Number of Integer Solutions to Inequality

CAT 2017 Slot 1 · Quantitative Ability · Hard · Inequalities

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

Answer

Explanation

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

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Number of Integer Solutions to Inequality

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