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GMAT Prep #2 - HELP

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Source: — Data Sufficiency |
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by mals24 » Sat Apr 18, 2009 10:04 am
Is 1/p > r/(r^2 + 2) ?

St 1: p = r
Plug in values for p

Let p = r = -2

LHS: 1/-2 RHS: -2/6

-0.5< -0.3
Answer to the question is No.

Let p = r = 2

LHS: 0.5 RHS: 0.3

0.5>0.3
Answer to the question is Yes

St 1 is insuff

St 2: r>0...not sufficient.

Combining we know that p and r are positive.
So 1/p > r/(r^2 + 2)

Answer is C
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Re: GMAT Prep #2 - HELP

by Ian Stewart » Sat Apr 18, 2009 12:52 pm
BeatGMATinGVA wrote:Is 1/p > r/(r^2 + 2) ?

1) p = r

2) r > 0

I would say 1) is enough but... OA is C

Thanks for help!
Or, proceeding algebraically, using only Statement 1: If p = r, we can rephrase the question:

Is 1/r > r/(r^2 + 2) ?

Note that we can't multiply both sides by r here, since we don't know whether r is negative (if r is negative, we would need to reverse the inequality). We can, however, multiply by r^2 + 2 on both sides, since r^2 + 2 must be positive. Rephrasing the question by doing that, we want to know if:

(r^2 + 2)/r > r
(r^2/r) + (2/r) > r
r + (2/r) > r
2/r > 0
r > 0

That is, using Statement 1, the question becomes "Is r > 0?" We need Statement 2 to be sure of the answer to that question. C.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by arora007 » Wed Dec 15, 2010 2:34 am
Ian you have infact shown a new way to counter DS problems.
Thanks!
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by bblast » Mon Jul 04, 2011 8:07 am
Hi IAN,


is'nt it legal to cross multiple the problem statement once we are given p=r ? we are no longer concerned about the sign of p and r once we know they are equal FROM THE STATEMENT.
Cheers !!

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by Frankenstein » Mon Jul 04, 2011 8:27 am
bblast wrote: is'nt it legal to cross multiple the problem statement once we are given p=r ? we are no longer concerned about the sign of p and r once we know they are equal FROM THE STATEMENT.
Hi,
Even if they are equal, cross multiplication by negative quantity changes the sign of the inequality.
For instance:1/(-2) > (-2)/3.
Cross multiplication gives 3 > 4(Incorrect)
This is because in essence, we are multiplying both sides by (-6).So, the sign of inequality should change.
Cheers!

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by bblast » Mon Jul 04, 2011 10:36 am
thanks frank, really need to polish my inequalities' concepts. :oops:
Cheers !!

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