Q5 REMAINDERS

Let b be a positive integer and a = b²-b. If b >=4, then a²-2a is divisible by

a. 15

b. 20

c. 24

We know that a = b^2-b

So a²-a = b(b^3 - 2b^2-b+2)=(b-2)(b-1)(b)(b+1)

The above given is a product of 4 consecutive numbers with the lowest number of the product being 2(given b>= 4)

In any set of four consecutive numbers, one of the numbers would be divisible by 3 and there would be two even numbers with the minimum value of the pair being (2,4).

Thus, for any value of b >=4, a² - 4 would be divisible by 3 x 2 x 4 = 24.

Thus, option C is the right choice Options A and B are definitely wrong as a set of four consecutive numbers need not always include a multiple of 5 eg:(6,7,8,9)

  

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