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GRE Quantitative Reasoning QUESTION #8178
Question 1

Given the equation $\dfrac{1-x}{x-1} = \dfrac{1}{x}$, compare:

Quantity A: $x$

Quantity B: $-\dfrac{1}{2}$

  • 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 $\dfrac{1-x}{x-1}$: note that $1 - x = -(x-1)$, so $\dfrac{1-x}{x-1} = -1$ (for $x \neq 1$).

The equation becomes: $-1 = \dfrac{1}{x}$

$x = -1$

Quantity A $= -1$. Quantity B $= -\dfrac{1}{2}$.

Since $-1 < -\dfrac{1}{2}$, Quantity B is greater.