In this number analogy, “5 is to 30 as 7 is to ______”. Select the number that completes the analogy by applying the same multiplication pattern used in the first pair.

Introduction / Context:
This question involves a simple multiplication based number analogy. The pair “5 : 30” suggests that the second number is derived from the first using a direct arithmetic rule. Once that rule is identified, we apply it to the number 7 in the second pair “7 : ?” and select the correct result from the options. Questions like this are designed to test quick recognition of standard multiplication patterns.

Given Data / Assumptions:

• First pair: 5 corresponds to 30. • Second pair: 7 corresponds to an unknown number. • Options: 54, 50, 49, 56. • We expect a single arithmetic rule applied consistently in both pairs.

Concept / Approach:
First, look at how to obtain 30 from 5. One common pattern in analogies is n multiplied by the next integer, that is, n * (n + 1). For 5, this gives 5 * 6 = 30, which matches the given pair. If we treat that as the rule, then we should apply the same formula to 7 to obtain the second number of the new pair and then match it with the correct option.

Step-by-Step Solution:
Step 1: Confirm the rule in the first pair. Compute 5 * (5 + 1) = 5 * 6 = 30. This exactly matches 30, so the rule works. Step 2: Apply the same rule to 7. Compute 7 * (7 + 1) = 7 * 8. 7 * 8 = 56. Step 3: Check the answer options. Among 54, 50, 49, and 56, only 56 matches the computed result.

Verification / Alternative check:
We can re express the analogy as “n : n * (n + 1)”. For n = 5, we have 5 : 30. For n = 7, we have 7 : 56. No other simple common pattern such as squaring or doubling fits both pairs as neatly. For example, 5² = 25 and 7² = 49, but 30 is not 25, and 49 is only one of the distractors, not the number that continues the pattern properly. Thus, n * (n + 1) is the most consistent rule here.

Why Other Options Are Wrong:
• 54: This equals 6 * 9 and does not arise from 7 * (7 + 1). • 50: This is not obtained by any direct extension of 5 * 6 = 30 for the number 7. • 49: This is 7², which might look tempting but breaks the specific pattern used in the first pair.

Common Pitfalls:
Candidates sometimes spot 49 as 7² and choose it, forgetting to check whether squaring also explains 30 from 5. Because 5² is 25 and not 30, squaring cannot be the underlying rule. The safer approach is to test any suspected pattern against both parts of the analogy before deciding on a final answer.

Final Answer:
The number that correctly completes the analogy is 56.