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tricky 1 from Prep

This topic has 3 expert replies and 0 member replies
mukherjee.tanuj3@gmail.co Master | Next Rank: 500 Posts
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tricky 1 from Prep

Post Mon Apr 28, 2014 8:34 pm

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sanju09 GMAT Instructor
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Post Fri May 02, 2014 11:02 pm
mukherjee.tanuj3@gmail.co wrote:
(1) If p = r, let’s plug in p = r = 2, and ask if ½ > 2/6, we get a YES. Or if we plug in p = r = -2, and ask if -½ > -2/6, and we get a NO. Hence, insufficient!

(2) It only tells about r, no info about p. Hence, insufficient!

When taken together, since both p and r are equal and positive, even if we now try a fraction for p and r, like if we plug in p = r = ½, and ask if 1/(½) > (½) /(¼ + 2) or “Is 2 > 2/9”, we still get a YES. Hence Sufficient!

Take C

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Post Thu May 01, 2014 3:11 am
Quote:
Is 1/p > r/(r^2 + 2) ?

(1) p = r
(2) r > 0
Alternate approach:

Statement 2 is clearly INSUFFICIENT.

Statement 1: p=r
Substituting p=r into the question stem, we get:
1/r > r/(r² + 2)?

(1/r) - r/(r² + 2) > 0?

(r² + 2 - r²) / [r(r² + 2)] > 0?

2 / [r(r² + 2)] > 0?

1 / [r(r² + 2)] > 0?

Case 1: r>0
1 / [r(r² + 2)] > 0
1/(positive*positive) > 0
1/positive > 0.
positive > 0.
In this case, the answer is YES.

Case 2: r<0
1 / [r(r² + 2)] > 0
1/(negative*positive) > 0
1/negative > 0
negative > 0.
In this case, the answer is NO.
INSUFFICIENT.

Statements combined:
Since only Case 1 is possible, the answer to the question stem is YES.
SUFFICIENT.

The correct answer is C.

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Post Wed Apr 30, 2014 11:27 am
There isn't an obvious way to rephrase this question. We can't cross-multiply because we don't know whether p is negative. (You could rephrase giving yourself a positive and negative case, but this can become confusing). The best thing to do it to try to PROVE INSUFFICIENCY when looking at the statements.

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

1) p = r

Test values to prove insufficiency:
If p and r both equal 1: (1/1) > 1/(1^2 + 2) --> 1 > 1/3 yes.
If p and r both equal -1: (1/-1) > -1/((-1)^2 + 2) --> -1 > -1/3 no.
Insufficient.

2) r > 0

This tells us nothing about p. Insufficient.

1 & 2) Together, if r > 0 then p > 0. We only need to test positive values:
If p and r both equal 1: (1/1) > 1/(1^2 + 2) --> 1 > 1/3 yes.
If p and r both equal 2: (1/2) > 2/(2^2 + 2) --> 1/2 > 2/6 yes.
If p and r both equal 3: (1/3) > 3/(3^2 + 2) --> 1/3 > 3/11 yes.

Any positive value we test would give us a "yes" result. The answer is C.

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