In this three-number group odd-man-out question, choose the group whose numbers do not follow the same decreasing pattern.

Introduction / Context:
This is a classification question involving groups of three numbers that decrease according to certain steps. In three of the groups, the numbers decrease by the same pair of fixed differences. One group uses a different set of differences, which makes it the odd-man-out. Detecting this requires us to find the difference between consecutive terms in each group and compare the patterns.

Given Data / Assumptions:

• Groups: (104, 101, 96), (109, 106, 101), (97, 94, 89) and (121, 118, 111).
• Each triple is ordered as (first, second, third).
• We analyse the sequence of differences first to second and second to third in each group.

Concept / Approach:
All sequences here are decreasing. The key observation is whether the differences are the same across groups. In three groups, the numbers decrease first by 3 and then by 5. In one group, the second decrease is bigger, breaking the pattern. Identifying this difference pattern reveals the odd group.

Step-by-Step Solution:
Step 1: Analyse (104, 101, 96). The first difference is 101 - 104 = -3. The second difference is 96 - 101 = -5. So this group uses steps of -3 and then -5. Step 2: Analyse (109, 106, 101). The first difference is 106 - 109 = -3. The second difference is 101 - 106 = -5. This group also decreases by -3 and then -5. Step 3: Analyse (97, 94, 89). The first difference is 94 - 97 = -3. The second difference is 89 - 94 = -5. So it again follows -3, then -5. Step 4: Analyse (121, 118, 111). The first difference is 118 - 121 = -3. The second difference is 111 - 118 = -7. Here, the decreases are -3 and then -7, not -3 and -5. Step 5: Summarise. Three groups share the same pattern of subtracting 3 and then subtracting 5, while one group subtracts 3 and then subtracts 7. Step 6: Conclude that (121, 118, 111) is the odd group because it does not follow the common -3, -5 decreasing pattern.

Verification / Alternative check:
We can also express the third term in terms of the first term. In the first three groups, the third term equals first - 8, because -3 and then -5 gives a net -8. For example, 104 - 8 = 96, 109 - 8 = 101 and 97 - 8 = 89. In the last group, however, 121 - 8 = 113, not 111. Instead, 111 = 121 - 10, which confirms the second step there is larger. Thus, under both the difference pattern and net change perspective, (121, 118, 111) fails to match the others.

Why Other Options Are Wrong:
(104, 101, 96) is not the odd group because it follows the standard -3, -5 pattern. (109, 106, 101) also decreases by the same amounts and fits in with the others. (97, 94, 89) is again perfectly consistent with -3, then -5. Since these three share identical difference patterns, they cannot be considered the odd-man-out. Only (121, 118, 111) uses -3 and then -7, which makes it different.

Common Pitfalls:
Students sometimes focus only on whether the numbers are prime or composite, or they may check only the first difference and ignore the second one. If you look only at the first step, all groups have -3 and appear similar. You must always check the second step as well to see the full pattern. Another issue is trying to invent complex formulas when a simple difference analysis is enough. Always compute both differences for each group to avoid missing such subtle mismatches.

Final Answer:
The odd group of numbers is (121, 118, 111), because in this group the numbers decrease by 3 and then 7, whereas in all the other groups they decrease by 3 and then 5.