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The annual rent collected by a corporation from a certain

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Manager
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The annual rent collected by a corporation from a certain [#permalink] New post 12 May 2006, 10:58
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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) (xy)/100 < x -y
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 [#permalink] New post 12 May 2006, 11:43
Let annual rent be 100 in 1997
In 1998 it was 100 + x
In 1999 it was 100 + x - y - xy/100

So, we are comparing 100 against (100 + x - y - xy/100)

From (1) not sufficient as we do not know value of x and y.
because if x=10 and y=2, then (100 + x - y - xy/100) >100
and if x=90 and y=80 then (100 + x - y - xy/100) < 100

From (2) if x=10 and y=2 , (x-y) = 8 and xy/100 = 0.2; so (100 + x - y - xy/100) > 100
and if x=90 and y=80 then (x-y) = 10 and xy/100=72 ---> but this does not meet (2) so as long as (xy)/100 < x -y, Annual rent in 1999 is always greater. Hence sufficient.

So, B
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 [#permalink] New post 12 May 2006, 11:44
Its B.
Suppose in 1997 rent = 100
rent in 1998 = 100+x
rent in 1999 = (100+x) -y(100+x)/100 = (100+x)(100-y)/100.

so expanding the rent in 1999: -
(10000+100x-100y-xy)/100.
(10000+100(x-y)-xy)/100 --Eqn 1

now from eqn 1, if 100(x-y)-xy > 0, eqn 1 will be more than 100.
so 100(x-y)>xy
or, xy/100<(x-y).
So B is SUFF.
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Re: DS - Percents - Tough [#permalink] New post 12 May 2006, 12:06
TOUGH GUY 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


seems B cuz from 2 we know that x>y.
Re: DS - Percents - Tough   [#permalink] 12 May 2006, 12:06
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