SAT Practice Math Questions: Number Systems

By Geraldine Woods, Ron Woldoff

Mathematics is based on numbers, and different groups of numbers work in different ways. It helps to know about number systems before taking the SAT Math exam.

You should be familiar with the following groups of numbers:

  • Whole numbers. The whole numbers are the ones you (hopefully) remember from grade school: 0, 1, 2, 3, 4, 5, 6 . . . you get the idea. Whole numbers, by definition, don’t include fractions or decimals, or negative numbers.
  • Prime numbers. Prime numbers are whole numbers divisible only by themselves and by 1. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, and 19. Zero and 1 aren’t prime numbers. They’re considered “special.” No negative number is ever prime because all negative numbers are divisible by –1.
  • Composite numbers. Any whole number that’s not prime or special is composite. If you can divide a number by some smaller whole number (other than 1) without getting a remainder, you have a composite number. A few composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, and so on.
  • Integers. The whole numbers and all their opposites — also known as negative numbers — are integers. Integers reach infinity in both directions on a number line.
  • Rational numbers. All integers are rational numbers. In addition, any number that can be written as a fraction — proper or improper — is a rational number. (In a proper fraction, the number on top is smaller than the number on the bottom, and in an improper fraction, the top number is greater than the bottom number.) Plus, any decimal that either ends, such as 1.2, or repeats, such as

1301

(the decimal for 1/3), is a rational number. The following are also rational: –2, 0.234, 787/23,

1302

  • Irrational numbers. Irrational numbers have decimals that never end or repeat. Practically speaking, you need to worry about only two kinds of irrational numbers: radicals, such as

1303

which you’ve seen from working with a circle

  • Real numbers. A real number can be found on the number line, and it includes both rational and irrational numbers.

Practice questions

  1. Which number is an element of the set of prime numbers but not of the set of odd numbers?
    • A. 0
    • B. 1
    • C. 2
    • D. 3
  2. The total number of even three-digit numbers is
    • A. 49
    • B. 100
    • C. 449
    • D. 450

Answers and explanations

  1. C. Because 2 is the only prime number that isn’t odd, Choice (C) is correct.
  2. D. Counting all the even three-digit numbers would take a really long time, so try to figure out this question logically. The three-digit numbers start with 100 and end with 999. How many numbers do you have? It’s 900, not 899. (Yes, there is a formula you can use here: Subtract the numbers and add 1. Works every time.) How many of these numbers are even? Well, because even and odd numbers alternate on this list, half of them are even, and half are odd. So you have 450 of each type. Choice (D) is right.