Question

In the given question, state whether the given statement is True or False.

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

Answer 1

False
$\because N÷5$ leaves remainder 3.
$\Rightarrow$ N = 5n + 3, where n = 0, 1, 2, 3, ....
Now, it is also given, $N÷2$ leaves remainder 0.
So, N must be an even number.
But N = 5n + 3
i.e. sum of two terms whose second term is odd.
So, for N should be even it is necessary that 5n must be odd.
which is possible, when n = 1, 3, 5, ....
So, in this case value of N should be
N = 8, 18, 28, 38, ....
i.e. N = 10n + 8, n = 0, 1, 2,3, .....
When $N÷10$ leaves remainder 8 always.