CA Foundation · Quantitative Aptitude · Linear Inequalities
Consider the region defined by 2x + 3y ≤ 12, x ≥ 0 and y ≥ 0. Which of the following points lies in this solution region?
The point (3, 2) lies in the region. Substituting it gives 2(3) + 3(2) = 12, which satisfies the non-strict inequality 2x + 3y ≤ 12 as a boundary point. The other points give 15 or 16, exceeding 12, so they fall outside the region.
- A(5, 2)
- B(2, 4)
- C(3, 2)Correct
- D(0, 5)
Explanation
Substitute each point into 2x + 3y. (5, 2) gives 16, (2, 4) gives 16 and (0, 5) gives 15, all greater than 12. (3, 2) gives 6 + 6 = 12, which satisfies ≤ because boundary points are included for a non-strict inequality.
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