Data Sufficiency

Please help with the question.. Please explain the answer...

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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

OA after some discussion...

This is how I tried,
Let's say
1997 -----> rent collected 100 $

1998 ----------> rent collected ( 100 +x )$

1999 ---------> (100+x) - (100+x)*y/100
==> 100 + (x-y) - xy/100

so if we can prove (x-y) - xy/100 > 0 we are done.
only thing we know is that x, y >0 hence xy/100 but x-y can be <0 and - xy/100 is definitely < 0
stmt 1. x>y hence x-y >0 but if xy/100 >x-y then expression is negative if xy/100 < x-y then expression is +ve. insufficient

stmt 2: xy/100 < (x-y) hence (x-y) - xy/100 >0 SUFFICIENT IMO it is B.
What is OA??

regards,
CBM

IMO D

Both are correct

1999 ---------> (100+x) - (100+x)*y/100
==> 100 + (x-y) - xy/100

(x-y) - xy/100

this value can be greater than 0 only when x>y

You can plug in any positive value of x and y and check,if this relation holds true,
then (x-y) - xy/100> 0

And why I say positive value of x and y because we cannot have percent values in negative

Hope this Helps

Karan

what about

x = 51

y = 50 ?

regards,
CBM

Opps!!

I missed this out

x = 51

y = 50 ?

regards,
CBM

Thanks CBM

it has to be B

thanks OA is B