Loading [MathJax]/jax/output/HTML-CSS/jax.js

IIFT 2019 Question Paper | Quants

IIFT Previous Year Paper | IIFT Quants Questions | Question 15

The best way to boost your IIFT prep is to practice the actual IIFT Question Papers. 2IIM offers you exactly that, in a student friendly format to take value from this. In the 2019 IIFT, quants were a mixed bag of questions of varying difficulty, with some routine questions and the others were very demanding. Some beautiful questions that laid emphasis on Learning ideas from basics and being able to comprehend more than remembering gazillion formulae and shortcuts.

Question 15: In triangle MNL,line NP bisects the angle MNL. If NP : NL = 2 : 3 and angle MNL= 120 degrees . Then NP: NL: MN is:

Triangle, angle bisector
  1. 2:3:4
  2. 2:3:6
  3. 2:3:5
  4. 2:3:9

Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!


2IIM : Best Online CAT Coaching.

Celebrate the festival of colors with a flat 25% OFF on all 2IIM CAT 25 & 26 Full Courses! ๐Ÿ“š๐Ÿ”ฅ Donโ€™t miss this golden opportunity to supercharge your preparation and crack the CAT! ๐Ÿš€ โœจ Grab the Offer & Make Your Success Colorful! โœจ

2IIM : Best Online CAT Coaching.


Video Explanation


Best CAT Coaching in Chennai


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


Explanatory Answer

We see that NP divides the angle MNL into two equal parts, so we use the angle bisector theorem.
So, MPPL = MNNL

In triangle NPL, PN : NL :: 2x : 3x
So lets say PN : NL : LP :: 2x : 3x : kx

Using cosine rule we can say that,
cos 60 = 12 = 22+32โˆ’k22ร—2ร—3
5 = 12 = 22+32โˆ’k22ร—2ร—3
6 = 13 โ€“ k2


So, k = โˆš7

Lets say the side MN is kx,
So, from angle bisector theorem:
MPPL = MNNL
= MPโˆš7 = kx3x
MP = โˆš7ร—k3

Now in triangle MNP,
Using cosine rule:
Cos 60 = 12 = k2+22โˆ’(โˆš7k/3)22ร—2ร—k
We get
2 k = k2 + 4 - 79 k2
2 k = 29 k2 + 4
Solving this quadratic equation,
k2+ 18 = 9 k
(k-3)(k-6) = 0
So k could be 3 or 6
Since the triangle cannot be isosceles, k cannot be 3
So k = 6
This, PN : NL : LP :: 2x : 3x : 6x
Or PN : NL : LP :: 2 : 3 : 6


The question is "The ratio NP: NL: MN is:"

Hence, the answer is, "2:3:6"
Best CAT Online Coaching
Try upto 40 hours for free
Learn from the best!

โ˜… Sign up Now!

Celebrate the festival of colors with a flat 25% OFF on all 2IIM CAT 25 & 26 Full Courses! ๐Ÿ“š๐Ÿ”ฅ Donโ€™t miss this golden opportunity to supercharge your preparation and crack the CAT! ๐Ÿš€ โœจ Grab the Offer & Make Your Success Colorful! โœจ

Check here!

Know all about CAT Syllabus and what to expect in CAT

โ˜… Download
CAT Syllabus PDF

Repeating CAT? Ace it with 2IIM! Get expert guidance & exclusive discounts. ๐Ÿš€

โ˜… Register Now

Best Indore IPM & Rohtak IPM Coaching
Signup and sample 9 full classes for free. Register now!

โ˜… Signup now

CAT Questions | CAT Quantitative Aptitude

CAT Questions | Verbal Ability for CAT


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?

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