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CA Foundation · Quantitative Aptitude · Linear Inequalities

Consider the system x + y ≤ 6, x − y ≥ 2, y ≥ 0, with x and y integers. How many ordered pairs (x, y) satisfy all three conditions?

There are 9 integer pairs. For each y, x runs from y + 2 to 6 − y: y = 0 gives 5 values, y = 1 gives 3 values, y = 2 gives 1 value, and larger y gives none. The sum is 5 + 3 + 1 = 9.

  1. A8
  2. B9
  3. C10Correct
  4. D12

Explanation

For each y ≥ 0, x must satisfy y + 2 ≤ x ≤ 6 − y. y = 0: x = 2 to 6 gives 5 values. y = 1: x = 3 to 5 gives 3 values. y = 2: x = 4 to 4 gives 1 value. y = 3: x from 5 to 3 gives none. Total is 5 + 3 + 1 = 9.

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