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CAT 2024 Slot 1 · Quant · Inequalities and Modulus · medium

Find the number of integers x satisfying the inequality 2x² − 11x + 12 ≤ 0.

Single correct option

Find the number of integers x satisfying the inequality 2x² − 11x + 12 ≤ 0.
  1. A. 2
  2. B. 3
  3. C. 4
  4. D. 5
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Answer: (B) 3

Solve 2x²−11x+12 = 0: x = [11 ± √(121−96)]/4 = [11±5]/4, giving x = 4 or x = 1.5. Since the parabola opens upward, the inequality holds between the roots: 1.5 ≤ x ≤ 4. Integers in this range: 2, 3, 4 — a total of 3 integers.
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Original question written in the CAT 2024 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake