OG 11 DATA SUFFICIENCY QNO 145

Question

GMATONIANS,

PL HELP

IS 1/P > R/(R^2+2) ?

(1) P = R
(2) R > 0

ANS IS C.
I UNDERSTOOD HOW OG 11 ARRIVED AT THIS,BUT I DONT UNDERSTAND WHY MY METHOD IS WRONG, WHICH IS

SUBSTITUTING (1),
1/R > R / (R^2 + 2)
CROSS MULTIPLYING
1>R^2/(R^2 +2)
OR
(R^2 +2)/R^2 > 1
WHICH IS TRUE FOR ALL CASES OF R, + OR - , HENCE ANS IS A

WELL,WHY NOT?

Vemuri · Answer

Because you did not consider the negative value of R. What if R<0, then the inequality will be:

R^2/(R^2+2)>1, which cannot be correct because (R^2+2) > R^2.

We need the second statement as well to answer the question.

Hope that helps.

Ian Stewart · Answer

georgy wrote:
SUBSTITUTING (1),
1/R > R / (R^2 + 2)
CROSS MULTIPLYING
1>R^2/(R^2 +2)

Ron just discussed this in another thread, but you can't 'cross-multiply' with inequalities unless you know whether your denominators are positive or negative. When you 'cross-multiply', you're really multiplying on both sides by both denominators. So in the above, when you cross-multiplied, you were multiplying on both sides by r^2 + 2, and by r. Well, r^2 + 2 is certainly positive, so no problem there, but r could be positive or could be negative. If r is negative, you'd need to reverse the inequality when you multiply by r on both sides. That's why you need the second statement, which guarantees that r is positive, and that you can multiply by r on both sides without needing to worry about reversing the inequality.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

georgy · Answer

I SEE,LEARNED SOMETHING NEW TODAY... THANK YOU

iamcste · Answer

Using stament 1, can this be simplified to 2/R>0 or have I over simplified it

Ian Stewart · Answer

iamcste wrote:Using stament 1, can this be simplified to

2/R>0

or have I over simplified it

Yes, that's perfect - you can even go further than that.

In detail, when we use Statement 1, we can rephrase the question, by rewriting it algebraically. Note that all we're doing is restating the question in different ways; what we're hoping to find is either:

-something we know to be true, like 2 > 0. Then we'll know we have sufficient information;
-something we don't know is true, like r > 0. Then we'll know we don't have sufficient information, and we'll know exactly what information we need.

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

Using S1, this becomes:

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

We can multiply by r^2 + 2, since we know that r^2 + 2 must be positive:

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

And now we see why we need Statement 2 as well.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

iamcste · Answer

Ian Stewart wrote:iamcste wrote:Using stament 1, can this be simplified to 2/R>0 or have I over simplified it Yes, that's perfect - you can even go further than that. In detail, when we use Statement 1, we can rephrase the question, by rewriting it algebraically. Note that all we're doing is restating the question in different ways; what we're hoping to find is either: -something we know to be true, like 2 > 0. Then we'll know we have sufficient information; -something we don't know is true, like r > 0. Then we'll know we don't have sufficient information, and we'll know exactly what information we need. Is 1/p > r/(r^2 + 2) ? Using S1, this becomes: Is 1/r > r/(r^2 + 2) ? We can multiply by r^2 + 2, since we know that r^2 + 2 must be positive: Is (r^2 + 2)/r > r ? Is (r^2/r) + (2/r) > r ? Is r + (2/r) > r ? Is 2/r > 0 ? Is r > 0? And now we see why we need Statement 2 as well. Thanks Ian!

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OG 11 DATA SUFFICIENCY QNO 145

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