Question

Find the value of $a+b+c$, if $373a$ is divisible by $9,473b$ is divisible by $11$ and $371c$ is divisible by $6.$

• A. $7$
• B. $6$
• C. $0$
• D. $9$

Answer 1

The correct option is D $9$

373a is divisible by 9.

$\Rightarrow$ $3+7+3+a=13+a$ should be divisible by 9.

$\Rightarrow$ a = 5

473b is divisible by 11.

$\Rightarrow$ 4 + 3 - 7 - b = 0 or 11

$\Rightarrow$ b = 0 or 11

$\therefore$ b = 0

371c is divisible by 6.

$\Rightarrow$ 371c is divisible by both 2 and 3.

$\Rightarrow$ c is an even number and 3 + 7 + 1 + c is divisible by 3.

$\Rightarrow$ c = 0, 2, 4, 6, 8 and 11 + c is divisible by 3.

$\Rightarrow$ c = 4

$\therefore$ a + b + c = 5 + 0 + 4 = 9