PSAT/SAT & ACT Math Attack – Percent of Integers

The PSAT & SAT are notorious for asking complicated questions about seemingly simple concepts; this is one reason the PSAT & SAT Math sections can be so difficult. Following College Compass’ SAT Math Attack series will help you understand the concepts behind the questions.

1. What percent of the integers from 3 to 12, inclusive, are neither primes nor multiples of 4?
   1. 20%
   2. 30%
   3. 40%
   4. 60%
   5. 70%

Explanation: The use of the word inclusive is meant to alert test-takers to the fact we are to include the numbers 3 & 12 in this problem. Including the numbers 3 & 12 brings the total number of integers being considered to 10:

3, 4, 5, 6, 7, 8, 9, 10, 11, 12

The first step is to get rid of all integers that are multiples of 4:

3, 4, 5, 6, 7, 8, 9, 10, 11, 12

The next step would be to eliminate all prime integers:

3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Of our initial integers, we have 3 remaining:

6, 9, 10

To determine the percentage we would simply take the number of remaining integers (3) and divide them by the number of integers we started with (10):

3/10 = 30%

The answer is thus (B).

Have a question? Ask the experts at Test Masters!

Interested in more PSAT and SAT Sample Questions? Check them out here! Learn more about the Test Masters PSAT/SAT course here!