In this number analogy, “96 is to 32 as 48 is to ______”. Select the number that completes the analogy by applying the same division rule used in the first pair.

Introduction / Context:
This is a straightforward numerical analogy from quantitative aptitude. The pair 96 : 32 shows how the first number is related to the second by a simple arithmetic operation. To solve the analogy, you must detect this operation and apply it to the second first number, 48, in order to find the matching second number from the options. Questions like this reward a calm, stepwise check of basic operations such as addition, subtraction, multiplication, and division.

Given Data / Assumptions:

• First pair of numbers: 96 and 32. • Second pair: 48 and an unknown number. • Options: 14, 12, 16, 18. • All numbers are ordinary positive integers and there is a single consistent rule that connects the pairs.

Concept / Approach:
Begin with the first pair and test natural operations. Notice that 32 is exactly one third of 96, because 96 / 3 = 32. No other simple integer operation is as clean or direct. This suggests that the rule might be “divide the first number by 3 to obtain the second number”. If that rule works well in the example, we apply the same operation to 48 and then match the result with the options provided.

Step-by-Step Solution:
Step 1: Work with the first pair 96 and 32. Check division: 96 / 3 = 32 exactly, with no remainder. Step 2: Record the pattern. Pattern: second number = first number / 3. Step 3: Apply the same pattern to 48. Compute 48 / 3. 48 / 3 = 16. Step 4: Compare with the options. The value 16 matches option C and no other option equals 48 / 3.

Verification / Alternative check:
To confirm, check whether any other simple rules such as subtracting a constant or taking a factor give more consistent results. For example, 96 − 32 = 64, but 48 − 16 = 32, which does not show a stable pattern that fits the analogy statement. Similarly, multiplying 32 by a constant does not recover 96 in a way that naturally extends to 48. Therefore, division by 3 is the clearest and most logical rule that satisfies the given pair and leads to a valid answer for the second pair.

Why Other Options Are Wrong:
• 14: This does not equal 48 / 3 and does not arise from any simple extension of 96 : 32. • 12: Corresponds to 48 / 4, which is not the rule in the first pair. • 18: Counts as 48 / 2.67 approximately and is not a clean integer division pattern.

Common Pitfalls:
Sometimes candidates try to overcomplicate the pattern by mixing operations or searching for advanced formulas. For many exam questions, especially where the numbers divide neatly, a single basic operation is enough. Always test simple division and multiplication first, particularly when the second number is smaller and appears to be an exact fraction of the first.

Final Answer:
The number that correctly completes the analogy is 16.