CBSE Class 10 Answered

We know that themultiples of 3 will differ by 3.

Also every multiple of 3 is either an odd number or an even number.

Suppose

out of the given numbers

 n,n+2,n+4

If n is a multiple of 3, there's nothing more to prove.

So, let's assume that  n is not a multiple of 3.

Then n-3 is not a multiple of 3, so

either n-1, or n-2 must be a multiple of 3.

So next multiple of 3 would be either (n-1)+3= n+2

or

(n-2)+3 =n+1

So we see that if n is not a multiple of 3 then n+2 may be a multiple of 3 or n+1 may be a multiple of 3

 Next,

if n+1 is a multiple of 3 , then (n+1)+3 must be a multiple of 3

i.e. n+4 must be a multiple of 3.

So we see that if n is not a multiple of 3 then either n+2 or n+4 is a multiple of 3.

Thus either of n, n+2 or n+4 is always a multiple of 3.

i.e. one out of n,n+2 or n+4 is divisible by 3.