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vaibhavjha
- Newbie | Next Rank: 10 Posts
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Consider first (1) alone.
It says P/Q > 0.
So (P > 0 and Q > 0) or (P < 0 and Q < 0).
Since P and Q are integers, P/Q <= (PQ)^2.
Take any example, let P = 2, Q = 3. So P/Q is 2/3.
Now (PQ)^2 = (2*3)^2 = 36.
Next let P = -2 and Q = -3. So P/Q is 2/3 and (PQ)^2 = 36
So P/Q <= (PQ)^2.
Or (1) alone is sufficient to answer the question.
Next consider (2) alone.
Q < 0.
Take P = -1, Q = -1. So P/Q = - 1/-1 = 1.
(PQ)^2 = (1)^2 = 1.
So P/Q = (PQ)^2.
Next let P = 1 and Q = -1. So P/Q = - 1/1 = -1. Also (PQ) ^2 = (1 *-1) ^2 = 1.
Again P/Q < (PQ)^2.
In any case P/Q <= (PQ)^2.
So answer to the main question is No.
Or (2) alone is also sufficient.
The correct answer is hence (D).
