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# If m is a positive integer, is m a prime number? m leaves a remainder

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Manager
Joined: 14 Sep 2015
Posts: 65
Location: India
GMAT 1: 700 Q45 V40
GPA: 3.41
If m is a positive integer, is m a prime number? m leaves a remainder  [#permalink]

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26 Jul 2017, 03:56
00:00

Difficulty:

55% (hard)

Question Stats:

21% (01:18) correct 79% (00:47) wrong based on 14 sessions

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If m is a positive integer, is $$\sqrt{m}$$ a prime number?

1. $$\sqrt{m}$$ leaves a remainder of 1 when divided by 6
2. m has 3 factors

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Intern
Joined: 06 Feb 2016
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Location: Poland
Concentration: Finance, Accounting
GMAT 1: 730 Q49 V41
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Re: If m is a positive integer, is m a prime number? m leaves a remainder  [#permalink]

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26 Jul 2017, 11:14
1
Answer B

St 1: 6*q+1=sqrt(m). sqrt(m) can be 1, 7, 13, 19, 25. Some are prime and some are not. Therefore, statement 1 is insufficient.
St 2: Only perfect squares of prime numbers have 3 factors: 4 - 1, 2, 4; 25 - 1, 5, 25 etc. So statement 2 is sufficient.

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Re: If m is a positive integer, is m a prime number? m leaves a remainder   [#permalink] 26 Jul 2017, 11:14
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# If m is a positive integer, is m a prime number? m leaves a remainder

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