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.)

(76, 152, 38)
(84, 168, 42)

The correct option is (68, 136, 34).

Step-by-step Explanation:

Let us analyze the relationship between the numbers in the given sets: (76, 152, 38) and (84, 168, 42).

Let the numbers in a set be represented as (A, B, C).

1. Analyzing the First Set: (76, 152, 38)

Notice the relationship between the first number (A = 76), the second number (B = 152), and the third number (C = 38):

$B=A\times 2$

$152=76\times 2$

And for the third number C:

$C=\frac{A}{2}$

$38=\frac{76}{2}$

2. Analyzing the Second Set: (84, 168, 42)

Checking the same pattern for the second set (A = 84, B = 168, C = 42):

$B=A\times 2$

$168=84\times 2$

And for the third number C:

$C=\frac{A}{2}$

$42=\frac{84}{2}$

Thus, the general rule/pattern followed by the numbers in each set is:

• The second number is twice the first number ($B=2A$).

• The third number is half of the first number ($C=\frac{A}{2}$).

3. Testing the Options:

• Option 1: (84, 178, 42)

$84\times 2=168\ne 178$ (Incorrect)

• Option 2: (96, 184, 46)

$96\times 2=192\ne 184$ (Incorrect)

• Option 3: (62, 132, 33)

$62\times 2=124\ne 132$ (Incorrect)

• Option 4: (68, 136, 34)

$68\times 2=136$ (Matches B)

$\frac{68}{2}=34$ (Matches C)

Therefore, the set (68, 136, 34) follows the exact same pattern.