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 their constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting / 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.)

(20, 46, 2)

(32, 136, 24)

The correct answer is (6, 42, 10).

Logic and Pattern Analysis:
Let the numbers in each set be represented as (First Number, Second Number, Third Number) or (A, B, C).

The relationship between the numbers follows the pattern:

$\mathrm{Second\; Number}=(2\times \mathrm{First\; Number})+(3\times \mathrm{Third\; Number})$

$B=2A+3C$

Let me verify this pattern with the given sets:

Set 1: (20, 46, 2)

$B=(2\times 20)+(3\times 2)$

$B=40+6=46$

This matches the middle term of the first set.

Set 2: (32, 136, 24)

$B=(2\times 32)+(3\times 24)$

$B=64+72=136$

This matches the middle term of the second set.

Now, let's test the options to find the set that follows the same rule:

Option 1: (6, 42, 10)

$B=(2\times 6)+(3\times 10)$

$B=12+30=42$

This matches the middle number 42 perfectly.

Option 2: (32, 93, 11)

$(2\times 32)+(3\times 11)=64+33=97\ne 93$

Option 3: (13, 25, 1)

$(2\times 13)+(3\times 1)=26+3=29\ne 25$

Option 4: (17, 78, 16)

$(2\times 17)+(3\times 16)=34+48=82\ne 78$

Therefore, the set (6, 42, 10) follows the exact same pattern as the original sets.