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IKMC 2013 - Grades 3-4 - Self-study

Question 1

In which figure is the number of black kangaroos greater than the number of white kangaroos?
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Question 2

Aline writes a correct calculation, then covers two identical digits with stickers as shown. Which digit is under each sticker?

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Question 4

How many triangles can be seen in the picture?

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  1. 9
  2. 10
  3. 11
  4. 13
  5. 12

Question 5

At London 2012 the USA won 46 gold, 29 silver and 29 bronze medals. China won 38 gold, 27 silver and 23 bronze medals. How many more medals did the USA win?
  1. 6
  2. 14
  3. 16
  4. 24
  5. 26

Question 6

Daniel divides all 36 candies equally among all his friends. Which cannot be the number of friends?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 7

Vero’s mum uses two bread slices per sandwich. A package has 24 slices. How many sandwiches can she make from two and a half packages?
  1. 24
  2. 30
  3. 48
  4. 34
  5. 26

Question 8

About 325, five boys say:
Andrei: “It is a three-digit number.”
Boris: “All digits are distinct.”
Vitya: “The sum of the digits is 10.”
Grisha: “The units digit is 5.”
Danya: “All digits are odd.”
Who is wrong?
  1. Andrei
  2. Boris
  3. Vitya
  4. Grisha
  5. Danya

Question 9

The rectangular mirror was broken. Which piece is missing from the figure?

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Question 10

Whenever Pinocchio lies his nose grows 6 cm; whenever he tells the truth it shortens by 2 cm. Starting at 9 cm, he tells three lies and two truths. How long is his nose afterwards?
  1. 14 cm
  2. 15 cm
  3. 19 cm
  4. 23 cm
  5. 31 cm

Question 11

Oranges are sold in boxes containing 5, 9 or 10 oranges. Pedro wants exactly 48 oranges. What is the smallest number of boxes he can buy?
  1. 8
  2. 7
  3. 6
  4. 5
  5. 4

Question 12

Ann starts in the arrow’s direction. At successive street intersections she turns right, left, left, right, left, left. Which pictured place is she finally walking towards?

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Question 13

Andy, Betty, Cathie and Dannie were born in the same year on February 20, April 12, May 12 and May 25, in some order. Betty and Andy share a birth month. Andy and Cathie share the day number but not the month. Who is oldest?
  1. Andy
  2. Betty
  3. Cathie
  4. Dannie
  5. Impossible to determine

Question 14

30 children from Adventure Park took part in events. 15 entered the moving-bridge contest and 20 went down the zip-wire. How many took part in both events?
  1. 25
  2. 15
  3. 30
  4. 10
  5. 5

Question 15

Which piece fits together with the given piece to form a rectangle?

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Question 16

35 is divisible by its units digit, since 35 divided by 5 is 7, but 38 is not divisible by its units digit. How many numbers greater than 21 and smaller than 30 have this property?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 17

Join the midpoints of a triangle’s sides to make a smaller triangle. Repeat with that smaller triangle. How many triangles of the smallest resulting size fit in the original triangle?

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  1. 5
  2. 8
  3. 10
  4. 16
  5. 32

Question 18

After 1 January 2013, how many years pass before the first year whose digit product is greater than its digit sum?
  1. 87
  2. 98
  3. 101
  4. 102
  5. 103

Question 19

In December, Tosha the cat slept for exactly three weeks. Which expression gives the number of minutes he stayed awake that month?
  1. $(31-7)\cdot3\cdot24\cdot60$
  2. $(31-7\cdot3)\cdot24\cdot60$
  3. $(30-7\cdot3)\cdot24\cdot60$
  4. $(31-7)\cdot24\cdot60$
  5. $(31-7\cdot3)\cdot24\cdot60\cdot60$

Question 20

Basil has the pictured dominoes. He wants to arrange as many as possible in one line so that touching squares on neighbouring tiles have the same number of dots. What is the largest number of tiles he can use?

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  3. 5
  4. 6
  5. 7