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# GMAT Math: Percentages

Written by Kelly Granson. Posted in GMAT Study Guide

Introduction

Percentage problems in mathematics can be solved by fractions or decimals, usually fractions. A rate given as 40% can be written as the fraction 40/100 or the decimal 0.4. To solve percentage problems, you will have to combine different topics. Here are a couple of sample problems.

Before solving the problems, let's review one important concept:

• To determine by what percentage X is greater than Y, use this formula —

Problem1:

An election was contested by Parties A and B. Party A secured 10% more votes than Party B. If the total votes secured by Party B were 270,000, by what number of votes did Party A win?

A. 50,000

B. 300,000

C. 600,000

D. 60,000

E. 10,000

Solution:

This problem can be solved using an assumption method in which you assume a percentage and find the answer based on that assumption.

Let us assume the percentage of the total votes secured by Party A was x%.

Given that the total number of votes secured by Party A is 10% more than Party B, the

percentage of votes secured by Party B can be written as (x-10)%.

As the question doesn't mention any other party than these two, you can assume that only two parties contested this election, so the combined total percentage of their votes should be 100%.

x% + (x – 10) % = 100%

x+(x-10) = 100

x+x-10 = 100

2x-10 = 100

2x-10+10 =100+10

2x=110

Divide by 2 on both sides

2x/2 = 110/2

x = 55

So percentage of votes secured by A is 55%.

If Party A got 55% of the votes, then Party B would have gotten (x-10)% = (55 - 10) % = 45% of the total votes.

Total number of votes secured by Party B is given as 270,000.

So, 45% * Total number of votes = 270,000.

(45/100) * Total number of votes = 270,000.

Multiply by 100 on both sides.

45* Total number of votes = 27,000,000.

Total number of votes = 27,000,000/45.

Total Number of votes = 600,000.

As Party A secured 10% votes more than Party B, that 10% will make the difference

between winning and losing.

Difference = 10% * Total number of votes.

Difference = 10% * 600,000.

Difference = 60,000.

Therefore, party A won the election by 60,000 votes.

Hence the answer is Option (D).

Problem2:

The owner of a pasture in the form of a rectangle wants to increase its area. What is the % change in the area of a pasture when its length increases by 20% and its width decreases by 20%?

A. No change in the area

B. 12% increase

C. 10% decrease

D. 4% decrease

E. Insufficient data

Solution:

At first glance, the question seems simple as the length is increased and width decreased by same percentage. But consider it more closely.

Percentage problems like this one are easier to manage if you assign numbers to the measurements. You can assume any number, but computation will be easier if you take 100 units as the length of the pasture and also the width. (There is no reason this has to be a square, but every square is a rectangle, and since percentage problems are based on 100, making this a 100x100 rectangle will be convenient.)

Area of the rectangle before altering its dimensions = length * width = 100 units * 100 units= 10,000 sq units.

If length is increased by 20%, then length = 120 units.

If width is decreased by 20%, then width = 80 units.

Area after altering the dimensions = 120*80 = 9600 sq. units.

Difference between original and altered two areas = 10000-9600 sq.units.

Difference in the two areas = 400 sq.units

Now use the formula to find the percentage change.

% change in area = (change in area/original area) * 100

= (400/10,000)*100 = 4% decrease in area

Hence the answer is Option (D).