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

$112$

Step 1: Explanation for the correct answer

Option (a): $112$

Let us assume the three consecutive multiples of $7$ be $7m,(7m+7),(7m+14)$ where $m$ is a natural number.

As per the condition in the question,

$\begin{array}{rcl}7m+(7m+7)+(7m+14)& =& 357\\ 21m+21& =& 357\\ 21(m+1)& =& 357\\ \frac{21(m+1)}{21}& =& \frac{357}{21}\\ m+1& =& 17\\ m& =& 17–1\\ m& =& 16\end{array}$

Therefore, the smallest multiple of $7$ is, $7\times 16=112$.

Thus, option (a) is the correct answer.

Step 2: Explanation for the incorrect answer

Option (b): $126$

Option (c): $119$

Option (d): $116$

By calculating the smallest multiple, we get $112$.

Thus, option (b), (c) and (d) are incorrect answers.

Hence, option (a) is the correct answer.