CAT 2017 Question Paper | Quants Slot 1

CAT Questions

Inequalities are crucial to understanding many topics that are tested in the CAT exam. Having a good foundation in this topic will help you enormously in Algebra. This question is about finding the number of integral solutions to an inequality. Make sure you practice this topic well because a range of questions can be asked in CAT Exam based on this simple concept.

Question 26 : For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied? [TITA]

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Inequalities

We have to find for how many integers n, will the inequality
(n – 5)(n – 10) – 3(n – 2) ≤ 0 be satisfied
(n – 5)(n – 10) – 3(n – 2) ≤ 0
n² – 15n + 50 – 3n + 6 ≤ 0
n² – 18n + 56 ≤ 0
(n – 4)(n – 14) ≤ 0
n = (4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14)
So n has to be between the two positive numbers 4 and 14 which is equal to 11.

The question is "For how many integers n, will the inequality (n – 5) (n – 10) – 3(n – 2) ≤ 0 be satisfied? [TITA]"

Hence, the answer is 11