tapanmittal wrote:127. 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
Statement 1 is a trap here. You could almost convince yourself that it is sufficient, because given that x > y it seems that the rent collected went up more than it went down.
However, Statement 1 incorporates a trick commonly used in GMAT data sufficiency questions, describing a situation in percentage terms and then asking a question about actual, rather than percentage, change.
You could approach Statement 1 mathematically, but I prefer to just be aware that when something increases to a higher level there is more of a percentage change than there is when going the other direction.
For instance, going from 80 to 100 is a 25% increase, but going from 100 to 80 is a 20% decrease.
So Statement 1 could be true if the rent collected in 1999 were higher, the same, or lower than that collected in 1997. So Statement 1 is insufficient.
Statement 2 is interesting. It constrains the difference between x and y, and so it immediately starts to look sufficient, but is it?
Let's pick a number, 100, for the rent in 1997 and see what we can do.
If the rent collected in 1997 is 100, then the rent collected in 1998 is 100 + 100(x/100) = 100 + x. So the change is x.
If the rent collected in 1998 is 100 + x, then the rent collected in 1999 is
(100 + x) - (y/100)(100 + x)
So the change from 1998 to 1999 is y + xy/100.
So the question becomes is the change from 1997 to 1998, x, greater than the change from 1998 to 1999, y + xy/100.
We can manipulate Statement 2 to get x > y + xy/100.
So the change from 1997 to 1998 is greater, and Statement 2 is sufficient, and the correct answer is
B.
Is that an "easier approach"? I guess that depends on what the alternative is.
