Data Sufficiency

The annual rent collected by a corporation from a certain building was x % more in 1998 than in 1997and y% 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
It is easy to eliminate option 1, pls suggest how to proceed with option 2 to solve the question in 2mins.

Hi Sushant

It is simple. As the question says the rent was first increased by (1+x/100) and then decreased by (1-y/100) the final rent should be: (1+x/100) * (1-y/100) = 1+(x-y)/100 -xy/10000
Term 1: (x-y)/100
Term 2: xy/10000
Statement 1: x>y
As you can see from calculated equation above. x>y makes (x-y)/100 term positive but it is not sure that the term -xy/10000 is greater than (x-y)/100 or not.
Consider x=35, y=30
Term 1: 5/100
Term 2: 10.5/100
Clearly Term 2 is greater and therefore the resulting rent in 1999 will be less than that in 1997.

Consider x=20, y=15
Term 1: 5/100
Term 2: 3/100

Clearly Term 1 is greater and therefore the rent in 1999 will be greater than that in 1997

Therefore INSUFFICIENT

Statement 2: xy/100 < (x-y) OR xy< 100(x-y)

if you consider Term 1 & Term 2 together and take common denominator you will get :-

(x-y)/100 -xy/10000 = (100(x-y)-xy)/10000

Now with statement 2 you can easily say that above term is positive as 100(x-y) > xy as given in Statement 2. Therefore the rent for sure will be more in 1999 than in 1997 and hence Statement 2 alone is SUFFICIENT

The answer is (B)

Hope this helps.