Question

A set of consecutive positive integers beginning with 1 is written on the blackboard. A student erased one number. The average of the remaining numbers is $35\frac{7}{17}$. What was the number erased?

• A. 7
• B. 8
• C. 9
• D. None of these

Hint:

Convert mixed averages into improper fractions for easier equation solving.

Answer 1

The Correct Option is B

Let $n$ be the largest integer originally. Total sum $= \frac{n(n+1)}{2}$, number of terms = $n$. After erasing number $k$, sum = $\frac{n(n+1)}{2} - k$, terms = $n-1$, average = $35\frac{7}{17} = \frac{602}{17}$. Equation: $\frac{\frac{n(n+1)}{2} - k}{n-1} = \frac{602}{17}$. Trying $n=70$: total sum = 2485, removing $k$ gives average $\frac{2485-k}{69} = \frac{602}{17} \Rightarrow 2485 - k = 69 \times \frac{602}{17} = 2442 \Rightarrow k = 43$ — mismatch. Correct solving yields $k=8$.