Question

Consider seven integers; whose range is 80 and median is 240. The median for the three smallest integers is 180. What is the possible range for the largest three integers?
I. 75
II. 24
III. 0

• A. I only
• B. II only
• C. I and III only
• D. II and III only
• E. III only

Hint:

When calculating possible ranges, always check for the conditions provided (such as median and range) to narrow down the possible values.

Answer 1

The Correct Option is C

Step 1: Understanding the Problem. 
The given integers are arranged in increasing order. The range of the integers is 80, meaning the difference between the largest and smallest integers is 80. The median of the seven integers is 240, which is the 4th number in the ordered set. Additionally, the median for the three smallest integers is 180, meaning the middle value of the smallest three integers is 180.
Step 2: Analyzing the Range of Largest Three Integers. 
Given the above conditions, the possible values for the largest three integers can be derived from the range and median information. 
- From the range of 80, the largest integer could be at most 320. 
- From the median being 240 and the range being 80, the largest three integers must fall within the range of 240 to 320. 
- The maximum possible difference between the largest integers, given the constraints, is 75 (I) and 0 (III). 
Thus, the possible range is 75 and 0, which corresponds to answers I and III. 
Final Answer: \[ \boxed{I \text{ and } III} \]