A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4?

(a) 2n
(b) 3n
(c) 2n + 4
(d) 3n + 1 ✓ UPSC's answer

Why the answer is (d)

• The digits greater than 3 are 4, 5, 6, 7, 8, and 9.

• Among these, the digits divisible by 3 are 6 and 9.

• Since n is not divisible by 6, n cannot be 6, so n = 9.

• Substituting n = 9 gives 2n = 18, 3n = 27, 2n + 4 = 22, and 3n + 1 = 28.

• Only 28 is divisible by 4, so option (d) follows.

Why the other options are wrong

(a) 2n: 2n equals 18 when n = 9, and 18 is not divisible by 4.
(b) 3n: 3n equals 27 when n = 9, and 27 is not divisible by 4.
(c) 2n + 4: 2n + 4 equals 22 when n = 9, and 22 is not divisible by 4.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2020, held on 4 October 2020. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.