Question

What is the average of all integers between 100 and 250 that are exactly divisible by 11?

• A. 176
• B. 175
• C. 165
• D. 187

Answer 1

Answer:

A. 176

Numbers divisible by 11 between 100 and 250 form an arithmetic sequence.

Find first and last terms

• First multiple of 11 ≥ 100 → $(11 \times 10 = 110)$

• Last multiple of 11 ≤ 250 → $(11 \times 22 = 242)$

• Use property of arithmetic sequence

The average of equally spaced numbers =
$\frac{\text{first term} + \text{last term}}{2}$

$= \frac{110 + 242}{2} = \frac{352}{2} = 176$

Final Answer:

176