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Percentage Increase

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by [email protected] » Thu Apr 24, 2014 6:10 pm
Hi Experts,

Can we just divide the sum of percentage given over three years to get percentage given for each year?

We are given that the percentage increase for each year was the same!
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Source: — Data Sufficiency |

by GMATGuruNY » Fri Apr 25, 2014 2:54 am
[email protected] wrote:Hi Experts,

Can we just divide the sum of percentage given over three years to get percentage given for each year?

We are given that the percentage increase for each year was the same!
No.
To see why, test a case with EASY VALUES.

Let the 3rd year profits = 100 and the annual percent increase = 10%.
Then:
4th year increase = 10% of 100 = 10.
4th year profits = 100 + 10 = 110.
5th year increase = 10% of 110 = 11.
5th year profits = 110 + 11 = 121.
Result:
From the 3rd year to the 5th year, the profits increase from 100 to 121, an increase of 21%.

As you can see, the annual percent increase (10%) is a bit LESS than 1/2 the total percent increase (21%).
The reason is that the percent increase is COMPOUNDED from year to year.

In the DS problem above:
Since the profits increase by a total of 60% over the course of 2 years, and the percent increase is the same each year, the annual percent increase is a bit less than 1/2 of 60% (about 26.25%).
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by [email protected] » Fri Apr 25, 2014 3:47 am
Thanks Mitch, so the answer is correct i.e. C but can we say say C where we aren't getting an exact solution I mean we are getting an approximate solution but not exact no!


GMATGuruNY wrote:
[email protected] wrote:Hi Experts,

Can we just divide the sum of percentage given over three years to get percentage given for each year?

We are given that the percentage increase for each year was the same!
No.
To see why, test a case with EASY VALUES.

Let the 3rd year profits = 100 and the annual percent increase = 10%.
Then:
4th year increase = 10% of 100 = 10.
4th year profits = 100 + 10 = 110.
5th year increase = 10% of 110 = 11.
5th year profits = 110 + 11 = 121.
Result:
From the 3rd year to the 5th year, the profits increase from 100 to 121, an increase of 21%.

As you can see, the annual percent increase (10%) is a bit LESS than 1/2 the total percent increase (21%).
The reason is that the percent increase is COMPOUNDED from year to year.

In the DS problem above:
Since the profits increase by a total of 60% over the course of 2 years, and the percent increase is the same each year, the annual percent increase is a bit less than 1/2 of 60% (about 26.25%).
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by GMATGuruNY » Fri Apr 25, 2014 5:14 am
[email protected] wrote:Thanks Mitch, so the answer is correct i.e. C but can we say say C where we aren't getting an exact solution I mean we are getting an approximate solution but not exact no!
When the two statements are combined, the annual percent increase CAN be determined.
But -- since this is a DS problem -- there is no need to calculate the exact percentage.
Since the two statements combined give SUFFICIENT information to determine the annual percent increase, select C and move on.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
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