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A rectangular floor is covered by a rug except fo a strip p

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by BTGmoderatorDC » Tue Dec 03, 2019 4:31 pm
A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by n meteres, What is the area of the rug in square meters?

A) mn - p(m+n)
B) mn - 2p(m+n)
C) mn - p^2
D) (m - p)(n - p)
E) (m - 2p)(n - 2p)

OA E

Source: Official Guide
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by Jay@ManhattanReview » Tue Dec 03, 2019 9:11 pm
BTGmoderatorDC wrote:A rectangular floor is covered by a rug except for fo a strip p meters along each of the four edges. If the floor is m meters by n meters, What is the area of the rug in square meters?

A) mn - p(m+n)
B) mn - 2p(m+n)
C) mn - p^2
D) (m - p)(n - p)
E) (m - 2p)(n - 2p)

OA E

Source: Official Guide
The length of the rug = m - 2p; and the width of the rug = n - 2p

Thus, the area of the rug = (m - 2p)(n - 2p) sq mtr

The correct answer: E

Hope this helps!

-Jay
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by [email protected] » Wed Dec 04, 2019 5:03 pm
Hi All,

We're told that a rectangular floor (that is M meters by N meters) is covered by a rug EXCEPT for a strip P meters along EACH of the four edges. We're asked for the area of the rug in square meters. This question can be solved in a couple of different ways, including by TESTing VALUES.

IF.... M=5 and N=4, then we have a 5x4 floor.

IF.... P=1, then there is a 1 meter space around EACH of the 4 sides, meaning that the area of the rug is....

(5-1-1) = 3 meters by (4-1-1) = 2 meters
Area of the rug is (3)(2) = 6 square meters

Based on the work I've done so far, you might recognize which answer is correct (since it's "formatted" almost identically to the above calculation). If you don't recognize it, then you just have to do enough work until you find the answer that equals 6 when you plug in M=5, N=4 and P=1... there's only one answer that matches. ..

Final Answer: E

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by Scott@TargetTestPrep » Mon Dec 09, 2019 5:33 pm
BTGmoderatorDC wrote:A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by n meteres, What is the area of the rug in square meters?

A) mn - p(m+n)
B) mn - 2p(m+n)
C) mn - p^2
D) (m - p)(n - p)
E) (m - 2p)(n - 2p)

OA E

Source: Official Guide

The area of the rug is:

[length - 2(strip)] x [width - 2(strip)]

(m - 2p)(n - 2p)

Answer: E

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by Brent@GMATPrepNow » Thu Dec 12, 2019 7:46 am
BTGmoderatorDC wrote:A rectangular floor is covered by a rug except fo a strip p meters along each of the four edges. If the floor is m meters by n meteres, What is the area of the rug in square meters?

A) mn - p(m+n)
B) mn - 2p(m+n)
C) mn - p^2
D) (m - p)(n - p)
E) (m - 2p)(n - 2p)

OA E

Source: Official Guide
When we sketch the given information, we get the following:
Image

So, the area of the rectangular rug equals = (base)(height) = (m - 2p)(n - 2p)

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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