Question

Question 62

$212x5$ is a multiple of 3 and 11. Find the value of x.

Answer 1

Since, $212x5$ is a multiple of 3.
2 + 1 + 2 + x + 5 = 0, 3, 6, 9, 12, 15, 18,
$\Rightarrow$ 10 + x = 0, 3, 6, ......
$\Rightarrow$ x = 2, 5, 8, ............(i)
Again, $212x5$ is a multiple of 11, (2 + 2 + 5) - (1 + x) = 0, 11, 22, 33
$\Rightarrow$ 8 - x = 0, 11, 22, ......
$\Rightarrow$ x = 8 ................(ii)
From Eqs. (i) and (ii), we have
x = 8