Number of Integer Solutions to Inequality

CAT 2017 Slot 1 · Quantitative Ability · Hard · Inequalities

This is a hard Quantitative Ability question from the CAT 2017 Slot 1 paper. It tests Inequalities. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

For how many integers nn, will the inequality (n5)(n10)3(n2)0(n - 5)(n - 10) - 3(n - 2) \le 0 be satisfied?

Answer

11

Explanation

Expand: n215n+503n+60n^2 - 15n + 50 - 3n + 6 \le 0 n218n+560n^2 - 18n + 56 \le 0 (n4)(n14)0(n - 4)(n - 14) \le 0 Integers satisfying 4n144 \le n \le 14. Number of integers = 144+1=1114 - 4 + 1 = 11.

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