Tip #18 to Get a Top ACT Math Score (page 3)
Dr. Evil: Finally we come to my number two man. His name? Number Two.
Austin Powers: International Man of Mystery (New Line Cinema, 1997)
If "Use the Answers" is our single most useful and important strategy, "Make It Real" is number two. You could say that if "Use the Answers" is Dr. Evil, then "Make It Real" is … well, Number Two.
Let's look at this question:
Solution: You'd have to be Einstein to get this question; it's too theoretical. So we take it out of theory and "Make It Real." We choose real numbers in place of the variables, and it becomes easier. We can choose any numbers that seem to fit the equation, and we might as well choose numbers that work evenly and avoid decimals. In this case, let's say b = 3 and e = 4. (Be careful of choosing 0, 1, or 2 for "Make It Real." These numbers behave in strange ways, as we'll see in Skill 46.) So when b = 3 and e = 4:
- c = –2b – 2(2e – b)
- c = –2(3) – 2(2(4) – 3)
- c = –6 – 2(5)
- c = –6 – 10
- c = –16
The question asks what happens when we add 2 to both b and e, so let's add 2 to both b and e and then solve the equation again. With b = 5 and e = 6:
- c = –2b – 2(2e – b)
- c = –2(5) – 2(2(6) – 5)
- c = –10 – 2(7)
- c = –10 – 14
- c = –24
Cake. C was –16 and is now –24, so it decreased by 8.
Correct answer: K
This strategy turns very difficult questions into much easier ones!
It's my single favorite ACT strategy.
- If t represents an odd integer, which of the following expressions also represents an odd integer?
- t – 3
- 2t – 1
- 2t – 2
- 3t –1
- 4t – 4
- If m < 0 and n > 0, then the product of m and n
- Is always even
- Is always odd
- Is always positive
- Is always negative
- Cannot be zero, but can be any other real number
- If b is any real number other than 3 and 7, then =
- There are k students in a class. If, among those students, q% have NOT seen the movie Monty Python and the Holy Grail, which of the following general expressions represents the number of students who have seen the movie?
- Let x equal –3m – 2n – 4. What happens to the value of x if the value of m increases by 2 and the value of n decreases by 1 ?
- It increases by 3.
- It increases by 2.
- It is unchanged.
- It decreases by 3.
- It decreases by 4.
- B This question intimidates some students; it seems too theoretical. But "Make It Real" makes it so easy. Just choose a real number for p (remember that the question says that the number that you choose has to be odd). Let's say p = 5. Then try p = 5 in all the answer choices to see which one does what the question asks, which one gives an odd number. The answer is B since 2(5) – 1 = 9.
- J First, "product" means "multiply." We will review this more in Skill 27. "Make It Real," let's say, m = –3 and n = 3. Now it's easy, the product (multiplication) of –3 and 3 is –9. Choice J looks good, but to be safe, try a few more possibilities. After you've done three, you can be sure that your answer is correct. And by then you might realize that "Of course, a positive times a negative is always a negative."
- D Choose a number for b, let's say b = 5 (notice the question states that b can be any real number besides 3 and 7). Now it's easy, solve:
- H We are into the "hards" now. But "Make It Real" will knock these down a notch to mediums or even easies. Let's say k = 100 and q = 20. So, of the 100 kids in a class, 20 have NOT seen Monty Python and the Holy Grail. Once we've "Made It Real," it becomes obvious that if 20 have NOT seen it, then 80 have seen it. (When you are using "Make It Real" with percents, use 100 when you can, it makes questions really easy.) Now, based on k = 100 and q = 20, we want an answer of 80. So try each answer choice, using k = 100 and q = 20 and find the one answer choice that equals 80.
- E Let's say m = 3 and n = 5. Then –3m – 2n – 4 = –3(3) – 2(5) – 4 = –23. The question asks what happens when m increases by 2 and n decreases by 1, so let's solve for m = 5 and n = 4. Now, –3m – 2n – 4 = –3(5) – 2(4) – 4 = –27. So the result changed from –23 to –27; it decreased by 4.
Skill 12 review: the value of b cannot equal 3 or 7 because either number would give us a 0 on the bottom of the fraction, which is illegal in math and would cause the equation to be "undefined" and would cause lots of important folks to get very upset.
Choice H is correct because
If two choices work, just choose new "Make It Real" numbers and have a tiebreaker.
People think that this might take forever to do, but try it; it takes like 30 seconds.
Go to: Tip #19
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