Four groups of three numbers are given. In each group the second and third numbers follow a rule based on the first number. Three groups share the same addition rule. Select the odd group of numbers.

Introduction / Context:
This question checks your understanding of simple number patterns and analogies. You are given small groups of numbers where the second and third numbers are derived from the first by a simple rule, and you must detect which group does not follow the dominant pattern.

Given Data / Assumptions:

• Groups: (2, 3, 4), (4, 5, 6), (6, 7, 8), (4, 6, 8).
• The second and third numbers should be related to the first using the same rule for most groups.
• We need to find the group that fails to follow that common rule.

Concept / Approach:
For such three term groups, a very common rule is to obtain the second and third terms by adding fixed numbers to the first term. We test if the second equals first plus some constant and the third equals first plus another constant across the groups and see which set breaks the pattern.

Step-by-Step Solution:
For (2, 3, 4): 3 = 2 + 1 and 4 = 2 + 2. For (4, 5, 6): 5 = 4 + 1 and 6 = 4 + 2. For (6, 7, 8): 7 = 6 + 1 and 8 = 6 + 2. For (4, 6, 8): 6 = 4 + 2 and 8 = 4 + 4, so the increments are +2 and +4, not +1 and +2. Thus three groups follow the pattern (first + 1, first + 2), but (4, 6, 8) does not.

Verification / Alternative check:
You can also subtract the first number from the other two numbers in each group and look only at the resulting pair of differences. The first three sets give difference pairs (1, 2), while the last gives (2, 4). Since only the last pair of differences is different, (4, 6, 8) is confirmed as the odd group.

Why Other Options Are Wrong:

• (2, 3, 4): Follows the rule second = first + 1 and third = first + 2.
• (4, 5, 6): Also matches the same +1, +2 pattern.
• (6, 7, 8): Again clearly follows +1, +2 from the first number.

Common Pitfalls:
Sometimes candidates only check if the numbers are consecutive and miss that the rule is specifically linked to the first term. (4, 6, 8) looks like a simple progression with difference 2, but the structure relative to the first element is different. Always express the second and third terms directly in terms of the first term to see the intended pattern clearly.

Final Answer:
(4, 6, 8)