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.)

(45, 15, 3)

(120, 40, 8)

The correct option is (165, 55, 11).

Let us analyze the relationship between the three numbers in the given sets: $(A,B,C)$.

First Set: $(45,15,3)$

If we divide the first number by the second number, we get:
$45÷15=3$ (which is the third number)

Also, notice that:
$3\times 15=45$

Second Set: $(120,40,8)$

Dividing the first number by the second number gives:
$120÷40=3$

Wait, let us re-examine the pattern across both sets:

In set 1: $45÷15=3$, and the third number is $3$.
In set 2: $120÷40=3$, but the third number is $8$? No, let us check another relation:

$A÷C=B$

For $(45,15,3)$:
$45÷3=15$

For $(120,40,8)$:
$120÷8=15$

Therefore, the logic following both given sets is:
First number ÷ Third number = Second number (or First number = Second number × Third number / 15 ... wait, $15\times 3=45$ and $40\times 8=320\ne 120$).

Let us check: $A÷C=15$? No, $45÷3=15$ (second number) and $120÷8=15$ (which is not 40, but $120÷40=3$ and $120÷15=8$).

Let's check the ratio:
$A=B\times 3$
For set 1: $15\times 3=45$
For set 2: $40\times 3=120$

So the relation between the first two numbers is $A=3\times B$ (or $A÷B=3$).

Now let's check the options for $A=3\times B$:
1. $55\times 3=165$ (Holds for 165, 55)
2. $54\times 3=162\ne 165$

Now let me check the third number $C$:
In set 1: $15÷5=3$ or $45÷15=3$
In set 2: $40÷5=8$
So, $C=B÷5$!

Let me verify:
For $(45,15,3)$:
$A=3\times 15=45$
$C=15÷5=3$

For $(120,40,8)$:
$A=3\times 40=120$
$C=40÷5=8$

Applying this rule to $(165,55,11)$:
$A=3\times 55=165$
$C=55÷5=11$

Thus, $(165,55,11)$ follows the exact same pattern.