SSC CGL 2024 PYQ — Question 55

The correct answer is option 1 i.e. 1

A number is divisible by 6 if it is divisible by both 2 and 3.

The term 2²ⁿ is always even.

The term 2n is also even.

Since the sum of two even numbers is always even, 2²ⁿ + 2n is divisible by 2.

A number is divisible by 3 if = 2²ⁿ + 2n ≡ 0     (mod 3)

For divisibility by 3 = 2²ⁿ + 2n ≡ 1 + 2n ≡ 0      (mod 3)

⇒ 2n ≡ −1 ≡ 2     (mod 3)

⇒ 2n ≡ 2   (mod 3)

⇒ n ≡ 1     (mod 3)

so

⇒ 2²⁽¹⁾ + 2(1) = 2² + 2 = 4 + 2 = 6

Hence answer is 1.