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# Is P a prime number?

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Math Expert
Joined: 02 Aug 2009
Posts: 7757
Is P a prime number?  [#permalink]

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04 Dec 2016, 19:29
1
2
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Difficulty:

65% (hard)

Question Stats:

36% (00:55) correct 64% (00:59) wrong based on 59 sessions

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Is P a prime number, if P is an integer?

(1) P has odd number of factors.
(2) P = R^2

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Joined: 12 Aug 2015
Posts: 2610
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: Is P a prime number?  [#permalink]

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04 Dec 2016, 19:44
1
Great Question chetan2u

Here is my solution ->

Given info=> P is an integer
We need to see if its prime or not

Statement 1
P has odd number of factors.
Rule -> A perfect square has odd number of factors
And conversely -> Any number that has odd number of factors must be a perfect square.
So So P can be => {1,4,9,16,25}
Hence P=x^2 where x is an integer.
Its Safe to say that P will never be prime.
Hence Sufficient

Statement 2
Here P=R^2
But no clue of R is given.
If R=√2 => P=2 which is prime
if R=2 => P=4 which is not a prime number.

Hence This statement is not sufficient.

Hence A

Also Can you post a solution to this one-> the-units-digit-of-n-p-and-n-q-are-6-and-4-respectively-what-is-the-229444.html

Regards
Stone Cold

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Re: Is P a prime number?  [#permalink]

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08 Jan 2019, 04:29
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Re: Is P a prime number?   [#permalink] 08 Jan 2019, 04:29
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