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naaga: Master | Next Rank: 500 Posts; Posts: 129; Joined: Mon Dec 15, 2008 11:43 pm; Location: Hyderabad; Thanked: 2 times

geometry

by naaga » Mon Feb 16, 2009 5:03 am

14. A rectangular floor is covered by a rug except for a strip p meters wide 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 – p2
(D) (m - p)(n - p)
(E) (m –2p)(n – 2p)

folks plz explain standard method for this kind of problems

thanks in advance

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Source: Beat The GMAT — Problem Solving | Mon Feb 16, 2009 5:03 am

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 am; Thanked: 712 times; Followed by:550 members; GMAT Score:770

by DanaJ » Mon Feb 16, 2009 6:05 am

You basically have two rectangles:
a. the bigger rectangle is the floor with a surface of m*n
b. the smaller rectangle is the rug. The are of this one is (are of floor) - (area not covered by the rug).
The are not covered by the rug will be 2*p*n + 2*(m - 2p)*p. This means that the surface of the rug will be mn - 2pn - 2pm + 4p^2 = (mn - 2pm) - (2pn - 4p^2) = m(n - 2p) - 2p(n - 2p) = (m - 2p)(n - 2p).

Another way of solving this is considering length of rug = x and width of rug = y. Then x = m - 2p (since you've got a strip of p length on the right and one on the left) and y = n - 2p (since you 've got a strip of p length on the top and one on the bottom). This makes area = (m - 2p)(n - 2p). This method is slightly faster.

My guess is E.