In this odd-man-out question on number pairs, four pairs are given: 48:134, 40:110, 18:48 and 30:80. In three of these, the second number is obtained from the first by applying the relation 3 × first number − 10. Which option represents the odd pair that does not follow this 3n − 10 pattern?

Introduction / Context:
This question is a numerical odd-man-out problem involving pairs of numbers related by a specific arithmetic rule. The pairs given in the stem are 48:134, 40:110, 18:48 and 30:80, and the options A, B, C and D correspond to these pairs respectively. In many aptitude tests, such pair relationships are based on expressions like 2n + k or 3n − k. Here, three pairs follow one consistent rule, while one pair does not. The aim is to identify the mismatched pair.

Given Data / Assumptions:
Option A represents the pair 48:134.
Option B represents the pair 40:110.
Option C represents the pair 18:48.
Option D represents the pair 30:80.
There is a suspected relationship of the form second number = 3 × first number − 10 in three of the pairs.
One pair does not satisfy this rule and is the odd one out.

Concept / Approach:
The core concept is to check a potential linear relationship between the first and second numbers of each pair. We test the expression second = 3 × first − 10 on each pair. If the expression holds for three pairs but fails for one, the failing pair is the odd one. This method is systematic and helps avoid random guessing.

Step-by-Step Solution:
Step 1: For 48:134, compute 3 × 48 − 10. This equals 144 − 10 = 134, which matches the second number. Step 2: For 40:110, compute 3 × 40 − 10. This equals 120 − 10 = 110, which matches the second number. Step 3: For 30:80, compute 3 × 30 − 10. This equals 90 − 10 = 80, which again matches the second number. Step 4: For 18:48, compute 3 × 18 − 10. This equals 54 − 10 = 44, but the second number is 48, not 44. Step 5: Conclude that the first, second and fourth pairs follow the relation 3n − 10, while the third pair does not. Therefore, option C is the odd one out.
Verification / Alternative check:
Another way to verify is to rearrange the relation as 3 × first = second + 10 and check if this is an integer equality. For 48:134, we have 3 × 48 = 144 and 134 + 10 = 144, which is true. For 40:110, 3 × 40 = 120 and 110 + 10 = 120, again true. For 30:80, 3 × 30 = 90 and 80 + 10 = 90, which holds. For 18:48, 3 × 18 = 54, but 48 + 10 = 58, which does not match. This clearly confirms that the pair in option C does not satisfy the rule.

Why Other Options Are Wrong:
Option A (48:134) satisfies the rule second = 3 × first − 10 and therefore belongs to the main consistent group.
Option B (40:110) also satisfies second = 3 × first − 10, so it is not the odd one out.
Option D (30:80) fits the same pattern, confirming that it belongs with options A and B.
Option C (18:48) alone does not match the 3n − 10 relationship and thus is the correct odd-man-out option.

Common Pitfalls:
A frequent mistake is to try random operations or to stop checking once one or two patterns are found. It is important to test the suspected rule across all pairs. Another pitfall is careless multiplication or subtraction, which can lead to incorrect conclusions. Always recheck the arithmetic with simple expressions like 3n − 10 or 3n = second + 10 to ensure accuracy. Focusing on a simple linear rule is usually sufficient in such pair-relation questions.

Final Answer:
The pair that does not follow the relation second = 3 × first − 10 and is therefore the odd one out is represented by option C, that is, 18:48.