Select the option that is related to the first letter-number cluster in the same manner as the fourth letter-number cluster is related to the third letter-number cluster and the sixth letter-number cluster is related to the fifth letter-number cluster. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits.)
JKL300 : ? :: MNO150 : PQR450 :: STU200 : VWX600

The correct answer is MNO900.

Step-by-step Explanation:

We are given the letter-number cluster analogy pattern:
JKL300 : ? :: MNO150 : PQR450 :: STU200 : VWX600

To find the missing cluster, let's analyze the relationship between the letter and number components in the established pairs.

1. Analyzing the Third and Fourth Clusters (MNO150 : PQR450):

Letter Shift:
M + 3 positions = P
N + 3 positions = Q
O + 3 positions = R
Each letter moves forward by 3 steps in the alphabetical order.

Number Operation:
The number component is multiplied by 3:

$150\times 3=450$

2. Analyzing the Fifth and Sixth Clusters (STU200 : VWX600):

Letter Shift:
S + 3 positions = V
T + 3 positions = W
U + 3 positions = X
Each letter moves forward by 3 steps in the alphabetical order.

Number Operation:
The number component is multiplied by 3:

$200\times 3=600$

3. Applying the Pattern to the First Cluster (JKL300 : ?):

Letter Shift:
J + 3 positions = M
K + 3 positions = N
L + 3 positions = O
The letter group becomes MNO.

Number Operation:
Multiply the numerical value 300 by 3:

$300\times 3=900$

Combining the transformed letters and number gives the final cluster: MNO900.