If n and m are positive, is m

Question

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

(1) m < n and mn = 81.

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

Archit3110 · Answer

#1
we can say that n=81 and m=1 so sufficient
#2
squaring both sides we get m < 9 < n 
sufficieint
IMO D

Rumsus · Answer

Why can't we take 3 and 27 as m and n respectively ?

TestPrepUnlimited · Answer

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

Chethan92 · Answer

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

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