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# The annual rent collected by a corporation from a certain

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Senior Manager
Joined: 07 Nov 2004
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The annual rent collected by a corporation from a certain [#permalink]  02 Feb 2005, 10:02
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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) (x * y)/100 < x - y

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficientE. Statements (1) and (2) TOGETHER are NOT sufficient.
VP
Joined: 13 Jun 2004
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Location: London, UK
Schools: Tuck'08
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B, Statement 2 is sufficient.

from Statement 1 we know that X>Y, however it is not sufficient, 2 cases :

A=annual rent=1000
x=20%
y=19%

97=1000
98=1200
99=1000-228=772
-> 97 > 99

A=1000
x=50%
y=10%

97=1000
98=1500
99=1350
-> 97 < 99

From statement 2, we know that (x * y)/100 < x - y
or xy < 100(x-y), so x>y

You can find fast by picking number that if you want to get 97 > 99
Y has to be close to X as much as possible, however without going more than X and the product XY must be inferior to 100 times the difference between X and Y.
Finally, you'll realize that if you go more than 9% with Y you need to give soon 2 points of difference to X

if Y=10, X must be at least more than 11
and it goes on like this more and more...after many numbers the gap between X and Y is more and more important so there's no way 97 > 99, 97 is always < to 99 because X tend to be higher and higher faster than Y

Sorry for not having a scientific or algebric explanation
Director
Joined: 07 Jun 2004
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Location: PA
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i think this ia a def candidtae for using picking numbers

good explanation
VP
Joined: 18 Nov 2004
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"B". I wud recommend solving using algebra, might be quicker.

let's say 100 was the resnt in 97, so in 98....we have 100+x ....and in 99...we have 100+x-(y+xy/100)

100+x-(y+xy/100) > 100

or

100(x-y) - xy > 0

(xy) /100 < x-y.....u can see B from here.
SVP
Joined: 03 Jan 2005
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Baner has good explantions.

1997: 1
1998: 1+x/100
1999: (1+x/100)(1-y/100)=1+(x-y)/100-xy/10000
S=1999-1997= (x-y)/100-xy/10000
(I) x>y insufficient
(II) (x-y)>xy/100
(x-y)/100>xy/10000
S>0
Sufficient

(B)
VP
Joined: 13 Jun 2004
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Location: London, UK
Schools: Tuck'08
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You got it. Thanks Banner
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