how many years from now will he be twice Ali’s age?
  1. 12
  2. 15
  3. 13
  4. 11
  5. 14