Number of Integer Solutions to Inequality

CAT 2017 Slot 1 · QA · Hard · Inequalities

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For how many integers nn, will the inequality (n−5)(n−10)−3(n−2)≤0(n - 5)(n - 10) - 3(n - 2) \le 0 be satisfied?

Answer

11

Explanation

Expand: n2−15n+50−3n+6≤0n^2 - 15n + 50 - 3n + 6 \le 0 n2−18n+56≤0n^2 - 18n + 56 \le 0 (n−4)(n−14)≤0(n - 4)(n - 14) \le 0 Integers satisfying 4≤n≤144 \le n \le 14. Number of integers = 14−4+1=1114 - 4 + 1 = 11.

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