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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]

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03 Dec 2006, 01:45
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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
Senior Manager
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03 Dec 2006, 01:56

statemnetI : x>y does not convey much

staement II says that

x-y-x*y/100 >0

this is nothing but the consolidated value in 1999............it eliminates the possibility of x% and y% adding upto a negative value........

hence we need II statement to evaluate what is being asked.
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03 Dec 2006, 08:01
Why is A not suff?

If we know the rent collected increases more between 97 - 98 than it decreases between 98-99 then isn't that sufficient to tell us that the rent in 99 is more than in 97?
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03 Dec 2006, 09:29
jyotsnasarabu wrote:

statemnetI : x>y does not convey much

staement II says that

x-y-x*y/100 >0

this is nothing but the consolidated value in 1999............it eliminates the possibility of x% and y% adding upto a negative value........

hence we need II statement to evaluate what is being asked.

Should this not be <?

Original equation is xy/100<x-y ----> (xy-/100)-(x-y)<0 ????
Manager
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03 Dec 2006, 10:06
Why not A is suff to say that the 1999 annual rent collected by the corporation from the building more??
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03 Dec 2006, 11:29
Let us assume that amt in '97=100, x=25% and y=21%
Then, '98=125, '99<100

But, y=10%
then, '99>100

Since it depends on the value A is insuff.

Hope it helps
Senior Manager
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03 Dec 2006, 16:05
Thanks - could you explain the reasoning for part 2 please?
Senior Manager
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03 Dec 2006, 18:10
I tried to substitute the same nos. as S1 in S2

xy/100 < x-y
25*21/100=5.25 which is greater than 25-21=4. So the rent in '99 is lesser

25*10/100=2.5 which is less than 25-10=15. So the rent is greater.

However, we do not need to find the result. All we need is that the equation is suff to answer the Q.

I could not derive an expl. algebraically.
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05 Dec 2006, 10:46
R98=[(100+x)/100]*R97
R98=R99*[(100/100-y)]

Thus,

R99*[(100/100-y)]=[(100+x)/100]*R97

Simplifying to,

R99=R97*[1+(100(x-y)-xy)/100000)]

According to B,

xy/100<x-y

100(x-y)-xy<0

Meaning

R99=R97*[1-(some value0]

Hence R97 is greater. B is sufficient.
05 Dec 2006, 10:46
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