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# If n = p/q where p and q are non zero integers, is n an

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Retired Moderator
Joined: 18 Jul 2008
Posts: 920
If n = p/q where p and q are non zero integers, is n an [#permalink]

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30 Nov 2008, 21:45
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If n = p/q where p and q are non zero integers, is n an integer?

(1) n^2 is an integer

(2) (2n+4)/2 is an integer

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

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Director
Joined: 14 Aug 2007
Posts: 704
Re: DS: Is n an integer? [#permalink]

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30 Nov 2008, 22:51
If n = p/q where p and q are non zero integers, is n an integer?

(1) n^2 is an integer

(2) (2n+4)/2 is an integer

Tricky Q!

1) n^2 = Integer, n = sqrt(Integer)

Square roots of integers that are not perfect squares are always irrational numbers i.e Square roots can either be integers or irrational numbers (i.e later meaning that they can not be expressed as p/q)

since n can be expressed as p/q, it must be an integer. and thus 1 is sufficient.

2) is straightforward n+1/2 = integer i.e n = 2*integer - 1 and thus n should be integer.

D for me.
Manager
Joined: 28 Apr 2008
Posts: 110
Re: DS: Is n an integer? [#permalink]

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01 Dec 2008, 04:05
D

1-->(p/q)^2= n^2, and n^2 is an integer

we know that p and q are non zero integers.

we also know that any non integer root of an integer is a irrational number, i.e., a number which cannot be expressed as a fraction m/n, where m and n are integers.

thus, p/q, which is the root of n^2, must be an integer becaus it can be expressed as a fraction p/q, where p and q are integers.

==>1 is suff

2--> suff

D

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: DS: Is n an integer?   [#permalink] 01 Dec 2008, 04:05
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