Question

4. Show that one and only one out of n, n + 4, n + 8, n + 12 and n + 16 is divisible by 5, where n is any positive integer.

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Answer 1

Heya!

Here is yr answer.....


Given,

n, n+4 , n+8 , n+12 , n+16

n is any positive integer......


If n = 1

=> 1 , 1+4, 1+8 , 1+12 , 1+16

=> 1 , 5 , 9 , 12 , 17

Here, 5 only divisible by 5




If n = 2

=> 2 , 2+4 , 2+8 , 2+12 , 2+16

=> 2 , 6 , 10 , 14 , 18

Here, 10 only divisible by 5



If n = 3

=> 3, 3+4 ,3+8 , 3+12 , 3+16

=> 3 , 7 , 11 , 15 , 19

Here, 15 only divisible by 5


By observing... the above values of 'n'

We, can say one and only out of n, n+4, n+8 , n+12 , n+16 is divisible by 5


Hope it hlpz...