Question

For how many integers n, will the inequality $(n – 5) (n – 10) – 3(n – 2) ≤ 0$ be satisfied?

• A. 11
• B. 14
• C. 21
• D. 13

Answer 1

Answer: (A)

11

Answer 2

The inequality $(n−5)(n−10)−3(n−2)≤0$ can be expressed as $n^2−18n+56≤0$, further simplified to $(n−4)(n−14)≤0.$
Since n is an integer, it can take values from 4 to 14 (inclusive), resulting in a total of 11 possible values.