Data Sufficiency

The annual rent collected by corp from certain rent was x percent more in 98 than in 97 and y percent less in 99 than 98. was the annual rent collected by corp in 99 more than in 97?

a. x > y
b. xy/100 < x -y

Correct answer is B.

Please explain logic.....

1)

By substitution, x = 10 & Y = 5 (x >y)

Rent collected in 99 will be more than rent collected in 97

If x = -10 & y = -5.

Rent collected in 99 will be less than rent collected in 97

Insufficient

2) xy > 100X-100Y

Substitute the same values for X = 10 & -10, get Y values. The Rent collected in 99 will be more than rent collected in 97

Answer is B

GHong14 wrote:The annual rent collected by corp from certain rent was x percent more in 98 than in 97 and y percent less in 99 than 98. was the annual rent collected by corp in 99 more than in 97?

a. x > y
b. xy/100 < x -y

Correct answer is B.

Please explain logic.....

Plug in that 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
Thus, the total change from 1997 to 1999 = increase in 1998 - decrease in 1999 = x - (y + xy/100) = x - y - xy/100.

The question then becomes: Is x - y - xy/100 > 0?

Statement 1:
If x=20 and y=10, then x - y - xy/100 = 20 - 10 - (20*10)/100 = 8.
If x=90 and y=80, then x - y - xy/100 = 90 - 80 - (90*80)/100 = -7.
Since the change from 1997 to 1999 could be positive or negative, insufficient.

Statement 2:
If x-y > xy/100, then x - y - xy/100 > 0. Sufficient.

The correct answer is B.

GMATGuruNY wrote:

GHong14 wrote:The annual rent collected by corp from certain rent was x percent more in 98 than in 97 and y percent less in 99 than 98. was the annual rent collected by corp in 99 more than in 97?

a. x > y
b. xy/100 < x -y

Correct answer is B.

Please explain logic.....

Plug in that 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
Thus, the total change from 1997 to 1999 = increase in 1998 - decrease in 1999 = x - (y + xy/100) = x - y - xy/100.

The question then becomes: Is x - y - xy/100 > 0?

Statement 1:
If x=20 and y=10, then x - y - xy/100 = 20 - 10 - (20*10)/100 = 8.
If x=90 and y=80, then x - y - xy/100 = 90 - 80 - (90*80)/100 = -7.
Since the change from 1997 to 1999 could be positive or negative, insufficient.

Statement 2:
If x-y > xy/100, then x - y - xy/100 > 0. Sufficient.

The correct answer is B.

I have seen many of your posts and you tend to substitute with such numbers that the problem looks simple. Can you please suggest on how, why and when you decide on the numbers. Thank you.

Unfortunately I simply don't see the underlying concept the problem is trying to test you other than just been a mind teaser during the test. Can someone explain what is the underlying significance of xy/100<x-y? Why does this statement tell us what we need to know?