Analogy: ____ : 9 :: 4 : 24

To solve this analogy, we need to identify the relationship between the given pair of numbers (____ and 9) and apply the same relationship to the second pair of numbers (4 and 24).

Step 1: Analyzing the first pair
The first pair consists of a blank space (____) and the number 9. We need to determine what number should replace the blank space to maintain the same relationship as between 9 and the blank space.

Step 2: Identifying the relationship
To find the relationship between 9 and the blank space, we can observe that 9 is the square of 3 (3 x 3 = 9). Therefore, the missing number in the first pair is 3.

Step 3: Applying the relationship to the second pair
Now that we have identified the relationship between 9 and the blank space as the square root of 9, we can apply the same relationship to the second pair.

To find the missing number in the second pair, we need to determine what number, when squared, equals 24. By calculating the square root of 24, we get approximately 4.899. However, since the options provided are whole numbers, we need to round this value to the nearest whole number.

Step 4: Finding the missing number
Rounding 4.899 to the nearest whole number gives us 5. Therefore, the missing number in the second pair is 5.

Conclusion:
The correct answer is option 'A' (3). The relationship between the first pair (____ and 9) is that 9 is the square of 3. Applying the same relationship to the second pair (4 and 24), we find that the missing number is 5, which corresponds to option 'A'.

Answer 3