In this number analogy, “5 is to 130 as 6 is to ______”. Choose the option that completes the analogy by applying the same cube plus number rule used for the first pair.

Introduction / Context:
This analogy transforms a number into a larger number using a rule based on cubes. The pair “5 : 130” hints that 130 can be expressed using 5³ in some way, perhaps with an additional small operation. Once we identify the exact formula for converting 5 into 130, we can apply the same formula to 6 to determine the correct answer in “6 : ?”. Such cube based patterns are common in numerical reasoning questions.

Given Data / Assumptions:

• First pair: 5 corresponds to 130. • Second pair: 6 corresponds to an unknown number. • Options: 210, 212, 222, 242. • We note that 5³ = 125, which is close to 130, suggesting a cube plus something pattern.

Concept / Approach:
Start by expressing 130 in terms of 5³. Since 5³ = 125, we see that 130 = 5³ + 5. This suggests the rule “n maps to n³ + n”. If that is the rule, then for n = 6, the corresponding number would be 6³ + 6. We compute that value and compare it with the given options to find the correct match.

Step-by-Step Solution:
Step 1: Check the rule for the first pair. Compute 5³ = 5 * 5 * 5 = 125. Add the original number: 125 + 5 = 130. So the rule is consistent with 5 mapping to 5³ + 5. Step 2: Apply the same rule to 6. Compute 6³ = 6 * 6 * 6 = 216. Add the original number: 216 + 6 = 222. Step 3: Check the answer options. The result 222 appears as option C.

Verification / Alternative check:
To confirm that this is the intended pattern, consider whether any simpler rule fits both pairs. A simple multiple of 5 would not equal 130, and a square based pattern such as 5² or 6² would not produce results close to the given numbers. The formula n³ + n fits 5 exactly and yields a value for 6 that is one of the answer choices. This makes it the most natural and consistent explanation of the analogy.

Why Other Options Are Wrong:
• 210: This equals 6 * 35 and does not match 6³ + 6. • 212: This is 6³ − 4 and does not align with the pattern derived from the first pair. • 242: This is 6³ + 26, which is unrelated to the addition of the original number 6.

Common Pitfalls:
Some test takers may search for repeated differences or ratios between 5 and 130 or 6 and the options, instead of looking for a clean expression using powers. When a small integer maps to a much larger number, it is often a hint to consider squares or cubes. Checking n³ and then n³ plus n for each candidate quickly leads to the correct rule without confusion.

Final Answer:
The number that correctly completes the analogy is 222.