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CA Foundation · Quantitative Aptitude · Linear Inequalities

The solution set of the pair of inequalities |x − 2| > 3 and x² ≤ 36, where x is real, is:

The solution set is [−6, −1) ∪ (5, 6]. The condition |x − 2| > 3 gives x < −1 or x > 5, while x² ≤ 36 gives −6 ≤ x ≤ 6. Their intersection keeps −6 and 6 but excludes −1 and 5.

  1. A[−6, −1) ∪ (5, 6]Correct
  2. B(−6, −1) ∪ (5, 6)
  3. C[−6, 6]
  4. D[−1, 5]

Explanation

|x − 2| > 3 gives x < −1 or x > 5. x² ≤ 36 gives −6 ≤ x ≤ 6. Intersecting gives −6 ≤ x < −1 or 5 < x ≤ 6. Option (−6,−1) ∪ (5,6) wrongly drops the included endpoints ±6. Option [−1, 5] is the solution of |x − 2| ≤ 3, the opposite case.

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