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IKMC 2005 - Grades 5-6 - Self-study

Question 1

What is $2005\times100+2005$?
  1. 2005002005
  2. 20052005
  3. 2007005
  4. 202505

Question 2

Ali and Amna have 10 sweets, but Amna has 2 more than Ali. How many sweets does Amna have?
  1. 8
  2. 7
  3. 6
  4. 4

Question 3

In the diagram any of the eight kangaroos can jump to another square. What is the least number that must jump so that each row and each column has exactly two kangaroos?

Question illustration
  1. 1
  2. 2
  3. 3
  4. 4

Question 4

Ali lives with his father, mother, brother and also one dog, two cats, two parrots and four goldfish. How many legs do they have altogether?
  1. 13
  2. 28
  3. 24
  4. 22

Question 5

A butterfly sat down on my correctly solved exercise. What number is the butterfly covering?

Question illustration
  1. 1825
  2. 2185
  3. 1775
  4. 1800

Question 6

The diagram shows a cube with sides of length 12 cm. An ant is walking across the cube’s surface from A to B on the route shown. How far does it walk?

Question illustration
  1. 40 cm
  2. 48 cm
  3. 60 cm
  4. It is impossible to determine

Question 7

Saima cut a sheet of paper into 10 pieces. Then she took one of the pieces and cut it into 10 pieces also. She repeated this twice more. How many pieces did she have in the end?
  1. 27
  2. 30
  3. 37
  4. 40

Question 8

Aisha chose a whole number and multiplied it by 3. Which number could not be her answer?
  1. 103
  2. 105
  3. 204
  4. 444

Question 9

Five cards numbered 1 to 5 lie in the row shown. In one move, any two cards may be interchanged. Find the smallest number of moves needed to put all cards in increasing order.

Question illustration
  1. 1
  2. 2
  3. 3
  4. 4

Question 10

How many hours are there in half of a third of a quarter of a day?
  1. $\frac13$
  2. $\frac12$
  3. 1
  4. 2

Question 11

Raza needs 40 minutes to walk from home to the sea and return on an elephant. Riding an elephant both ways takes 32 minutes. How long would walking both ways take?
  1. 36 minutes
  2. 42 minutes
  3. 46 minutes
  4. 48 minutes

Question 12

The sum of five consecutive positive integers is 2005. What is the largest?
  1. 401
  2. 403
  3. 405
  4. 2001

Question 13

How many different factors, including 1 and 100, does 100 have?
  1. 6
  2. 7
  3. 8
  4. 9

Question 14

Count all possible triangles and all possible squares in the picture. How many more triangles than squares are there?

Question illustration
  1. The same quantity
  2. 1
  3. 2
  4. 3

Question 15

Which equality means that m is 30% of k?
  1. $10m-3k=0$
  2. $3m-10k=0$
  3. $7m-10k=0$
  4. $7m-3k=0$

Question 16

If you fold up the net on the right, which cube can you make?

Question illustration
  1. Question illustration
  2. Question illustration
  3. Question illustration
  4. Question illustration

Question 17

Different figures represent different digits. Find the digit corresponding to the square.

Question illustration
  1. 9
  2. 8
  3. 7
  4. 6

Question 18

In a trunk there are 5 chests, each containing 3 boxes, each box containing 10 gold coins. The trunk, chests and boxes are locked. How many locks must be opened to get 50 coins?
  1. 5
  2. 7
  3. 8
  4. 9

Question 19

A caterpillar starts from home and moves in a straight line on the ground, turning 90° left or right after each hour. It moves 1 m in the first hour,2 m in the second, and so on. What is its minimum possible distance from home after six hours?
  1. 0 m
  2. 1 m
  3. 1.5 m
  4. 2.5 m

Question 20

The sum of ten distinct positive numbers is 100. The largest of these numbers can be:

Editorial clarification for this self-study item: interpret “positive numbers” as positive integers, the intended domain needed for a unique choice.
  1. 10
  2. 13
  3. 55
  4. 60