Select the set in which the numbers are related in the same way as are the numbers of the following sets.

(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)

(288, 144, 24)

(432, 216, 36)

The correct answer is (504, 252, 42).

Let us analyze the relationship between the numbers in the given sets:
1) (288, 144, 24)
2) (432, 216, 36)

Let each set be represented as ($A$, $B$, $C$).

If we look at the relationship between the first and the second numbers:
In the first set:
$\frac{288}{2}=144$
In the second set:
$\frac{432}{2}=216$
So, $B=\frac{A}{2}$.

Now, let us examine the relationship between the second and third numbers, or between the first and third numbers:
In the first set:
$\frac{288}{24}=12$
In the second set:
$\frac{432}{36}=12$
This gives the relation:
$\frac{A}{C}=12$ or $A=12\times C$.

Alternatively, the relationship between the second and third numbers is:
In the first set:
$\frac{144}{24}=6$
In the second set:
$\frac{216}{36}=6$
This gives the relation:
$B=6\times C$.

Thus, the logic followed by each set ($A$, $B$, $C$) is:
$B=\frac{A}{2}$ and $B=6\times C$ (which means $A=12\times C$).

Let us check the options to find the set that follows this logic:
Option 1: (504, 252, 42)
Checking $B=\frac{A}{2}$:
$\frac{504}{2}=252$ (This is correct)
Checking $B=6\times C$:
$6\times 42=252$ (This is correct)

Therefore, the set (504, 252, 42) follows the same relationship.