Select the odd one out from the following four digit numbers based on the pattern of even and odd digits in each number: 1356, 5497, 8764, 9943.

Introduction / Context:
Odd one out questions check the ability to recognize patterns and classify numbers according to specific properties. Here, we are given four digit numbers and asked to select the one that does not fit the same pattern as the others. The key is to look for a simple property that three of the numbers share, such as the count of even and odd digits, and then identify the exception.

Given Data / Assumptions:

• Numbers given: 1356, 5497, 8764, 9943, and an additional number 7534 as a distractor option.
• Each number contains exactly four digits.
• We are to focus on properties related to the digits, not on larger mathematical structures like prime status of the whole number.
• The most natural property to inspect is whether each digit is even or odd.

Concept / Approach:
We examine each number digit by digit and count how many digits are even and how many are odd. If three of the numbers share the same count pattern, and one differs, that differing number is the odd one out. For four digit numbers, the possible patterns include three odds and one even, three evens and one odd, two evens and two odds, and so on. The simplest workable pattern usually gives the intended answer.

Step-by-Step Solution:
Step 1: Consider 1356. Digits are 1, 3, 5, and 6. Here 1, 3, and 5 are odd, and 6 is even, so the pattern is three odd digits and one even digit. Step 2: Consider 5497. Digits are 5, 4, 9, and 7. Here 5, 9, and 7 are odd, and 4 is even, so again we have three odd digits and one even digit. Step 3: Consider 9943. Digits are 9, 9, 4, and 3. Here 9, 9, and 3 are odd, and 4 is even, so the pattern remains three odd digits and one even digit. Step 4: Consider 8764. Digits are 8, 7, 6, and 4. Here 8, 6, and 4 are even, and 7 is odd, so this number has three even digits and one odd digit. Step 5: The majority of numbers 1356, 5497, and 9943 share the pattern three odd and one even, while 8764 has the reverse pattern, so 8764 is the odd one out.

Verification / Alternative check:
We can quickly check the distractor 7534. Digits are 7, 5, 3, and 4. Here 7, 5, and 3 are odd, and 4 is even, so it also follows the three odd, one even pattern. This confirms that only 8764 breaks the dominant pattern among the given options. Counting procedures are straightforward, so if we re count 8764 and still get three even digits, our conclusion remains stable.

Why Other Options Are Wrong:
1356: Matches three odd digits and one even digit, consistent with the dominant pattern.
5497: Again matches three odd digits and one even digit, so it is not special.
9943: Follows the same pattern of three odd and one even digit.
7534: Included as an extra option but also has three odd digits and one even digit, so it is not the odd one out.

Common Pitfalls:
A common error is to inspect properties like divisibility by 2, 3, or 5 of the entire number, which may not lead to a clear unique choice. Another pitfall is mis classifying digits like 0 or mis counting under exam stress. In such pattern questions, it is often best to write a small table and count the number of odd and even digits for each candidate.

Final Answer:
The only number that has three even digits and one odd digit, while the others have three odd digits and one even digit, is 8764.