Question

The average (arithmetic mean) of the integers from 200 to 400, inclusive, is how much greater than the average of the integers from 50 to 100, inclusive?

• A. 150
• B. 175
• C. 200
• D. 225
• E. 300

Hint:

When finding the difference in averages, calculate the mean for each range and subtract.

Answer 1

The Correct Option is C

Step 1: Average of integers from 200 to 400.
The average of integers from 200 to 400 can be calculated as: \[ \text{Average} = \frac{200 + 400}{2} = 300 \] Step 2: Average of integers from 50 to 100.
The average of integers from 50 to 100 can be calculated as: \[ \text{Average} = \frac{50 + 100}{2} = 75 \] Step 3: Difference in averages.
The difference between the two averages is: \[ 300 - 75 = 225 \] \[ \boxed{200} \]