Simple algebra @ Variable Question: Need help

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pardeep_10sharma: Senior | Next Rank: 100 Posts; Posts: 36; Joined: Tue Mar 02, 2010 9:38 amFollowed by: 1 member; Location: India; GMAT Score:540

by pardeep_10sharma » Fri May 14, 2010 5:58 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) 100xy < x - y

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Source: Beat The GMAT — Quantitative Reasoning | Fri May 14, 2010 5:58 am

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon May 17, 2010 4:25 am

pardeep_10sharma 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) 100xy < x - y

If it was 100 in 1997, then it has to be (100 + x) in 1998 and (100 + x) (100 - y)/100 in 1999. The question is:

Was (100 + x) (100 - y)/100 > 100? Or

Was 10000 + 100 (x - y) - x y > 10000? Or

Was 100 (x - y) > x y?

As there's no ambiguity expected, hence x and y each is positive.

(1) Take suitable set of numbers for x and y, when x = 2, y = 1, 100 (x - y) > x y; but when x = 25 and y = 20, 100 (x - y) = x y, and when x = 50 and y = 40, 100 (x - y) < x y. Insufficient

(2) If 100 x y < x - y, then x and y are proper fractions of the order x = 0.2 and y = 0.001 etc, and in such cases, 100 times the difference 0.199 is greater than their product. [spoiler]Sufficient

B[/spoiler]

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