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DS rent from a corporation

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DS rent from a corporation

by cceci » Wed Aug 01, 2012 9:24 pm
Dear all struggling with GMAT,

in the 12th edition of the review book there is a question which answer I can't understand:

the annual rent collected by a corporation from a 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

what i don't understand is why the first statement is not sufficient (according to the answer in the book). that is my explanation:

1998 = (1+x%).1997
1998 = (1+y%).1999

since x > y it means that 1999 must be greater than 1997, so that when both years are musltiplied with the percentage we get the same value - where am I wrong? on page 329 fron the book there is another explanation i don't really understand to be honest...

i hope you can help me with my "wrong" answer :)

best regards,
Tsveti
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by niketdoshi123 » Thu Aug 02, 2012 2:28 am
cceci wrote:Dear all struggling with GMAT,

in the 12th edition of the review book there is a question which answer I can't understand:

the annual rent collected by a corporation from a 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

what i don't understand is why the first statement is not sufficient (according to the answer in the book). that is my explanation:

1998 = (1+x%).1997
1998 = (1+y%).1999

since x > y it means that 1999 must be greater than 1997, so that when both years are musltiplied with the percentage we get the same value - where am I wrong? on page 329 fron the book there is another explanation i don't really understand to be honest...

i hope you can help me with my "wrong" answer :)

best regards,
Tsveti
While solving DS questions always try to rephrase the question stem in its most simplified form.

Let's try rephrasing what the question is actually asking

It says , the rent collected was x% more in 1998 than in 1997

Assume the rent collected in 1997 (A)= $100,

then the rent collected in 1998 (B)= $100 + x% of $100 = 100 + x

and the rend collected was y% less in 1999 than in 1998

So rent collected in 1999 (C)= (100+x) - y% of (100+x) = 100 + x - y - x*y/100

Question asked : was the annual rent collected more in 1999 than in 1997
=> was C - A > 0

=> Is (100 + x - y - x*y/100) - (100) > 0
=> Is x - y > x*y/100

From statement 1 we know that x - y > 0 , but (x - y) can be greater than or less than x*y/100. Hence this statement is not sufficient

Statement 2 clearly states that x - y is greater than x*y/100. Hence it is sufficient to answer our rephrased question.
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by GMATGuruNY » Thu Aug 02, 2012 2:40 am
cceci wrote: the annual rent collected by a corporation from a 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
Let the 1997 rent = 100.
Increase in 1998 = (x/100)*100 = x.
Rent in 1998 = 100+x.
Decrease in 1999 = y/100*(100+x) = y + xy/100
The problem asks whether the increase is greater than the decrease.

Question rephrased: Is x > y + xy/100?

Statement 1: x > y
If x=20 and y=10, then y + xy/100 = 10 + (20*10)/100 = 12.
Is 20 > 12? Yes.

If x=90 and y=80, then y + xy/100 = 80 + (90*80)/100 = 152.
Is 90 > 152? No.
Since the answer in the first case is YES, and the answer in the second case is NO, INSUFFICIENT.

Statement 2: x-y > xy/100
Thus, x > y + xy/100.
SUFFICIENT.

The correct answer is B.

It is helpful to be able to recognize the following formulas for repeated percent change:

If a value increases by x% and then by another y%, the total percent change = x + y + xy/100.
If a value increases by x% and then decreases by y%, the total percent change = x - y - xy/100.
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