. CAT 2018 Question Paper Quants Slot 2 - CAT Polynomials and Inequalities Questions, 2IIM CAT 2022 online classes for CAT, CAT coaching in Chennai | 2IIM CAT Online Classes

# CAT 2018 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Polynomials and Inequalities Questions | Question 14

This is a question from Polynomails that appeared in the CAT 2018 Question Paper. There are essentially two ways to solve the question. Try it yourself before looking at the video explanation where both the ways to solve this questionare explained.
To know about the exam's blueprint, visit 2IIM's CAT Blueprint.

Question 14 : The smallest integer n such that n3 - 11n2 + 32n - 28 ＞ 0 is [TITA]

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now!

##### Method of solving this CAT Question from Polynomials and Inequalities

We have to find the smallest integer n such that n3 - 11n2 + 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
n3 - 11n2 + 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
n3 - 11n2 + 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 n3 - 11n2 + 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 n3 - 11n2 + 32n - 28 is a multiple of n-2

(n-2)(n2 – 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 n3 - 11n2 + 32n - 28 ＞ 0 is [TITA]"

##### Hence, the answer is 8

###### CAT Coaching in ChennaiCAT 2022

Classroom Batches Starting Now! @Gopalapuram

###### Best CAT Coaching in Chennai Introductory offer of 5000/-

Attend a Demo Class

##### Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

##### How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com