8 : 28 :: 27 : ?

Answer: Option D

The correct answer is (C) 64

Let's break down why:

The problem is an analogy, meaning we need to find a similar relationship between the numbers.

First, let's analyze the first pair: 8 : 28
* Notice that 8 is 2 cubed (2 * 2 * 2 = 8) or 2³
* 28 is close to 27, which is 3 cubed (3 * 3 * 3 = 27) or 3³. It's actually 3³ + 1

So, the relationship seems to be: x³ : (x+1)³ + 1

Now, let's apply this relationship to the second pair: 27 : ?
* 27 is 3 cubed (3 * 3 * 3 = 27) or 3³
* Following the pattern, the next number should be (3+1)³ + 1

Calculate (3+1)³ + 1:
* (3+1) = 4
* 4³ = 4 * 4 * 4 = 64
* Therefore, 3³ : 4³ + 1 is 3³ : 65is equal to 27 : 65

Hence, the answer is 65.