Problem Solving

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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pmFollowed by: 6 members

by BTGmoderatorRO » Sat Feb 10, 2018 4:52 am

If the sides of a rectangle are increased by 15%, what is the percentage increase in the area?

A. 32.25%
B. 40%
C. 37.50%
D. 36.75%
E. 32%
OA is C

What formula do I need for this? An Expert contribution is needed please.

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Source: Beat The GMAT — Problem Solving | Sat Feb 10, 2018 4:52 am

EconomistGMATTutor: GMAT Instructor; Posts: 555; Joined: Wed Oct 04, 2017 4:18 pmFollowed by: 12 members; Thanked: 180 times

answer

by EconomistGMATTutor » Sun Feb 11, 2018 2:51 am

Roland2rule wrote:If the sides of a rectangle are increased by 15%, what is the percentage increase in the area?

A. 32.25%
B. 40%
C. 37.50%
D. 36.75%
E. 32%
OA is C

What formula do I need for this? An Expert contribution is needed please.

Hello Roland.

There is a mistake with the answer. Let's see why.

Let's call the sides of the rectangle "x" and "y". Hence the area is A=x*y.

Now, if each side is increased by 15%, the measure of the sides will be $$X=x+15\%\cdot x=x+0.15\cdot x=1.15\cdot x$$ $$Y=y+15\%\cdot y=y+0.15\cdot y=1.15\cdot y$$ Therefore, the area of the new rectangle is $$A_2=X\cdot Y=1.15\cdot x\cdot1.15\cdot y=1.3225\cdot xy.$$ Now,

xy----------------100%
1.3225xy---------- ?

Hence, the new area represents $$\frac{1.3225xy\cdot100\%}{xy}=132.25\%\ \ \text{of}\ \text{the}\ \text{first}\ \text{area}$$ This implies that the new area is 132.25%-100% = 32.25% biger than the first rectangle.

So, the correct answer is A.

I hope this answer may help you.

I'm available if you'd like a follow-up.

Regards.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Feb 11, 2018 3:17 am

Roland2rule wrote:If the sides of a rectangle are increased by 15%, what is the percentage increase in the area?

A. 32.25%
B. 40%
C. 37.50%
D. 36.75%
E. 32%

Since 15% = 15/100 = 3/20, let the rectangle be a SQUARE with a side of 20.
Original area = sÂ² = 20Â² = 400.
After each side is increased by 15% to 23, the new area = sÂ² = 23Â² = 529.
Percent increase from 400 to 529 = (Difference/Smaller) * 100 = (129/400) * 100 = 129/4 = 32.25.

The correct answer is A.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8156; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Sun Jun 23, 2019 6:26 pm

BTGmoderatorRO wrote:If the sides of a rectangle are increased by 15%, what is the percentage increase in the area?

A. 32.25%
B. 40%
C. 37.50%
D. 36.75%
E. 32%
OA is C

We can let each side of the rectangle = 100, so the area is 10,000.

With a 15 percent increase the new area is 115 x 115 = 13,225.

Thus, the percent increase is:

(13,225 - 10000)/10000 x 100% = 3225/10000 x 100 = 32.25%

Answer: A

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