Problem Solving

Hi ziyuenlau,

This question can be solved by TESTing VALUES.

Let's start with a population of 100 on May 1st...
The population grows by 50%.... 100 + 100(.5) = 150
Then it grows by another 50%... 150 + 150(.5) = 225
Then it decreases by 11.11%.... 225 - 225(1/9) = 200

In total, the population grew from 100 to 200. You might recognize that that is a 100% increase, but you can also use the Percent Change Formula to prove it...

(200 - 100)/100 = 100/100 = 1 = 100%

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

Here is some general advice that I always have my students follow: LOOK AT THE ANSWER CHOICES FOR TRAPS & CLUES BEFORE STARTING TO SOLVE.

On a PERCENT CHANGE problem, the most common trap that test writers will set is to include a trap answer for PERCENT OF rather than percent CHANGE. And 'percent of' is always 100 more than 'percent change.'

As the other posters have demonstrated, the initial population of x doubles to 2x by the end of the season. It would be tempting to pick 200%... and that's an answer option! But going from x --> 2x is an increase of 100%.

When I looked at the answer choices before doing any math, I noticed that 100 and 200 are the only two answer options that are 100 apart. So - without doing any work - I figured that 100 was probably the right answer, and 200 was probably the trap.

hazelnut01 wrote: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%

We can let the initial population = n.

After the town grows by 50%, then another 50%, and then decreases by 11.11%, we have:

n(3/2)(3/2)(8/9) = 72n/36 = 2n

Let's determine the percentage increase:

(2n - n)/n x 100 = n/n x 100 = 100%

Answer: C

ceilidh.erickson wrote:Here is some general advice that I always have my students follow: LOOK AT THE ANSWER CHOICES FOR TRAPS & CLUES BEFORE STARTING TO SOLVE.

Here is another post that exemplifies the importance of this strategy: https://www.beatthegmat.com/m-is-the-sum ... tml#793900

And here is an article you should read to help you practice: https://www.manhattanprep.com/gmat/blog ... -pen-down/

hazelnut01 wrote: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%

Source : Veritas Prep
OA=C

Another approach to this question.

Since we have to deal with 50% = 1/2; 50% = 1/2; and 11.11% = 1/9, we can assume that the initial population is 36 (multiple of denominators of 1/2, 1/2, and 1/9).

Thus,

Population by June 1 = 36 + 36x1/2 = 54
Population by July 1 = 54 + 54x1/2 = 81
Population by Aug 1 = 81 - 81x1/9 = 72

We see that population doubles ( 72 from 36). Or the population rose by 100%.

The correct answer: C

Hope this helps!

Relevant book: Manhattan Review GMAT Math Essentials Guide

-Jay
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