In the following question, select the odd number group from the alternatives given below. In most options, the third number is 2.5 times the second number (or follows a consistent ratio). Identify the group that breaks this relationship. (A) (4, 16, 48) (B) (6, 36, 90) (C) (8, 64, 160) (D) (12, 144, 360) (E) (10, 100, 250)

Introduction / Context:
This odd-one-out problem involves number triples. Such questions typically hide a consistent relationship between the 2nd and 3rd values (ratio or multiplier), while the 1st and 2nd values may follow another pattern (like square). The odd group is the one that does not match the dominant shared relationship.

Given Data / Assumptions:

• Each option is a triple (a, b, c).
• We check whether b relates to a (often b = a^2).
• We then check whether c relates to b by a consistent multiplier.

Concept / Approach:
First, observe that b equals a^2 in all options (for example, 6^2=36). Then identify the dominant pattern between b and c. In options B, C, D, and E, c = 2.5 * b. The option that does not satisfy c = 2.5 * b is the odd one out.

Step-by-Step Solution:

Verification / Alternative check:
Compute the ratio c/b. For B: 90/36 = 2.5. For C: 160/64 = 2.5. For D: 360/144 = 2.5. For E: 250/100 = 2.5. For A: 48/16 = 3. Since A has ratio 3 while the others have ratio 2.5, A is clearly the odd group.

Why Other Options Are Wrong:

Common Pitfalls:
Many learners stop after noticing b = a^2 and assume that is the only rule. But the oddness is not there, because all options satisfy the square relation. You must also examine b-to-c. Another pitfall is using multiplication by 3 for all, which fails for most. Always look for the dominant multiplier that appears repeatedly across the set.

Final Answer:
(4, 16, 48)