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AMO 2024 Primary 4 (Grade 4)

Question 1

Three numbers satisfy $AB=20$, $BC=35$ and $CA=28$. What is $ABC$? Clarification: use the intended positive numbers; the source does not explicitly state positivity.

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  1. 120
  2. 140
  3. 180
  4. 215

Question 2

Which number is smallest: $3/2,4/3,5/6,3/4$?

Question illustration
  1. $3/2$
  2. $4/3$
  3. $5/6$
  4. $3/4$

Question 3

A square is folded into the shown pattern. The marked points are midpoints or quarter-points. What fraction of the whole square is shaded?

Question illustration
  1. $1/3$
  2. $5/16$
  3. $1/2$
  4. $1/4$

Question 4

Nancy’s machine first adds 12, then takes one third of the result and subtracts 5. What is the output for input 36?

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  1. 25
  2. 21
  3. 11
  4. 10

Question 5

Five distinct positive whole numbers have average 12. The smallest is 3. What is the greatest possible largest number?

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  1. 42
  2. 45
  3. 52
  4. 57

Question 6

Emily walks 500 m north, turns right 30° and walks 400 m, turns right 45° and walks 300 m, then turns right 60° and walks 200 m. Which direction is she facing at the end?

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  1. East
  2. Southeast
  3. Southwest
  4. West

Question 7

Marbles form the sequence of triangular patterns shown. How many marbles are in the tenth pattern?

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  1. 91
  2. 66
  3. 55
  4. 36

Question 8

The pie chart shows the after-school preferences of 50 students. How many prefer sports?

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  1. 36
  2. 24
  3. 18
  4. 12

Question 9

Which is greatest among $1.25,1\frac{2}{3},\frac{5}{3},\frac{7}{5},1\frac{4}{5}$?

Question illustration
  1. $7/5$
  2. $5/3$
  3. $1\frac45$
  4. $1\frac23$