The best questions to practice for CAT Exam are the actual CAT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. If you would like to take the same inside a testing engine (for **Free**) head out here: **CAT Official Question Mocks**. In CAT 2018 we saw some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts. Original CAT Question paper is the best place to start off your CAT prep practice. This page provides exactly that. To check out about 1000 CAT Level questions with detailed video solutions for free, go here: **CAT Question Bank**

Question 14 : The smallest integer n such that n^{3} - 11n^{2} + 32n - 28 ＞ 0 is [TITA]

Get CAT Last Mile Prep Course for 799 /-

CAT Online Coaching

Starts Sat, November 2nd, 2019

We have to find the smallest integer n such that n^{3} - 11n^{2} + 32n - 28 > 0

For this we can assume some values for n, such that n = 10 , 9 , 8 ,.. so on and can find the smallest integer

n^{3} - 11n^{2} + 32n - 28 > 0

Let us now assume that n = 10

1000 – 1100 + 320 - 28 > 0

192 > 0 Hence this n = 10 works out

Similarly n = 9 , 8 also works so we can try out with n = 8 and if it works we can try for lower numbers otherwise we can try with 9

n^{3} - 11n^{2} + 32n - 28 > 0

512 – 704 + 256 – 28 > 0

36 > 0

Since n = 8 works lets check for n = 7

343 – 539 + 224 – 28 = 0

Hence the smallest integer was found to be 8

The other way of thinking about it can be by substituting it with smaller numbers and checking if something can factorize it

So \\frac{P(x)}{x-a}) where remainder = 0

Let's substitute n = 1 with n^{3} - 11n^{2} + 32n - 28

1 – 11 + 32 – 28 = -6 this doesn’t work and now we can substitute n = 2 and check it out

8 – 44 – 64 – 28 = 0

So this number n^{3} - 11n^{2} + 32n - 28 is a multiple of n-2

(n-2)(n^{2} – 9n + 14)

(n – 2)(n - 2)(n - 7) > 0

This will be greater than 0 when n = 7 and when n is between 2 and 7 it will be negative

When n = 1 ,

1 - 11 + 32 - 28 = -6 so this doesn’t work

Hence the smallest integer which will work is n = 8

The question is **"The smallest integer n such that n ^{3} - 11n^{2} + 32n - 28 ＞ 0 is [TITA]"**

CAT 2020

Enroll at 44,000/-

Next Weekend Batch Starts Sat, Nov 2nd, 2019

Register Online, get Rs 4000/- off

Attend a Demo Class

Copyrights © 2019 All Rights Reserved by 2IIM.com - A Fermat Education Initiative.

Privacy Policy | Terms & Conditions

CAT^{®} (Common Admission Test) is a registered trademark of the Indian Institutes of Management. This website is not endorsed or approved by IIMs.

2IIM Online CAT Coaching

A Fermat Education Initiative,

58/16, Indira Gandhi Street,

Kaveri Rangan Nagar, Saligramam, Chennai 600 093

**Phone:** (91) 44 4505 8484

**Mobile:** (91) 99626 48484

**WhatsApp:** WhatsApp Now

**Email: **prep@2iim.com