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FMO 2026 - Grade 6 - International - Paper 06

Question 1

The pie chart shows the occupations of members of a book club. If 22 members are students, how many members are there altogether?

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  1. 100
  2. 220
  3. 110
  4. 89
  5. 200

Question 2

Which measuring cylinder contains the most water?

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Reading convention: the bottom is zero and successive graduation intervals in each cylinder represent equal volumes.
  1. Cylinder 1
  2. Cylinder 2
  3. Cylinder 3
  4. Cylinder 4
  5. Cylinder 5

Question 3

The numbers 9,53,15,22,49,33,40,47,29,13 are paired so that every pair has the same sum. Which number is paired with 13?
  1. 40
  2. 47
  3. 49
  4. 53
  5. 33

Question 4

Joey cuts ropes of lengths 52 cm and 60 cm into pieces of one common length, using all of both ropes. What is the least number of pieces?
  1. 14
  2. 28
  3. 16
  4. 7
  5. 8

Question 5

A prime is special if reversing its digits still gives a prime. For example, 13 is special because 31 is prime. How many two-digit special primes are there?
  1. 6
  2. 5
  3. 8
  4. 9
  5. 10

Question 6

Helen forms the solid from identical cubes as shown. What is the least number of unit squares visible when viewed directly from the right?

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  1. 13
  2. 15
  3. 12
  4. 14
  5. 11

Question 7

Wendy has identical 7 cm by 5 cm paper rectangles. Joining two gives a rectangle of width 5 cm and area 65 cm². She joins ten in the same end-to-end way with the same overlap at every join. Find the resulting area.
  1. 650 cm²
  2. 300 cm²
  3. 350 cm²
  4. 305 cm²
  5. 325 cm²

Question 8

Cakes of the same type have equal weights. Which cake type is heaviest?

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Question 9

The picture is an excerpt of a repeating animal ribbon. In the complete ribbon, the 2022nd drawing from the left is a crab. What is the first drawing of the complete ribbon?

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Question 10

Lucy inputs M into the calculator shown and obtains 74. Which statement about M is correct?

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  1. M < 400
  2. 400 < M < 440
  3. 440 < M < 480
  4. 480 < M < 520
  5. M > 520

Question 11

Nathan, Cecilia, Lily, Mike and Jack are born in the same year, in distinct months March, April, July, August and October. Nathan and Lily’s birth months are consecutive. Jack is born on the 31st. Mike is the oldest. Who is born in October?
  1. Nathan
  2. Cecilia
  3. Lily
  4. Mike
  5. Jack

Question 12

Joanna tries to fold the five six-square paper shapes into six-faced cubes. What is the greatest number of cubes she can make?

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  1. 1
  2. 2
  3. 3
  4. 4
  5. 5

Question 13

M is a positive integer. How many possible values of M make $\frac{180}{2M-3}$ an integer?
  1. 7
  2. 5
  3. 6
  4. 8
  5. 10

Question 14

Find the total shaded area in the rectangle, whose perimeter is 130 units.

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  1. 400
  2. 360
  3. 420
  4. 480
  5. 450

Question 15

Define $a\otimes b=\frac{ab}{a+b}$ for $a+b\ne0$. For example, $5\otimes20=4$. Find $1\otimes1+2\otimes2+\cdots+100\otimes100$.
  1. 400
  2. 360
  3. 420
  4. 2525
  5. 5050

Question 16

One box of doughnuts needs 3 kg flour and 4 kg sugar; one box of birthday cakes needs 4 kg flour and 5 kg sugar. Using exactly 25 kg flour to make whole boxes, what is the least sugar needed?
  1. 28 kg
  2. 29 kg
  3. 31 kg
  4. 32 kg
  5. 33 kg

Question 17

A large cube consists of 4×4×4 small cubes. Ruby removes the sixteen central cubes to form the tunnel shown, then paints every exposed surface. If the painted area is 480 cm², find the remaining solid’s volume.

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  1. 48 cm³
  2. 384 cm³
  3. 3072 cm³
  4. 512 cm³
  5. None of the above

Question 18

A sheep is tied by a 10-m rope at a corner of a 10 m by 20 m rectangular barn. The nearest edge of the open doorway is 6 m from that corner, as shown. Ignore wall thickness. What total area can the sheep reach, in m²?

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  1. $93\pi$
  2. $79\pi$
  3. $58\pi$
  4. $83\pi$
  5. $75\pi$

Question 19

Henry’s calculator uses the digit shapes shown. He writes a four-digit number whose reflected reading in a mirror has the same value. How many numbers can he write?

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  1. 20
  2. 16
  3. 36
  4. 54
  5. 25

Question 20

A box has 1225 cards. Angela, Bruno, Cindy, Henry and Freya take turns in that order, drawing 1,2,3,4,5 cards respectively, then 6,7,…, one more on each turn. Who draws the last cards?
  1. Angela
  2. Bruno
  3. Cindy
  4. Henry
  5. Freya