DS rent from a corporation

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cceci: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sun Mar 27, 2011 6:13 am

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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Source: Beat The GMAT — Data Sufficiency | Wed Aug 01, 2012 9:24 pm

niketdoshi123: Master | Next Rank: 500 Posts; Posts: 210; Joined: Thu Mar 08, 2012 11:24 pmFollowed by: 3 members; Thanked: 62 times

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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