Question

Which of the positive integers below gives a remainder of 0 when it is divided by 3, if the positive integer n is divided by 3, the remainder is 1.

A. n – 1

B. n + 1

C. n + 2

D. n – 3

1. A and C are correct
2. Only C is correct
3. Only A is correct
4. All are correct

Answer 1

Correct Answer - Option 2 : Only C is correct

Formula Used:

Remainder Theorem

Dividend = (Divisor × Quotient) + Remainder           

Calculation:

Using above formula,

n = 3k + 1, where k = 0,1,2,…

There are two possibilities for the number to be divided by 3 completely

n - 1 and n + 2

n – 1 = 3k + 1 – 1 = 3k where k = 0,1,2,…

But if k = 0, n – 1 = 0 which is not a positive integer.

(∵ n - 1 is negative for n = 0)

n + 2 = 3k + 1 + 2 = 3k + 3 = 3(k +1) where k = 0,1,2,…

n + 2 is the positive integer that gives a remainder of 0 when divided by 3.

∴ Only C is correct