Your Most Important Back-up Plan on SAT Math

pretty young college student writing on the chalkboard/blackboard during a math class

You don’t need to know every math formula or math procedure to do well on the math portions of the SAT (or ACT, or PSAT). Many of these math problems can be solved using a strategy known as backsolving.

With backsolving, you substitute numeric answer choices back into the question to determine which one makes sense based on given information. This strategy is useful for questions that involve solving an equation for an unknown, or for solving word problems that have numeric answer choices. Backsolving often involves less complicated math formulas and less complicated calculations, and therefore leaves room for less errors in computations.

So, how do you go about using backsolving? If the question involves solving an equation for x, substitute one answer choice at a time for x into the equation until you find the one that makes the equation true.

It often makes most sense to start with an answer choice that is in the middle numerically. This is typically choice C. If the answer for choice C is is too small, you can eliminate all other smaller answer choices and back solve with next larger answer choice. Likewise, if the first answer choice you check is too large, you can eliminate all other larger answer choices and back solve with the next smaller choice.

Here’s an example of a word problem where the backsolving strategy is useful.

In the junior class, 3/8 of the students play a musical instrument. Of these students, 1/5 of them play a percussion instrument. If a total of 21 students in the junior class play a percussion instrument, how many total students are in the junior class?

(A) 240

(B) 250

(C) 260

(D) 280

(E) 300

Here you have some options when it comes to answering this question. You can try to figure out how the given information is related and attempt to write and solve proportions or equations based on this. Or, you can use the strategy of backsolving and substitute a specific answer choice as the total number of students to see if 21 students results when the fractions 3/8 and 1/5 are applied. The former method is a bit involved and leaves room for possible error, whereas the latter method is a more straitforward approach that involves simpler math computations.

Start with answer choice (C) and assume there are a total of 260 students in the junior class. Then, the number of students that play a musical instrument is 3/8(260) = 97.5. You know that you cannot have a fraction of a student, so that means 260 is not correct and choice (C) is not the correct answer. So, pick another answer choice and check that one. In this case, it doesn’t matter which direction you go from choice (C), so try choice (D).

With answer choice (D), you assume there are a total of 280 students in the junior class. The number of students that play a musical instrument is 3/8(280) = 105. Of these 105 students, 1/5 play a percussion instrument, which is 1/5(105) = 21. This matches the given information that 21 students in the junior class play a percussion instrument. So, you know that there must be 280 total students in the junior class and choice (D) is the correct answer.