The Official SAT Question of the Day™

Read the following SAT test question, 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

Answer is E

Here's Why:

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 × 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.


Difficulty: Medium
Question Type: Standard Multiple Choice

(Mathematics)