In the group of ordered triples 5-20-25, 10-40-50, 4-15-24 and 25-100-125, which triple is the odd one out?

Introduction / Context:
This question is about recognising a proportional relationship within ordered triples of numbers. Three of the triples follow a common multiplicative rule, while one does not. This is a standard style of odd one out problem used to test understanding of ratios and simple multiplication patterns.

Given Data / Assumptions:
- The triples are 5-20-25, 10-40-50, 4-15-24 and 25-100-125.
- Each triple is of the form a b c, where a, b and c are positive integers.
- Exactly one triple does not follow the pattern satisfied by the other three.

Concept / Approach:
Look for a simple relationship between the three numbers in each triple. The most natural idea is that b and c are fixed multiples of a. For example, b could be 4 times a and c could be 5 times a. If three of the triples satisfy the same set of ratios and one does not, that one will be the odd one out.

Step-by-Step Solution:
Step 1: Check the triple 5-20-25. 20 = 4 * 5 and 25 = 5 * 5, so b = 4a and c = 5a. Step 2: Check the triple 10-40-50. 40 = 4 * 10 and 50 = 5 * 10, again b = 4a and c = 5a. Step 3: Check the triple 25-100-125. 100 = 4 * 25 and 125 = 5 * 25, once more b = 4a and c = 5a. Step 4: Check the triple 4-15-24. If the same pattern held, b should be 4 * 4 = 16 and c should be 5 * 4 = 20. Instead, b = 15 and c = 24, which are not equal to 16 and 20. Therefore, 4-15-24 does not follow the pattern.

Verification / Alternative check:
Rewriting the valid triples as (a, 4a, 5a) makes the pattern very clear: (5,20,25), (10,40,50) and (25,100,125) all fit this structure. The triple (4,15,24) would have to be (4,16,20) to be consistent but it is not, so it is definitely the odd one.

Why Other Options Are Wrong:
Option B (5-20-25) follows the b = 4a and c = 5a pattern perfectly.
Option C (10-40-50) also satisfies the same proportional relationships.
Option D (25-100-125) is again consistent with b = 4a and c = 5a.
Option A (4-15-24) alone does not match this rule, so it is the correct odd one out.

Common Pitfalls:
Sometimes students compare absolute differences such as 20 - 5 or 25 - 20 without noticing the multiplicative structure. Others may check random patterns like a + b = c, which does not hold here. The key is to think in terms of ratios because many real world relationships like speed, density or scaling work multiplicatively, and exam questions mirror that idea.

Final Answer:
The odd triple is 4-15-24.