Bunuel wrote:

Positive integer n is divisible by 5.

What is the remainder when dividing 4(n + 1)(n + 8) by 5?

A. 0

B. 1

C. 2

D. 3

E. 4

Kudos for a correct solution.

Given : Possible values of n = 5, 10, 15, 20, 15, 20, 25, .... etc = 5aQuestion : Remainder when 4(n + 1)(n + 8) is divided by 5 = ? CONCEPT: (Remainder when a is divided by x)*(Remainder when b is divided by x) = (Remainder when a*b is divided by x)

Also (Remainder when a is divided by x)+(Remainder when b is divided by x) = (Remainder when {a+b} is divided by x)Method-1i.e. Remainder [\(\frac{4(n + 1)(n + 8)}{5}\)] = 4*Remainder [\(\frac{(n + 1)}{5}\)]*Remainder [\(\frac{(n + 8)}{5}\)]

i.e. Remainder [\(\frac{4(n + 1)(n + 8)}{5}\)] = 4*Remainder [\(\frac{(5a + 1)}{5}\)]*Remainder [\(\frac{(5a + 8)}{5}\)]

i.e. Remainder [\(\frac{4(n + 1)(n + 8)}{5}\)] = 4*1*Remainder [\(\frac{(8)}{5}\)] = 4*1*3 = 12

i.e. Remainder [\(\frac{4(n + 1)(n + 8)}{5}\)] = Remainder (12/5) =

2Answer: option C

Method-2Let, n=5

then, 4(n + 1)(n + 8) = 4(5 + 1)(5 + 8) = 4*6*13 = 312

i.e. Remainder [\(\frac{4(n + 1)(n + 8)}{5}\)] = i.e. Remainder [\(\frac{312}{5}\)] =

2Answer: option C

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