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is y prime number?

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is y prime number?  [#permalink]

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New post 26 Jul 2018, 22:52
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A
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E

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Question Stats:

50% (00:52) correct 50% (00:19) wrong based on 4 sessions

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is y prime number?

1) \(y^2\) has exactly 3 factors.
2) y is of form 6q+1
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Re: is y prime number?  [#permalink]

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New post 26 Jul 2018, 23:00
To determine whether y is a prime number

Statement 1

\(y^2\) has exactly 3 factors

=> y * y has exactly 3 factors

=> the factors are 1, y and \(y^2\)

=> y must be a prime number because if y is not prime then there exist a factor other that 1 and y. Lets call it x

=> x must be a factor of \(y^2\) contradicting the given information that \(y^2\) has only 3 factors

=> y doesn't have any factor x such that 1 < x < y

=> y is a prime number

Statement 2

y is of the form 6q + 1

=> y = 6(2) + 1 = 13 a prime number

=> y = 6(4) + 1 = 25 not a prime number

Statement 2 is insufficient

Hence option A
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Re: is y prime number?  [#permalink]

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New post 26 Jul 2018, 23:02
1
is y prime number?

1) \(y^2\) has exactly 3 factors.
number of factors of \(y^2\) is \((2+1)=3\)
possible only when y is prime...
for knowledge the factors are 1, y and y^2
suff

2) y is of form 6q+1
all prime numbers are of the form \(6K+1\) or \(6K-1\)
but vice versa may not be true..
\(k=1, 6*1+1=7...\) prime
\(k=4, 6*4+1=25...\) not a prime
insuff

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: is y prime number? &nbs [#permalink] 26 Jul 2018, 23:02
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