GMAT Math - Word problem; Geometry

GMAT Math - Word problem; Geometry 

Question

A circle is divided into four sections. If 3 sections constitute 1/4, 2/5, and 3/20 of its total area, what is the fractional value of the area of the 4th section?

a) 1/2

b) 1/3

c)1/4

d)1/5

e)1/6

Solution

For this one, fight the urge to draw out the circle. This isn't really a geometry question, despite the fact that it mentions a circle. It's really just a fraction question.

Add the 3 known sections of the circle's area. To do so, find the lowest common demonimator and add the fractions. 1/4 = 5/20, 2/5 = 8/20 and 3/20 The total fractional value of the 3 sections is 16/20. Therefore, the area of the 4th section must be 1 - 16/20 = 1/5.

You could also backsolve if this one's confusing. Look for the choice that, when added to the three given fractions, equals 1.

Answer is D

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