In this basic divisibility based odd one out question, you must choose the number that is not a multiple of 8 from the set of numbers 56, 72, 90 and 64.

Introduction / Context:
This question belongs to the number system and divisibility category in aptitude. You are required to identify which number does not share the same property of being a multiple of 8. Such questions build fluency in mental arithmetic and knowledge of common multiplication tables, which are critical for many competitive exams.

Given Data / Assumptions:

• The numbers are 56, 72, 90 and 64.
• We assume standard arithmetic in base 10.
• The suspected pattern is that three numbers are multiples of 8, and one is not.

Concept / Approach:
A multiple of 8 can be written as 8 * n for some integer n. For two and three digit numbers, you can check quickly by dividing or by remembering the 8 times table. The approach is to test each number for divisibility by 8 and identify which one fails this test. The number that is not divisible by 8 will be the odd one out.

Step-by-Step Solution:
Step 1: Check 56. 8 * 7 = 56, so 56 is a multiple of 8.Step 2: Check 72. 8 * 9 = 72, so 72 is a multiple of 8.Step 3: Check 64. 8 * 8 = 64, so 64 is a multiple of 8.Step 4: Check 90. When we divide 90 by 8 we get 11.25, which is not an integer. Therefore, 90 is not a multiple of 8.Step 5: Since 56, 72 and 64 are exact multiples of 8 and 90 is not, 90 is the odd one out.
Verification / Alternative check:
Another verification approach is to use remainders. Compute 56 mod 8, 72 mod 8 and 64 mod 8, which all give 0. For 90 mod 8, the remainder is 2, confirming that it is not divisible by 8. This matches the earlier conclusion derived from direct multiplication table knowledge.

Why Other Options Are Wrong:
56 is not the odd one out because it is 7 times 8 and clearly a multiple of 8.
72 is not the odd one out as it equals 9 times 8 and fits the common pattern.
64 is also not the odd one out because it is 8 times 8, another standard multiple of 8.

Common Pitfalls:
Some learners may look only at whether a number is even, but all four numbers given here are even. Being even is not enough; the focus must be on being a multiple of 8 specifically. Another mistake is performing division too quickly and miscalculating the quotient for 90. Remember that 8 * 11 = 88 and 8 * 12 = 96, so there is no whole number n for which 8 * n = 90. Careful mental calculation prevents such errors.

Final Answer:
The only number that is not a multiple of 8 is 90, so 90 is the odd one out.