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

Question

(1) pq = 2(p+q)

(2) p – q = 0

Cutemon · Answer

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.

Answer is A

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Cutemon · Answer

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.

Answer is A

Posted from my mobile device

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We are asked if  (p-2) (q-2)  is square of an integer or not 
  (p-2) (q-2)=pq-2p-2q+4=pq-2(p+q)+4  
 We are asked  if  pq-2(p+q)+4  is square of an integer or not

Statement 1:    pq = 2(p+q) 
   pq-2(p+q)+4 
 =2(p+q)-2(p+q)+4 
 =4  
 We know 4 is square of integer 2 
 Thus,  statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2:    p – q = 0 
   p-q=0  means  p=q  
  pq-2(p+q)+4 
 =p^2-2(p+p)+4 
 =p^2-4p+4 
 =p^2-4(p-1)  
 We are not sure if  p^2-4(p-1)  is square of an integer or not 
 Thus,  statement 2 alone is not sufficient

Hence the right answer is    Option A

NickelMue · Answer

I would argue with this, as the question is not if (p-2)(q-2) is a perfect square (defined as the product of two positive integers), but simply if it is the quare of an integer (nowhere defined if positive or anything alike). And the last time I checked, 0 is a an integer and 0 is also the square of 0 (0*0=0)...

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

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GMAT Data Sufficiency (DS) Questions

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

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