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Bunuel
If n and m are positive, is m < 9 < n ?

(1) m < n and mn = 81.

(2) m^2 < 81 < n^2

Analyzing the question:
Note information like m > n or 9 > n is automatically sufficient as we would answer "no" to the question.

Statement 1:
If m = n was true we would have m = n = 9 but since m must be smaller than n, we must have m < 9 and n > 9. Hence m = 3 or 1. Sufficient.

Statement 2:
We know m and n are both positive so we are allowed to square root one inequality at a time. The left part of the inequality simplifies to m < 9, the right side simplifies to 9 < n.
Combine again to get m < 9 < n. Sufficient.

Ans: D
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Rumsus
Why can't we take 3 and 27 as m and n respectively ?

Even if you take m as 3 and n as 27. It satisfies the condition- m<9<n

So A is sufficient.

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