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/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) (33, 1089, 17) (21, 441, 11) 4902

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The correct option is (27, 729, 14).

Pattern Analysis:
Let the given sets of numbers be represented as (A, B, C).

By analyzing the relationship between the numbers in the given sets, we can establish the following rules:

1. The second number (B) is the square of the first number (A):

$B=A^2$

2. The third number (C) is obtained by adding 1 to the first number (A) and dividing by 2:

$C=\frac{A+1}{2}$

Verification with Given Sets:

Set 1: (33, 1089, 17)

${33}^2=1089$

$\frac{33+1}{2}=\frac{34}{2}=17$

Both relations hold true for Set 1.

Set 2: (21, 441, 11)

${21}^2=441$

$\frac{21+1}{2}=\frac{22}{2}=11$

Both relations hold true for Set 2.

Checking the Options:

Now, let's test option (27, 729, 14) with the same rules:

${27}^2=729$

$\frac{27+1}{2}=\frac{28}{2}=14$

Since both mathematical relations hold true, (27, 729, 14) follows the exact same pattern as the given sets.

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The correct option is (27, 729, 14).

Pattern Analysis:
Let each set of numbers be represented in the general format (A, B, C).

By observing the given sets, we can establish two key relationships among the numbers:

1. The second number (B) is the square of the first number (A):

$B=A^2$

2. The third number (C) is calculated by adding 1 to the first number (A) and dividing the result by 2:

$C=\frac{A+1}{2}$

Verification with the Given Sets:

First Given Set: (33, 1089, 17)

${33}^2=1089$

$\frac{33+1}{2}=\frac{34}{2}=17$

Both rules hold true for the first set.

Second Given Set: (21, 441, 11)

${21}^2=441$

$\frac{21+1}{2}=\frac{22}{2}=11$

Both rules hold true for the second set.

Testing the Option (27, 729, 14):

${27}^2=729$

$\frac{27+1}{2}=\frac{28}{2}=14$

Since both conditions are satisfied, the set (27, 729, 14) follows the exact same logical rule as the original sets.