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# If m is a positive integer, is √m a prime number?

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Director
Joined: 18 Feb 2019
Posts: 607
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
If m is a positive integer, is √m a prime number?  [#permalink]

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23 Mar 2019, 22:46
00:00

Difficulty:

45% (medium)

Question Stats:

58% (01:26) correct 42% (01:33) wrong based on 12 sessions

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If m is a positive integer, is √m a prime number?

I. √m leaves a remainder of 1 when divided by 6
II. m has 3 factors
Math Expert
Joined: 02 Aug 2009
Posts: 8320
Re: If m is a positive integer, is √m a prime number?  [#permalink]

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23 Mar 2019, 22:54
If m is a positive integer, is √m a prime number?

I. √m leaves a remainder of 1 when divided by 6
That is √m=6x+1
If a number is a prime number greater than 3, it will surely be of the form 6k+1 or 6k-1, but give versa is not true.
For example, if √m could be 7, 13, that is a prime number, but √m as 25=6*4+1 or 49, it is not aprime .
Insufficient

II. m has 3 factors
Any number having three factors will always be a perfect square of a prime number.
The three factors will be 1√m and m..
Thus √m is a prime number.
Sufficient

B
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Re: If m is a positive integer, is √m a prime number?   [#permalink] 23 Mar 2019, 22:54
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