Question

The sum of three consecutive multiples of 7 is 357. Find the smallest multiple.

• A. 112
• B. 126
• C. 119
• D. 116

Answer 1

The correct option is A 112

Let the three consective multiples of 7 be $7x$, $7x+7$, and $7x+14$ where $x$ is a natural number.
According to the condition given in the question,
$7x+(7x+7)+(7x+14)=357$
$\Rightarrow 21x+21=357\Rightarrow 21(x+1)=357\Rightarrow (x+1)=\frac{357}{21}\Rightarrow x+1=17\Rightarrow x=17-1\therefore x=16$
Hence, the smallest multiple of 7 is $7\times 16,$ i.e. $112$.