OG-12 DS (Inequalities)

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OG-12 DS (Inequalities)

by Elena89 » Mon Dec 26, 2011 12:07 am
The annual rent collected by a corporation from a certain building was x percent more in 1998 than in
1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997 ?

(1) x > y

(2)(xy/100) < x - y

Again, OG gives a very cumbersome approach to compute this one.

In need of a quick explanation!

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by [email protected] » Mon Dec 26, 2011 12:18 am
Elena89 wrote:The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997 ?

(1) x > y

(2)(xy/100) < x - y

Again, OG gives a very cumbersome approach to compute this one.

In need of a quick explanation!
Let us assume that rent in 1997 = 100
Then in 1998, rent = 100 + x
Rent in 1999 = (100 - y)(100 + x)/100
Now the question can be rephrased as: Is (100 - y)(100 + x)/100 > 100?
100x - 100y - xy > 0
100(x - y) > xy
(1) x > y does not imply whether 100(x - y) > xy or not; NOT sufficient.

(2) (xy/100) < x - y, which clearly implies that 100(x - y) > xy; SUFFICIENT.

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