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.)

(5, 25, 50)

(8, 64, 128)

The correct option is (12, 144, 288).

Logic and Pattern Analysis:

Let the set of numbers be denoted as ($A$, $B$, $C$).

Analyzing the relationship between the numbers in the given sets:

1. First Set: (5, 25, 50)

Second number ($B$): $5^2=25$

Third number ($C$): $25\times 2=50$

2. Second Set: (8, 64, 128)

Second number ($B$): $8^2=64$

Third number ($C$): $64\times 2=128$

Pattern:

$B=A^2$

$C=B\times 2=2\times A^2$

Checking the Options:

Applying the same logic to option (12, 144, 288):

First number ($A$) = 12

Second number ($B$) = ${12}^2=144$

Third number ($C$) = $144\times 2=288$

This follows the exact pattern defined by the given sets.