If the length and width of a rectangular garden plot

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Tue Oct 17, 2017 5:12 pm

If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

How will i start the formula here?

OA E

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Source: Beat The GMAT — Problem Solving | Tue Oct 17, 2017 5:12 pm

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

Answer

by EconomistGMATTutor » Tue Oct 17, 2017 7:09 pm

Hello lheiannie07.

I will show you with an example how to determine the correct answer.

Let's take a rectangular garden whose length is 20 and its width is 10. So, its area is equal to 200.

Now, if we increase each dimension by 20%, we will obtain that the new dimensions are 24 and 12 (length and width respectively).

The new area is equal to 288.

Now, if 200 is the 100% of the firts area, which percent represents 288?

It is the same as $$x=\frac{288\cdot100}{200}=144%.$$

So, the new area excess the first area by 44% percent.

So, the answer is E.

I hope this answer can help you.

I'm available if you'd like any follow up.

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by [email protected] » Wed Oct 18, 2017 8:37 pm

Hi lheiannie07,

We're told that the length and width of a rectangular plot were each increased by 20 percent. We're asked for the percent increase in the area of the plot. This question can be solved rather easily by TESTing VALUES (as EconomistGMATTutor has shown). It can also be solved Algebraically.

The original Length and Width of the rectangle would give us an area of (L)(W).

By increasing both of those values by 20%, we would have an area of (1.2L)(1.2W) = 1.44(L)(W). Comparing 1.44(L)(W) to (L)(W), the increase is clearly 44%

Final Answer: E

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Rich

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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 » Thu Oct 19, 2017 2:59 am

lheiannie07 wrote:If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

A square is a type of rectangle.
To make the math easier, let the rectangular garden be a SQUARE with a side of 10.
Area of the square garden = 10Â² = 100.
If the length and width of the square each increase by 20% -- in other words, if each SIDE of the square increases by 20% -- the new area = 12Â² = 144.
Since the area increases from 100 to 144 -- an increase of 44% -- the correct answer is E.

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by Scott@TargetTestPrep » Sun Oct 22, 2017 3:44 pm

lheiannie07 wrote:If the length and width of a rectangular garden plot were each increased by 20 percent, what would be the percent increase in the area of the plot?

(A) 20%
(B) 24%
(C) 36%
(D) 40%
(E) 44%

If we let L = the original length and W = the original width, then the original area of the rectangle is LW.

The new area is 1.2L x 1.2W = 1.44LW.

Thus, we see that there is a 44% increase in the area.

Alternate Solution:

We can let the original length = 10 and the original width = 10. We see that the increased length will be 12, and the increased width will be 12.

The original area is length x width = 10 x 10 = 100. The new area is 12 x 12 = 144.

We find the percentage increase in the area by using the formula (new - old)/old x 100, and we obtain:
(144 - 100)/100 x 100 = 44/100 x 100 = 44%.

Answer:E

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