Question

A student was asked to divide a number by 6 and add 12 to the quotient. He however, first added 12 to the number and then divided it by 6, getting 112 as the answer. The correct answer should have been?

• A. 124
• B. 172
• C. 118
• D. 122

Hint:

When a problem involves misinterpretation of operations, carefully set up both the intended and the mistaken operations. Always verify with the final options to avoid errors.

Answer 1

The Correct Option is D

Step 1: Express condition mathematically.
Let the number be \(N\). Correct operation: \(\frac{N}{6} + 12\). Mistaken operation: \(\frac{N+12}{6} = 112\). 

Step 2: Solve for \(N\).
\[ \frac{N+12}{6} = 112 \quad \Rightarrow \quad N+12 = 672 \quad \Rightarrow \quad N=660. \] 

Step 3: Compute correct answer.
\[ \frac{N}{6} + 12 = \frac{660}{6}+12 = 110+12=122. \] \[ \boxed{122} \]