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# If p is an integer, is q an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 47898
If p is an integer, is q an integer?  [#permalink]

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24 Dec 2017, 01:27
00:00

Difficulty:

35% (medium)

Question Stats:

76% (00:41) correct 24% (00:36) wrong based on 33 sessions

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If p is an integer, is q an integer?

(1) pq is an integer.
(2) p + q is not an integer.

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Intern
Joined: 07 Oct 2017
Posts: 47
Re: If p is an integer, is q an integer?  [#permalink]

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24 Dec 2017, 01:33
Imo B

St1:
p=4 q=4
Yes

p=4 q=1/4
No

Not sufficient

St2:
Integer + q= not integer
Therefore, q can never be an integer
Sufficient

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Manager
Joined: 05 Oct 2014
Posts: 60
Location: India
Concentration: General Management, Strategy
GMAT 1: 580 Q41 V28
GPA: 3.8
WE: Project Management (Energy and Utilities)
Re: If p is an integer, is q an integer?  [#permalink]

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24 Dec 2017, 07:19
Statement 1: pq is an integer.
Lets say p=2
Thus p X q = 2 X 2, q =integer
p X q = 2 X 1/2, q =non- integer, INSUFFICIENT
Statement 2: p + q is not an integer
P is Integer, So Q must be non-integer. SUFFICIENT
Manager
Joined: 24 Nov 2016
Posts: 152
Re: If p is an integer, is q an integer?  [#permalink]

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24 Dec 2017, 13:55
1
Bunuel wrote:
If p is an integer, is q an integer?

(1) pq is an integer.
(2) p + q is not an integer.

(1) pq is an integer. If p = 2, q = 1/2 (not-integer), $$pq=2*1/2=1=integer$$, answer is no. If p = 2 q = 3, $$pq=2*3=6=integer$$ answer is a yes; insufficient.

(2) p + q is not an integer. If $$p+q = non-integer$$ and p = integer, then q must be a non-integer; sufficient.

Re: If p is an integer, is q an integer? &nbs [#permalink] 24 Dec 2017, 13:55
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