The largest possible number by which the expression n3-n is divisible for all the possible integral values of n is?

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answer is C.

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Detailed Solution

Concept- To solve this problem, you need to split the given expression into three consecutive numbers. This is the logic. If there are three consecutive numbers, and the number to be acquired is odd, the consecutive numbers will be even.
The given expression is

For further simplification, we get

Above that there are three consecutive numbers
If there are three consecutive numbers and the numbers drawn are odd, then the consecutive numbers are even. One of them has an even number. Therefore, it is divisible by 2. If there are three consecutive numbers and the number to be acquired is an even number, the consecutive numbers will be odd. Since there are three consecutive numbers, one of the values is odd, which means it is divisible by three.

or later it is divisible by 2 and 3, so

Divisible by 6.
Hence, the correct answer is option 3) .

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