If 3^(2x-1) = 27^y and x and y are positive integers, which of the following must be true?

A 2x - 1 = 3y

B 2x - 1 = 27y

C 3x - 1 = 9y

D 9x - 3 = y

✓ Correct Answer: Option A

Rewrite 27 as 3^3. The equation becomes 3^(2x-1) = (3^3)^y. Using exponent rules, this simplifies to 3^(2x-1) = 3^(3y). Since the bases are equal, the exponents must be equal: 2x - 1 = 3y.

💡 Why is A) the correct answer?

The correct answer to the question "If 3^(2x-1) = 27^y and x and y are positive integers, which of the following must be true?" is Option A: 2x - 1 = 3y.

The other options — B) 2x - 1 = 27y, C) 3x - 1 = 9y, D) 9x - 3 = y — are incorrect for this GRE Exam Prep question. As explained above: Rewrite 27 as 3^3. The equation becomes 3^(2x-1) = (3^3)^y. Using exponent rules, this simplifies to 3^(2x-1) = 3^(3y). Since the bases are equal, the exponents must be equal: 2x - 1 = 3y.

📚 About This GRE Exam Prep Practice Question

This 4-level GRE Exam Prep question from the Quantitative Reasoning topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free GRE Exam Prep practice test or use flashcards for spaced repetition review.

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If 3^(2x-1) = 27^y and x and y are positive integers, which of the following must be true?

✓ Correct Answer: Option A

📚 About This GRE Exam Prep Practice Question

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