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Problem 12 - Entrance Test
If 3ˣ⁺ˣ = 27 and 9ˣ⁻ˣ = 81, find xy.
A. 2
B. 3
C. 4
D. 5
E. 6
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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.