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

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Math Expert
Joined: 02 Sep 2009
Posts: 50730
If p is an integer, is q an integer?  [#permalink]

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24 Dec 2017, 00:27
00:00

Difficulty:

15% (low)

Question Stats:

78% (00:43) correct 22% (00:38) wrong based on 55 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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Senior Manager
Joined: 07 Oct 2017
Posts: 265
Re: If p is an integer, is q an integer?  [#permalink]

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24 Dec 2017, 00:33
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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Re: If p is an integer, is q an integer?  [#permalink]

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24 Dec 2017, 06:19
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
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Re: If p is an integer, is q an integer?  [#permalink]

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24 Dec 2017, 12:55
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.

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Re: If p is an integer, is q an integer?  [#permalink]

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16 Nov 2018, 13:37
Bunuel wrote:
If p is an integer, is q an integer?

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

Statement 1)

p * q = integer.

let p = 3
q = 1

yes q is integer.

However, let q = 1/3

3 * 1/3 = 1

q is not an integer. Insufficient.

p + q = not integer.

if q were an integer, it would not satisfy the condition of the second statement so it must be non-integer.

B is sufficient.
Re: If p is an integer, is q an integer? &nbs [#permalink] 16 Nov 2018, 13:37
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