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Re: Is (p-2) (q-2) square of an integer? [#permalink]
Expert Reply
kiran120680 wrote:
Is (p-2) (q-2) square of an integer?

(1) pq = 2(p+q)

(2) p – q = 0

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
GMAT Club Bot
Re: Is (p-2) (q-2) square of an integer? [#permalink]
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