Question 58

If a positive integer n is divided by 7, the remainder is 2. Which of the numbers in the options yields a remainder of 0 when it is divided by 7?

Solution

Given, when 'n' is divided by 7 the remainder is 2.

Let n = 7k + 2 where k is an positive integer

By Trial and Error method,

Option A

n + 3 = 7k + 2 + 3 = 7k + 5

$$\Rightarrow$$ When n + 3 is divided by 7, the remainder is 5.

Option B

n + 5 = 7k + 2 + 5 = 7k + 7 = 7(k+1)

$$\Rightarrow$$ When n + 5 is divided by 7, the remainder is 0.

Hence, the correct answer is Option B

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