For 11 years you've been trained to solve math problems the long way. "No shortcuts!" Mrs. Nicholas always said. Mrs. Nicholas was the best math teacher that I ever had, and her advice was correct for math class. But the ACT is multiple-choice, and we can save time and energy by using the answers; simply test the answer choices to see which one works. To make this even easier, when there are fractions, π, or square roots in the questions or answers, you can convert them to decimals. "Use the Answers" works best when there are variables or unknowns in the question and numbers in the answer choices.
Let's look at this question:
Solution: This question looks pretty tough to many students, but "Use the Answers" makes it easy! You can answer this question by setting up an algebraic equation, or you can just "Use the Answers." We want 3 consecutive even integers that add up to 36. That means we want 3 even numbers in a row, like 2, 4, and 6. Try each choice as the shortest side and see which one makes the situation work:
- 7 is not even.
- 8 + 10 + 12 ≠ 36
- 10 + 12 + 14 = 36
- 12 + 14 + 16 ≠ 36
- 14 + 16 + 18 ≠ 36
Choice C is correct since 10 + 12 + 14 = 36. Careless error buster: Notice that the question asks for the shortest, not the longest, side.
Correct answer: C
- If 3x – 4 = – 10, then x = ?
- If n , then n = ?
- What is the largest integer value of p that satisfies the inequality ?
- Jaleesa earned a score of 160 on a recent 50-question spelling contest. The scoring for the contest was +4 for each correct answer, –1 for each incorrect answer, and 0 for each unanswered question. If she answered every question, what is the maximum number of questions that Jaleesa could have answered correctly?
Translate each answer choice. Whichever is closest to 18.97 is correct. Choice F is correct, since 6 = 18.97.
Notice that the ≥ sign allowed us to use 10 as an answer, since the answer could be "greater than or equal to." If there had only been a > sign, the answer would be 9.
- A You can answer this question quickly and easily by using simple algebra and solving for x. If, however, that is difficult or daunting, "Use the Answers." Just plug each choice in to see which one makes the equation work. Choice A is correct: 3(–2) – 4 =–10.
- F This question looks pretty tough to some students, but "Use the Answers" makes it EASY! Just use your calculator to convert each √ into a decimal, and then see which answer choice works. (We will also briefly discuss the "math class" way to answer this question in Skill 29.)
- D You can answer this question by using algebra and solving for n. Or "Use the Answers" to make this "medium" question EASY! Just use your calculator to convert each fraction to a decimal, and then plug each answer choice into the question to see which one makes the equation work. Choice D is correct:
- H You can answer this question by using algebra and solving for p, but "Use the Answers" makes this "medium" question EASY! Just plug in each choice to see which one makes the inequality work. Choice H is correct since
- D You can answer this question by setting up two equations and using algebra to solve for the variables, but "Use the Answers" makes this "hard" question EASY! Just plug in each choice to see which one makes the situation work. Choice D is correct since 42 correct questions earn 168 points, and 8 incorrect questions subtract 8 points, which equals 160 points.