GMAT MATH - Geometry Question

Question - GMAT MATH - Geometry Question

Volume of a rectangle

The volume of a rectangular solid is x. If the length and width are each increased by 25% and the height is increased by 300%, what is the volume of the new rectangle formed?

a) x
b) 4x
c) 6x
d) 6.25x
e) 10x

Solution:

Formula for volume of a rectangle = length (ln) * width (b) * height (h)

Given, Volume of rectangle = x

ln*b*h =x

Here we need to understand percentage increase.

For example, if 10 increases by 10% then we calculate it as

10 + (10 *(10/100)) = 10 + 1

Similarly
 25 % length increase = ln + ((25/100)*ln) = ln + 0.25ln = 1.25ln
 25 % width increase = w + ((25/100)*w) = w + 0.25w = 1.25w
200% height increase = h + ((300/100)*h) = h + 3h =4h

New Volume = 1.25ln * 1.25w * 4h
                       = 6.25 (ln*w*h)

If ln*b*h =x;
then 6.25 (ln*b*h) = 6.25x

Correct Answer: D