Question

If $A$ is the set of prime numbers and $B$ is the set of two-digit positive integers whose units digit is 5, how many numbers are common to both sets?

• A. None
• B. One
• C. Two
• D. Five
• E. Nine

Answer 1

The correct option is A None

Set A {1,3,5,7,11,13,17,19,......} --> Set of Prime Numbers (Numbers that have only two factors: "$1$" and "itself")

Set B {15,25,35,45,55,......} -->Set of two digit positive integers whose unit digit (ones place) is "$5$"

Each two digit positive integer with a unit digit of $5$ has more than $2$ factors, each of these numbers is Set B has $1,5$ and "itself" as a factor. Therefore these two sets are disjoint (sharing no common element).

Therefore choice A is the correct answer.