When positive integer f is divided by 6, the remainder is 1. Which of the following must be true?
I. f is a prime number
II. f is odd
III. f is divisible by 7  Choose the most appropriate option: A) I only B) II only C) III only D) I and II only E) II and III only
f=6q+1   Examine II) put q=0,1,2,3....... we have f=1,7,13,...25 so f must be odd   Examine III) 14/6 has reminder 249/7 has reminder 1 so not always true   Examine I) f= 7 true but while 2 is prime, it does not give reminder 1   Answer: II only
<result>B</result>
When positive integer f is divided by 6, the remainder is 1. Which of the following must be true?
I. f is a prime number
II. f is odd
III. f is divisible by 7