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# Is (p-2) (q-2) square of an integer?

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Senior Manager
Joined: 18 Feb 2019
Posts: 284
Location: India
GMAT 1: 490 Q47 V13
GPA: 3.6
Is (p-2) (q-2) square of an integer?  [#permalink]

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29 Mar 2019, 12:42
1
1
00:00

Difficulty:

65% (hard)

Question Stats:

45% (01:35) correct 55% (01:50) wrong based on 20 sessions

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Is (p-2) (q-2) square of an integer?

(1) pq = 2(p+q)

(2) p – q = 0
Intern
Joined: 12 Jul 2016
Posts: 17
Location: India
GMAT 1: 690 Q50 V32
GPA: 3.74
Re: Is (p-2) (q-2) square of an integer?  [#permalink]

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29 Mar 2019, 14:17
5
Statement 1

pq = 2(p+q)
So for only value of 4 for both p and q, the condition satisfy.
i.e. 4*4 = 2(4+4)
16 = 16
Statement 1 is sufficient.

Statement 2:
p - q = 0
This implies that p and q are of same value and same sign.There can be any range of values for p and q, i.e. (2,2), (4,4), (100,100).
But for p and q having value 2, the condition (p-2)(q-2)=square of an integer doesn't satisfy, as 0*0 is not a perfect square.
Statement 2 is insufficient condition.

Posted from my mobile device
Intern
Joined: 12 Jul 2016
Posts: 17
Location: India
GMAT 1: 690 Q50 V32
GPA: 3.74
Re: Is (p-2) (q-2) square of an integer?  [#permalink]

### Show Tags

29 Mar 2019, 14:19
1
Statement 1

pq = 2(p+q)
So for only value of 4 for both p and q, the condition satisfy.
i.e. 4*4 = 2(4+4)
16 = 16
Statement 1 is sufficient.

Statement 2:
p - q = 0
This implies that p and q are of same value and same sign.There can be any range of values for p and q, i.e. (2,2), (4,4), (100,100).
But for p and q having value 2, the condition (p-2)(q-2)=square of an integer doesn't satisfy, as 0*0 is not a perfect square.
Statement 2 is insufficient condition.

Posted from my mobile device
Re: Is (p-2) (q-2) square of an integer?   [#permalink] 29 Mar 2019, 14:19
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