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by abhishek.pati » Sun Jul 03, 2011 8:17 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
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Source: — Data Sufficiency |
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by Jim@Knewton » Sun Jul 03, 2011 9:17 pm
Let 1997 rent = p
From the question:
rent in 1998 = p*(1+x/100)
rent in 1999 = p*(1+x/100)*(1-y/100)
Difference between 1999 and 1997 = p*(1+x/100)*(1-y/100) - p

Question is: Is p*(1+x/100)*(1-y/100) - p > 0 ? (is the difference between 1999 and 1997 positive? )
=>Is p*(1 - y/100 + x/100 - xy/10000) - p > 0?
=> Is p*(x/100 - y/100 - xy/10000) > 0?
Since p cannot be 0
=> Is (x/100 - y/100 - xy/10000) > 0? ........................................................(1)

From #1: x>y
using x>y in (1), we are unable to conclude if (x/100 - y/100 - xy/10000) > 0?
Hence #1 by itself is insufficient.

From #2: xy/100 < x - y
Rearranging terms in (1) we get
Is (x/100 - y/100 - xy/10000) > 0?
=>Is x/100 - y/100 > xy/10000
=> Is x- y > xy/100 ?
But #2 states precisely that x- y > xy/100

Hence p*(1+x/100)*(1-y/100) - p > 0 => the difference between 1999 and 1997 is positive
=> 1999 rent > 1997 rent

Hence #2 alone is sufficient
Hence B
:-)

Thx. for posting - interesting question!
Best, Jim
Please "thank" this post if it helps you!
https://www.knewton.com/people/jims
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