Question

the HCF of two numbers is 1 and the sum of the numbers is 86.What are the numbers if their difference is less than 20.

Answer 1

There could be three such combinations that can satisfy the question.

First of all as it is mentioned that the HCF is 1. So it is quite obvious that either of the number or both has to be a prime number followed by their sum has to be 86.

Now we can consider three prime numbers : 37, 41, 47 Now you may be wondering the reason why I chose only these three but not before it or beyond it. The reason is if you consider 31 the very succesive prime number of 37 then the pair will be (31, 55) So it satisfies that the HCF is 1 but their difference is greater than 20. Similarly we cannot select 53.

Therefore the 3 possible pairs are as follows:

(37, 49), (41, 45) & (47, 39)........ (Ans)