If p is an integer, is q an integer?

Question

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

sumit411 · Answer

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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merajul · Answer

Answer is B.
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

exc4libur · Answer

(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.

(B) is the answer.

Salsanousi · Answer

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.

If p is an integer, is q an integer?

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GMAT Data Sufficiency (DS) Questions

If p is an integer, is q an integer?

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