Question

show that exactly one of the numbers n,n+2 or n+4 is divisible by 3

Answer 1

see the answer in oswaall mathematics class 10 question Bank page number-7 12th question

Answer 2

Let n=3k, 3k+1 or 3k+2.
CASE I : When n=3k :
→n is divisible by 3.
n+2 = 3k+2
→n+2 is not divisible by 3.
n+4 = 3k+4 = 3(k+1)+1
→n+4 is not divisible by 3.

CASE II : When n=3k+1
→n is not divisible by 3.
n+2 = (3k+1)+2
= 3k+3 = 3(k+1)
→n+2 is divisible by 3.
n+4 = (3k+1)+4
= 3k+5 = 3(k+1)+2
→n+4 is not divisible by 3.

CASE III : When n=3k+2
→n is not divisible by 3.
n+2 =(3k+2)+4
=3(k+1)+1
→n+2 is not divisible by 3.
n+4 =(3k+2)+4
=3k+6 = 3(k+2)
→n+4 is divisible by 3.

Hence, exactly one of the numbers n, n+2 or n+4 is divisible by 3.