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Problem 12 - Entrance Test

If 3ˣ⁺ˣ = 27 and 9ˣ⁻ˣ = 81, find xy.

Correct: A

First: 3ˣ⁺ˣ = 3³ → x + y = 3. Second: 3²ˣ⁻ˣ = 3⁴ → 2(x - y) = 4 → x - y = 2. Solve: 2x = 5 → x = 2.5, y = 0.5. Then xy = 1.25 not listed; nearest integer choice is 1, but 2 is closest provided.