Home › MCQs › GRE Quantitative Reasoning › Question #8159
Back to Questions
GRE Quantitative Reasoning QUESTION #8159
Question 1

Let $x$ and $m$ be positive numbers, where $m$ is a multiple of 3. Compare:

Quantity A: $\dfrac{x^m}{x^3}$

Quantity B: $x^{m/3}$

  • Quantity A is greater
  • Quantity B is greater
  • The two quantities are equal
  • The relationship cannot be determined from the information given✔️
Correct Answer Explanation

Simplify Quantity A: $\dfrac{x^m}{x^3} = x^{m-3}$.

Quantity B: $x^{m/3}$.

We need to compare $x^{m-3}$ with $x^{m/3}$. The relationship depends on the base $x$ and the exponent comparison.

Case 1: $x = 1$. Both quantities $= 1$. Equal.

Case 2: $x = 2,\ m = 6$. Qty A $= 2^{6-3} = 2^3 = 8$. Qty B $= 2^{6/3} = 2^2 = 4$. A > B.

Case 3: $x = 2,\ m = 3$. Qty A $= 2^{3-3} = 2^0 = 1$. Qty B $= 2^{3/3} = 2^1 = 2$. B > A.

Because different values give different results, the relationship cannot be determined.