Question

If N ÷ 5 leaves remainder 3 and N ÷ 2 leaves remainder 0, then N ÷ 10 leaves remainder 4.

Options

• True

• False

Answer 1

This statement is False.

Explanation:

Here it’s given N ÷ 5 leaves remainder 3

⇒ N = 5n + 3,where n = 0, 1, 2, 3, ...

And N ÷ 2 leaves remainder 0

⇒ N is an even number

But N = 5n + 3, it’s sum of two terms whose second term is odd.

Therefore, 5n should be an odd number.

5n can be odd when n = 1, 3, 5, ...

So, in this case when N = 5n + 3

⇒ N = 5(1) + 3 = 8 when (n = 1)

Hence when we substitute n = 1, 3, 5, ... in N = 5n + 3, we get 8, 18, 28 etc

Now, when we divide N by 10, N can be written as

N = 10 × n + 8, when n = 0, 1, 2, 3, ...

Therefore, when N ÷ 10, always leaves remainder 8.