# CAT 1997 | Question: 116

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$P$ and $Q$ are two integers such that $P \times Q = 64$. Which of the following cannot be the value of $P+Q$?

1. $20$
2. $65$
3. $16$
4. $35$

Possible values of P,Q are (1,64), (2,32), (4,16), (8,8)

Possible values of P+Q are 65, 34, 20, 16

35 is not possible. Hence, option D would be the answer

Factor of $64$ are: $1,2,4,8,16,32,64$.

It is given that $P\times Q=64$. The number of pairs of $(P\times Q)=64$ are:

 Options $(P\times Q)=64$ $P+Q$ A $16\times 4=64$ $20$ B $64\times 1=64$ $65$ C $8\times 8=64$ $16$ D $32\times 2=64$ $34$

So from above Option (D) is not possible.

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