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