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

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