Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

If S is the set of positive integers that are multiples of 7, and if T is the set of positive integers that are multiples of 13, how many integers are in the intersection of S and T?

(A) None

(B) One

(C) Seven

(D) Thirteen

(E) More than thirteen

The correct answer is E

Explanation

The intersection of sets S and T is the set of integers that are in S and also in T. Set S consists of all positive integers that are multiples of 7, and set T consists of all positive integers that are multiples of 13, so the intersection of S and T is the set of positive integers that are multiples of both 7 and 13. This is the set of all positive integers that are multiples of 7 times 13 = 91. There are an infinite number of positive integers that are multiples of 91, so there are more than thirteen integers in the intersection of S and T.