Select the number that completes the given numerical analogy in the same way as the second… — State PSC Exam

Select the number that completes the given numerical analogy in the same way as the second term is related to the first term:

14 : 350 :: 18 : ?

594

The relation governing the first pair is

N : N \times (N + S(N) + 6)

, where

S(N)

represents the sum of digits of

N

. For

14

S(14) = 1 + 4 = 5

, giving

14 \times (14 + 5 + 6) = 14 \times 25 = 350

. Applying this exact rule to

18

yields

S(18) = 1 + 8 = 9

, and

18 \times (18 + 9 + 6) = 18 \times 33 = 594

Analyze the relation between the first pair

14 : 350

Calculate the digit sum of

14

1 + 4 = 5

Identify sub-components of the multi-step operation.

Determine the composite multiplier rule for the first term

Add the term, its digit sum, and the constant offset

6

14 + 5 + 6 = 25

Establish the exact pattern mapping

14

350

via

14 \times 25 = 350

Apply the established pattern to the third term

18

Calculate the digit sum of

18

1 + 8 = 9

. Then compute the multiplier:

18 + 9 + 6 = 33

Maintain structural consistency with the original analogy.

Compute the final missing term

18 \times 33 = 594

Obtain the required missing term for the second pair.

Multi-step Numerical Analogy based on Positional Digit Operations and Constant Shift

Question