GMAT Prep Pract Test #2

[abby.perlman]

Hello,

Had trouble with this one--just have my notes with me but this is what I had written down:

If 0<r<1 and 1<s<2 which MUST be less than 1?

1) R/S
2) RS
3) S-R

I just plugged in 1/2 for R and 3/2 for S and tested each option which got me to the conclusion that 1 & 2 must be less than 1 but the actual answer is A that only 1 is less than 1. Can you please explain? Thank you!

[rajivbhatia2007]

You also have to consider extreme possibilities.

You plugged in 0.5 for r.
But r could be 0.01 or 0.99

You plugged in 1.5 for s
But s could be 1.01 or 1.99

Choice I:

0 < r < 1, 1 < s < 2 implies that r < s and that r and s are both positive. We have a case where the numerator is less than the denominator. This implies that r/s < 1. TRUE

Choice II

If r = 0.1 and s=1.01, then rs < 1
If r = 0.99 and s=1.99, then rs > 1
Thus, FALSE

Choice III
If s = 1.99 and r = .01, then s-r = 1.98. 1.98 > 1
If s = 1.01 and r = .99, then s-r = .02. .02 < 1
Thus, FALSE


Thus, the answer is I only.

Best,
Rajiv
my gmat story

[jnelson0612]

Very nice Rajiv! Excellent point about needing to test out extremes rather than middle numbers.

[amarroy]

Thanks a lot Rajib...We all know that we need to plug numbers in these kind of problems, however we often forget to consider the boundary conditions. This is a perfect example...

By the way I got it Wrong :)

[tim]

well, you don't HAVE to plug in numbers, but it certainly helps in a lot of cases..