The sum of three consecutive integers is 24. What is the greatest of these three consecutive integers?

Introduction / Context:
This problem tests understanding of consecutive integers and simple linear equations. When the sum of three consecutive integers is known, we can represent them in terms of a variable and solve for that variable. This is a standard type of question in basic algebra and aptitude tests.

Given Data / Assumptions:
We have three consecutive integers.Their sum is 24.We need to find the largest of these three integers.

Concept / Approach:
Three consecutive integers can be represented as n, n + 1 and n + 2, where n is an integer. Their sum is then 3n + 3. By equating this sum to the given total, we obtain an equation that can be solved for n. Once n is found, the greatest of the three is n + 2.

Step-by-Step Solution:
Step 1: Let the three consecutive integers be n, n + 1 and n + 2.Step 2: Write their sum: n + (n + 1) + (n + 2) = 3n + 3.Step 3: Set this equal to 24: 3n + 3 = 24.Step 4: Subtract 3 from both sides to isolate the term with n: 3n = 21.Step 5: Divide both sides by 3: n = 21 / 3 = 7.Step 6: Therefore the three integers are 7, 8 and 9.Step 7: Among these, the greatest integer is 9.

Verification / Alternative check:
Add the found integers to confirm the sum: 7 + 8 + 9 = 24, which matches the given total. This verifies that the numbers have been identified correctly and that 9 is indeed the largest of the three.

Why Other Options Are Wrong:
If we choose 8 as the greatest integer, the three consecutive integers would be 6, 7 and 8, whose sum is 21, not 24. If we choose 7, the numbers 5, 6 and 7 sum to 18. If we choose 6, the numbers 4, 5 and 6 sum to 15. None of these match the required sum. Hence only 9 is consistent with the condition.

Common Pitfalls:
Some learners mistakenly assume that the middle number is 24 divided by 3 and then misidentify which of the three is the greatest. Others mis-handle the representation of consecutive integers, sometimes writing n − 1, n and n + 1 unnecessarily. The direct representation n, n + 1 and n + 2 keeps the algebra simple.

Final Answer:
The greatest of the three consecutive integers is 9.