In the following number analogy, 4 is related to 44 using a specific multiplication rule. Using the same rule, which number should be related to 77?

Introduction / Context:
This number analogy problem checks your ability to detect a simple arithmetic relationship between two numbers. You are told that 4 is related to 44, and must find what number corresponds to 77 under the same rule. Recognising common patterns such as multiplication by a constant is key to solving such questions quickly in aptitude exams.

Given Data / Assumptions:
- Known pair: 4 and 44.
- Second known number: 77.
- Options for the missing number: 3, 6, 7 and 5.
- We assume a single consistent arithmetic rule is responsible for the mapping.

Concept / Approach:
Observe that 44 is 4 multiplied by 11. That is, 4 * 11 = 44. This suggests a pattern where each base number is multiplied by 11 to get the second number in the pair. If that is correct, then we must find the number which, when multiplied by 11, gives 77.

Step-by-Step Solution:
Step 1: Confirm the pattern for the first pair: 4 * 11 = 44. Step 2: Formulate the rule as related number = base number * 11. Step 3: Apply this rule in reverse to 77 by dividing 77 by 11. Step 4: Compute 77 / 11 = 7. Step 5: Check that 7 appears among the given options. Step 6: Conclude that 7 is the base number that relates to 77 in the same way 4 relates to 44.

Verification / Alternative check:
Verify that no other simple pattern fits as neatly. For example, adding a fixed constant to 4 to obtain 44 would require 40, while to obtain 77 from the same constant would give 37, which does not match any option. The multiplication by 11 pattern is widely recognised and works consistently across both pairs, which confirms it as the intended rule.

Why Other Options Are Wrong:
Option A 3 would give 3 * 11 = 33, not 77. Option B 6 would give 66, and option D 5 would give 55. None of these results match 77, so they cannot be correct under the identified rule. Therefore they fail the consistency requirement of number analogies.

Common Pitfalls:
Some candidates overcomplicate simple problems by looking for digit manipulation, such as repeating digits or concatenation, instead of testing basic multiplication. Another mistake is to try multiple inconsistent rules for different pairs, which is not allowed in a valid analogy. Always confirm the same operation works for all pairs involved before finalising your answer.

Final Answer:
Since 4 relates to 44 by the rule 4 * 11, the number that relates to 77 must satisfy n * 11 = 77, giving n = 7.