Home › MCQs › GRE Quantitative Reasoning › Question #8186
Back to Questions
GRE Quantitative Reasoning QUESTION #8186
Question 1

If $0 < a < 1 < b$, which inequality correctly describes the reciprocals of $a$ and $b$?

  • $1 < \dfrac{1}{a} < \dfrac{1}{b}$
  • $\dfrac{1}{a} < 1 < \dfrac{1}{b}$
  • $\dfrac{1}{b} < \dfrac{1}{a} < 1$
  • $\dfrac{1}{b} < 1 < \dfrac{1}{a}$✔️
Correct Answer Explanation

Since $0 < a < 1$: taking the reciprocal reverses the inequality, so $\dfrac{1}{a} > 1$.

Since $b > 1$: taking the reciprocal reverses the inequality, so $\dfrac{1}{b} < 1$.

Therefore: $\dfrac{1}{b} < 1 < \dfrac{1}{a}$.

For example, $a = 0.5,\ b = 2$: $\dfrac{1}{a} = 2,\ \dfrac{1}{b} = 0.5$. Indeed $0.5 < 1 < 2$. ✓