Which of the statements (A)-(D) are true in the context of number series I and II given below :

Series I: 6, 24, x, 720, 5040

Series II: 432, 250, 128, y, 16

(A) The sum of x and y is 164

(B) x exceeds the double of y by 12

(C) Both x and y are exactly divisible by 6

(D) Either x or y is a perfect square

Choose the correct answer from the options given below :

Given:

Series I: 6, 24, x, 720, 5040

Series II: 432, 250, 128, y, 16

We need to find the values of x and y and verify the given statements.

Calculation:

Finding x:

Observing the factorial pattern:

6 = 3!

24 = 4!

x = 5! = 120

720 = 6!

5040 = 7!

Finding y:

The given series follows the following pattern

2 × 63 = 432

2 × 53 = 250

2 × 43 = 128

2 × 33 = 54 = y

2 × 23 = 16

Verifying the Statements:

(A) The sum of x and y is 164

⇒ 120 + 54 = 174  (False)

(B) x exceeds the double of y by 12

⇒ 120 = (2 × 54) + 12

⇒ 120 = 120 (True)

(C) Both x and y are exactly divisible by 6

⇒ 120 % 6 = 0, 54 % 6 = 0  (True)

(D) Either x or y is a perfect square

⇒ 120 is not a perfect square

⇒ 54 is not a perfect square  (False)

∴ The correct statement are (B) and (C) Only​.