Distance reasoning — estimating Alexis’s distance from the airport Danielle has been visiting friends in Ridge-wood for two weeks and flies out early tomorrow. Most of her friends live fairly close to the airport. Madison lives 10 miles away. Frances lives 5 miles away. Samantha lives 7 miles away. Alexis lives farther from the airport than Frances, but closer than Samantha. Approximately how far from the airport is Alexis?

Introduction / Context:
This critical-reasoning question tests your ability to interpret relational distance constraints and choose a value that satisfies all conditions simultaneously. The prompt names multiple friends and fixes their distances from the airport. You must locate Alexis on the number line relative to those anchor points.

Given Data / Assumptions:

• Madison is 10 miles from the airport.
• Frances is 5 miles from the airport.
• Samantha is 7 miles from the airport.
• Alexis is farther than Frances (so > 5 miles) but closer than Samantha (so < 7 miles).
• We are selecting an approximate distance from the given options.

Concept / Approach:
The strategy is to translate the text into inequalities and then check which answer options are within the valid interval. Because the statements are strict (farther than, closer than), Alexis must lie strictly between 5 and 7 miles from the airport. Any option equal to 5 or 7 or outside this range must be eliminated.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• nine miles: 9 is not less than 7, so Alexis would not be closer than Samantha.
• seven miles: Alexis must be closer than 7, not equal to 7.
• eight miles: 8 is greater than 7, violating the ‘‘closer than Samantha’’ condition.
• five miles: Alexis must be farther than Frances; equality fails.

Common Pitfalls:

Final Answer:
six miles