2014-09-24 09:00:47

The first term of a certain sequence of integers is 75. Every term after the first is equal to twice the preceding term if that term is even, or is equal to 1/3 of the preceding term rounded to the nearest integer if that term is odd. What is the fifth term of the sequence?

(A) 8
(B) 9
(C) 25
(D) 32
(E) 64

The correct answer is D
Explanation: Just find the first five terms in the sequence, since it is not that much work.

Term 1: 75 – this is given

Term 2: 25 — 75 was odd, so the next term is 1/3 of the first term rounded to the nearest integer

Term 3: 8 — 25 was odd, so the next term is 1/3 of the first term rounded to the nearest integer, and 1/3 of 25 is 8.

Term 4: 16 — 8 was even, so the next term is twice the preceding term

Term 5: 32 — 16 was even, so the next term is twice the preceding term

This means the fifth term is 32, making D right.