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