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The product of the predecessor and succe...

The product of the predecessor and successor of an odd natural number is always divisible by

A

3

B

4

C

6

D

8

Text Solution

Verified by Experts

The correct Answer is:
D
An odd natural number can be expressed as 2n-1 , n=1,2,..N.
Its predecessor and successior are 2-2 and 2n respectively
`(2n-2)xx(2n)xx=4n(n-1)`
If n is idd, (n-1) is even,i.e. it yields atleast one power of 2
`n(n-1)=2k,k in N`
`(2n-2)xx2n=8k`
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