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

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