The sum of three consecutive odd integers is 93. What is the value of the middle odd number?

Introduction:
This question is about consecutive odd numbers and simple algebra. When you know the sum of three consecutive odd integers, you can find the middle one quickly using a straightforward equation. This is a very common type of question in basic aptitude tests.

Given Data / Assumptions:

• We have three consecutive odd integers.
• Their sum is 93.
• We must find the middle number.

Concept / Approach:
Consecutive odd numbers can be represented using a single variable. If the middle odd number is n, then the three consecutive odd numbers are n − 2, n and n + 2. Their sum becomes a simple linear expression in n, which we can solve easily.

Step-by-Step Solution:
Step 1: Represent the three consecutive odd integers.Let the middle number be n.Then the three consecutive odd numbers are n − 2, n, n + 2.Step 2: Write the sum expression.(n − 2) + n + (n + 2) = 93.Step 3: Simplify the left-hand side.(n − 2) + n + (n + 2) = 3n.So 3n = 93.Step 4: Solve for n.n = 93 / 3 = 31.

Verification / Alternative check:
Check the three numbers: n − 2 = 29, n = 31, n + 2 = 33. Sum = 29 + 31 + 33 = 93, which agrees with the given information. Thus the middle number is indeed 31.

Why Other Options Are Wrong:
33, 29 and 27 do not produce a sum of 93 when used as the middle term of three consecutive odd integers. For instance, if 33 were the middle number, the numbers would be 31, 33 and 35, whose sum is 99, not 93.

Common Pitfalls:
Some students mistakenly take the numbers as n, n + 1, n + 2 instead of odd-only spacing, or try guessed triples rather than setting up the simple equation. Remember that consecutive odd numbers differ by 2, not 1.

Final Answer:
The middle odd number is 31.