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If x is an integer, is x a prime number? 1. x is a multiple

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If x is an integer, is x a prime number? 1. x is a multiple [#permalink]

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New post 30 Sep 2008, 10:58
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If \(x\) is an integer, is \(x\) a prime number?

1. \(x\) is a multiple of a prime number
2. \(x\) is a product of two integers

if x is a multiple of a prime number, doesn't it mean that x is NOT prime. isn't the first statement alone sufficient ? Am I missing something ??
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Re: DS: Is x prime ? [#permalink]

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New post 30 Sep 2008, 11:29
[quote="amitdgr"]If \(x\) is an integer, is \(x\) a prime number?

1. \(x\) is a multiple of a prime number
2. \(x\) is a product of two integers

if x is a multiple of a prime number, doesn't it mean that x is NOT prime. isn't the first statement alone sufficient ? Am I missing something ??[/quote]

A prime number is a multiple of itself. That is the reason, stmt1 cannot be sufficient.

From stmt1, x can be 2,3, 4,5, 6,7,8,9,10,11.......and hence not sufficient as x can be a prime or a non-prime.

From stmt2, again x can be anything (e.g. 2 = 2*1, 3 = 3*1, and so on).

Hence, to me, the answer should be E.

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Re: DS: Is x prime ? [#permalink]

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New post 30 Sep 2008, 11:32
i think the answer is E

1) x is a multiple of a prime

2 is the first multiple of 2: 2 is prime
4 is the second multiple of 2: 4 is not prime
insuff

2) x is a product of 2 int.

2*1 is prime
2*2 is not prime

together insufficient
same reasons as stmnt 2

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Re: DS: Is x prime ? [#permalink]

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New post 30 Sep 2008, 11:44
scthakur wrote:
amitdgr wrote:
If \(x\) is an integer, is \(x\) a prime number?

1. \(x\) is a multiple of a prime number
2. \(x\) is a product of two integers

if x is a multiple of a prime number, doesn't it mean that x is NOT prime. isn't the first statement alone sufficient ? Am I missing something ??


A prime number is a multiple of itself. That is the reason, stmt1 cannot be sufficient.

From stmt1, x can be 2,3, 4,5, 6,7,8,9,10,11.......and hence not sufficient as x can be a prime or a non-prime.

From stmt2, again x can be anything (e.g. 2 = 2*1, 3 = 3*1, and so on).

Hence, to me, the answer should be E.


FROM 1: X can be any integer > 1.
FROM 2: X can be any integer.

neither each alone nor togather is sufficient to answer.

//E//
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Re: DS: Is x prime ? [#permalink]

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New post 30 Sep 2008, 11:45
IMO E.

1. Consider x = 3, so multiple of 3 and PRIME ...
Consider x=6, not a prime....
1 is insuff

2. Consider x=3, product of two integers 1 and 3.
COnsider x=6, product of two integers 2 and 3
2 in insuff

SO A, D, B are out and left with C and E

Lets consider x=3 and x=6 again. suffice and insuffice for 1 and 2. Hence E.
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Re: DS: Is x prime ? [#permalink]

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New post 30 Sep 2008, 20:10
OA is E. Thank you for explanation guys ! I fell into the trap designed in this question.
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Re: DS: Is x prime ?   [#permalink] 30 Sep 2008, 20:10
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