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GRE Quantitative Reasoning QUESTION #8105
Question 1

Given that $x \neq 0$, compare the two quantities below.

Column A: $\dfrac{x}{|x|}$

Column B: $1$

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

The expression $\dfrac{x}{|x|}$ is the sign function of $x$:

  • If $x > 0$: $\dfrac{x}{|x|} = \dfrac{x}{x} = 1$ → equal to Column B
  • If $x < 0$: $\dfrac{x}{|x|} = \dfrac{x}{-x} = -1$ → less than Column B

Since $x$ can be positive or negative, and we get different results, the relationship cannot be determined from the information given.