In this three digit number reasoning question, select the odd number from the given alternatives based on the relationship between its digits.

Introduction / Context:
This question tests your ability to detect internal digit relationships in three digit numbers. Each option is a three digit number, and you must pick the number that does not follow the same internal rule as the others. Such digit based patterns are frequently tested in aptitude exams because they encourage careful observation rather than direct calculation of large expressions.

Given Data / Assumptions:
- The options are 325, 437, 246, and 564.- Each number has three digits that may be related through simple arithmetic operations.- A common pattern is that the third digit is obtained from the first two digits.

Concept / Approach:
One classic pattern with three digit numbers is that the third digit equals the sum of the first two digits. If three numbers satisfy this rule and one does not, that non matching number is the odd one out. We will therefore check each number to see whether the sum of the first two digits equals the third digit.

Step-by-Step Solution:
Step 1: For 325, add the first two digits: 3 + 2 = 5. This matches the third digit, so 325 follows the rule.Step 2: For 437, add 4 + 3 = 7. This equals the third digit, so 437 also follows the rule.Step 3: For 246, add 2 + 4 = 6. This matches the third digit, so 246 follows the same pattern.Step 4: For 564, add 5 + 6 = 11, which does not equal the third digit 4. So 564 does not follow the sum pattern.Step 5: Therefore, three numbers satisfy the rule third digit = sum of first two digits, while one number does not.

Verification / Alternative check:
You can quickly verify by checking whether subtracting the second digit from the third gives the first digit. For 325, 5 minus 2 equals 3; for 437, 7 minus 3 equals 4; for 246, 6 minus 4 equals 2. For 564, 4 minus 6 equals minus 2, which does not match the first digit 5. This confirms that 564 is the odd one.

Why Other Options Are Wrong:
325: Correctly follows third digit = sum of first two digits.437: Also follows the same relationship.246: Again matches the sum relationship.

Common Pitfalls:
Many candidates look only at even or odd digits and miss the more meaningful sum rule. Always check simple arithmetic relations between digits when you see patterns in three digit numbers.

Final Answer:
The odd number is 564 because its third digit is not equal to the sum of its first two digits, unlike the other three numbers.