The average age of a group of 10 students is 15 years.\nWhen 5 more students join the group, the average age increases by 1 year.\nWhat is the average age of the 5 new students?

Introduction / Context:
This problem tests understanding of averages and how adding new members with a different average age affects the overall group average. We relate the total ages before and after new students join.

Given Data / Assumptions:

• Average age of 10 students = 15 years.
• Therefore total age of the 10 students = 10 * 15 years.
• 5 more students join the group.
• New average age of all 15 students = 16 years.
• We must find the average age of these 5 new students.

Concept / Approach:
Average age = total age / number of students. From the given averages, we first compute the total age of the original 10 students. Then we compute the total age of all 15 students after the new ones join. The difference between these totals gives the combined age of the 5 new students, from which we can find their average.

Step-by-Step Solution:
Total age of original 10 students = 10 * 15 = 150 years. After 5 more students join, total students = 15. New average age = 16 years. Total age of 15 students = 15 * 16 = 240 years. Combined age of 5 new students = 240 - 150 = 90 years. Average age of new students = 90 / 5 = 18 years. Thus the required average is 18 years.

Verification / Alternative check:
We can also reason that the overall average increased by 1 year for all 15 students, which adds 15 years more total age than if the original 10 had just grown. The original group had a total of 150 years. If the new 5 students had also been 15 on average, the new total would be 225. Instead, it is 240, which is 15 more, meaning those 5 students contribute an extra 3 years each on average, giving 15 + 3 = 18 as their average. This matches the earlier calculation.

Why Other Options Are Wrong:
Options 19, 20 and 21 years would give total ages for the new students of 95, 100 and 105 respectively, which would lead to different overall totals and averages that do not match the given increase to 16 years.

Common Pitfalls:
Learners sometimes mistakenly add 1 to the original average for the new group only or misinterpret how the average changes. Another common issue is not using total sums consistently when dealing with averages. Always convert average information into total sums, do the arithmetic, and then convert back.

Final Answer:
The average age of the 5 new students is 18 years.