In this number analogy question, select the related number pair from the given alternatives: 36 : 12 :: 72 : ?

Introduction / Context:
This is a simple number analogy question from quantitative aptitude and reasoning exams. We are given one pair of numbers, 36 and 12, and asked to extend the same relationship to find the missing number that should pair with 72. Problems like this test your ability to recognise arithmetic patterns such as multiplication, division, and proportional relationships between numbers.

Given Data / Assumptions:

• First pair of numbers: 36 : 12.
• Second pair of numbers: 72 : ?.
• We assume the same mathematical rule connects both pairs.
• Only one option should satisfy the same rule consistently.

Concept / Approach:
The usual approach in such analogy questions is to check for a simple operation between the first and second numbers in the known pair. We try division, multiplication, and combinations of basic operations to see which pattern works neatly. Once the pattern is discovered for 36 and 12, we apply the same rule to 72 to get the missing number. The key idea is that the rule must be consistent and not artificially adjusted for each pair.

Step-by-Step Solution:
Step 1: Examine the first pair 36 and 12.Step 2: Compute 36 / 3 = 12, which gives an exact integer result.Step 3: This suggests the rule may be “second number = first number / 3”.Step 4: Apply the same rule to 72: 72 / 3 = 24.Step 5: Check that 24 is present among the answer options and that no other option fits a simpler consistent rule.

Verification / Alternative check:
We can briefly test other possible patterns to ensure the division by 3 rule is indeed the most natural. For example, 36 - 24 = 12, so a subtraction pattern like “second = first - 24” would not generalise well, because then 72 - 24 = 48, which does not match any intuitive relation with 36 : 12. Similarly, trying multiplication such as first * 2, first * 4, or adding fixed numbers does not produce 12 from 36 in a neat way. Division by 3 is the cleanest and most consistent pattern, and applying it to 72 yields 24, which is one of the options.

Why Other Options Are Wrong:
Option A (20): There is no simple rule that converts 36 to 12 and 72 to 20 simultaneously by the same arithmetic operation.
Option C (17): This is not a result of dividing 72 by any simple factor that also converts 36 to 12, so it breaks the analogy.
Option D (16): Again, 16 does not follow from 72 under the rule 36 → 12 by division. It would require a completely different pattern, so it is not consistent.

Common Pitfalls:
Candidates sometimes look for complicated number patterns when a very simple rule such as multiplication or division is sufficient. Another common mistake is to apply different rules to each pair, which is not allowed in analogy questions. You must always use the same transformation for both pairs. Forgetting this requirement can easily lead to an incorrect choice even if the second pair seems superficially reasonable.

Final Answer:
The consistent rule is “divide the first number by 3 to obtain the second.” Therefore, 36 : 12 :: 72 : 24, and the correct answer is 24.