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Source: — Data Sufficiency |
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by vk_vinayak » Wed Aug 29, 2012 11:14 am
nroy347 wrote:If p is a positive integer is P > 4 ?
(1)p^4 = 246
(2)(p^2 -1)(p-4) = 0
After I solved I got A but it was D...
1. 4^4 = 256 => So, if p^4 = 246 then p is less than 4. SUF

2. (p^2 -1)(p-4) = 0 => (p^2 -1)=0 OR (p-4)=0

If(p^2 -1)=0 then p=+1 or -1

If (p-4)=0 then p=4. So, in both the cases p<4. SUF

Ans D.

P.S: Question says p is a positive integer. But according A, p is not an integer. So, I think the option A should be p^4 = 256.
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by nisagl750 » Thu Aug 30, 2012 2:36 am
nroy347 wrote:If p is a positive integer is P > 4 ?
(1)p^4 = 246
(2)(p^2 -1)(p-4) = 0
After I solved I got A but it was D...
P>4 means Is P>=5 ?
Statement1: P^4 = 246 that means P<4, as 4^4 = 256 - Sufficient
Statement2: (P^2 -1)(p-4) = (p-1)(p+1)(p-4)=0
So P=1, -1, 4
All the values are less than 5
Even P=4 means that P is at least not greater than 4
Sufficient

So, D
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by Brent@GMATPrepNow » Fri Aug 31, 2012 5:31 am
nroy347 wrote:If p is a positive integer is P > 4 ?
(1)p^4 = 246
(2)(p^2 -1)(p-4) = 0
After I solved I got A but it was D...
This could never be a true GMAT question since statement 1 contradicts the given statement that p is an integer. There is no integer such that p^4 = 246

Aside: Statement 2 is great. Notice that the equation yields 3 different values of p (p= -1, 1, or 4). Since we're told that p is a positive integer, we can rule out p = -1, but we're still left with p = 1 or 4.
At this point, many students will think, "Well, since p can have 2 different values, statement 2 is not sufficient. However, notice that the question doesn't ask "What is the value of p?" It asks, "Is p > 4?" Since both possible values of p are less than 4, we can answer the target question with certainty (no, p is definitely not greater than 4), even though we don't actually know the value of p.

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by nroy347 » Sun Sep 09, 2012 1:19 am
But if we would change the question to - 2) (p^2-1)(p-4) > 0 how would the answer change...
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by neelgandham » Sun Sep 09, 2012 1:30 am
If 2) (p^2-1)(p-4) > 0, then
p<-1 or p>4. So, statement II would be insufficient to answer the question and the answer would be A
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