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Source: — Data Sufficiency |
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by Frankenstein » Fri Jul 01, 2011 2:48 am
Hi,
From(1): p=r
Consider 1/p - r/(r^2 + 2) = 1/r - r/(r^2 + 2) = [(r*r+2) - r*r]/r*(r^2 + 2) = 2/r(r^2+2)
r^2+2 is always positive
So, sign of 2/r(r^2 + 2) depends on sign of r.
If r is positive it will be positive, if r is negative, it will be negative
Not sufficient
From(2): r>0
No info. about p
Not sufficient
Both (1)&(2):
1/p - r/(r^2 + 2) = 2/r(r^2+2)
As r>0, 2/r(r^2+2) > 0
So, 1/p - r/(r^2 + 2) > 0
Sufficient

Hence, C
Cheers!

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by Brent@GMATPrepNow » Fri Jul 01, 2011 11:30 am
Mumbai wrote:Is 1/p > r/(r^2 + 2) ?
a. p = r
b. r > 0
Answer C
Statement 1:
If we replace p with r, the target question becomes "Is 1/r > r/(r^2 + 2)?"
In this form, it might be tough to answer the new target question.
However, since (r^2 + 2) must be positive, we can multiply both sides of the target question by (r^2 + 2) to get a new target question: Is (r^2 + 2)/r > r?
From here, we can simplify the left-hand-side to get Is r + 2/r > r?
Finally, if we subtract r from both sides of the target question, we get Is 2/r > 0?
At this point, it's easy to answer the target question.
2/r can be greater than zero or it can be less than zero.
As such, statement 1 is not sufficient.

Statement 2:
Since we are given no information about p, statement 2 is not sufficient.

Statements 1 AND 2:
Statement 1 allowed us to rewrite the question as Is 2/r > 0?
Since statement 2 tells us that r is positive, we can now answer the new target question with certainty (2/r is definitely greater than zero).

So, the answer is C
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by gauravbhandari.86 » Mon Jul 18, 2011 12:00 am
Brent@GMATPrepNow wrote:
Mumbai wrote:Is 1/p > r/(r^2 + 2) ?
a. p = r
b. r > 0
Answer C
Statement 1:
If we replace p with r, the target question becomes "Is 1/r > r/(r^2 + 2)?"
In this form, it might be tough to answer the new target question.
However, since (r^2 + 2) must be positive, we can multiply both sides of the target question by (r^2 + 2) to get a new target question: Is (r^2 + 2)/r > r?
From here, we can simplify the left-hand-side to get Is r + 2/r > r?
Finally, if we subtract r from both sides of the target question, we get Is 2/r > 0?
At this point, it's easy to answer the target question.
2/r can be greater than zero or it can be less than zero.
As such, statement 1 is not sufficient.

Statement 2:
Since we are given no information about p, statement 2 is not sufficient.

Statements 1 AND 2:
Statement 1 allowed us to rewrite the question as Is 2/r > 0?
Since statement 2 tells us that r is positive, we can now answer the new target question with certainty (2/r is definitely greater than zero).

So, the answer is C

Hi Brent,

I'am getting the ans as A...don't know where I'm going wrong..

(r^2+2)/p > r

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

Ques rephrased...

Is r^2+2-rp > 0 (Is this step wrong)
Now, if r=p then,

r^2 + 2 - r^2 >0
i.e 2>0 (Sufficient)

Plz help me to find where I'm going wrong
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by dabral » Mon Jul 18, 2011 11:52 am
You can't multiply both sides of an inequality by a variable (p here) unless you know it is positive or negative.

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

Ques rephrased...

Is r^2+2-rp > 0 (Is this step wrong? Yes)

Here is a video explanation:
https://www.gmatquantum.com/shared-posts ... ty-15.html

Dabral
Free Video Explanations: 2021 GMAT OFFICIAL GUIDE.
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