# Quantitative Aptitude – Algebra – Inequalities – For how many integers n

## Question

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

11

## Solution

From CAT 2017 – Quantitative Aptitude – Algebra – Inequalities, we can see that,
On solving the equation, we get n^2 – 18n + 56 ≤ 0
Factorize and we get, (n-4)(n-14) ≤ 0
4 ≤ n ≤ 14
No of values of n =11

## CAT 2017 Questions from Quantitative Aptitude – Algebra

Quantitative Aptitude – Algebra – Inequalities – Ques: The number of solutions (x, y, z) to the equation x – y – z = 25, where x, y, and z are positive integers such that x ≤ 40, y ≤ 12, and z ≤ 12 is
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