Question

Shakeel has 60 toys which he wants to arrange equally on the shelves such that each shelf must contain more than 1 toy but less than 20 toys. How many ways can he do this ?

• A. 6
• B. 7
• C. 4
• D. 8

Answer 1

The correct option is D 8

To find the number of possible arrangements we need to find the factors of number 60.

Factors pairs of 60 = 1 x 60, 2 x 30, 3 x 20, 4 x 15, 5 x 12, 6 x 10, 10 x 6, 12 x 5, 15 x 4, 20 x 3, 30 x 2, 60 x 1

So the number of toys in each shelf are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The shelf must contain more than 1 toy but less than 20 toys, thus the possible number of toys on each shelf can be: 2, 3, 4, 5, 6, 10, 12, 15

⇒ No. of arrangements = 8