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how would you solve this one? OG DS #127

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by zashley777 » Mon Feb 23, 2015 7:08 pm
The annual rent collected by a corporation from a certain building was x percent more in 198 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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Source: — Data Sufficiency |
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by GMATGuruNY » Mon Feb 23, 2015 7:17 pm
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
Let the 1997 rent = 100.
Increase in 1998 = (x/100)*100 = x.
Thus, rent in 1998 = 100+x.
Decrease in 1999 = y/100*(100+x) = y + xy/100/

The question stem asks whether the increase is greater than the decrease.
Question stem, rephrased:
Is x > y + xy/100?

Statement 1: x > y
Case 1: x=20 and y=10
Here, y + xy/100 = 10 + (20*10)/100 = 12.
Is 20 > 12?
YES.

Case 2: x=90 and y=80
Here, y + xy/100 = 80 + (90*80)/100 = 152.
Is 90 > 152?
NO.

Since the answer is YES in Case 1 but NO in Case 2, INSUFFICIENT.

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

The correct answer is B.
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by ravihanda » Mon Feb 23, 2015 8:36 pm
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)
Let us say that the rent that was collected in 1997 was 100
Rent in 1998 = 100(1 + x/100) = 100 + x
Rent in 1999 = (100 + x)(1 - y/100) = 100 + x - y - xy/100
Rent in 1999 - Rent in 1997 = x - y - (xy)/100
We have to figure out if the above value is > 0 or not.

Statement 1: x > y
We cannot comment about x - y - (xy)/100 from this information.
Statement 1 is not sufficient.

Statement 2: (xy)/100<(x-y)
=> x - y - xy/100 > 0
=> Rent in 1999 - Rent in 1997 > 0
=> Statement 2 is sufficient.
[spoiler]Correct Answer: B[/spoiler]
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