There are also other special Kaplan strategies you might use, such as picking numbers and backsolving.
Picking Numbers
This strategy is based on the idea that instead of always trying to wrap your head around abstract variables, you can pick numbers for them.
This way you end up making calculations with real numbers and you can really see the answer. The strategy of picking numbers works especially well with even/odd questions. For example:
If a is an odd integer and b is an even integer, which of the following must be odd?
(A) 2a + b (B) a + 2b (C) ab (D) a2b
By picking numbers to represent a and b, you may come to the solution more easily. When you are adding, subtracting, or multiplying even and odd numbers, you can generally assume that what happens with one pair of numbers happens with similar pairs of numbers. Let’s say, for the time being, that a = 3 and b = 2. Plug those values into the answer choices, and there’s a good chance that only one choice will be odd:
(A) 2a + b = 2(3) + 2 = 8 (B) a + 2b = 3 + 2(2) = 7 (C) ab = (3)(2) = 6
(D) a2b = (32)(2) = 18
Choice (B) is the only odd answer when the numbers 2 and 3 are used to represent the variables; thus, it is fair to assume that it must be the only odd-answer choice, no matter what odd number you plug in for a and even number you plug in for b. The answer is (B).
Picking numbers is a helpful strategy in several other situations, such as when:
The answer choices for problems involving percentages are all percents.
The answer choices for word problems are algebraic expressions.
Here are a few rules to remember when picking numbers:
Pick easy numbers rather than ones that might be used or suggested in the problem. Keep the numbers small and manageable. You should avoid zero and 1; these often give several answers that are possibly correct.
Remember that you have to try all the answer choices. If more than one works, pick another set of numbers.
Don’t pick the same number for more than one variable.
Always pick 100 for questions involving percents.
Backsolving
With some math questions, it’s easier to work backward from the answer choices than to try and trudge through the question. Basically, with
backsolving, you are plugging the answer choices back into the question until you find a solution. This method works best when the question is a complex word problem and the answer choices are numbers, or when your only other choice is to set up multiple algebraic equations.
Backsolving is not ideal:
If the answer choices include variables.
If the answer choices are radicals or fractions (plugging them in takes too much time).
Here’s an example of how backsolving works:
A music club draws 27 patrons. If there are 7 more males than females in the club, how many patrons are male?
(A) 8 (B) 10 (C) 14 (D) 17
Try each of the answers as a substitute for the number of males in the club. Plugging in choice (C) gives you 14 males in the club. Since there are 7 more males than females, there are 7 females in the club, but 14 + 7 < 27, so 14 doesn’t work. You know the solution has to be higher, so you can eliminate (A), (B), and (C). Already you’ve found the right
answer. Now, if you plug in (D) you see that it gives you 17 males and 10 females. 17 + 10 = 27. That’s the right answer.
Now that you have reviewed the best math strategies, it’s time to test how much you have learned by answering the following review questions.
REVIEW QUESTIONS
The following questions are not meant to mimic actual test questions.
Instead, these questions will help you review the concepts and terms covered in this chapter.
1. Match the number type with its definition.
____ Real numbers ____ Rational numbers ____ Consecutive numbers
(A) Any number that can be written as a ratio of two integers, including whole numbers, integers, terminating decimals, and repeating decimals.
(B) Numbers that follow one after another, in order, without any skipping.
(C) Any number that can name a position on a number line regardless of whether that position is positive or negative.
2. Fill in the blank. When you multiply an even number by an odd number the product is _____________.
3. True or false? The product of three negative numbers is positive. _____________
4. Define the term Greatest Common Factor.
_____________________________________
5. Write the steps of the Order of Operations.
_____________________________________
_____________________________________
_____________________________________
_____________________________________
_____________________________________
6. True or False? To convert a fraction to a decimal, you divide the numerator by the denominator.
_____________________________________
7. Write the formula for calculating an average.
_____________________________________
8. Fill in the blank. In algebra, the ____________ is the letter that stands for an unknown.
9. Write the formula for calculating distance.
_____________________________________
10. What is 20% of 10% of 500?
(A) 5 (B) 10 (C) 15 (D) 20
11. Solve 3x2 + 5 (3 – y) – 2z if x = 3, y = 8, and z = 2.
(A) –20 (B) –2 (C) 12 (D) 48
12.
(A) (B) (C) (D) 2
13. Which fraction is equivalent to 25%?
(A) (B) (C) (D)
REVIEW ANSWERS
1. (C) Real numbers are any number that can name a position on a number line regardless of whether that position is positive, negative, or zero.
(A) Rational numbers are any number that can be written as a ratio of two integers, including whole numbers, integers, terminating decimals, and repeating decimals.
(B) Consecutive numbers are numbers that follow one after another, in order, without any skipping.
2. When you multiply an even number by an odd number the product is even.
3. False. The product of three negative numbers is negative.
4. The Greatest Common Factor is the largest factor that goes into two or more numbers.
5. Parentheses Exponents
Multiplication and Division (from left to right) Addition and Subtraction (from left to right)
6. True. To convert a fraction to a decimal, you divide the numerator by the denominator.
7.
8. In algebra, the variable is the letter that stands for an unknown.
9. Distance = Rate × Time
10. (B) This question is a little tricky, because it requires you to find the percentage of a
percentage of a number. The easiest way to work a problem like this is to go backwards.
Start with 500, and calculate 10%: 10% of 500 = 500 × 0.10 = 50. Then, taking this answer, calculate 20%: 20% of 50 = 0.20 × 50 = 10.
11. (B) To solve this problem, simply substitute the given values for each letter provided in the question: 3x2 + 5 (3 – y) – 2z = 3(3)2 + 5(3 – 8) – 2(2) = 3(9) + 5(–5) – 4 = 27 – 25 – 4 = – 2.
12. (C)
13. (D) To find out which fraction is equivalent to 25%, you can do the division for every answer choice and see if any of them match up to the decimal equivalent of 25% (which is 0.25).
However, the easier way is to convert 25% to a fraction and see if it matches any of the answer choices. 25% = , which can be reduced to . Since is not one of the answer choices, see if any of the answer choices can be reduced to . The fractions , choice (A), and , choice (B), cannot be further reduced, while , choice (C), can be reduced to
. Only , choice (D), can be reduced to .
• Biology Review
• Anatomy and Physiology Review
• Physical Science Review