CA Foundation · Quantitative Aptitude · Linear Inequalities
Consider the feasible region defined by x + y ≤ 8, x − y ≥ 0, x ≥ 0 and y ≥ 0. How many points (x, y) with both x and y non-negative integers lie in this region?
The region contains 25 integer points. Counting by y from 0 to 4 with y ≤ x ≤ 8 − y gives 9, 7, 5, 3 and 1 points respectively, and these add up to 25. Values of y above 4 leave no valid x.
- A15
- B25
- C20Correct
- D18
Explanation
We need 0 ≤ y ≤ x and x + y ≤ 8. For y = 0, x runs 0 to 8: 9 points. For y = 1, x runs 1 to 7: 7 points. For y = 2, x runs 2 to 6: 5 points. For y = 3, x runs 3 to 5: 3 points. For y = 4, x runs 4 to 4: 1 point. Total = 9+7+5+3+1 = 25.
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