SAT: Multiple-Choice Math Questions

The Mathematics multiple-choice questions test your ability to solve mathematical problems involving arithmetic, algebra I and II, geometry, data interpretation, basic statistics and probability, and word problems by using problem-solving insight, logic, and the application of basic skills. You should have a total of about 42 to 46 multiple-choice questions spread throughout the three Math sections that count toward your score.

Basic Skills Necessary

The basic skills necessary to do well on this section include high school algebra I and II and intuitive or informal geometry. No calculus is necessary. Logical insight into problem-solving situations is also necessary.

The Inside Scoop

Here are some details to keep in mind as you approach multiple-choice math questions on the SAT:

  • All numbers used are real numbers.
  • Calculators may be used.
  • Some problems may be accompanied by figures or diagrams. These figures are drawn as accurately as possible EXCEPT when it is stated in a specific problem that a figure is not drawn to scale. The figures and diagrams are meant to provide information useful in solving the problem or problems. Unless otherwise stated, all figures and diagrams lie in a plane.
  • A list of data that may be used for reference is included.
  • All scratch work is to be done in the test booklet; get used to doing this because no scratch paper is allowed into the testing area.
  • You are looking for the one correct answer; therefore, although other answers may be close, there is never more than one right answer.

Suggested Approaches with Samples

Circle or Underline

Take advantage of being allowed to mark on the test booklet by always underlining or circling what you are looking for. This will ensure that you are answering the right question.

SAMPLE QUESTION: If x + 6 = 9, then 3x + 1 =

  1. 3
  2. 9
  3. 10
  4. 34
  5. 46

You should first circle or underline 3x + 1 because this is what you are solving for. Solving for x leaves x = 3, then substituting into 3x + 1 gives 3(3) + 1, or 10. The most common mistake is to solve for x, which is 3, and mistakenly choose A as your answer. But remember, you are solving for 3x + 1, not just x. You should also notice that most of the other choices would all be possible answers if you made common or simple mistakes. Make sure that you are answering the right question. The correct answer is C.

Pull Out Information

"Pulling" information out of the word problem structure can often give you a better look at what you are working with; therefore, you gain additional insight into the problem. When pulling out information, actually write out the numbers and/or letters to the side of the problem, putting them into some helpful form and eliminating some of the wording.

SAMPLE QUESTION: Bill is ten years older than his sister. If Bill was twenty-five years of age in 1983, in what year could he have been born?

  1. 1948
  2. 1953
  3. 1958
  4. 1963
  5. 1968

The key words here are in what year and could he have been born. Thus, the solution is simple: 1983 - 25 = 1958, answer C. Notice that you pulled out the information twenty-five years of age and in 1983. The fact about Bill's age in comparison to his sister's age was not needed, however, and was not pulled out. The correct answer is C.

Work Backward

In some instances, it will be easier to work from the answers. Do not disregard this method because it will at least eliminate some of the choices and could give you the correct answer.

SAMPLE QUESTION: What is the approximate value of the square root of 1596?

  1. 10
  2. 20
  3. 30
  4. 40
  5. 50

Without the answer choices, this could be a difficult problem. By working up from the answer choices, however, the problem is easily solvable. Since you need to know what number times itself equals 1596, you can take any answer choice and multiply it by itself. As soon as you find the answer choice that when multiplied by itself approximates 1596, you've got the correct answer. You may want to start working from the middle choice, since the answers are usually in increasing or decreasing order. In the problem above, start with choice C, 30. Since 30 ´ 30 = 900, which is too small, you can now eliminate A, B, and C as too small. But 40 ´ 40 = 1600, approximately 1596. Choice D is correct. If your calculator computes square roots, you could have used it to compute the square root and then rounded off.

Substitute Simple Numbers

Substituting numbers for variables can often be an aid to understanding a problem. Remember to substitute simple numbers, since you have to do the work.

SAMPLE QUESTION: If x is a positive integer in the equation 12x = q, then q must be

  1. a positive even integer.
  2. a negative even integer.
  3. zero.
  4. a positive odd integer.
  5. a negative odd integer.

At first glance, this problem appears quite complex. But plug in some numbers and see what happens. For instance, first plug in 1 (the simplest positive integer) for x.

12x = q
12(1) = q
12 = q

Now try 2,

12x = q
12(2) = q
24 = q

Try it again. No matter what positive integer is plugged in for x, q will always be positive and even. Therefore, the correct answer is A.