In the four digit numbers 5210, 7214, 9218 and 7426, find the odd one out based on a double of the first digit pattern.

Introduction / Context:
Some odd one out questions hide a neat arithmetic pattern relating specific digits within each number. Here, each number has four digits and we can think of it as abcd. A common type of pattern relates the first digit to the last two digits, for example the last two digits may equal twice the first digit. If three numbers follow this rule and one fails, the one that fails is the odd one out. This question is a classic example of that kind of digit relationship puzzle.

Given Data / Assumptions:
The numbers are 5210, 7214, 9218 and 7426. We interpret each number as a four digit sequence abcd. We test whether the last two digits form a number equal to 2 times the first digit.

Concept / Approach:
Let the first digit be a and the last two digits together be a two digit number k. In three of the numbers, k equals 2 * a. For example, if a = 5, then twice the first digit is 10 and the last two digits are 10. The number in which this relationship does not hold is the odd one out. This pattern is simple yet effective in reasoning exams because it forces candidates to connect different parts of the number rather than treat it as a whole.

Step-by-Step Solution:
Step 1: Consider 5210. The first digit is 5 and the last two digits are 10. Twice the first digit is 2 * 5 = 10, which matches the last two digits. Step 2: Consider 7214. The first digit is 7 and the last two digits are 14. Twice the first digit is 2 * 7 = 14, again matching the last two digits. Step 3: Consider 9218. The first digit is 9 and the last two digits are 18. Twice the first digit is 2 * 9 = 18, which also matches the last two digits. Step 4: Consider 7426. The first digit is 7 and the last two digits are 26. Twice the first digit is 2 * 7 = 14, which does not match 26. Step 5: Therefore, 5210, 7214 and 9218 follow the pattern last two digits = 2 * first digit, while 7426 does not. So 7426 is the odd one out.

Verification / Alternative check:
We can check the middle digit for completeness, but it is not needed for this pattern and does not affect the rule. Recomputing twice the first digit for each number confirms that only 7426 breaks the relationship. Since the pattern is exact and simple arithmetic, the conclusion is secure.

Why Other Options Are Wrong:
5210 is not the odd one out because it perfectly satisfies the pattern 2 * first digit = last two digits. 7214 is not the odd one out because it also obeys the same rule. 9218 is not the odd one out because its last two digits equal twice the first digit. 7426 alone fails this rule, which makes it different.

Common Pitfalls:
A common mistake is to focus only on the sum or product of all four digits instead of exploring targeted relationships, such as first digit to last two digits. Another error is to treat the last two digits separately rather than as a two digit number, which hides the intended pattern. Carefully checking simple linear relationships between digits is an efficient strategy for such reasoning questions.

Final Answer:
The number that does not satisfy the rule last two digits = double the first digit and is therefore the odd one out is 7426.