CAT Quantitative Aptitude Questions | CAT Number Systems - HCF and LCM questions

CAT Questions | Number Theory | HCF basics

The question is about HCF basics. Given the sum of numbers with their HCF, we need to find out number of possible pairs. In CAT Exam, one can generally expect to get 1~2 questions from CAT Number Systems: HCF and LCM. In multiple places, extension of HCF and LCM concepts are tested by CAT Exam and one needs to understand HCF and LCM to be able to answer the same. CAT Number theory is an important topic with lots of weightage in the CAT Exam. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score.

Question 7: The sum of two non co–prime numbers added to their HCF gives us 91. How many such pairs are possible?

  1. 2
  2. 4
  3. 3
  4. 6

Rs. 2500 off on 2IIM Ultimate DI LR Course for CAT 2019. Offer valid till March 24th.

Signup to sample the Best CAT Online Coaching

Video Explanation

Best CAT Coaching in Chennai

Starts Sat, Mar 23, 2019

Explanatory Answer

Method of solving this CAT Question from Number Theory - HCF and LCM: Given sum of two numbers and their GCD, how do we find the two numbers.

Let HCF of the numbers be h. The numbers can be taken as ha + hb, where a, b are coprime.
h + ha + hb = 91
h(1 + a + b) = 91
h ≠ 1
h = 7
=> 1 + a + b = 13 a + b = 12

h = 13
=> 1 + a + b = 7
=> a + b = 6

Case 1: h = 7, a + b = 12
(1, 11), (5, 7) => Only 2 pairs are possible as a, b have to be coprime.

Case 2: h = 13, a + b = 6
(1, 5) only one pair is possible as a, b have to be coprime.

Overall, 3 pairs of numbers are possible – (7, 77) (35, 49) and (13, 65)

The question is "How many such pairs are possible?"

Hence the answer is "3 Pairs"

Choice C is the correct answer.


Online CAT Coaching
Try it free!

Register in 2 easy steps and start learning in 30 seconds!

★ Sign up for Free

Already have an Account?

★ Login to Continue

CAT Coaching in Chennai

Next Weekend Batch Starts Sat, Mar 23rd, 2019

★ CAT Coaching Info

Best CAT Coaching in Chennai

Sign up for a Free Demo of our CAT Coaching in Chennai

★ Schedule Demo

CAT Online Coaching | CAT Number Systems questions Videos On YouTube

Other useful sources for Number System Questions | Number Theory HCF and LCM Sample Questions

CAT Questions | CAT Quantitative Aptitude

CAT Questions | CAT DILR

CAT Questions | Verbal Ability for CAT

Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
10-C, Kalinga Colony, Bobbili Raja Salai
K.K.Nagar, Chennai. India. Pin - 600 078

How to reach 2IIM?

Phone: (91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now