The GATE Grind

GATE 2023 XH5 (Psychology) – Question 19

Reasoning and Comprehension · Quantitative reasoning · 2 marks · Multiple choice

Select the correct relation between E and F.

$E = \frac{x}{1+x}$ and $F = \frac{-x}{1-x}$, $x > 1$

  1. E > F
  2. E < F
  3. E = F
  4. E < -F

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) E < F

Explanation

For $x > 1$, $F = \frac{-x}{1-x} = \frac{x}{x-1}$, which is positive. Both fractions have the same numerator, and $x - 1 < x + 1$, so $F = \frac{x}{x-1} > \frac{x}{x+1} = E$.