If n is an odd natural number greater than 1, then which of the following is correct about the product of its successor and predecessor?

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Is an odd natural number

Is an even natural number

Can be even or odd

None of these

answer is B.

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Detailed Solution

Let n, an odd natural number higher than 1, be the specified odd natural number.
The following number after the specified number "n," that is, the number after this number, shall be

(n + 1)

.
The predecessor of the number n will be

(n − 1)

.
The required product will be,

(n + 1) (n − 1) = n 2 − 12 = n 2 − 1

We know that the square of an odd number will be an odd number and the if we subtract 1 from any odd number, we get an even number.
Thus, the required product will always be even.
Therefore, the correct option is 2.

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