In this number classification question, select the odd number from the given alternatives based on divisibility properties.

Introduction / Context:
This is a basic arithmetic odd one out question that checks your understanding of divisibility rules. You are given four numbers and must decide which number does not share a common divisibility property with the others. This type of problem is frequently seen in aptitude tests because it can be solved quickly if you are familiar with divisibility by small integers like 2, 3, 5, and 9.

Given Data / Assumptions:
- The numbers given are 18, 45, 54, and 55.- All numbers are two digit integers.- We are looking for a common divisibility rule that applies to three of them but not to one.

Concept / Approach:
One of the quickest checks is divisibility by 9 or by 3 using digit sum rules. A number is divisible by 3 if the sum of its digits is a multiple of 3. The same digit sum rule with multiples of 9 works for divisibility by 9. We try these simple checks first because they are fast and often used in competitive exam questions.

Step-by-Step Solution:
Step 1: For 18, the sum of digits is 1 + 8 = 9, which is a multiple of 3, so 18 is divisible by 3.Step 2: For 45, the sum of digits is 4 + 5 = 9, again a multiple of 3, so 45 is divisible by 3.Step 3: For 54, the sum of digits is 5 + 4 = 9, so 54 is also divisible by 3.Step 4: For 55, the sum of digits is 5 + 5 = 10, which is not a multiple of 3, so 55 is not divisible by 3.Step 5: Thus, three numbers are divisible by 3 and one is not.

Verification / Alternative check:
You can divide each number by 3 directly. 18 / 3 = 6, 45 / 3 = 15, 54 / 3 = 18, all whole numbers. However, 55 / 3 gives a non integer result. This confirms that 55 breaks the common divisibility pattern.

Why Other Options Are Wrong:
18: Multiples of 3 and fits the pattern.45: Also a multiple of 3, so it fits.54: Clearly divisible by 3, again fitting the group.

Common Pitfalls:
Some students focus only on even and odd status, but here both even and odd numbers appear among those divisible by 3. Looking only at parity will not give a clear answer, so divisibility rules are essential.

Final Answer:
The odd number is 55 because it is not divisible by 3, whereas the other three numbers are.