In the sequence 35, 48, 54, 63, 81, 105, which number is the odd one out?

Introduction / Context:
This is a straightforward odd one out question based on divisibility. The task is to detect which number in the list does not share a common divisibility property with the others. Such questions are common in basic number system sections and are usually solved quickly with simple divisibility tests.

Given Data / Assumptions:

• List of numbers: 35, 48, 54, 63, 81, 105.
• Exactly one number in this group behaves differently.
• Divisibility by 3 is often a useful property to check when many numbers are multiples of 3.

Concept / Approach:
A number is divisible by 3 if the sum of its digits is divisible by 3. Looking at the list, several numbers appear to be multiples of 3 at first glance. We apply the sum of digits test to each term and see which one fails this condition. The number that is not divisible by 3 while all others are will be the odd one out.

Step-by-Step Solution:
Check 35: Sum of digits = 3 + 5 = 8, which is not divisible by 3. So 35 is not a multiple of 3.Check 48: Sum of digits = 4 + 8 = 12, which is divisible by 3. So 48 is a multiple of 3.Check 54: Sum of digits = 5 + 4 = 9, which is divisible by 3. So 54 is a multiple of 3.Check 63: Sum of digits = 6 + 3 = 9, divisible by 3. So 63 is a multiple of 3.Check 81: Sum of digits = 8 + 1 = 9, divisible by 3. So 81 is a multiple of 3.Check 105: Sum of digits = 1 + 0 + 5 = 6, divisible by 3. So 105 is a multiple of 3.

Verification / Alternative check:
We can also divide each number directly by 3. We find that 48 divided by 3 is 16, 54 divided by 3 is 18, 63 divided by 3 is 21, 81 divided by 3 is 27 and 105 divided by 3 is 35, all exact integers. However, 35 divided by 3 gives a non integer result with remainder. This confirms that 35 alone is not divisible by 3, while all other numbers in the list are.

Why Other Options Are Wrong:
48, 54, 63, 81 and 105 are all divisible by 3, so they share the common property and cannot be the odd one out.

Only 35 fails the test for divisibility by 3, so it is the only number that does not belong to the group defined by this property.

Common Pitfalls:
Sometimes candidates look at prime factorizations or at divisibility by other numbers such as 5 or 7 and become confused. While 35 is divisible by 5 and 7, some of the others are also divisible by 3 and 5 or 3 and 7. The simplest and most consistent identifying feature here is divisibility by 3 for five of the numbers and lack of it for only one number.

Final Answer:
The odd one out in the sequence is 35.