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CAT 2023 Slot 2 · Quant · Inequalities and Modulus · medium

How many integers x satisfy both (x−3)(x−7) ≤ 0 and x² − 9 > 0?

Single correct option

How many integers x satisfy both (x−3)(x−7) ≤ 0 and x² − 9 > 0?
  1. A. 3
  2. B. 4
  3. C. 5
  4. D. 6
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Answer: (B) 4

(x−3)(x−7) ≤ 0 gives 3 ≤ x ≤ 7. x² − 9 > 0 gives x < −3 or x > 3 (this excludes x = 3 since equality gives 0, not >0). Combining: 3 < x ≤ 7, so integers are 4, 5, 6, 7 — a total of 4 values.
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Original question written in the CAT 2023 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake