Brent@GMATPrepNow wrote:Here's a question I just made up.
Difficulty level: 700ish
If 2^m = 5 and 5^(1/n) = 3, then (3^n)/2^(-2m) =
A) 1/25
B) 1/5
C) 5
D) 25
E) 125
An alternate approach is to BALLPARK.
Since the answer choices are very spread out, we can approximate with integer values.
Since 2² = 4, 2^m = 5 implies that m ≈ 2.
Since √5 ≈ 2.24, 5^(1/n) = 3 implies that n ≈ 2.
Thus:
(3^n)/2^(-2m) ≈ (3²)/2¯� = (9)(16) = 144.
Only
E is viable.
The correct answer is
E.
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