CA Foundation · Quantitative Aptitude · Linear Inequalities
How many ordered pairs (x, y) of positive integers satisfy 3x + 2y ≤ 12?
There are 8 such pairs. For x = 1, 2 and 3 the allowed positive values of y are 4, 3 and 1 respectively, and x = 4 leaves no positive y. Adding gives 8. Counting non-negative solutions instead would wrongly include zero values and give 19.
- A6
- B8Correct
- C10
- D19
Explanation
Take x = 1: 2y ≤ 9, so y = 1 to 4 (4 pairs). For x = 2: 2y ≤ 6, so y = 1 to 3 (3 pairs). For x = 3: 2y ≤ 3, so y = 1 (1 pair). For x = 4, y would have to be 0, which is not positive. Total = 4 + 3 + 1 = 8. The figure 19 counts non-negative integer pairs, including zeros.
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