The question is about HCF and LCM. We need to find out the possible pairs of (x,y), which satisfies the given conditions about the sum of their HCF and LCM. 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.

Question 5: How many pairs of positive integers x, y exist such that HCF (x, y) + LCM (x, y) = 91?

- 10
- 8
- 6
- 7

8

Try upto 40 hours for free

Learn from the best!

Limited Seats Available - Register Now!

Let us x = h * a; y = h * b

a and b are co-prime. So, LCM of (x, y) = h * a * b

So, in essence h + h * a * b = 91. Or h(ab + 1) = 91

Now, 91 can be written as 1 * 91 or 7 * 13

Or, we can have HCF as 1, LCM as 90 -

There are 4 pairs of numbers like this (2, 45), (9, 10), (1, 90) and (5, 18)

We can have HCF as 7, ab + 1 = 13 => ab = 12 => 1 * 12 or 4 * 3

Or, the pairs of numbers are (7, 84) or (21, 28)

The third option is when HCF = 13, ab + 1 = 7 => ab = 6

Or (a, b) can be either (1, 6) or (2, 3)

The pairs possible are (13, 78) and (26, 39)

There are totally 8 options possible - (2, 45), (9, 10), (1, 90), (5, 18), (7, 84), (21, 28), (13, 78) and (26, 39).

8 Pairs.

The question is **"How many pairs of positive integers x, y exist such that HCF (x, y) + LCM (x, y) = 91?"**

Choice B is the correct answer.

CAT 2024

Classroom Batches Starting Now! @Gopalapuram and @Anna nagar

Copyrights © 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