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IKMC 2027 - Grades 5-6 - Self-study SET 16 - Thematic Batch 3

Question 1

The first two balances shown are level. Which choice balances the third scale?

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Question 2

I am the smallest natural number greater than 50 that is divisible by each of two consecutive positive integers. What number am I?

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Editorial correction: answer the literal divisibility question. The source’s different consecutive-product interpretation is preserved and assessed in the solution.
  1. 52
  2. 51
  3. 56
  4. 72
  5. 90

Question 3

Bon accidentally spills ink on a calendar, covering most dates as shown. On which weekday does the 25 th fall?

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  1. Monday
  2. Wednesday
  3. Friday
  4. Saturday
  5. Cannot be determined

Question 4

Ann has nine pencils, at least one blue. Every selection of four contains two of the same colour, while every selection of five contains at most three of any one colour. How many pencils are blue?

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  1. 2
  2. 3
  3. 4
  4. 1
  5. Cannot be determined

Question 5

Bình joins five strips, each 20 cm wide, into Figure 1. Each successive strip is 15 cm taller. He rearranges them as Figure 2. How much do the two perimeters differ?

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  1. 15cm
  2. 20cm
  3. 25cm
  4. 30cm
  5. 35cm

Question 6

How many three-digit numbers have a digit product less than 2?

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The source computes 172 but prints the wrong answer letter; its arithmetic and the printed choices are reconciled in the solution.
  1. 1
  2. 81
  3. 90
  4. 171
  5. 172

Question 7

Alice has four identical straight pieces, each made of three unit squares. Which pictured shape cannot be assembled from them?

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Question 8

How many different directed paths spell 2006 in the illustrated arrow diagram?

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  1. 12
  2. 11
  3. 10
  4. 8
  5. 6

Question 9

Square ABCD is divided into a smaller central square and four surrounding grey rectangles. Each grey rectangle has perimeter 40 cm. What is the area of ABCD?

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  1. 400
  2. 200
  3. 160
  4. 100
  5. 80

Question 10

Firefighter Peter starts on the middle stair. He goes up 3 steps, down 5, then up 7. Six more steps remain to reach the top stair. How many stairs are there?

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  1. 15
  2. 20
  3. 22
  4. 23
  5. 24

Question 11

There are 17 trees on Basil’s route to school. Going to school, he marks the first tree and then every other tree. Returning, he marks the first tree and then every third tree. How many trees are never marked?

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  1. 4
  2. 5
  3. 6
  4. 7
  5. 8

Question 12

Hoà harvests longans and lychees and packs six crates, each containing just one fruit. Their masses are 13, 23, 28, 40, 32, 24 kg. After selling all longans in one crate, the remaining lychees weigh four times the remaining longans. What were the original totals?

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  1. 69 kg longans and 91 kg lychees
  2. 36 kg longans and 124 kg lychees
  3. 64 kg longans and 96 kg lychees
  4. 81 kg longans and 79 kg lychees
  5. Cannot be determined

Question 13

Nick partitions 2, 3, 4, …, 10 into disjoint groups, each with at least two numbers, so every group has the same sum. What is the greatest possible number of groups?

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  1. 2
  2. 3
  3. 4
  4. 6
  5. Another answer

Question 14

Tom folds the regular hexagon so that its three marked vertices meet at the centre. What shape is the resulting outline?

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  1. Hexagon
  2. Square
  3. Triangle
  4. Six-pointed star
  5. Twelve-vertex polygon

Question 15

Plates A, B, C contain circles, squares and triangles as shown. Equal shapes have equal masses, and the plates are arranged in increasing total mass. Where should plate D be inserted?

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  1. Between A and B
  2. Between B and C
  3. Before A
  4. After C
  5. D and C have equal masses

Question 16

How many different paths through the illustrated arrows form the number 2017?

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

Question 17

David’s T-shirt is embroidered with BENJAMIN. He wears it inside out. Which option shows the lettering seen from the reverse side?

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The shirt remains upright; only its front/back side is reversed.
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Question 18

Ben makes four claims about a natural number m: divisible by 5; divisible by 55; divisible by 11; less than 10. Exactly two claims are true. What is m?

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  1. 0
  2. 5
  3. 10
  4. 11
  5. 55

Question 19

Tom writes the illustrated letters on a sheet and holds it upright in front of a mirror. Which reflected image does he see?

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Question 20

Positive integers satisfy a<b<c<d. You may increase exactly one of them by 1. Which choice makes the new product as small as possible?

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  1. a
  2. b
  3. c
  4. d
  5. Depends on the numbers