Question: Population Increase

Comment on Population Increase

Hi Brent! In this question, I think you have used the wrong value. It should be $712.80 instead of 237..

https://greprepclub.com/forum/kathleen-s-weekly-salary-was-increased-by-8-percent-to-13649.html#p33761

greenlight-admin's picture

Question link: https://greprepclub.com/forum/kathleen-s-weekly-salary-was-increased-by-...

The question (with $237.60) is from the 2nd edition of the GRE Official Guide.
When the test-makers published the 3rd edition, they changed $237.60 to $712.80
I'm not sure why they did that.
The solution is the same, except we divide $712.80 by 1.08 to get an answer of $660

Cheers,
Brent

Hi Brent, I did it differently. I took the 2008 value and divided it by the 2007 value to get a 325% increase, then multiplied the 2008 value by 3.25. I got D. Is this an incorrect way to do the question?
greenlight-admin's picture

Your solution is perfectly valid. However, just to be clear about the terms, we can't say there was a 325% INCREASE, since it was actually a 225% increase.

However, we CAN say that the 2008 population was 3.25 TIMES the 2007 population.
Then, to find the 2009 population, we just MULTIPLY the 2008 population by 3.25

Cheers,
Brent

Why did we add one in the new value and multiplyed it by 65000?
greenlight-admin's picture

Here are a few similar examples:

If x is increased by 10%, then the NEW value = x + (10% of x)
= x + 0.1x
= 1.1x

If x is increased by 50%, then the NEW value = x + (50% of x)
= x + 0.5x
= 1.5x

If x is increased by 90%, then the NEW value = x + (90% of x)
= x + 0.9x
= 1.9x

If x is increased by 100%, then the NEW value = x + (100% of x)
= x + x
= 2x

Likewise, if x is increased by 225%, then the NEW value = x + (225% of x)
= x + 2.25x
= 3.25x

Does that help?

Cheers,
Brent

Hi Brent! I also completed this a little different as follows:
1. (65,008-19,984)/65,008 * 100 = about 69%
2. Then, I plugged in each answer choice to see which matches/is close to 69%
3. For ex: (210,000-65,008)/210,000 * 100 = 67%, so I went with choice D.

Is my technique applicable for these types of questions or was this a coincidence?
Thanks!
greenlight-admin's picture

You got a little lucky on that question, because you calculated the percent increase incorrectly. However, you also tested the answer choices incorrectly, which allowed you to arrive at the correct answer :-)

In your solution, you are saying that percent increase = (100)(new - old)/NEW

The actual formula is as follows:
Percent increase = (100)(new - old)/OLD

So, as a percent increase = (65,008-19,984)/19,984 * 100
≈ 225%

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