Among four students sitting in a row, the average age of the last three students is 20 years and the average age of the first three students is 21 years. If the age of the first student is 26 years, what is the age in years of the last student?

Introduction / Context:
This problem uses averages of overlapping groups to find an individual value. Four students sit in a row, and we know the average age of the first three and the last three. Using these overlapping averages and the age of the first student, we can determine the age of the last student at the end of the row.

Given Data / Assumptions:

• There are four students in a row, call them A, B, C and D in order.
• The average age of the last three students B, C and D is 20 years.
• The average age of the first three students A, B and C is 21 years.
• The age of the first student A is 26 years.
• We must find the age of the last student D.

Concept / Approach:
When we know averages of overlapping groups, we can convert them to equations using sums. From the average of the last three students we get B + C + D. From the average of the first three students we get A + B + C. Substituting the given value of A lets us find B + C, which can then be used to find D. This is a standard technique for handling overlapping averages in aptitude questions.

Step-by-Step Solution:
Step 1: From the last three students, (B + C + D) / 3 = 20, so B + C + D = 60. Step 2: From the first three students, (A + B + C) / 3 = 21, so A + B + C = 63. Step 3: The age of A is 26, so B + C = 63 - 26 = 37. Step 4: Substitute B + C = 37 into B + C + D = 60 to get 37 + D = 60. Step 5: Therefore D = 60 - 37 = 23.

Verification / Alternative check:
Check that these ages are consistent. We do not know the exact values of B and C, but we know B + C is 37. So A + B + C = 26 + 37 = 63, whose average is 63 / 3 = 21. Also B + C + D = 37 + 23 = 60, whose average is 60 / 3 = 20. Both match the original conditions, confirming the value of D as 23 years.

Why Other Options Are Wrong:
If D were 37, then B + C would have to be 23 to keep B + C + D = 60, which would make A + B + C less than 63 and the first average smaller than 21. If D were 24 or 29, similar checks break one of the two given average conditions. Only D = 23 satisfies both equations at the same time.

Common Pitfalls:
Learners sometimes try to treat the averages as simple independent values and forget to convert them to sums. Others mistakenly assume that B and C must have the same age. The safe method is to set up equations using sums, substitute known values step by step, and solve for the unknown age carefully.

Final Answer:
The age of the last student is 23 years.