When positive integer x is divided by 6, the remainder is 1. Which of the following must be true?
I. x is a prime number
II. x is odd
III. x is divisible by 7
Choose the correct choice from the following choices:
A) I only  B) II only  C) III only  D) I and II only  E) II and III only
X=6q+1   Examine II) put q=0,1,2,3....... we have x=1,7,13,...25 so x must be odd   Examine III) 14/6 has reminder 2 &amp; 49/7 has reminder 1 so not always true   Examine I) X= 7 true but while 2 is prime, it does not give reminder 1   Answer: II only
<result>B</result>
When positive integer x is divided by 6, the remainder is 1. Which of the following must be true?
I. x is a prime number
II. x is odd
III. x is divisible by 7