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IMAS 2012 — Upper Primary Grades 5–6 — Round 1

Question 1

What is the value of 101010−10101?
  1. 90909
  2. 10101
  3. 100000
  4. 900000
  5. 10000

Question 2

The following figures are formed by identical squares. Which figure has the longest perimeter?
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  5. Question illustration

Question 3

Which of the following sets of fractions has sum greater than 1?
  1. $ \frac{1}{3} $, $ \frac{1}{4} $, $ \frac{1}{5} $
  2. $ \frac{1}{2} $, $ \frac{1}{4} $, $ \frac{1}{6} $
  3. $ \frac{1}{2} $, $ \frac{1}{3} $, $ \frac{1}{6} $
  4. $ \frac{1}{2} $, $ \frac{1}{4} $, $ \frac{1}{5} $
  5. $ \frac{1}{2} $, $ \frac{1}{3} $, $ \frac{1}{5} $

Question 4

The diagram to the right shows two squares AMND and PQRS inside a rectangle ABCD. The areas of the two squares are $ 16 \, cm^2 $ and $ 4 \, cm^2 $ respectively. What is the sum of area of the shaded regions in $ cm^2 $?

Question illustration
  1. 3
  2. 4
  3. 5
  4. 6
  5. 7

Question 5

Mike jogs at constant speed along a road with lamp posts which are evenly spaced. It takes him 2 minutes to go from the first lamp post to the fifth lamp post. He continues jogging to the n-th lamp post before turning back. If he has been jogging for 12 minutes when he returns to the first lamp post, what is the value of n?
  1. 6
  2. 9
  3. 11
  4. 12
  5. 13

Question 6

The smallest interior angle of a triangle is $50^{\circ}$. Which of the following statements about this triangle is correct?
  1. It must be isosceles.
  2. It must be right angled.
  3. It must be acute angled.
  4. It must be obtuse angled.
  5. None of these is correct.

Question 7

Each of A, B, C and D has a watch.

(1) A's watch is 10 minutes faster than standard time but A believes that it is 5 minutes slower.

(2) B's watch is 5 minutes slower than standard time but B believes that it is 10 minutes faster.

(3) C's watch is 5 minutes faster than standard time but C believes that it is 3 minutes faster.

(4) D's watch is 5 minutes slower than standard time but D believes that it is 10 minutes slower.

According to their watches and their beliefs, they go to school in order to be just in time. Who is late?
  1. A
  2. B
  3. C
  4. D
  5. No one

Question 8

The diagram below shows four squares with numbers which exhibit a certain pattern. What number should be inside the fourth box?

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  1. 210
  2. 260
  3. 288
  4. 308
  5. 330

Question 9

A piece of square paper is folded along a straight line, dividing it into two regions with the same area and the same shape. How many such straight lines are there?
  1. 1
  2. 2
  3. 3
  4. 4
  5. infinitely many

Question 10

The three figures in the diagram below have equal perimeters. What is $a:b:c$?

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  1. 1:1:1
  2. 2:4:5
  3. 4:6:5
  4. 16:20:25
  5. 20:25:24

Question 11

A triangle is formed with 10 matchsticks of equal length connected end to end. No matchsticks are bent or broken. How many different triangles can be formed?
  1. 2
  2. 3
  3. 4
  4. 5
  5. 6

Question 12

The total weight of 5 apples is equal to that of 6 bananas, and the total weight of 3 bananas is equal to that of 4 oranges. How many apples have the same total weight as 16 oranges?
  1. 8
  2. 9
  3. 10
  4. 11
  5. 12

Question 13

Jane begins observing a hyacinth plant on last Friday, when some of its flowers bloom. Thereafter, the number of flowers which bloom on any day is equal to the number of flowers which have already bloomed. No flowers wither. All the flowers have bloomed by the following Thursday. On which day of the week have exactly half of the flowers bloomed?
  1. Saturday
  2. Sunday
  3. Monday
  4. Tuesday
  5. Wednesday

Question 14

The side length of each square in the diagram below is 1 unit. An ant needs 5 seconds to crawl 1 unit horizontally, and 6 seconds to crawl 1 unit vertically. It requires 1 second to change direction. What is the minimum number of seconds for the ant to crawl from point A to point B?

Question illustration
  1. 43
  2. 45
  3. 46
  4. 47
  5. 48

Question 15

During the holidays, Dick worked part-time washing bowls in a restaurant. He got paid 3 dollars for washing one bowl. If he broke a bowl, he got no pay for washing it, and must pay 9 dollars to the owner. In one week, Dick washed 500 bowls and earned 1368 dollars. How many bowls did he break?
  1. 7
  2. 8
  3. 9
  4. 10
  5. 11

Question 16

Four coloured lamps are arranged in a $2\times2$ array, where the letters R, Y, B and W represent the colours red, yellow, blue and white respectively. Each lamp changes its colour every minute. In the first minute, the colours of the lamps in the two rows are interchanged. In the second minute, colours of the lamps in the two columns are interchanged. See the diagram below. This cycle is then repeated. What are the colours of the four lamps at the $60^{\text{th}}$ minute?

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Question 17

The elder sister is 12 years old, the younger sister is 8 years old and brother is 3 years old. Their birthdays are in the same day. When the sum of their ages equal 50, what is the age of the younger sister?
  1. 14
  2. 15
  3. 16
  4. 17
  5. 18

Question 18

Mrs. Wong worked at the airport. She had two consecutive days of rest after working for eight days. If she rests on Saturday and Sunday this week, at least how many weeks later will she rest on Sunday again?
  1. 4
  2. 5
  3. 6
  4. 7
  5. 8

Question 19

The diagram below shows four cups in a row, labelled 1, 2, 3 and 4. Initially, there is a ball inside cup #3. In each move, the ball may be transferred to an adjacent cup. From cup #1, the ball can only go to cup #2, and from cup #4, the ball can only go to cup #3. After 2012 moves, which of the following statements about the ball is correct?

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1

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2

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3

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4
  1. It cannot be in cup #1 and cannot be in cup #2
  2. It cannot be in cup #1 and cannot be in cup #3
  3. It cannot be in cup #2 and cannot be in cup #3
  4. It cannot be in cup #2 and cannot be in cup #4
  5. It cannot be in cup #3 and cannot be in cup #4

Question 20

On a 4×4 chessboard shown in the diagram below on the left, we wish to place a minimum number of copies of the shape shown in the diagram below on the right, so that no more copies of this shape can be placed. Copies may be rotated. What is this minimum number of copies?

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  1. 2
  2. 3
  3. 4
  4. 5
  5. 6