Numbers -3

Find the following assumptions:
1. Every two consecutive positive numbers are co-prime
2. Every two consecutive positive odd numbers are co-prime
3. Every two consecutive positive even numbers are co-prime
  Choose the correct answer from the following:                                    
(A) Assumptions 1 & 2 are correct
(B) Assumptions 2 & 3 are correct      
(C) Assumptions 1 & 3 are correct         
(D) All Assumptions  are correct 
(E) Only the first assumption is correct 
Solution follows here:

Solution:

‘Co-prime numbers are numbers with no common factors’ (rather we can say that the only common factor is ‘1’)

Better approach for this type of problems is going for examples and trying out.

First case - consecutive positive numbers: check out any two consecutive numbers. We find that they are always co-prime.

Second case - consecutive odd numbers: check out any two, for example, 3 and 5 are co-prime. 31 and 33 are co-prime.

Third case consecutive even numbers: consecutive even numbers are never co-prime. For that case, any two even numbers are never co-prime because at the least ‘2’ is a common factor.

Answer (A)