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# If x is a positive interger greater than 1, does x have any

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Manager
Joined: 22 Feb 2006
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If x is a positive interger greater than 1, does x have any [#permalink]  02 Apr 2006, 12:41
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If x is a positive interger greater than 1, does x have any integer factor n such that 1 < n < x?

1) x is even

2) 47 < x < 53

Thanks!
Intern
Joined: 02 Jun 2005
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B

X can be anything from 48 to 52. Each value in this range has a factor > 1.
Manager
Joined: 21 Dec 2005
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Kudos [?]: 1 [0], given: 0

E

Statement 1 has factors such that both x<n<x exist

Statement 2 has the same factors too. For example, 48 is a factor of x such that n<48 is not satisfied.

Statement 1 and 2 put together is not sufficient either, thus answer E.
Manager
Joined: 20 Nov 2004
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jodeci wrote:
E

For example, 48 is a factor of x such that n<48 is not satisfied.

The question is not whether the condition is true for ALL factors,
but if it's true for AT LEAST ONE of the factors. Since 48, 49, 50, 51 and
52 all have at least one factor with 1 < n < x, (2) is sufficient.

(1) is not sufficient since 2 has no factor smaller than 2 and bigger
than 1.

So as khush stated, it is B.
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1) x is even. Smallest possible integer = 2. Factors = 1 and 2. So x does not have an integer factor between 1 and x.

But if x = 6, then factors = 1,2,3,6 and there are factors between 1 and x.

Insufficient.

2) x can be 48-52.

48 will have factors between 1 and 48.
49 will have factors between 1 and 49
50 will have factors between 1 and 50
51 will have factors between 1 and 51
52 will have factors between 1 and 52.

Sufficient.

Ans B
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