Problem Solving

The population of a small beach town on Australia's east coast grows by 50% from May 1 to June 1 and then grows by another 50% from June 1 to July 1. The population then decreases by 11.11% from July 1 to August 1. By approximately what percentage has the population grown from May 1 to August 1?

a) 50%
b) 90%
c) 100%
d) 200%
e) 225%

Please assist with above problem.

Hi,

The easiest way to solve the question would be to assume that the population of the town was 100 on May 1st:

May 1st: 100
June 1st: It grew by 50%. This implies 100 + 50/100 * 100 = 100 + 50 = 150
July 1st: It grew by 50% again. This implies 150 + 50/150 = 150 + 75 = 225
August 1st: The population fell by 11.11%. For convenience remember 11.11% is approximately 1/9. Thus, reduce the population by 1/9.
225 * 1/9 = 25. 225 - 25 = 200

Thus, the population on August 1st is 200, whereas the population on May 1st was 100.
While rule of thumb shows that it is a straight 100% increase, you can see it by the below calculation as well:

Change in population = 200 - 100 = 100
Base population = 100
%age change = 100/100 * 100 = 100%

Thus, the answer is C, 100%.

Hi Alanforde800Maximus,

There are two things which you have to note in this question.

1.Remember when ever GMAT tests you on percentages you can try to start value with 100 or multiples of 100.

2.The word approximately is the key - GMAT next your reasoning skills than your mathematical skills. So you can approximate and eliminate answer choices accordingly.

So let's solve this question,

Let take the value on May 1 as 100.

Then the value on June 1 will be 100 + 50% of 100 = 150

Similarly the value on July 1 will be 150 + 50% of 150 = 225

From July 1st to August 1st there is a decrease of 11.11%.

Since the question says approximately, instead of 11.11 % just approximate it as 10 % decrease( here the answer choices are wide enough so we can approximate to 10).

So approximately the new value is 225 - 10% 0f 225 = 202.5.

At this stage you can eliminate all the answer choices except C. Because 202.5 is little more than a 100 percent increase from May.

If you are looking how to find the percentage change, the rule is, (Difference/ original)* 100 = {(202.5-100)/100}* 100

That is approximately 100%.Bingo �

So the answer is C.

I hope this is clear�