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?
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?"
Choice C is the correct answer.
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