ACT Math: Test Answer Choices Backwards to Find the Right Answer Faster

Instead of solving an equation, substitute each answer choice into the problem and see which one works. Example: "If 3x+5=20, what is x?" Instead of solving 3x=15, x=5, you can test the answer choices. If the choices are 3, 5, 7, 10: test x=5 → 3(5)+5=20. Correct! This method is 30% faster for some students because there is no algebraic manipulation, just arithmetic. Working backwards is especially fast on word problems where solving algebraically is tedious but checking is straightforward.

Example word problem: "A store sells apples for $2 each. Sarah bought some apples and a $3 notebook, totaling $19. How many apples did she buy?" Instead of setting 2a+3=19, test answer choices. a=5: 2(5)+3=13. No. a=8: 2(8)+3=19. Yes! Answer is 8.

Backwards is faster when: (1) answer choices are simple numbers, (2) substituting is quicker than solving, (3) you are error-prone at algebra. Backwards is slower when: (1) answer choices are complex fractions or expressions, (2) algebraic solving is straightforward, (3) you need to test multiple choices before finding the right one. Learn to judge quickly; if you sense backwards testing will be faster, use it. If not, solve algebraically.

On your next practice test, try both methods on a few problems. Notice: some you solve faster, some you test faster. This awareness trains strategic problem-solving.

Solve ten ACT Math problems using backwards testing exclusively. Time yourself; aim for 45-60 seconds per problem. Check your answers. Do you notice any patterns about when backwards testing is fastest? This drill trains backwards testing speed so that during the real test, you can deploy it strategically on problems where it shines.

Do this drill once per week for two weeks. By test day, you will have a backup method for problems where algebra is slow or confusing.

One or two word problems per ACT Math section can be solved backwards faster than algebraically. Each is worth 1 point. Using backwards testing on these problems saves you 60 seconds total, time you can reinvest in harder problems, raising your Math score by 1-2 points per test section.

This week, learn backwards testing. By test day, you will have two powerful problem-solving methods and know when to use each.