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

###### CAT Questions | Number Theory | HCF basics CAT Questions

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

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##### 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.

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