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Inequality DS ; Little help

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by soni_pallavi » Sat Nov 17, 2012 5:29 am
Q) If p is a positive is p > 4 ?

1) p^4 = 256

2) (p^2 - 1)(p - 4) >0

I get Statement 1 is sufficient.But how's statement 2 sufficient ? Answer is D

Thanks
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Source: — Data Sufficiency |
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by jkaustubh » Sat Nov 17, 2012 7:16 am
Statement 2 is not sufficient

as the inequality can be satisfied by the following ranges

p-> (-1,1)U(4,infinity)

for eg.
P=0 satisfies the inequality and also any value of p greater than 4

hence this statement is insufficient.

The OA should be A and not D

what is the source of the problem??
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by soni_pallavi » Sat Nov 17, 2012 8:11 am
Its from a mock test given to us at an institute...

I chose A ; the answer at the back is D.

Need an expert's advice to clarify this.
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by Brent@GMATPrepNow » Sat Nov 17, 2012 8:52 am
soni_pallavi wrote:Q) If p is a positive is p > 4 ?
1) p^4 = 256
2) (p^2 - 1)(p - 4) > 0
Target question: Is p > 4 ?

Statement 1: p^4 = 256
256 = (4)(4)(4)(4)
So, if p^4 = 256 (and p is positive), then we can be certain that p = 4
Once we know the value of p, we can answer the target question with certainty, which means statement 1 is SUFFICIENT

Statement 2: (p^2 - 1)(p - 4) > 0
Factor to get: (p-1)(p+1)(p-4) > 0
There are several values of p that meet this condition. Here are two:
Case a: p = 1/2 in which case p is not greater than 4
Case b: p = 5 in which case p is greater than 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Aside: jkaustubh noted that p=0 satisfies the given inequality, but the question tells us that p is positive. As such, p cannot equal 0

Answer = A

Cheers,
Brent
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by jkaustubh » Sat Nov 17, 2012 9:12 am
Thanks Brent for reminding me that 0 is not positive. I always make this mistake.

Thank you
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by soni_pallavi » Fri Nov 23, 2012 1:41 am
Hi Brent

I just noticed I forgot to mention that in the question,P is a positive integer...Hence the answer should infact be D :)
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by Brent@GMATPrepNow » Fri Nov 23, 2012 7:25 am
soni_pallavi wrote:Hi Brent

I just noticed I forgot to mention that in the question,P is a positive integer...Hence the answer should infact be D :)
Agreed. If the question had read...

If p is a positive integer, is p > 4 ?
1) p^4 = 256
2) (p^2 - 1)(p - 4) > 0

...the answer would have been D

Cheers,
Brent
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