In this aptitude number series question, find the odd number out from the series: 71, 88, 113, 150, 203, 277.

Introduction / Context:
This reasoning problem asks you to identify the odd number out in the series 71, 88, 113, 150, 203, 277. Instead of a positional number pattern, the key idea here is to use divisibility properties to see which term behaves differently from the others.

Given Data / Assumptions:

• Series: 71, 88, 113, 150, 203, 277
• Exactly one number does not share a common property with the rest.
• We look for a simple and consistent numerical property, such as divisibility by a small integer.

Concept / Approach:
A common technique in odd one out questions is to examine divisibility by small primes like 2, 3, 5, 7 or 11. The goal is to find a property that all but one number either satisfy or fail to satisfy. Often, divisibility by 3 is the simplest and most revealing check.

Step-by-Step Solution:
Step 1: Check divisibility by 3 using the sum of digits rule.71: 7 + 1 = 8, not divisible by 3.88: 8 + 8 = 16, not divisible by 3.113: 1 + 1 + 3 = 5, not divisible by 3.150: 1 + 5 + 0 = 6, which is divisible by 3.203: 2 + 0 + 3 = 5, not divisible by 3.277: 2 + 7 + 7 = 16, not divisible by 3.Step 2: Interpret the results.Only 150 has digit sum divisible by 3 and therefore is divisible by 3 itself. All other numbers are not divisible by 3.

Verification / Alternative check:
You can directly divide each number by 3 as a secondary check. 150 / 3 = 50 exactly, while all the other numbers leave a remainder when divided by 3. No comparable simple property (such as divisibility by 2, 5, or 7) isolates exactly one number in this set as clearly as divisibility by 3 does.

Why Other Options Are Wrong:
71: Not divisible by 3, so it shares the main property with 88, 113, 203 and 277.
113: Also not divisible by 3, so it fits the common group pattern.
203: Again not divisible by 3, remaining consistent with the majority of the series.
277: Not divisible by 3, so it cannot be the odd one out based on this key property.

Common Pitfalls:
Many learners initially search for complex patterns involving squares, cubes or differences between terms and overlook simpler divisibility patterns. Another frequent mistake is to accept a property that applies to more than one candidate, which violates the requirement of a single odd term. Always validate that your chosen property isolates exactly one number in the series.

Final Answer:
The odd number out in the given series is 150.