CAT Exam Model Paper 7 with solutions for free online practice

Question : 23 of 60

Marks: +1, -0

The lengths of the three edges of a cuboid are increased by a%, b% and c%. The volume increases by V%, where V is an integer. How many values can V take if a, b, c are real numbers and 10 ≤ a, b, c ≤ 20?

11
39
41
Cannot be determined

Validate

Solution:

The increase in volume will be minimum when a, b and c are 10% each.
The new volume will be

1.1×1.1×1.1 = 1.331

times of the old volume. So the percentage increase in volume will be 33.1%.
Similarly, the increase in volume will be maximum when a, b and c are 20% each.
The new volume will be

1.2 × 1.2 × 1.2 = 1.728

times of the old volume. So the percentage increase in volume will be 72.8%.
As the final percentage increase in volume is an integer, the value must be an integer from 34 to 72 i.e. 39 distinct values are possible.

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