SSAT & ISEE Prep 2023 - Princeton Review 2023

SSAT math
The SSAT

INTRODUCTION

This section will provide you with a review of the math strategy that you need to know to do well on the SSAT. When you get started, you may feel that the material is too easy. Don’t worry. The SSAT measures your basic math skills, so although you may feel a little frustrated reviewing things you have already learned, basic review is the best way to improve your score.

We recommend that you work through these Math sections in order, reading each section and then doing each set of drills. If you have trouble with one section, mark the page so you can come back later to go over it again. Keep in mind that you shouldn’t breeze over pages or sections just because they look familiar. Take the time to read over all of the Math sections, so you’ll be sure to know all the math you’ll need!

Lose Your Calculator!

You will not be allowed to use a calculator on the SSAT. If you have developed a habit of reaching for your calculator whenever you need to add or multiply a couple of numbers, follow our advice: put your calculator away now and take it out again after the test is behind you. Do your math homework assignments without it, and complete the practice sections in this book without it. Trust us, you’ll be glad you did.

Write It Down

Do not try to do math in your head. You are allowed to write in your test booklet if you are taking a paper-based test, and you are allowed scratch paper if you are taking an online test. You should write in your test booklet or on your scratch paper. Even when you are just adding a few numbers together, write them down and do the work on paper. Writing things down will not only help eliminate careless errors but also give you something to refer to if you need to check over your work.

Don’t Get Stuck

Make sure you don’t spend too much time working on one tough question; there might be easier questions left in the section.

One Pass, Two Pass

Within any Math section you will find three types of questions:

· those you can answer easily without spending too much time

· those that, if you had all the time in the world, you could do

· some questions that you have absolutely no idea how to tackle

When you work on a Math section, start out with the first question. If you think you can do it without too much trouble, go ahead. If not, save it for later. Move on to the second question and decide whether or not to do that one. In general, the questions in each Math section are in a very rough order of difficulty. This means that earlier questions tend to be somewhat easier than later ones. You will likely find yourself answering more questions toward the beginning of the sections and leaving more questions blank toward the end.

Once you’ve made it all the way through the section, working slowly and carefully to do all the questions that come easily to you, go back and try some of the ones that you think you can do but will take a little longer. You should pace yourself so that time will run out while you’re working on the second pass through the section. By working this way, you’ll know that you answered all the questions that were easy for you. Using a two-pass system is a smart test-taking strategy.

Guesstimating

Sometimes accuracy is important. Sometimes it isn’t.

Which of the following fractions is less than ?

(A)

(B)

(C)

(D)

(E)

Some Things Are Easier Than They Seem

Guesstimating, or finding approximate answers, can help you eliminate wrong answers and save lots of time.

Before making any kind of calculation, think about this question. It asks you to find a fraction smaller than . Even if you’re not sure which one is actually smaller, you can certainly eliminate some wrong answers.

Start simple: is less than 1, right? Are there any fractions in the choices that are greater than 1? Get rid of (D) and (E).

Look at (C). equals 1. Can it be less than ? Eliminate (C). Already, without doing any math, you have a 50 percent chance of guessing the right answer. If you have a few extra seconds, you can evaluate the remaining two answer choices. Which one is easier to work with? Look at (B). reduces to , which is bigger than . You might also think about the fact that would be , so must be bigger. The answer is (A).

Here’s another good example.

A group of three people buys a one-dollar raffle ticket that wins $400. If the one dollar that they paid for the ticket is subtracted and the remainder of the prize money is divided equally among the people, how much will each person receive?

(A) $62.50

(B) $75.00

(D) $133.00

(E) $200.00

This isn’t a terribly difficult question. To solve it mathematically, you would take $400, subtract $1, and then divide the remainder by three. But by using a little bit of logic, you don’t have to do any of that.

The raffle ticket won $400. If there were four people, each one would have won about $100 (actually slightly less because the problem tells you to subtract the $1 price of the ticket, but you get the idea). So far so good?

However, there weren’t four people; there were only three. This means fewer people among whom to divide the winnings, so each one should get more than $100, right? Look at the choices. Eliminate (A), (B), and (C).

Two choices left. Choice (E) is $200, half of the amount of the winning ticket. If there were three people, could each one get half? Unfortunately not. Eliminate (E). What’s left? The right answer!

Guesstimating also works very well with some geometry questions, but we’ll save that for the Geometry section.

WORKING WITH CHOICES

In Chapter 2, Fundamental Math Skills for the SSAT & ISEE, we reviewed the concepts that will be tested on the SSAT tests. However, the questions in those practice drills were slightly different from the ones that you will see on your exam. In this chapter, we’ll look at how to apply test strategy to those math concepts. Questions on test day are going to give you five answers to choose from. And as you’ll soon see, there are many benefits to working with multiple-choice questions.

A Tip About Choices

Notice that the choices are often in numerical order.

For one, if you really mess up calculating the question, chances are your choice will not be among the ones given. Now you have a chance to go back and try that problem again more carefully. Another benefit is that you may be able to use the information in the choices to help you solve the problems (don’t worry—we’ll tell you how soon).

We are now going to introduce to you the type of multiple-choice questions you will see on the SSAT. Each one of the following questions will test some skill that we covered in the Fundamental Math Skills chapter. If you don’t understand the underlying concept, take a look back at Chapter 2 for help.

Math Vocabulary

1.Which of the following is the greatest even integer less than 25?

(A) 26

(B) 24.5

(D) 21

(E) 0

The first and most important thing you need to do on this—and every—problem is to read and understand the question. What important vocabulary words did you see in the question? There is “even” and “integer.” You should always underline the important words in the questions on paper-based tests, or jot them down on your scratch paper for online tests. This way you will make sure to pay attention to them and avoid careless errors.

Now that we understand that the question is looking for an even integer, we can eliminate any answers that are not even or an integer. Cross out (B) and (D). We can also eliminate (A) because 26 is greater than 25 and we want a number less than 25. Now all we have to do is ask which is greater—0 or 22. Choice (C) is the right answer.

Try it again.

Set A = {All multiples of 7}

Set B = {All odd numbers}

2.All of the following are members of both Set A and Set B above EXCEPT

(A) 7

(B) 21

(D) 59

(E) 77

Did you underline or jot down the words multiples of 7 and odd ? Did you note that this is an EXCEPT question? Because all the choices are odd, they are all in Set B, but only (D) is not a multiple of 7. You’re looking for the answer choice that doesn’t match the others on EXCEPT questions. So (D) is the right answer.

The Rules of Zero

3.x, y, and z stand for three distinct numbers, where xy = 0 and yz = 15. Which of the following must be true?

(A) y = 0

(B) x = 0

(D) xyz = 15

(E) It cannot be determined from the information above.

Remember the Rules of Zero

Zero is even. It’s neither positive nor negative, and anything multiplied by 0 = 0.

Because x times y is equal to zero, and x, y, and z are different numbers, we know that either x or y is equal to zero, which means that z cannot be zero and xyz cannot be 15. Cross out choices (C) and (D). If y was equal to zero, then y times z should also be equal to zero. Because it is not, we know that it must be x that equals zero. Choice (B) is correct.

The Multiplication Table

4.Which of the following is equal to 6 × 5 × 2?

(A) 60 ÷ 3

(B) 14 × 7

(D) 12 × 10

(E) 3 × 3 × 3 × 9

6 × 5 × 2 = 60. The original expression is a multiple of 5, so the answer must also contain a multiple of 5. Cross out (B) and (E). Now evaluate the remaining answer choices. is smaller than 60, so cross out (A). 2 × 2 × 15 = 60. Choice (C) is correct.

Don’t Do More Work Than You Have To

When looking at answer choices, start with what’s easiest for you; work through the harder ones only when you have eliminated all the others.

Working with Negative Numbers

5.7 — 9 is the same as

(A) 7 — (—9)

(B) 9 — 7

(D) —7 — 9

(E) —9 — 7

Remember that subtracting a number is the same as adding its opposite. Choice (C) is correct.

Order of Operations

6.9 + 6 ÷ 2 × 3 =

(A) 7

(B) 9

(D) 13

(E) 18

Remember your PEMDAS rules? Left to right, since this problem has no parentheses (P) or exponents (E), you can proceed to MD (multiplication and division). 6 ÷ 2 is 3, and 3 × 3 is 9. Finally, perform the addition. 9 + 9 is 18. The correct answer is (E).

Factors and Multiples

7.What is the sum of the prime factors of 42 ?

(A) 18

(B) 13

(D) 10

(E) 7

The best way to find the prime factors is to draw a factor tree. Need to review? Revisit Chapter 2! Then we will see that the prime factors of 42 are 2, 3, and 7. Add them up and we get 12, (C).

Factors Are Few; Multiples Are Many

The factors of a number are always equal to or less than that number and there’s a limited quantity of them. The multiples of a number are always equal to or greater than that number and there are infinitely many of them. Be sure not to confuse the two!

Fractions

8.Which of the following is less than ?

(A)

(B)

(C)

(D)

(E)

When comparing fractions, you have three choices. You can find a common denominator and then compare the fractions (such as when you add or subtract fractions). Use the Bowtie method from Chapter 2 to find one easily. You can also change the fractions to decimals. If you have memorized the fraction-to-decimal chart from Chapter 2, you probably found the right answer without too much difficulty. It’s (A).

Percents

9.Thom’s playlist contains 15 jazz songs, 45 rap songs, 30 funk songs, and 60 pop songs. What percent of the songs on Thom’s playlist are funk?

(A) 10%

(B) 20%

(D) 30%

(E) 40%

Start with some Process of Elimination. Since there are fewer funk songs than there are rap songs or pop songs, funk will definitely be less than . Cross out (D) and (E). To narrow the answers down further find the fractional part that represents Thom’s funk songs. He has 30 out of a total of 150. We can reduce to . As a percent, is 20%, (B).

Exponents

10.2⁶ =

(A) 2³

(B) 3²

(D) 4⁴

(E) 8²

Expressions with the same base but different exponents will never have the same value. Eliminate choice (A). To be equivalent, the answer would need to have a base that is a multiple of 2. Eliminate choice (B). Now expand 26 out and multiply to find that it equals 64. Look for which of the remaining answer choices also equals 64. Choice (E) is correct.

Elementary Level

You shouldn’t expect to see exponents or roots on your tests.

Square Roots

11.The square root of 75 falls between what two integers?

(A) 5 and 6

(B) 6 and 7

(D) 8 and 9

(E) 9 and 10

If you know your perfect squares, you’ll see that 75 falls between 64 and 81. The square root of 64 is 8 and the square root of 81 is 9. If you have trouble with this one, try using the choices and working backward. As we discussed in Chapter 2, a square root is just the opposite of squaring a number. 52 is 25 and 62 is 36, so cross out (A). 72 is 49, so cross out (B). 82 is 64, so cross out (C). Then we find that 75 falls between 8² (64) and 9² (81). Choice (D) is correct.

Simple Algebraic Equations

12.11x = 121. What does x = ?

(A) 2

(B) 8

(D) 11

(E) 12

To isolate x, divide both sides by 11. 121 ÷ 11 = 11. If you find the equation confusing or you’re better at multiplying than dividing, use the choices and work backward. Each one provides you with a possible value for x. Start with the middle choice and replace x with it: 11 × 10 = 110. That’s too small. Now we know that not only is (C) incorrect, but also that (A) and (B) are incorrect because they are smaller than (C). Now test 11 × 11 = 121, so the correct choice is (D).

The Case of the Mysteriously Missing Sign

If there is no operation sign between a number and a variable (letter), the operation is multiplication.

Solve for Variable

13.If 3y + 17 = 25 — y, then y =

(A) 1

(B) 2

(D) 4

(E) 5

Add y to both sides to consolidate the variables. Now you have 4y + 17 = 25. Subtract 17 from both sides. 4y = 8. Divide both sides by 4. y = 2. Just as above, if you get stuck, substitute the answer choices in for y to see which one makes the expression true. The correct answer is (B).

Percent Algebra

14.25% of 30% of what is equal to 18 ?

(A) 1

(B) 36

(D) 240

(E) 540

Use translation to turn the sentence into an equation. Need to review? Go back to Chapter 2! . Reduce to and to so they are easier to work with. Multiply both sides by . Now you have × x = 72. Multiply both sides by . x = 240. You can also use the choices and work backward. Start with (C) and find out that 25% of 30% of 120 is 9. This result is too small, so cross out (A), (B), and (C). 25% of 30% of 240 is 18. The correct answer is (D).

Percent

Percent means “out of 100,” and the word of in a word problem tells you to multiply.

Geometry

15.BCDE is a rectangle with a perimeter of 44. If the length of BC is 15, what is the area of BCDE?

(A) 105

(B) 17

(D) 14

(E) It cannot be determined.

If you know the length and the perimeter, you can figure out the area. Cross out (E). Need to review your Geometry definitions? Go back to Chapter 2! If the perimeter is 44, the length and width must add up to 22. Since the length is 15, the width must be 7. 7 × 15 = 105. The correct answer is (A).

Don’t Cut Corners: Estimate Them

Make sure to guesstimate on geometry questions! This is a quick way to make sure you’re not making calculation errors.

16.If the perimeter of this polygon is 37, what is the value of x + y ?

(A) 5

(B) 9

(D) 16

(E) 20

Use the figure to guesstimate that the sum of x and y is less than half of the perimeter. Cross out (E). x and y also aren’t dramatically smaller than the other sides, so cross out (A). Perimeter is the sum of the sides, so 37 = 6 + 8 + 7 + x + 6 + y. Consolidate into 37 = 27 + x + y. x + y = 10. Choice (C) is correct.

Word Problems

17.Jada is walking to school at a rate of 3 blocks every 14 minutes. When Omar walks at the same rate as Jada and takes the most direct route to school, he arrives in 56 minutes. How many blocks away from school does Omar live?

(A) 3

(B) 5

(D) 9

(E) 12

Start with some POE. Since Omar walks at the same rate and takes longer than 14 minutes, he must live farther than 3 blocks away. Cross out (A). Now recognize that this is a proportion question because you have two sets of data that you are comparing. Set up your fractions.

Remember that the units match on the top and on the bottom.

We know that we must do the same thing to the top and bottom of the first fraction to get the second fraction. Notice that the denominator of the second fraction (56) is 4 times the denominator of the first fraction (14). Therefore, the numerator of the second fraction must be 4 times the numerator of the first fraction (3).

So Omar walks 12 blocks in 56 minutes. This makes (E) the correct answer.

18.Half of the 30 students in Mrs. Whipple’s first-grade class got sick on the bus on the way back from the zoo. Of these students, of them were sick because they ate too much cotton candy. The rest were sick because they sat next to the students who ate too much cotton candy. How many students were sick because they sat next to the wrong student?

(A) 5

(B) 10

(D) 20

(E) 25

This is a really gooey fraction problem, and not just because it’s about cotton candy! Break it down into chunks, and work through one piece of information at a time. Make sure to write each step down! Because we’ve seen the word of, we know we have to multiply. First we need to multiply by 30, the number of students in the class. This gives us 15, the number of students who got sick. Now we have another of, so we must multiply the fraction of students who ate too much cotton candy, , by the number of students who got sick, 15. This gives us 10. So then the remainder, those who were unlucky in the seating plan, is 15 — 10 or 5, (A).

19.A piece of rope is 18 inches long. It is cut into 2 unequal pieces. The longer piece is twice as long as the shorter piece. How long, in inches, is the shorter piece?

(A) 2

(B) 6

(D) 12

(E) 18

Be strategic—start with some POE. If the rope is cut into unequal pieces, cross out (C) since 9 would be the length of two equal pieces. Since the question is asking for the shorter piece, cross out (D) and (E). Now test one of the remaining answer choices. If the shorter piece were 2, and the longer piece is twice the shorter piece, it would be 4, but that doesn’t add up to 18, so the answer must be (B). 12 is double 6, and 12 + 6 = 18.

PRACTICE DRILL 1—MULTIPLE CHOICE (ALL SSAT LEVELS)

When you are done, check your answers in Chapter 9. Don’t forget to time yourself!

Remember to time yourself during this drill!

1.The sum of five consecutive positive integers is 30. What is the square of the largest of the five positive integers?

(A) 16

(B) 25

(D) 64

(E) 80

2.How many factors does the number 24 have?

(A) 2

(B) 4

(D) 8

(E) 10

3.If 12 is a factor of a certain number, what must also be factors of that number?

(A) 2 and 6 only

(B) 3 and 4 only

(D) 1, 2, 3, 4, and 6

(E) 1, 2, 3, 4, 6, and 24

4.What is the smallest number that can be added to the number 1,024 to produce a result divisible by 9 ?

(A) 1

(B) 2

(D) 4

(E) 6

5.Which of the following is a multiple of 3 ?

(A) 2

(B) 6

(D) 14

(E) 16

6.Which of the following is NOT a multiple of 6?

(A) 12

(B) 18

(D) 24

(E) 42

7.Which of the following is a multiple of both 3 and 5 ?

(A) 10

(B) 20

(D) 45

(E) 50

8.A company’s profit was $75,000 in 2014. In 2021, its profit was $450,000. The profit in 2021 was how many times as great as the profit in 2014 ?

(A) 2

(B) 4

(D) 10

(E) 60

9.Valentina owns one-third of the pieces of furniture in the apartment she shares with her friends. If there are 12 pieces of furniture in the apartment, how many pieces does Valentina own?

(A) 2

(B) 4

(D) 8

(E) 12

10.A tank of oil is one-third full. When full, the tank holds 90 gallons. How many gallons of oil are in the tank now?

(A) 10

(B) 20

(D) 40

(E) 50

11.Tigger the Cat sleeps three-fourths of every day. In a four-day period, he sleeps the equivalent of how many full days?

(A)

(B)

(D) 3

(E) 4

12.Which of the following has the greatest value?

(A)

(B)

(C)

(D)

(E)

13.

(A)

(B) 1

(D) 3

(E) 12

14.The product of 0.34 and 1,000 is approximately

(A) 3.50

(B) 35

(D) 350

(E) 650

15.2.398 =

(A)

(B)

(C)

(D)

(E) None of the above

Stop. Record your time for this drill:

When You Are Done

Check your answers in Chapter 9, this page.

HOW DID YOU DO?

That was a good sample of some of the kinds of questions you’ll see on the SSAT. Now there are a few things to check other than your answers. Remember that taking the test involves much more than just getting answers right. It’s also about guessing wisely, using your time well, and figuring out where you’re likely to make mistakes. Once you’ve checked to see what you’ve gotten right and wrong, you should then consider the points that follow to improve your score.

Time and Pacing

How long did it take you to do the 15 questions? 15 minutes? It’s okay if you went a minute or two over. However, if you finished very quickly (in fewer than 10 minutes) or slowly (more than 20 minutes), look at any problems that may have affected your speed. Which questions seriously slowed you down? Did you answer some quickly but not correctly? Your answers to these questions will help you plan which and how many questions to answer on the SSAT.

Question Recognition and Selection

Did you use your time wisely? Did you do the questions in an order that worked well for you? Which kinds of questions were the hardest for you? Remember that every question on the SSAT, whether you know the answer right away or find the question confusing, is worth one point, and that you don’t have to answer all the questions to get a good score. In fact, because of the guessing penalty, skipping questions can actually raise your score. So depending on your personal speed, you should concentrate most on getting right as many questions you find easy or sort-of easy as possible, and worry about harder problems later. Keep in mind that in Math sections, the questions generally go from easiest to hardest throughout. Getting right the questions you know you can answer takes time, but you know you can solve them—so give yourself that time!

POE and Guessing

Did you actively look for wrong answers to eliminate, instead of just looking for the right answer? (You should.) Did you physically cross off wrong answers to keep track of your POE? Was there a pattern to when guessing worked (more often when you could eliminate one wrong answer, and less often when you picked simpler-looking over harder-looking answers)?

Be Careful

Did you work problems out? Did you move too quickly or skip steps on problems you found easier? Did you always double-check what the question was asking? Often students miss questions that they know how to do! Why? It’s simple—they work out problems in their heads or don’t read carefully. Work out every SSAT math problem on the page. Consider it double-checking, because your handwritten notes confirm what you’ve worked out in your head.

PRACTICE DRILL 2—MULTIPLE CHOICE (UPPER LEVEL ONLY)

While doing the next drill, keep in mind the general test-taking techniques we’ve talked about: guessing, POE, order of difficulty, pacing, and working on the page and not in your head. At the end of the section, check your answers. But don’t stop there. Investigate the drill thoroughly to see how and why you got your answers wrong. And check your time. You should be spending about one minute per question on this drill. When you are done, check your answers in Chapter 9. Don’t forget to time yourself!

Remember to time yourself during this drill!

1.How many numbers between 1 and 100 are multiples of both 2 and 7 ?

(A) 6

(B) 7

(D) 9

(E) 10

2.What is the smallest multiple of 7 that is greater than 50 ?

(A) 7

(B) 49

(D) 56

(E) 63

3.2³ × 2³ × 2² =

(A) 64

(B) 2⁸

(D) 2¹⁶

(E) 2¹⁸

4.For what integer value of m does 2m + 4 = m³?

(A) 1

(B) 2

(D) 4

(E) 5

5.One-fifth of the students in a class chose recycling as the topic for their science projects. If four students chose recycling, how many students are in the class?

(A) 4

(B) 10

(D) 20

(E) 24

6.If 6x — 4 = 38, then x + 10 =

(A) 7

(B) 10

(D) 17

(E) 19

7.If 3x — 6 = 21, then what is x ÷ 9 ?

(A) 0

(B) 1

(D) 6

(E) 9

8.Only one-fifth of the chairs in a classroom are in working order. If three additional working chairs are brought in, there are 19 working seats available. How many chairs were originally in the room?

(A) 16

(B) 19

(D) 80

(E) 95

9.If a harvest yielded 60 bushels of corn, 20 bushels of wheat, and 40 bushels of soybeans, what percent of the total harvest was corn?

(A) 50%

(B) 40%

(D) 30%

(E) 25%

10.At a local store, an item that usually sells for $45 is currently on sale for $30. By what percent is that item discounted?

(A) 10%

(B) 25%

(D) 50%

(E) 66%

11.Which of the following is most nearly 35% of $19.95 ?

(A) $3.50

(B) $5.75

(D) $9.95

(E) $13.50

12.Of the 50 hotels in the Hilltop Hotels chain, 5 have indoor swimming pools and 15 have outdoor swimming pools. What percent of all Hilltop Hotels have either an indoor or an outdoor swimming pool?

(A) 40%

(B) 30%

(D) 15%

(E) 5%

13.For what price item does 40% off equal a $20 discount?

(A) $50.00

(B) $100.00

(D) $800.00

(E) None of the above

14.A pair of shoes is offered on a special blowout sale. The original price of the shoes is reduced from $50 to $20. What is the percent change in the price of the shoes?

(A) 60%

(B) 50%

(D) 25%

(E) 20%

15.Destiny buys a silk dress regularly priced at $60, a cotton sweater regularly priced at $40, and four pairs of socks regularly priced at $5 each. If the dress and the socks are on sale for 20% off the regular price and the sweater is on sale for 10% off the regular price, what is the total amount of her purchase?

(A) $90.00

(B) $96.00

(D) $102.00

(E) $108.00

16.Thirty percent of $17.95 is closest to

(A) $2.00

(B) $3.00

(D) $9.00

(E) $12.00

17.Fifty percent of the 20 students in Mrs. Schweizer’s third-grade class are boys. If 90 percent of these boys ride the bus to school, which of the following is the number of boys in Mrs. Schweizer’s class who ride the bus to school?

(A) 9

(B) 10

(D) 16

(E) 18

18.On a test with 25 questions, Marc scored an 88 percent. How many questions did Marc answer correctly?

(A) 22

(B) 16

(D) 4

(E) 3

19.Four friends each pay $5 for a pizza every Friday night. If they were to start inviting a fifth friend to come with them and still bought the same pizza, how much would each person then have to pay?

(A) $1

(B) $4

(D) $20

(E) $25

20.A stop sign has 8 equal sides of length 4. What is its perimeter?

(A) 4

(B) 8

(D) 32

(E) It cannot be determined from the information given.

21.If the perimeter of a square is 56, what is the length of each side?

(A) 4

(B) 7

(D) 28

(E) 112

22.The perimeter of a square with a side of length 4 is how much less than the perimeter of a rectangle with sides of length 4 and width 6 ?

(A) 0

(B) 2

(D) 6

(E) 8

23.What is the perimeter of an equilateral triangle, one side of which measures 4 inches?

(A) 12 inches

(B) 8 inches

(D) 4 inches

(E) It cannot be determined from the information given.

24.x =

(A) 8

(B) 30

(D) 65

(E) 180

25.If b = 45, then v² =

(A) 32

(B) 25

(D) 5

(E) It cannot be determined from the information given.

26.One-half of the difference between the number of degrees in a square and the number of degrees in a triangle is

(A) 45

(B) 90

(D) 240

(E) 360

27.If the area of a square is equal to its perimeter, what is the length of one side?

(A) 1

(B) 2

(D) 8

(E) 10

28.The area of a rectangle with width 4 and length 3 is equal to the area of a triangle with a base of 6 and a height of

(A) 1

(B) 2

(D) 4

(E) 12

29.Two cardboard boxes have equal volume. The dimensions of one box are 3 × 4 × 10. If the length of the other box is 6 and the width is 4, what is the height of the second box?

(A) 2

(B) 5

(D) 12

(E) 24

30.If the area of a square is 64p², what is the length of one side of the square?

(A) 64p²

(B) 64p

(D) 8p

(E) 8

31.If AB = 10 and AC = 15, what is the perimeter of the figure above?

(A) 25

(B) 35

(D) 50

(E) It cannot be determined from the information given.

32.If ABCD, shown above, is a rectangle, what is the value of w + x + y + z?

(A) 90°

(B) 150°

(D) 190°

(E) 210°

33.What is the area of the figure above if all the angles shown are right angles?

(A) 38

(B) 42

(D) 88

(E) 96

34.In the figure above, the length of side AB of square ABCD is equal to 4 and the circle has a radius of 2. What is the area of the shaded region?

(A) 4 — π

(B) 16 — 4π

(D) 4π

(E) 8π

35.The distance between points A and B in the coordinate plane above is

(A) 5

(B) 6

(D) 9

(E) 10

Stop. Check your time for this drill:

When You Are Done

Check your answers in Chapter 9, this page.

Now we’re going to transition into concepts that go beyond what was covered in the Fundamentals (Chapter 2).

RATIOS

A ratio is like a recipe. It tells you how much of each ingredient goes into a mixture.

For example:

To make punch, mix two parts grape juice with three parts orange juice.

This ratio tells you that for every two units of grape juice, you will need to add three units of orange juice. It doesn’t matter what the units are; if you were working with ounces, you would mix two ounces of grape juice with three ounces of orange juice to get five ounces of punch. If you were working with gallons, you would mix two gallons of grape juice with three gallons of orange juice. How much punch would you have? Five gallons.

To work through a ratio question, first you need to organize the information you are given. Do this using the Ratio Box.

In a club with 35 members, the ratio of people wearing purple shirts to people wearing yellow shirts is 3:2. To complete your Ratio Box, fill in the ratio at the top and the “real value” at the bottom.

	Purple	Yellow	Total
Ratio	3 +	2 =	5
Multiplier
Real Value			35

Then look for a “magic number” that you can multiply by the ratio total to get the real value total. In this case, the magic number is 7. That’s all there is to it!

	Purple	Yellow	Total
Ratio	3 +	2 =	5
Multiplier	× 7	× 7	× 7
Real Value	21	14	35

PRACTICE DRILL 3—RATIOS

Remember to time yourself during this drill!

1.In a jar of lollipops, the ratio of red lollipops to blue lollipops is 3:5. If only red lollipops and blue lollipops are in the jar and if the total number of lollipops in the jar is 56, how many blue lollipops are in the jar?

(A) 35

(B) 28

(D) 8

(E) 5

2.At Jed’s Country Hotel, there are three types of rooms: singles, doubles, and triples. If the ratio of singles to doubles to triples is 3:4:5, and the total number of rooms is 36, how many doubles are there?

(A) 4

(B) 9

(D) 24

(E) 36

3.Matt’s Oak Superstore has exactly three times as many large oak desks as small oak desks in its inventory. If the store sells only these two types of desks, which could be the total number of desks in stock?

(A) 10

(B) 13

(D) 18

(E) 25

4.In Janice’s tennis club, 8 of the 12 players are right-handed. What is the ratio of right-handed to left-handed players in Janice’s club?

(A) 1:2

(B) 1:6

(D) 2:3

(E) 3:4

5.One-half of the 400 students at Booth Junior High School are girls. Of the girls at the school, the ratio of those who ride a school bus to those who walk is 7:3. What is the total number of girls who walk to school?

(A) 10

(B) 30

(D) 120

(E) 140

6.A pet goat eats 2 pounds of goat food and 1 pound of grass each day. When the goat has eaten a total of 15 pounds, how many pounds of grass will it have eaten?

(A) 3

(B) 4

(D) 15

(E) 30

Stop. Check your time for this drill:

When You Are Done

Check your answers in Chapter 9, this page.

PLUGGING IN

The SSAT will often ask you questions about real-life situations in which the numbers have been replaced with variables. One of the easiest ways to tackle these questions is with a powerful technique called Plugging In.

Mark is two inches taller than John, who is four inches shorter than Terry. If t represents Terry’s height in inches, then in terms of t, an expression for Mark’s height is

(A) t + 6

(B) t + 4

(D) t

(E) t — 2

The problem with this question is that we’re not used to thinking of people’s heights in terms of variables. Have you ever met someone who was t inches tall?

Whenever you see variables used in the question and in the choices, just plug in a number to replace the variable.

1.Choose a number for t.

2.Using that number, figure out Mark’s and John’s heights.

3.Draw a box around Mark’s height because that’s what the question asked you for.

4.Plug your number for t into the choices and choose the one that gives you the number you found for Mark’s height.

Take the Algebra Away, and Arithmetic Is All That’s Left

When you plug in for variables, you won’t need to write equations and won’t have to solve algebra problems. Doing simple arithmetic is always easier than doing algebra.

Here’s How It Works

Mark is two inches taller than John, who is four inches shorter than Terry. If t represents Terry’s height in inches, then ~~in terms of t~~, an expression for Mark’s height is

(A) t + 6

(B) t + 4

(D) t

(E) t — 2

For Terry’s height, let’s pick 60 inches. This means that t = 60.

Remember, there is no right or wrong number to pick. 50 would work just as well.

If Terry is 60 inches tall, now we can figure out that, because John is four inches shorter than Terry, John’s height must be (60 — 4), or 56 inches.

The other piece of information we learn from the problem is that Mark is two inches taller than John. If John’s height is 56 inches, that means Mark must be 58 inches tall.

Here’s what we’ve got:

Terry: 60 inches = t

John: 56 inches

Mark: inches

Now, the question asks for Mark’s height, which is 58 inches. The last step is to go through the choices substituting 60 for t and choose the one that equals 58.

(A) t + 6: 60 + 6 = 66: ELIMINATE

(B) t + 4: 60 + 4 = 64: ELIMINATE

(D) t: 60: ELIMINATE

(E) t — 2: 60 — 2 = 58: PICK THIS ONE!

After reading this explanation, you may be tempted to say that Plugging In takes too long. Don’t be fooled. The method itself is often faster and (more importantly) more accurate than regular algebra. Try it out. Practice. As you become more comfortable with Plugging In, you’ll get even quicker and better results. You still need to know how to do algebra, but if you do only algebra, you may have difficulty improving your SSAT score. Plugging In gives you a way to break through whenever you are stuck. You’ll find that having more than one way to solve SSAT math problems puts you at a real advantage.

Don’t worry about timing yourself on this drill.

Focus on the strategy.

Plug in for each question so you learn how to use the technique.

PRACTICE DRILL 4—PLUGGING IN

1.At a charity fund-raiser, 200 people each donated x dollars. In terms of x, what was the total number of dollars donated?

(A)

(B) 200

(C)

(D) 200 + x

(E) 200x

2.If 10 magazines cost d dollars, then in terms of d, how many magazines can be purchased for 3 dollars?

(A)

(B) 30d

(C)

(D)

(E)

3.The zoo has four times as many monkeys as lions. There are four more lions than there are zebras at the zoo. If z represents the number of zebras in the zoo, then in terms of z, how many monkeys are there in the zoo?

(A) z + 4

(B) z + 8

(D) 4z + 16

(E) 4z + 4

Elementary Level

While some of these problems may seem harder than what you will encounter, Plugging In and Plugging In the Answers (the next section) are great strategies. Be sure you understand how to use these strategies on your test.

Occasionally, you may run into a Plugging In question that doesn’t contain variables. These questions usually ask about a percentage or a fraction of some unknown number or price. This is the one time that you should Plug In even when you don’t see variables in the answers!

Also, be sure you plug in good numbers. Good doesn’t mean right because there’s no such thing as a right or wrong number to plug in. A good number is one that makes the problem easier to work with. If a question asks about minutes and hours, try plugging in 30 or 60, not 128. Also, whenever you see the word percent, plug in 100!

4.The price of a suit is reduced by half, and then the resulting price is reduced by 10%. The final price is what percent of the original price?

(A) 5%

(B) 10%

(D) 40%

(E) 45%

5.On Wednesday, Miguel ate one-fourth of a pumpkin pie. On Thursday, he ate one-half of what was left of the pie. What fraction of the entire pie did Miguel eat on Wednesday and Thursday?

(A)

(B)

(C)

(D)

(E)

6.If p pieces of candy costs c cents, then in terms of p and c, 10 pieces of candy will cost

(A) cents

(B) cents

(D) cents

(E) 10 + p + c cents

7.If J is an odd integer, which of the following must be true?

(A) (J ÷ 3) > 1

(B) (J — 2) is a positive integer.

(D) J² > J

(E) J > 0

8.If m is an even integer, n is an odd integer, and p is the product of m and n, which of the following is always true?

(A) p is a fraction.

(B) p is an odd integer.

(D) p is between m and n.

(E) p is greater than zero.

When You Are Done

Check your answers in Chapter 9, this page.

PLUGGING IN THE ANSWERS (PITA)

Plugging In the Answers (PITA for short) is similar to Plugging In. When you have variables in the choices, you Plug in. When you have numbers in the choices, you should generally Plug In the answers. The only time this may get tricky is when you have a question that asks for a percent or fraction of some unknown number.

Plugging In the Answers works because on a multiple-choice test, the right answer is always one of the choices. On this type of question, you can’t plug in any number you want because only one number will work. Instead, you can plug in numbers from the choices, one of which must be correct. Here’s an example.

Sydney baked a batch of cookies. She gave half to her friend Malik and six to her mother. If she now has eight cookies left, how many did Sydney bake originally?

(A) 8

(B) 12

(D) 28

(E) 32

See what we mean? It would be hard to just start making up numbers of cookies and hope that eventually you guessed correctly. However, the number of cookies that Sydney baked originally must be either 8, 12, 20, 28, or 32 (the five choices). So pick one—always start with (C)—and then work backward to determine whether you have the right choice.

Let’s start with (C): Sydney baked 20 cookies. Now work through the events listed in the question.

She had 20 cookies—from (C)—and she gave half to Malik. That leaves Sydney with 10 cookies.

What next? She gives 6 to her mom. Now she’s got 4 left.

Keep going. The problem says that Sydney now has 8 cookies left. But if she started with 20—(C)—she would only have 4 left. So is (C) the right answer? No.

No problem. Choose another choice and try again. Be smart about which choice you pick. When we used the number in (C), Sydney ended up with fewer cookies than we wanted her to have, didn’t she? So the right answer must be a number larger than 20, the number we took from (C). Eliminate (A), (B), and (C).

Now you only have two answer choices left. The good news is that it doesn’t matter which one you try next. If it works, it’s your answer. If it doesn’t work, the other one is the answer! If you can’t tell whether you need a bigger number or smaller number, just pick either (B) or (D) to test next, and pay attention to whether it gets you closer to your target or farther away.

Back to Sydney and her cookies. We need a number larger than 20. So let’s go to (D)—28.

Sydney started out with 28 cookies. The first thing she did was give half, or 14, to Malik. That left Sydney with 14 cookies.

Then she gave 6 cookies to her mother. 14 — 6 = 8. Sydney has 8 cookies left over. Keep going with the question. It says, “If she now has eight cookies left….” She has eight cookies left and, voilà—she’s supposed to have 8 cookies left.

What does this mean? It means you’ve got the right answer! Pick (D) and move on.

If (D) had not worked, and you were still certain that you needed a number larger than (C), you also would be finished. Since you started with the middle, (C), which didn’t work, and then you tried the next larger choice, (D), which didn’t work either, you could pick the only choice bigger than (C) that was left—in this case (E)—and be done.

This diagram helps illustrate the way you should move through the choices.

To wrap up, Plugging In the Answers should always go the following way:

1.Start with (C). This number is now what you are working with.

2.Work the problem. Go through the problem with that number, using information to help you determine if it is the correct answer.

3.If (C) doesn’t work, try another answer. Remember to think logically about whether you should try a bigger number or smaller number next.

4Once you find the correct answer, STOP.

PRACTICE DRILL 5—PLUGGING IN THE ANSWERS

Remember to time yourself during this drill!

1.Ted can read 60 pages per hour. Naomi can read 45 pages per hour. If both Ted and Naomi read at the same time, how many minutes will it take them to read a total of 210 pages?

(A) 36

(B) 72

(D) 145

(E) 180

2.If the sum of y and y + 1 is greater than 18, which of the following is one possible value for y ?

(A) —10

(B) —8

(D) 8

(E) 10

3.Mohammad is 5 years older than Vivek. In 5 years, Mohammad will be twice as old as Vivek is now. How old is Mohammad now?

(A) 5

(B) 10

(D) 25

(E) 35

4.Three people—Elliott, Vinita, and Cole—want to put their money together to buy a $90 radio. If Vinita agrees to pay twice as much as Cole, and Elliott agrees to pay three times as much as Vinita, how much must Vinita pay?

(A) $10

(B) $20

(D) $45

(E) $65

5.Four less than a certain number is two-thirds of that number. What is the number?

(A) 1

(B) 6

(D) 12

(E) 16

Stop. Check your time for this drill:

When You Are Done

Check your answers in Chapter 9, this page.

GEOMETRY

Guesstimating: A Second Look

Guesstimating worked well back in the introduction when we were just using it to estimate the size of a number, but geometry problems are undoubtedly the best place to guesstimate whenever you can.

Elementary Level

This question is harder than what you will encounter, but it’s a good idea to learn how guesstimating can help you!

Let’s try the next problem. Remember, unless a particular question tells you otherwise, you can safely assume that figures are drawn to scale.

A circle is inscribed in square PQRS. What is the area of the shaded region?

(A) 16 — 6π

(B) 16 — 4π

(D) 16 — 2π

(E) 16π

Wow, a circle inscribed in a square—that sounds tough!

It isn’t. Look at the picture. What fraction of the square looks like it is shaded? Half? Three-quarters? Less than half? Looks like about one-quarter of the area of the square is shaded. You’ve just done most of the work necessary to solve this problem.

Now, let’s just do a little math. The length of one side of the square is 4, so the area of the square is 4 × 4 or 16.

So the area of the square is 16, and we said that the shaded region was about one-fourth of the square. One-fourth of 16 is 4, right? So we’re looking for a choice that equals about 4. Let’s look at the choices.

(A) 16 — 6π

(B) 16 — 4π

(D) 16 — 2π

(E) 16π

This becomes a little complicated because the answers include π. For the purposes of guesstimating, and in fact for almost any purpose on the SSAT, you should just remember that π is a little more than 3.

Try these values when guesstimating:

π ≈ 3+

Let’s look back at those answers.

(A) 16 — 6π is roughly equal to 16 — (6 × 3) = —2

(B) 16 — 4π is roughly equal to 16 — (4 × 3) = 4

(D) 16 — 2π is roughly equal to 16 — (2 × 3) = 10

(E) 16π is roughly equal to (16 × 3) = 48

Now let’s think about what these answers mean.

Choice (A) is geometrically impossible. A figure cannot have a negative area. Eliminate it.

Choice (B) means that the shaded region has an area of about 4. Sounds pretty good.

Choice (C) means that the shaded region has an area of about 7. The area of the entire square was 16, so that would mean that the shaded region was almost half the square. Possible, but doubtful.

Choice (D) means that the shaded region has an area of about 10. That’s more than half the square and in fact, almost three-quarters of the entire square. No way; cross it out.

Finally, (E) means that the shaded region has an area of about 48. What? The whole square had an area of 16. Is the shaded region three times as big as the square itself? Not a chance. Eliminate (E).

At this point you are left with only (B), which we feel pretty good about, and (C), which seems a little large. What should you do?

Pick (B) and pat yourself on the back because you chose the right answer without doing a lot of unnecessary work. Also, remember how useful it was to guesstimate and make sure you do it whenever you see a geometry problem, unless the problem tells you that the figure is not drawn to scale!

Weird Shapes

Whenever the test presents you with a geometric figure that is not a square, rectangle, circle, or triangle, draw a line or lines to divide that figure into the shapes that you do know. Then you can easily work with shapes you know all about.

Shaded Regions—Middle and Upper Levels Only

Sometimes geometry questions show you one figure inscribed in another and then ask you to find the area of a shaded region inside the larger figure and outside the smaller figure (like the problem at the beginning of this section). To find the areas of these shaded regions, find the area of the outside figure and then subtract from that the area of the figure inside. The difference is what you need.

ABCE is a rectangle with a length of 10 and width of 6. Points F and D are the midpoints of AE and EC, respectively. What is the area of the shaded region?

(A) 25.5

(B) 30

(D) 52.5

(E) It cannot be determined from the information given.

Start by labeling your figure with the information given if you’re working in a test booklet, or by drawing the figure on your scratch paper. The next step is to find the area of the rectangle. If you multiply the length by the width, you’ll find the area is 60. Now we need to find the area of the triangle that we are removing from the rectangle. Because the height and base of the triangle are parts of the sides of the rectangle, and points D and F are half the length and width of the rectangle, we know that the height of the triangle is half the rectangle’s width, or 3, and the base of the triangle is half the rectangle’s length, or 5. Using the formula for area of a triangle, we find the area of the triangle is 7.5. Need to review your formulas? Go back to Chapter 2! Now subtract the area of the triangle from the area of the rectangle. 60 — 7.5 = 52.5. The correct choice is (D). Be careful not to choose (E) just because the problem looks tricky!

PRACTICE DRILL 6—FUNCTIONS (MIDDLE AND UPPER LEVELS ONLY)

Remember to time yourself during this drill!

Questions 1 and 2 refer to the following definition.

The function h is defined as h(x) = 10x — 10

1.h(7) =

(A) 70

(B) 60

(D) 7

(E) 0

2.If h(x) = 120, then x =

(A) 11

(B) 12

(D) 120

(E) 130

Questions 3—5 refer to the following definition.

For all real numbers d and y, d ¿ y = (d × y) — (d + y).

[Example: 3 ¿ 2 = (3 × 2) — (3 + 2) = 6 — 5 = 1]

3.10 ¿ 2 =

(A) 20

(B) 16

(D) 8

(E) 4

4.If K (4 ¿ 3) 30, then K =

(A) 3

(B) 4

(D) 6

(E) 7

5.(2 ¿ 4) × (3 ¿ 6) =

(A) (9 ¿ 3) + 3

(B) (6 ¿ 4) + 1

(D) (8 ¿ 4) + 2

(E) (9 ¿ 4) + 3

Stop. Check your time for this drill:

When You Are Done

Check your answers in Chapter 9, this page.

Middle Level

Some of the questions here are harder than what you will see on your test. Still, give them all a try. The skills you have learned should help you do well on most of the questions.

PRACTICE DRILL 7—MIDDLE AND UPPER LEVELS ONLY

When you are done, check your answers in Chapter 9. Don’t forget to time yourself!

Remember to time yourself during this drill!

1.If p is an odd integer, which of the following must be an odd integer?

(A) p² + 3

(B) 2p + 1

(D) p — 3

(E) 2(p²)

2.If m is the sum of two positive even integers, which of the following CANNOT be true?

(A) m < 5

(B) 3m is odd.

(D) m³ is even.

(E) m ÷ 2 is even.

3.The product of b and a² can be written as

(A) (AB)²

(B)

(C)

(D)

(E)

4.Damon has twice as many records as Graham, who has one-fourth as many records as Alex. If Damon has d records, then in terms of d, how many records do Alex and Graham have together?

(A)

(B)

(C)

(D)

(E) 2d

5.x^a = (x³)³

What is the value of a × b ?

(A) 17

(B) 30

(D) 45

(E) 72

6.One six-foot roast beef sandwich serves either 12 children or 8 adults. Approximately how many of these sandwiches do you need to feed a party of 250, 75 of whom are children?

(A) 21

(B) 24

(D) 30

(E) 32

7.Liam and Noel are traveling from New York City to Dallas. If they traveled of the distance on Monday and of the distance that remained on Tuesday, what percentage of the trip do they have left to travel?

(A) 25%

(B) 30%

(D) 50%

(E) 80%

8. of a bag of potato chips contains 10 grams of fat. Approximately how many grams of fat are in of that same bag of chips?

(A) 5.5

(B) 6.5

(D) 8.5

(E) 9.5

9.Students in Mr. Greenwood’s history class are collecting donations for a school charity drive. If the total number of students in the class, x, donated an average of y dollars each, in terms of x and y, how much money was collected for the drive?

(A)

(B) xy

(C)

(D)

(E) 2xy

10.If e + f is divisible by 17, which of the following must also be divisible by 17 ?

(A) (e × f) — 17

(B) e + (f × 17)

(D) (e + f) ÷ 17

(E) (e × 3) + (f × 3)

11.Joe wants to find the mean number of pages in the books he has read this month. The books were 200, 220, and 260 pages long. He read the 200 page book twice, so it will be counted twice in the mean. If he reads one more book, what is the fewest number of pages it can have to make the mean no less than 230 ?

(A) 268

(B) 269

(D) 271

(E) 272

12.Sayeeda is a point guard for her basketball team. In the last 3 games, she scored 8 points once and 12 points in each of the other two games. What must she score in tonight’s game to raise her average to 15 points?

(A) 28

(B) 27

(D) 25

(E) 15

13.What is the greatest common factor of (3xy)³ and 3x²y⁵ ?

(A) xy

(B) 3x²y⁵

(D) 27x³y³

(E) 27x⁵y⁸

14.The town of Mechanicville lies due east of Stillwater and due south of Half Moon Crescent. If the distance from Mechanicville to Stillwater is 30 miles, and from Mechanicville to Half Moon Crescent is 40 miles, what is the shortest distance from Stillwater to Half Moon Crescent?

(A) 10

(B) 50

(D) 100

(E) It cannot be determined from the information given.

15.PQRS is a square with an area of 144. What is the area of the shaded region?

(A) 50

(B) 72

(D) 120

(E) It cannot be determined from the information given.

16.PO and QO are radii of the circle with center O. What is the value of x ?

(A) 30

(B) 45

(D) 90

(E) It cannot be determined from the information given.

17.What is the value of x ?

(A) 360

(B) 100

(D) 67

(E) It cannot be determined from the information given.

18.ABC is an equilateral triangle. What is the perimeter of this figure?

(A) 4 + 2π

(B) 4 + 4π

(D) 8 + 4π

(E) 12 + 2π

19.What is the perimeter of this figure?

(A) 120

(B) 44

(D) 36

(E) It cannot be determined from the information given.

20.How many meters of police tape are needed to wrap around a rectangular crime scene that measures 6 meters wide by 28 meters long?

(A) 34 meters

(B) 68 meters

(D) 136 meters

(E) 168 meters

21.Billy Bob’s Beans are currently packaged in cylindrical cans that contain 9 servings. The cans have a height of 20 cm and a diameter of 18 cm. Billy Bob wants to introduce a new single-serving can. If he keeps the height of the can the same, what should the diameter of the single-serving can be?

(A) 3

(B) 3

(D) 6

(E) 6

Stop. Check your time for this drill:

When You Are Done

Check your answers in Chapter 9, this page.

MATH REVIEW

Make sure you can confidently answer all of the following questions before you take your test.

1.Is zero an integer?

2.Is zero positive or negative?

3.What operation do you perform to find a sum?

4.What operation do you perform to find a product?

5.What is the result called when you divide?

6.Is 312 divisible by 3 ?

Is 312 divisible by 9 ?

(Actually dividing isn’t fair—use your divisibility rules!)

7.What does the “E” in PEMDAS stand for?

8.Is 3 a factor of 12 ?

Is 12 a factor of 3 ?

9.Is 3 a multiple of 12 ?

Is 12 a multiple of 3 ?

10.What is the tens digit in the number 304.275?

11.What is the tenths digit in the number 304.275?

12.2³ =

13.In “math language,” the word percent means __________________.

14.In “math language,” the word of means ___________________.

15.In a Ratio Box, the last column on the right is always the ___________________.

16.Whenever you see a problem involving averages, draw the ___________________.

17.When a problem contains variables in the question and in the answers, I will ___________________.

18.To find the perimeter of a square, I ___________________ the length(s) of ___________________ side(s).

19.To find the area of a square, I ___________________ the length(s) of ___________________ sides(s).

20.There are ___________________ degrees in a straight line.

21.A triangle has ___________________ angles, which total ___________________ degrees.

22.A four-sided figure contains ___________________ degrees.

23.An isosceles triangle has ___________________ equal sides; a(n) ___________________ triangle has three equal sides.

24.The longest side of a right triangle is called the ________________ and is located opposite the ___________________.

25.To find the area of a triangle, I use the formula ________________.

When You Are Done

Check your answers in Chapter 9, this page.

SSAT & ISEE Prep 2023 - Princeton Review 2023

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