In this number trio reasoning question, four groups of three numbers are given: (4, 8, 16), (5, 10, 20), (6, 12, 24) and (7, 14, 21). In each valid group, the second and third numbers follow a simple rule based on the first number. Select the odd group that does not follow the same rule.

Introduction / Context:
This question focuses on number relationships inside small groups of three numbers. The groups given are (4, 8, 16), (5, 10, 20), (6, 12, 24) and (7, 14, 21). In three of these groups, the second and third numbers are simple multiples of the first number, following the same multiplication rule. One group deviates from that consistent pattern and must be identified as the odd one out.

Given Data / Assumptions:

• Number groups: (4, 8, 16), (5, 10, 20), (6, 12, 24), (7, 14, 21).
• The first number acts as a base for generating the second and third numbers.
• We expect a simple rule such as second = 2 * first and third = 4 * first.
• Exactly one group does not satisfy this common rule.

Concept / Approach:
The straightforward approach is to express each second and third number as a multiple of the first number. If in three groups the pattern is second = 2 * first and third = 4 * first, while in one group the third number does not equal 4 * first, that group becomes the odd one. Multiplication by small integers is all that is needed to solve this problem quickly.

Step-by-Step Solution:
Step 1: Examine (4, 8, 16).Second number = 8 = 2 * 4, and third number = 16 = 4 * 4. So the pattern is (n, 2n, 4n) with n = 4.Step 2: Examine (5, 10, 20).Second number = 10 = 2 * 5, and third number = 20 = 4 * 5. Again, the pattern is (n, 2n, 4n) with n = 5.Step 3: Examine (6, 12, 24).Second number = 12 = 2 * 6, and third number = 24 = 4 * 6. The same (n, 2n, 4n) pattern holds with n = 6.Step 4: Examine (7, 14, 21).Second number = 14 = 2 * 7, so the second number is correct if the rule is 2n. However, third number = 21 = 3 * 7, not 4 * 7. Thus this group does not follow the same (n, 2n, 4n) pattern.Step 5: Identify the odd group.The group (7, 14, 21) breaks the established rule for the third number, so it is the odd one out.

Verification / Alternative check:
You can also check by computing the ratios of second to first and third to first in each group. In the first three groups, the ratios are 2 and 4 respectively. For the last group, the ratios are 2 and 3. Since the ratio for the third number is different in the last group, that group does not belong with the others. This ratio based view reinforces the conclusion reached using simple multiplication.

Why Other Options Are Wrong:
(4, 8, 16): Exactly follows the rule second = 2n and third = 4n, where n is the first number.
(5, 10, 20): Again satisfies the same relationship as the first group.
(6, 12, 24): Continues the same pattern and is fully consistent with the other two correct groups.

Common Pitfalls:
Some students may focus only on differences between numbers, for example 4, 8, 16 having differences 4 and 8, which can be inconsistent and confusing. In many such questions, looking at ratios or direct multiplication relationships is more reliable than examining differences. Always try simple multiples first, especially when numbers appear to grow rapidly like 4, 8, 16 or 5, 10, 20.

Final Answer:
The odd group of numbers is (7, 14, 21), because it follows the pattern (n, 2n, 3n) instead of the consistent (n, 2n, 4n) pattern followed by the other three groups.