## Cracking the SSAT & ISEE - The Princeton Review 2019

# Answers and explanations for SSAT practice drills

The SSAT

**SSAT MATH**

**Practice Drill 1—Multiple Choice**

1.**D**

Use PITA to solve this question. Since the question asks for *the square of the largest of the five consecutive integers*, label the choices as such. Then, start with (C) to get rid of choices more effectively. If 49 were the square of the largest integer, the integer would be 7, and other consecutive integers would be 6, 5, 4, and 3. The sum of these numbers 3 + 4 + 5 + 6 + 7 = 25, which is less than 30. Therefore, eliminate (A), (B), and (C), since these are too small. Try (D): the square root of 64 is 8, and the other integers would therefore be 7, 6, 5, and 4. 4 + 5 + 6 + 7 + 8 = 30, so the correct answer is (D).

2.**D**

List the factors of 24: 1 and 24, 2 and 12, 3 and 8, and 4 and 6. This totals 8 different factors of 24. The correct answer is (D).

3.**D**

Since 12 is a factor of a certain number, Plug In for that certain number. For instance, Plug In 36, since 12 is a factor, and use POE. 2 and 6 are factors of 36, but they are not the only factors of 36 listed in the choices. Eliminate (A). Similarly, 3 and 4 are not the only factors of 36 listed, so eliminate (B). 12 is a factor, but it is not the only factor listed, so eliminate (C). 24 is not a factor of 36, so eliminate (E). Choice (D) contains all the other factors listed in previous choices. The correct answer is (D).

4.**B**

Use long division to find the remainder of 1,024 divided by 9. The remainder is 7, so add 2 to the total to make the number be divisible by 9. The correct answer is (B). Alternatively, you can use the divisibility rule for 9—the sum of the digits is divisible by 9. 1 + 0 + 2 + 4 = 7, so if 2 is added to that, the sum is 9, which is divisible by 9. Remember, the question asks for the *smallest* number that can be added to 1,024.

5.**B**

A multiple of 3 will be 3 times a number. 2 is not a multiple of 3, so eliminate (A). 3 × 2 = 6, so (B) is a multiple of 3. 10, 14, and 16 are not divisible by 3, and therefore cannot be multiples of 3. The correct answer is (B).

6.**C**

The question asks which number is NOT a multiple of 6. 6 × 2 = 12 and 6 × 3 = 18, so (A) and (B) are multiples. 6 does not divide evenly into 23, so keep (C). 6 × 4 = 24 and 6 × 7 = 42, so (D) and (E) are also multiples. The correct answer is (C).

7.**D**

The question is essentially asking for a number that is divisible by both 3 and 5. 10, 20, and 25, and 50 are all divisible by 5, but not by 3. Eliminate (A), (B), (C), and (E). 45 ÷ 3 = 15 and 45 ÷ 5 = 9, so 45 is divisible by both 3 and 5. The correct answer is (D). Remember, you can also use the divisibility rules for 3 and 5 to help with this question! All the numbers end in either 5 or 0, so they are all divisible by 5. However, only (D) has digits that add up to a number divisible by 3.

8.**C**

Since the question is asking for a specific amount and has real numbers in the choices, one way to solve this problem is to use PITA to test the answers, starting with (C). 75,000 × 6 = 450,000, which works. The correct answer is (C). Alternatively, you can translate the words. *How many times as great as* means divide the two numbers, so .

9.**B**

Use PITA since the question is asking for a specific value and there are real numbers in the choices. The question asks for Joanna’s portion of the furniture, which is one-third of the total. Therefore, 3 times however many pieces she owns will equal the total (12 pieces). Start with (C): 6 × 3 = 18, which is too large. Eliminate (C), (D), and (E). Try (B): 4 × 3 = 12, which works. The correct answer is (B).

10.**C**

Since the question asks for a specific value, use PITA to answer the question, starting with (C). The choices represent the amount of oil in the tank now, which is one-third of the total amount. Choice (C) is 30. Is 30 one-third of the total amount (90 gallons) the tank holds? 30 = (90) is true, so the correct answer is (C).

11.**D**

Tigger sleeps of each day. To find how many days he sleeps over the course of four days, multiply: × 4. Simplify to solve: = = 3. The correct answer is (D).

12.**A**

To find the greatest value, use the choices and ballpark wherever possible to help. Choice (A) is close to 1, so use this as a comparison point. Choice (B) is smaller, since it is less than . Pay attention to the division sign in (C): ÷ = × = , which is also less than . In (D), multiply the fractions: × = = , which is equal to (C) and therefore less than . Do the same with (E): × 2 = = . This is even smaller than (C) and (D), so eliminate (E). The greatest value is (A).

13.**D**

Rearrange these values by grouping together fractions with like denominators: + = 1, + = = 1, and + = = 1. Then add the whole numbers: 1 + 1 + 1 = 3. The correct answer is (D).

14.**D**

When multiplying by a factor of 10, simply move the decimal point to the right for each zero. In this case, you are multiplying by 1,000, so move the decimal point to the right three places for the three zeros in 1,000. The decimal 0.34 becomes 340, which is closest to 350. The correct answer is (D).

15.**C**

The question is testing knowledge of decimal places. The answer should not have multiplication in it, so eliminate (A). Eliminate (D) as well since it does not have 2 included. In the number 2.398, 0.3 is equivalent to , 0.09 to , and 0.008 to . This correlates to (C), which is the correct answer.

**Practice Drill 2—Multiple Choice—Upper Level Only**

1.**B**

First, since there are fewer multiples of 7, list the multiples of 7 from 1 to 99. The multiples are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, and 98. The multiples that would also be multiples of 2 would be the even numbers: 14, 28, 42, 56, 70, 84, and 98. This is a total of 7 numbers. The correct answer is (B).

2.**D**

Let the choices help here. Since the number must be greater than 50, eliminate (A) and (B). 51 is not a multiple of 7, so eliminate (C). 56 is a multiple of 7, and it is the smallest of the remaining choices. Therefore, the correct answer is (D). Note, 63 is a multiple of 7, but it is not the *smallest* multiple *greater than 50*.

3.**B**

Remember, with exponents, you can write it out! 2^{3} = 2 × 2 × 2 and 2^{2} = 2 × 2, so you have (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2). Count up the number of 2s that you have, which is 8, and make that number the new exponent: 2^{8}. The correct choice is (B). Alternatively, you can use MADSPM: when multiplying the same base, add the exponents. Simply add 3 + 3 + 2 = 8. The answer will be 2^{8}.

4.**B**

Use PITA to Plug In the choices for *m*, starting with (C). Plug 3 in for *m*: 2(3) + 4 = 10 and 3^{3} = 27, which are not equal. Since 3 is too large, eliminate (C), (D), and (E). Next try (B): 2(2) + 4 = 8 and 2^{3} = 8. Since this works, stop here. The correct answer is (B).

5.**D**

For word problem questions, translate the words to their math equivalents. If 4 (the students who chose recycling) is equal to one-fifth of the students in the class, then 4 = × *n*, where *n* is the number of students in the class. To solve, multiply both sides by 5, and *n* = 20. There are 20 students in the class. The correct choice is (D).

6.**D**

First, solve for *x* and then find what the question is asking: *x* + 10. Start with 6*x* — 4 = 38. Add 4 to each side, and 6*x* = 42. Divide by 6 on each side to find that *x* = 7. Now plug 7 into *x* + 10 to find that 7 + 10 = 17. The correct answer is (D).

7.**B**

Note that the question asks for , not just for *x*. Start with 3*x* — 6 = 21. Add 6 to both sides, and 3*x* = 27. Divide by 3 on each side, and *x* = 9. Plug this into the equation: = = 1. The correct answer is (B).

8.**D**

Since the question asks for a specific value, use PITA to answer the question, starting with (C). The choices represent the original number of chairs. Notice that with (C), there is a problem. If there were 22 chairs originally and only one-fifth worked, that would leave a remainder—22 does not divide by 5 evenly. Eliminate (C). Next try (D) since 80 is a multiple of 5. If there were 80 chairs originally, there would be 16 chairs in working order since × 80 = = 16. The problem states that 3 more chairs were added: 16 + 3 = 19, which is the number of available working seats. Since this works, stop here. The correct answer is (D).

9.**A**

To find a percentage, find the portion the question asks for out of the total. First, find the total of all the grains: 60 bushels of corn + 20 bushels of wheat + 40 bushels of soybeans = 120 total bushels. The question asks for the percent of corn, so = = , which is equal to or 50%. The correct answer is (A).

10.**C**

To find percent change, use the formula % change = × 100. The difference here is $45 — $30 = $15, and the item was originally $45, so × 100. This reduces to × 100. To solve, = = 33%. The correct answer is (C).

11.**C**

Use Ballparking! 19.95 is roughly 20 and 35% is close to , so of 20 is between 6 and 7. Eliminate (D) and (E) since both are too big. Choices (A) and (B) are too small, so that leaves (C) as the closest. The correct answer is (C).

12.**A**

The question asks for the percentage of hotels that have swimming pools, indoor or outdoor. There are 5 indoor pools and 15 outdoor pools, making a total of 20 pools. There are 50 total hotels, so = = = 0.4, or 40%. The correct answer is (A).

13.**A**

Use the choices to see which original value will yield $20. Just by Ballparking, you can eliminate (B), (C), and (D) since these are too large. 40% of any of these numbers will be greater than $20. Try (A): 40% of 50 translates into (50) = (50) = = = 20. This matches the information in the question, so the correct answer is (A).

14.**A**

To find percent change, use the formula % change = × 100. The original value is $50 and the final value is $20, so the difference is $30. × 100 reduces to × 100 = = = 60. The correct answer is (A).

15.**C**

Take this question in bite-sized pieces. The dress is originally priced at $60 and is 20% off. 20% of 60 is the same as saying (60) = = 12. Therefore, the discounted dress price is $60 — $12 = $48. Do the same to the other items. The cotton sweater is regularly $40 and is on sale for 10% off. (40) = = 4, so the discounted sweater price is $40 — $4 = $36. There are four pairs of socks for $5 each, and these are also 20% off. (5) = = 1, so the discounted price of each pair of socks is $5 — $1 = $4. There are four pairs, so multiply 4 by 4 to find the total for the socks on sale, which is $16. The question asks for the total, so find the sum: $48 + $36 + $16 = $100. The correct answer is (C).

16.**C**

Use Ballparking to answer this question. $17.95 is close to $18. 30% is close to , so (18) = = 6. The correct answer is (C).

17.**A**

Take this question in bite-sized pieces. 50% of the 20 students are boys. This means that half of the students are boys, so (20) = = 10. Since there are 10 boys, 90% of the 10 boys take the bus to school, which is equal to (10) = = 9. The correct answer is (A).

18.**A**

To find how many questions Marc answered correctly, ballpark! 88% is a large percentage, so eliminate anything too small. Eliminate (C), (D), and (E) since they are all less than half (or 50%) of 25. 88% is close to 80%, which is . What’s of 25? (25) = = 20. So the closest answer will be a little bigger than 20. That leaves (A), which is the correct answer.

19.**B**

Take this question in bite-sized pieces. If four friends each pay $5 for a pizza, the pizza costs 4 × 5 = $20. Therefore, if a fifth friend joins, then 5 × *p* = 20. Divide both sides by 5, and each friend pays $4. The correct answer is (B).

20.**D**

To find the perimeter, add all of the sides. Since there are 8 lengths of 4, 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 32, or 8 × 4 = 32. The correct answer is (D).

21.**C**

The perimeter is all the sides added together. The sides of a square are all equal, so divide 56 by 4 to find that each side has a length of 14. The correct answer is (C).

22.**C**

Take this question in bite-sized pieces. First, find the perimeter of a square with a side length of 4 by adding up all the sides: 4 + 4 + 4 + 4 = 16. Next, the perimeter of the rectangle with length 4 and width 6 is 4 + 4 + 6 + 6 = 20. The question asks for the difference between the two, so 20 — 16 = 4. The correct answer is (C).

23.**A**

An equilateral triangle has equal sides. Therefore, if one side has a length of 4, all three sides have a length of 4. Add all the sides to find the perimeter: 4 + 4 + 4 = 12. The correct answer is (A).

24.**C**

All triangles have a total of 180º. This triangle is isosceles since two sides are equal. This means that the two angles opposite the sides are equal as well. Therefore, there are two angles that equal 65º. 65º + 65º = 130º. The remaining side is 50º since 180 — 130 = 50. The correct answer is (C).

25.**A**

If *b*º = 45º, the other angle must also be 45º since 180 — 90 — 45 = 45, which makes this an isosceles right triangle. Therefore, the other leg of the triangle is also 4. From here, use the Pythagorean Theorem to find *v*^{2}: 4^{2} + 4^{2} = *v*^{2}. Simplify the left side of the equation to get 16 + 16 = 32. The correct answer is (A).

26.**B**

Translate this question into math: *One-half of something* means to multiply by , *difference between* means to subtract, *degrees in a square* is 360º, and *degrees in a triangle* is 180º. Thus, the equation will be (360 − 180). Simplify to get (180) = 90. The correct answer is (B).

27.**C**

Since the question asks for a specific value, use PITA to answer this question, starting with (C). If the side length of a square is 4, its perimeter is 16 because 4 + 4 + 4 + 4 = 16 and its area is also 16 because 4^{2} = 16. Since those are equal, stop here. The correct answer is (C).

28.**D**

First find the area of the rectangle with a width of 4 and length of 3: *A* = *l* × *w* = 3 × 4 = 12. The area of the triangle is also equal to 12, so *A* = *bh* = 12. Plug in the given value for the base: (6)*h* = 12. Simplify to find that 3*h* = 12, and then divide both sides by 3. The height must be 4, so the correct answer is (D).

29.**B**

First, find the volume of the box that has all dimensions known. *V* = *lwh*, so *V* = 3 × 4 × 10 = 120. Since the other box has the same volume, 120 = 6 × 4 × *h*. 120 = 24*h*, so *h* = 5. The correct answer is (B).

30.**D**

Use the formula for the area of a square: *A* = *s*^{2}. If *A* = 64*p*^{2}, then to find the side length of the square, take the square root: = 8. Eliminate (A) and (B) since both choices have 64. For the square root of *p*^{2}, you can plug in for *p*. Pick an easy number like 2. If *p* = 2, then *p*^{2} = 4. So = = 2, which means your answer should equal 2 when you plug in for *p*. Choice (C) has *p*^{2}, which would be 4, so eliminate (C). Choice (D) has *p*, which is 2. Keep it! Choice (E) is missing *p*, so it can’t be correct. The correct answer is (D).

31.**D**

The length of *AB* is the same as all the different heights added together on the right-hand side of the figure. Therefore, the perimeter will contain two lengths of 10. Similarly, the length of *AC* is the same as all the different lengths added together that are across the figure (in this case, above) *AC*, so there will be two lengths of 15. To find the perimeter, add all the sides: *P* = 10 + 10 + 15 + 15 = 50. The correct answer is (D).

32.**C**

Notice the three triangles that have been created within the rectangle. Look at the two right triangles that surround the larger (possibly) equilateral triangle in the middle. Since each triangle has a right angle, the other two angles must equal 90º since 180º — 90º = 90º. Thus, in the triangle on the left side that includes side *AB*, *w* + *x* = 90º, and in the triangle on the right side that includes side *CD*, *y* + *z* = 90º. Add all these together to find that 90º + 90º = 180º. The correct answer is (C).

33.**D**

Notice that the part that juts out on the left side of the shape would fit into the indented part on the right side of the shape. Filling in the hole would make a rectangle with a length of 8 and a width of 4 + 3 + 4 = 11. To find the area of a rectangle, use the formula *A* = *l × w*. Therefore, *A* = 8 × 11 = 88. The correct answer is (D).

34.**B**

Take this question in bite-sized pieces. The question asks for the shaded region, so you want the part inside the square but outside the circle. In other words, if you find the area of the square and the area of the circle, you can find the shaded region by removing what you do not need (the area of the circle). First, find the area of the square. The side of the square is equal to 4, so *A* = *s*^{2} = 4^{2} = 16. Eliminate (A), (C), (D), and (E), since these do not contain 16. For added security, find the area of the circle. The radius is 2, so *A* = π*r*^{2} = π(2)^{2} = 4π. Remember to subtract that from the area of the square, so the full answer is 16 — 4π. The correct answer is (B).

35.**E**

To find the distance between two points, draw a right triangle and use the Pythagorean Theorem. Draw a line straight down from point *B* and directly right from point *A*. That point will be (7, 1), which you can label *C*. The distance from *A* to *C* is 6, and the distance from *C* to *B* is 8. Use the Pythagorean Theorem to find the missing side: 6^{2} + 8^{2} = *c*^{2}. Simplify the left side to get 36 + 64 = 100. Take the square root of both sides to get *c* = 10. The correct answer is (E).

**Practice Drill 3—Ratios**

1.**A**

When the question asks about ratios, make a Ratio Box. The ratio of red to blue lollipops is 3:5, so place this information in the ratio row. Add across to find that 3 + 5 = 8, and put 8 in the total column for this row. The question states that the total number of lollipops is 56. Put this number in the total column in the actual number row. Now, ask yourself what times 8 equals 56. Well, 7 × 8 = 56, so the multiplier is 7. To find the number of blue lollipops, multiply 5 × 7 = 35. The correct answer is (A).

2.**C**

The ratio of single rooms to doubles to triples is 3:4:5, so label the boxes and place this ratio in the top row. Add 3 + 4 + 5 to find the total for the room types is 12. Put 12 in the total column for the ratio row. The question states that there are 36 total rooms in the hotel, so this number goes in the total column for the actual number row. 12 times what equals 36? Since 12 × 3 = 36, the multiplier is 3. Find the number of doubles by multiplying: 4 × 3 = 12. The correct answer is (C).

3.**C**

The question states that the superstore *has exactly three times as many large oak desks as small oak desks*, so the ratio of large desks to small desks is 3:1. Write this information into the ratio row, and add the two numbers together to get the total for the ratio row: 3 + 1 = 4. So 4 goes into the total column for the ratio row. The actual total is not given; however, that number will have to be a multiple of 4 since 4 times the multiplier will equal the total actual number. Since the question asks for the total number of desks, look at the choices. You can eliminate (A), (B), (D), and (E) because these numbers are not multiples of 4. Only 16 is a possible actual total because the multipliers must be integers. You can check to see that 16 works by plugging it into the ratio box. Remember, the desks must be integers since the store isn’t selling partial desks!

4.**C**

This question gives information about the total number of players first, so place this information in the bottom row and add 8 and 4 to find the total for the actual number row. Be careful to order the ratio in the way the question asks. There are more right-handed players, so the first number should be the bigger of the two numbers. Eliminate (A) and (B)! Next, divide out the largest possible common denominator, in this case 4, to find the most reduced form of the ratio. That means the ratio of right-handed players to left-handed players is 2:1. The correct answer is (C). Note: If you chose (A), you set up the Ratio Box backwards, showing left-handed players to right-handed players. Read carefully!

5.**C**

Take the question one step at a time: Half of the 400 students are girls, so there are 200 girls. This number will go in the total column for the actual number row. The ratio of the girls who ride the bus to those who walk is 7:3, which will go in the ratio row of the box. Add 7 and 3 to find the total number: 10. 10 times what equals 200? If 10 × 20 = 200, then the multiplier is 20. The question asks how many girls walk to school, so multiply 3 × 20 = 60 to get the total girls walking to school. The correct answer is (C).

6.**C**

The ratio of goat food to grass is 2:1, so place this in the ratio row of the box. The question also states that the goat eats 15 total pounds per day, so place this number in the total column of the actual number row. To find the multiplier, find the total of the ratio, 2 + 1 = 3, and find what times 3 equals 15. Since 3 × 5 = 15, the multiplier is 5. The question asks for the total amount of grass the goat eats, so 1 × 5 = 5. The correct answer is (C).

**Practice Drill 4—Averages**

1.**A**

Use an Average Pie to solve this question: . Place 3 in the *# of items* portion and 18 in the *average* place. Multiply these numbers to find the total, which is 54. The question asks for twice the sum, which is the same as twice the total, so 2 × 54 = 108. The correct answer is (A).

2.**D**

Whenever a question mentions average, use an Average Pie to solve . Place 4 in the *# of items* portion, and 7 in the *average* place. Find the total by multiplying the two together: 4 × 7 = 28. Eliminate (E) right away because that is the total. The question asks for the largest number the set could contain, so start with the largest remaining number in the choices: 25. If 25 were the largest number in the set, the other numbers would be 1, 1, and 1. This is a possibility, since the problem does not say the numbers have to be distinct. Since this works, the correct answer is (D).

3.**B**

Use two Average Pie to organize the information in this question—every time you see the word *average* draw an Average Pie . The first pie represents the information about the boys: 4 boys average 2 projects each, so place 4 in the *# of items* place and 2 in the *average* place. To find the total number of projects the boys complete, multiply 4 and 2 to find a total of 8 projects. Repeat this same process with the girls in the second pie. The 5 girls average 3 projects each, so place these numbers in their respective places in the average pie, and multiply to find a total of 15 projects. The question asks for the total number of projects in the class, so 8 + 15 = 23. The correct answer is (B).

4.**A**

Use two Average Pie to organize the information in this question—every time you see the word *average* draw an Average Pie . There are 6 students with an average test score of 72. Place 6 in the *# of items* place and 72 in the *average* place. Find the total number of points by multiplying 6 × 72 = 432. Make a separate Average Pie for the next portion of the question. If a seventh student joins the class, the *# of items* place now contains 7, and the desired *average* is 76. Multiply these together to find that 7 × 76 = 532. The difference between 532 and 432 is 100, so the seventh student must score 100 to change the average to 76. The correct answer is (A).

5.**A**

First, add the three scores to find Catherine’s current point total. 84 + 85 + 88 = 257. Next, make an Average Pie with 4 in the *# of items* place since there will be a fourth test, and 89 as the desired *average*. Multiply 4 × 89 to find a total of 356. Subtract the totals to find that 356 — 257 = 99. This means that she must score a 99 on the fourth test to raise her average to an 89. The correct answer is (A).

**Practice Drill 5—Percent Change**

1.**E**

The question is testing percent change since it asks *by what percent did the temperature drop?* To find percent change, use the formula % change = × 100. The change in temperature was 20 degrees: 10° — (—10°) = 20°. Since the question asks for the percent the temperature *dropped*, the *larger* number will be the original number. Thus, the equation should read × 100, which reduces to 2 × 100 = 200. The correct answer is (E).

2.**C**

The question is testing percent change since it asks *by what percent did the patty increase?* To find percent change, use the formula % change = × 100. The change in patty size is 4, which is given in the question. The new patty size is 16 oz, so the original patty size must have been 12 oz since 16 — 4 = 12. The equation will read × 100, which reduces to × 100 = 33. The correct answer is (C).

**Practice Drill 6—Plugging In**

1.**E**

This is a Plugging In question because there are variables in the choices and the question stem contains the phrase *in terms of*. Plug In a value, work through the problem to find a target answer, and then check each of the choices to see which yields the target answer. For instance, Plug In *x* = $3. The question asks for the total amount of money donated, so 3 × 200 = 600. The target answer is $600. Now, plug 3 into the choices for *x* to see which choice matches your target answer (600). Eliminate (A) because is way too small. Eliminate (B) as well because 200 ≠ 600. Eliminate (C) because is still too small. Eliminate (D) because 200 + 3 or 203 ≠ 600. Choice (E) works because 200(3) = 600. The correct answer is (E).

2.**D**

This is a Plugging In question because there are variables in the choices and the question stem contains the phrase *in terms of*. Plug In a value, work through the problem to find a target answer, and then check each of the choices to see which yields the target answer. For instance, Plug In 6 for *d* dollars. If 10 magazines cost $6, then $3 would buy 5 magazines—you spend half as much money, so you can get only half as many magazines. So 5 is the target answer. Now, plug 6 into the choices to see which answer yields 5, the target answer. Eliminate (A) because = = 1.8 does not equal 5. Eliminate (B) because 30(6) is way too large. Choice (C) is a fraction, = , so it will not equal 5. Choice (D) works, as = 5, so keep this choice. Remember to try all five choices when Plugging In, so check (E) as well: = = 20. Eliminate (E) since 20 ≠ 5. The correct answer is (D).

3.**D**

This is a Plugging In question because there are variables in the choices and the question stem contains the phrase *in terms of*. Plug In a value, work through the problem to find a target answer, and then check each of the choices to see which yields the target answer. *The zoo has four times as many monkeys as lions*, so, for instance, Plug In 40 for the monkeys, which translates to 4 × lions, = 40, so there are 10 lions. *There are four more lions than zebras*, which means that 10 — 4 = 6 zebras, so *z* = 6. The question asks *how many monkeys are there in the zoo*, so the target answer is 40. Now, plug 6 into the choices for *z* to see which choice matches your target answer (40). Eliminate (A) because 6 + 4 = 10 is too small. Eliminate (B) because 6 + 8 = 14 is still too small. In (C), 4 × 6 = 24 is still not equal to 40, so eliminate (C). Since 4(6) + 16 = 40, keep (D). Remember to try all five choices when Plugging In, so check (E) as well. 4(6) + 4 = 28, which is too small, so eliminate (E). The correct answer is (D).

4.**E**

When there are percents or fractions without a starting or ending value in the question stem, feel free to Plug In. For instance, Plug In $100 for the starting price of the suit. It is *reduced by half*, so one-half of $100 is $50, and the new price of the suit is $50. The suit is then *reduced by 10%*, so 10% of $50 is (50) = (50) = = 5. Subtract this from $50 to find the new price of the suit: 50 — 5 = 45. The final price is $45. The *final price is what percent of the original* translates to 45 = (100), which makes the math easy! 45 = *x*, so the correct answer is (E).

5.**C**

When there are percents or fractions without a starting or ending value in the question stem, feel free to Plug In. What number would make the math easy? 8 is a common denominator for and , so draw a circle and divide it into 8 equal parts. Shade in the number of pieces he has eaten. On Wednesday, he ate of the pie, so of 8 is 2 slices, leaving 6 slices for later. The next day, he ate of what was left. Half of 6 slices is 3, so he ate 3 slices. There are now 3 out of 8 slices left. Beware of choosing (A), however! The question asks how much he ate, so add up the slices he consumed. There should be 5 slices shaded (2 + 3 = 5), so the correct answer is (C).

6.**B**

This is a Plugging In question because there are variables in the choices and the question stem contains the phrase *in terms of*. Plug In a value, work through the problem to find a target answer, and then check each of the choices to see which yields the target answer. For instance, say that *p* pieces of candy is equal to 5 pieces, and *c* cents is 10 cents. Therefore, 10 pieces of candy will cost 20 cents—you have twice as many pieces, so it will cost twice as much money. So, the target answer is 20. Now, Plug In your values for *p* and *c* into the choices to find the choice that equals your target answer (20). Eliminate (A) because = = 5, which is too small. = = 20, so keep (B). Remember to check the remaining choices when Plugging In. Cross off (C) because 10(5)(10) = 500, which is way too large. = = 5, so eliminate (D) as well. Finally, eliminate (E) because 10 + 5 + 10 or 25 ≠ 20. The correct answer is (B).

7.**C**

In this question, *J* is an odd integer, so Plug In an odd integer for *J*. Since this is a *must be* question, see if there is a number that would make the answer untrue. Plug In 1 for *J* to make (A) untrue, since is not greater than 1. This number for *J* will also eliminate (B) since 1 — 2 = —1, which is not a positive integer. Choice (C) is true since 2 × 1 = 2, which is an even integer. Eliminate (D) since 1^{2} = 1 is not greater than 1. Finally, eliminate (E) since *J* could be negative. For example, if *J* = −3, −3 is not greater than 0. Check that value for (C) to be sure it always works. Again, if *J* = −3, then 2 × −3 = −6, which is still an even integer. Since it always works, the correct answer is (C).

8.**C**

Try Plugging In values that satisfy the question stem, and eliminate choices. It may be necessary to Plug In twice on *must be true* or *always true* questions. If *m* is an even number, let *m* = 2, and let *n* = 3 since it must be an odd integer. If *p* is the product of *m* and *n*, then *p* = (2)(3) = 6. Now check the choices. Eliminate (A) because *p* is not a fraction. Eliminate (B) as well since *p* is not an odd integer. Keep (C) because 6 is divisible by 2. 6 is not between 2 and 3, so eliminate (D). Finally, keep (E) because 6 is greater than zero. Plug In again to compare the remaining choices. Perhaps keep one number the same, so *n* = 3, but make *m* = −2 instead of 2. Now *p* = (−2)(3) = −6. Choice (C) still works since −6 is divisible by 2, but (E) no longer works since *p* is less than zero. Since it is always true, the correct answer is (C).

**Practice Drill 7—Plugging In The Answers**

1.**C**

The question is asking for a specific value and there are real numbers in the choices, so use PITA to solve. Ted can read 60 pages per hour, which is 60 pages in 60 minutes, and Naomi can read 45 pages in 60 minutes. Combined, they can read 105 pages (60 + 45) in 60 minutes. Now, start with (C) to see which answer will yield a total of 210 pages. If they read for 120 minutes, they will read double the amount they did in 60 minutes: 105 × 2 = 210. This satisfies the question, so (C) is correct.

2.**E**

The question is asking for a specific value and there are real numbers in the choices, so use PITA to solve, starting with (C). If *y* = 2, then *y* + (*y* + 1) = 2 + (2 + 1) = 2 + 3 = 5, which is too small. Therefore, eliminate (C) as well as (A) and (B) since those values for *y* are also too small. Now try (D): if *y* = 8, then *y* + (*y* + 1) = 8 + (8 + 1) = 8 + 9 = 17, which is still too small, so eliminate (D). The correct answer must be (E). If you’re pressed for time, pick (E) and move on. If you have time later to come back and check, great! It’s okay to be aggressive and go with (E) if you know the other choices don’t work. There has to be a correct answer!

3.**C**

The question is asking for a specific value and there are real numbers in the choices, so use PITA to solve, starting with (C). The choices represent Kenny’s age now. If Kenny is 15 years old and he is 5 years older than Greg, then Greg must be 10. In 5 years, Kenny will be 20. *Twice as old as Greg is now* would be 2(10) = 20. Since the two numbers match, stop here. The correct answer is (C).

4.**B**

The question is asking for a specific value and there are real numbers in the choices, so use PITA to solve, starting with (C). The choices represent how much Sara pays. If Sara pays $30 and she pays twice as much as John, then John would have paid $15 since × 30 = 15. Paul paid three times as much as Sara, so he would have paid 3 × 30 = 90. This added together is more than $90, so eliminate (C), (D), and (E), as all of these will amount to a total that is too much. Try (B): if Sara paid $20, John would have paid $10 since × 20 = 10. Paul paid 3 × 20 = 60. Add these amounts together to find that $20 + $10 + $60 = $90, which satisfies the question. The correct answer is (B).

5.**D**

First, translate the English into math and then use PITA to test the choices. *Four less than a certain number* translates to *n* — 4, and two-thirds of a number translates to × *n*. So the equation is *n* − 4 = × *n*. Now, Plug In the Answers to find the one that satisfies the equation, starting with (C). If *n* = 8, then the equation will read 8 − 4 = (8). Since 4 ≠ , eliminate (C) and try another choice. Try (D). If *n* = 12, then 12 − 4 = (12), which is 8 = or 8 = 8. Since 12 works, stop here. The correct answer is (D).

**Practice Drill 8—Functions**

1.**B**

Don’t be scared off by these types of questions! Simply follow the directions and plug numbers into the equation where specified. In this case, replace *n* with the given number (7). Thus, the equation should read $7 = 10(7) — 10. Simplify the equation to $7 = 70 — 10 = 60. The correct answer is (B).

2.**C**

The question asks which of the choices will yield a result of 120. Therefore, use PITA to solve, starting with (C). If *n* = 13, then replace 13 for *n* in the given equation: $13 = 10(13) — 10. Simplify to find that $13 = 130 — 10 = 120. This works, so the correct answer is (C).

3.**D**

In this function, simply plug in the number to the left of the weird symbol for *d* and the number to the right of the weird symbol for *y* exactly as the example directs. The function should read *d* ¿ *y* = 10 ¿ 2 = (10 × 2) — (10 + 2), which simplifies to (20) — (12) = 8. The correct answer is (D).

4.**D**

This question asks to first find the result of the function, and then to find the unknown *K*. Take this question in bite-sized pieces. Start with the parentheses first. Solve for 4 ¿ 3: (4 × 3) — (4 + 3) = (12) — (7) = 5. Next, plug 5 into the equation to find *K*: *K*(5) = 30. Divide by 5 on both sides to find that *K* equals 6. The correct answer is (D).

5.**A**

You will need to set the equation up based on the function defined, and then use PEMDAS to simplify and solve for the end result. Take this question in bite-sized pieces. Start with the first set of parentheses: (2 ¿ 4) = (2 × 4) — (2 + 4) = (8) — (6) = 2. Next, work with the second set of parentheses: (3 ¿ 6) = (3 × 6) — (3 + 6) = (18) — (9) = 9. Put these values back into the original equation: (2 ¿ 4) × (3 ¿ 6) = (2) × (9) = 18. Now, test the choices to see which expression yields 18 as well. Try (A): (9 × 3) — (9 + 3) + 3 = (27) — (12) + 3 = 18. Since this matches, stop here. The correct answer is (A). Remember, if you find a question too time consuming, skip it and move on! You can come back to it later if you have time.

**Practice Drill 9—Charts and Graphs**

1.**E**

First, find what District A spent in 1990: $400,000 (pay attention to the note below the table: the numbers are in thousands of dollars). Look for double this amount. $800,000 is listed in the table for the value in 1991 for District E. The correct answer is (E).

2.**D**

Add across to find which district spent the most, keeping in mind that these are all in the thousands (though this doesn’t really matter to find the largest sum). District E has the largest sum: $600,000 + $800,000 = $1,400,000. The correct answer is (D).

3.**E**

Remember that these numbers are in the thousands. Add down to find the sum of the values in 1990: $1,800,000. Do the same with the values in 1991 to find a sum of $2,600,000. Find the difference of these values: $2,600,000 — $1,800,000 = $800,000. The correct answer is (E).

4.**D**

Check the graph. Carl owns 5 CDs, so the other two people together must own a total of 5 CDs. Eliminate (A) because Abe has 2 and Ben has 4, totaling 6. Eliminate (B) as well because Ben has 4 and Dave has 3, which is 7. Choice (C) is incorrect since both Abe and Ed have 2, so this only amounts to 4. Choice (D) works because Abe has 2 and Dave has 3, amounting to 5. There can be only one correct answer, so the correct answer is (D).

5.**B**

To find which student owns one-fourth of all the CDs, first add all the CDs to find a total. Your work from the previous question will help! Abe = 2, Ben = 4, Carl = 5, Dave = 3, and Ed = 2, which yields a total of 16 CDs. of 16 is × 16 = = 4, so Ben is the student who has 4 CDs. The correct answer is (B).

6.**E**

To find Matt’s earnings for the week, first add up all his hours and then multiply by his hourly salary ($6/hour). He works 3.5 + 4 + 3.5 + 3 = 14 hours over the week, so 14 × 6 = 84. The correct answer is (E).

7.**B**

Remember, if you see the word average, you can use an Average Pie . The previous question helped you find the total number of hours Matt worked: 14. Put that number in the *total* place. He worked 4 days—note the question says *on the days he worked* not the number of days in a week. Put 4 in the *# of items* place. Divide these two numbers to find the average: = 3.5. If you’re pressed for time, instead of doing the long division, let the choices help! Since 14 is not divisible by 4, eliminate all the integers. The correct answer is (B).

8.**C**

One way to solve this problem is to translate the words into math: *the hours he worked on Monday* is 3.5, a*ccounted for* is equals, *what percent* is , and the *total hours he worked* is 14. The equation is 3.5 = × 14. Simplify the right side: × 14 = = . Multiply both sides by 100 to get 350 = 14*x*. Divide both sides by 14, and *x* = 25. The correct answer is (C). You can also find a percent by dividing the desired amount by the total amount: Matt worked 3.5 hours on Monday and a total of 14 hours, so = = , or 25%.

**Practice Drill 10—Middle and Upper Levels Only**

1.**B**

Since there are variables in the choices, Plug In a value for *p*, paying attention to the restrictions in the question. If *p* is an odd integer, make sure to Plug In an odd integer, for instance *p* = 3. Now, test the choices to see which ones can be eliminated. Cross off (A) because (3)^{2} + 3 = 9 + 3 = 12, which is not odd. Choice (B) works since 2(3) + 1 = 6 + 1 = 7, which is odd. Choice (C) works since = 1. Choice (D) does not work since 3 — 3 = 0. Remember 0 is even, not odd. Eliminate (E) because 2(3^{2}) = 2(9) = 18, which is not odd. Plug In a second time for the remaining choices. Try *p* = 5. Choice (B) still works because 2(5) + 1 = 10 + 1 = 11, but eliminate (C) because is no longer an integer. The correct answer is (B).

2.**B**

The wording on this problem is tricky. It asks for which CANNOT be true, so try to find examples that COULD be true to eliminate choices. Pay attention to the restrictions in the problem, and Plug In two positive even integers: say 4 and 6. Thus, 4 + 6 = 10 = *m*. Next, eliminate choices that WORK. Choice (A) does not work since 10 is greater than 5. Keep it. Choice (B) does not work because 3(10) = 30, which is even, not odd. Keep it. Eliminate (C) because *m* = 10, which is even, so it works. Eliminate (D) as well because 10^{3} ends in a zero, which is also even, so this statement works. Choice (E) doesn’t work because = 5, which is odd. Keep it. Now, Plug In a second time for the remaining choices. Try new numbers, and remember that the numbers do not have to be distinct from one another. Try Plugging In 2 for both positive even integers. Thus, 2 + 2 = 4 = *m*. Check the remaining answers and eliminate the choices that WORK. For (A), 4 is less than 5. That works, so eliminate (A). For (B), 3(4) = 12, which does not work since it’s even, so keep it. Finally for (E), = 2 is even, which works, so eliminate (E). The only choice left is (B), which is the correct answer.

3.**D**

This is a Plugging In question because there are variables in the choices. Plug In a value, work through the problem to find a target answer, and then check each of the choices to see which yields the target answer. Let *b* = 4 and *a* = 3. Finding the *product* means multiply, so (4) × 3^{2} = 2 × 9 = 18. The target answer is 18. Now, Plug In your values for *b* and *a* into the choices to find the choice that equals your target answer (18). Eliminate (A) since (3 × 4)^{2} = (12)^{2} = 144, which is too big. Eliminate (B) since = and is not equal to 18. Also eliminate (C) since 2(3) × (4) = 6 × 2 = 12, which does not equal 18. Choice (D) works: = = = 18. Keep it. Remember to try all five choices when Plugging In, so check (E) as well. = = = 72, which is too big, so eliminate (E). The correct answer is (D).

4.**D**

There are variables in the choices, so Plug In here. For instance, say that Damon has 10 records, so *d* = 10. That means Graham has half as many records, so he has 5 records. Graham has as many records as Alex, so Alex has 4 times as many as Graham: 5 × 4 = 20, or 20 records. Together, Graham and Alex have 5 + 20 = 25 records. So, 25 is the target answer. Now, Plug In 10 for *d* and find which choice yields 25, your target answer. Eliminate (A) because = = 15, which is not 25. Eliminate (B) since = is even smaller than (A). Choice (C) is too large since = = 45. Choice (D) works because = = 25. Remember to try all five choices when Plugging In, so still check (E). 2(10) = 20, which does not work, so eliminate (E). The correct answer is (D).

5.**E**

Use MADSPM to simplify the exponents in the equations first. When raising a power to a power, multiply the exponents together. For the first equation, (*x*^{3})^{3} = *x*^{3 × 3} = *x*^{9}, so *a* = 9. When dividing by the same base, subtract the exponents. For the second equation, = *y*^{10 − 2} = *y*^{8}, so *b* = 8. The question asks to find *a* × *b*, so 9 × 8 = 72. The correct answer is (E).

6.**C**

Take this question one step at a time. If there are 250 people and 75 are children, then there are 175 adults. If one hero sandwich could feed 12 children and there are 75 children at the party, find how many sandwiches are needed for the 75 children: 12 goes into 75 six times evenly since 6 × 12 = 72, which leaves a remainder of 3 children. Part of another sandwich will be needed to feed those children. Therefore, the 75 children will need 6+ sandwiches. Now, do the same for the adults. There are 175 adults at the party. Each hero sandwich can feed 8 adults. 8 only goes into 175 twenty-one times evenly since 8 × 21 = 168. That will leave a remainder of 7 adults (175 − 168 = 7). Remember, 1 sandwich feeds 8 adults, so if there are 7 adults left, you need almost an entire sandwich more. That makes about 22 sandwiches to feed all the adults. 22 + 6 = 28. Remember that a little more than 6 sandwiches were needed to feed all the children (no half-sandwich orders allowed!). Round up, so 29 sandwiches will be needed to feed the entire group. The correct answer is (C). Ballparking is okay here! Note that the next closest answer is 30, which is too many (3 extra sandwiches are not needed), so both (D) and (E) are too large. Choices (A) and (B) are too small even before taking the remainders into account, which makes (C) is the best answer!

7.**C**

When there are percentages in the choices with no starting or ending value, go ahead and Plug In a number. Even though it’s not realistic, try Plugging In 100 miles for the distance between New York and Dallas. Yes, it’s further, but make the math easy when Plugging In your own number! Liam and Noel drive of the distance on Monday, so of 100 is (100) = = 20. Subtract this from the total they must drive: 100 — 20 = 80 miles left. On Tuesday, they drive half the remaining distance; half of 80 is 40, so subtract this from 80: 80 — 40 = 40, so there are 40 miles remaining. To find the percentage they still need to drive, divide the remaining mileage from the total to find = . Multiply by 100 to convert to a percent: × 100 = 40%. The correct answer is (C).

8.**B**

Work step by step here. If of the bag contains 10 grams of fat, then the entire bag must contain 40 grams of fat since 10 × 4 = 40. To find of the bag, divide 40 by 6. This will not be a whole number, but it will be between 6 and 7 using Ballparking (6 × 6 = 36 and 6 × 7 = 42). Thus, the correct answer is (B).

9.**B**

There are variables in the choices, so Plug In here. Say there are 20 students in the class, so *x* = 20. If each donates an average of $3, *y* = 3. Next, find the total amount of money donated: 20 × 3 = 60. This is the target answer. Now, Plug In your values for *x* and *y* to see which choice yields the target (60). Eliminate (A) because is not an integer and is much too small. Choice (B) works because (20)(3) = 60. Eliminate (C) because = = 3, which is too small. Cross off (D) since it equals , and (E) is way too large: (2)(20)(3) = 120. The correct answer is (B).

10.**E**

There are variables in the answers, so Plug In here. If *e* + *f* = 17, then 17 is divisible by 17, so choose two numbers that add together to equal 17. For instance, 13 + 4 = 17, so let *e* = 13 and *f* = 4. Now, Plug In to the choices and see which one works. Eliminate (A) because (13 × 4) — 17 = 52 — 17 = 35, which is not divisible by 17. Similarly, eliminate (B) because 13 + (4 × 17) = 13 + (68) = 81, which is not divisible by 17 either. Choice (C) does not work because (13 × 17) + 4 = (221) + 4 = 225, which is not divisible by 17. Eliminate (D) because = = 1, which is not divisible by 17. Keep (E) because (13 × 3) + (4 × 3) = 39 + 12 = 51, which is divisible by 17. The correct answer is (E).

11.**C**

Since the question mentions the mean, create an Average Pie . Joe wants to have an average of 230 or more, so place 230 in the *average* spot of the pie. In the *# of items* place, write in 5 because he has already read 4 books that were 200, 200, 220, and 260 pages long, and he is going to read one more. Multiply to find the total number of pages he must read: 5 × 230 = 1,150. He has already read 200 + 200 + 220 + 260 = 880 pages, so find the difference between these two totals to see how many pages long the fifth book must at least be: 1,150 — 880 = 270. The correct answer is (C).

12.**A**

Since the question mentions average, create an Average Pie . Sayeeda wants to raise her average to 15 on the fourth game, so write 15 in the *average* spot and 4 in for the *# of items*. Multiply these two numbers together to find the total points: 4 × 15 = 60. In the first three games, she scored 8 + 12 + 12 = 32 points. The difference that she must score in the fourth game is 60 — 32 = 28 points. The correct answer is (A).

13.**C**

First, simplify the first expression: (3*xy*)^{3} = 3^{3}*x*^{3}*y*^{3} = 27*x*^{3}*y*^{3}. While comparing it to the other expression, 3*x*^{2}*y*^{5}, you can work in bite-sized pieces. Start with the coefficients. The greatest common factor of 3 and 27 is 3. Eliminate (A), (D), and (E) since those don’t contain 3. Both of the remaining answers contain *x*^{2}, so compare *y* in the two expressions. One has *y*^{3} = *y* × *y* × *y* and the other has *y*^{5} = *y* × *y* × *y* × *y* × *y*. The greatest common factor is *y*^{3} since both expressions have at least 3 *y*’s. Eliminate (B). The correct answer is (C).

14.**B**

To start, draw a picture for this question. Mechanicville must be due east of Stillwater, so draw Mechanicville directly to the right of Stillwater. Mechanicville is also due south of Half Moon Crescent, so draw Half Moon Crescent directly above Mechanicville. Connect each of these cities to form a right triangle. Label the lengths of the sides, 30 miles and 40 miles according to the problem. The length of the hypotenuse will equal the shortest distance from Stillwater to Half Moon Crescent. Use the Pythagorean Theorem to find the hypotenuse (30^{2} + 40^{2} = *c*^{2}), or recognize that this is a 3-4-5 right triangle. Therefore, the sides are 30, 40, and 50. The correct answer is (B).

15.**B**

Ballparking is one way to work through this problem. The shaded region looks to be about half the square, and half of 144 is 72, (B). To be more precise, the side of the square must be 12 since *A* = *s*^{2} and 12^{2} = 144, so the height of each shaded triangle is 12. The base for one triangle ends at *P* and the base for the other triangle ends at *Q*, and *PQ* = 12 since it’s a side of the square. So make the base for each triangle 6 since the two bases must add up to 12. Plug those values into the formula: *A* = *bh* = (6)(12) = 36. Since both areas equal 36, the total area of the shaded region is 36 + 36 = 72. The correct answer is (B).

16.**B**

Even though the length of the radius is unknown, it is still possible to find the angle measurements. There is a 90º angle in the center of the circle, and *OQ* and *OP* are both radii of the circle, which means they are the same length. Therefore, this is an isosceles right triangle, meaning the two smaller angles are equal. All triangles have 180º, so 180º — 90º = 90º. The two smaller angles add up to 90º, so = 45º. The correct answer is (B).

17.**D**

Notice that the four intersecting lines form a quadrilateral. All quadrilaterals contain 360º, so keep a tally of the vertices and find the missing angle. 80º is already provided, so 360º — 80º = 280º. All straight lines add up to 180º, so use the exterior angles to find the interior angles. If one of the exterior angles is 75º, the supplementary angle must be 105º. Subtract this from 280º to find that 280º — 105º = 175º. The other exterior angle, 108º, is opposite the interior vertex. Since opposite angles are equal, the interior vertex must also be 108º. Subtract this from the current total to find that 175º — 108º = 67º. The missing angle is 67º. The correct answer is (D).

18.**C**

The question states that triangle *ABC* is equilateral, so all three sides are equal to 4. Label *AC* as 4 and *BC* as 4. The question asks for perimeter, not area. So, there are two sides of the triangle that are part of the perimeter, so add them together: *AB* + *AC* = 4 + 4 = 8. Eliminate (A), (B), and (E) since the choice must have an 8 in it. Now, find the rounded portion. The rounded portion is half of the circumference (i.e., a semicircle). Since you labeled *BC* as 4, you should see that the diameter of the circle must also be 4. If *C* = π*d*, then half of the circumference is π*d*. Plug in the value for the diameter and simplify: π(4) = 2π. The full expression for the perimeter will then read 8 + 2π. The correct answer is (C).

19.**B**

To find the perimeter, it doesn’t matter how the right-hand vertical segments are broken up. Since everything meets at right angles, those segments will all add up to the same height as *AB*, which is 12. Similarly, it does not matter how the top horizontal lines are divided. They will still add up to the same length as *AC*, which is 10. Therefore, simply add 10 + 10 + 12 + 12 to find the perimeter of 44. The correct answer is (B).

20.**B**

The length of police tape wrapping around a rectangle is the same as the perimeter. Draw a rectangle and label the length as 28 and the width as 6. Remember, in a rectangle, opposite sides are equal to each other. Calculate the perimeter by adding all the sides: 6 + 6 + 28 + 28 = 68. The correct answer is (B).

21.**D**

Beware! The question asks for the diameter, not the radius. First, find the volume of the cylinder as it is now. The equation for the volume of a cylinder is *V* = π*r*^{2}*h*. Plug in the values for *r* and *h* from the question. The question states that the diameter is 18 cm, so the radius is 9 cm, and the height is 20 cm. The equation will read *V* = π(9^{2})(20). Simplify to get *V* = π(81)(20). Do not bother doing all this multiplication yet! Since the question asks for the diameter of a single serving which has the same height, take this volume (the volume of 9 servings) and divide by 9 to find the volume of a single serving can: *V* = , which simplifies to *V* = π(9)(20). To find the diameter, isolate the radius: *r*^{2} = 9, which means *r* = 3. Multiply by 2 to find the diameter, so *d* = 6 cm. The correct answer is (D). Remember, for any question that may seem difficult or time consuming, skip it and come back to it later if you have time!

**Math Review**

1.Yes

2.It is neither positive nor negative.

3.Addition

4.Multiplication

5.The quotient

6.Yes 3 + 1 + 2 = 6, which is divisible by 3;

No 3 + 1 + 2 = 6, which is not divisible by 9.

7.Exponents

8.Yes 3 goes into 12 evenly 4 times;

No 12 cannot go into 3.

9.No No integer times 12 is equal to 3;

Yes 3 × 4 = 12

10.0 The tens digit is two places to the left of the decimal.

11.2 The tenths digit is one place to the right of the decimal.

12.8 Write it out! 2 × 2 × 2 = 8

13.Over 100, or

14.Multiplication

15.Total column

16.Average Pie

17.Plug In a number

18.Add; all four

19.Multiply; two (or square one side, since the sides of a square are the same)

20.180

21.3; 180

22.360

23.2; equilateral

24.Hypotenuse; right angle

25.*A* = (*base*)(*height*)

**SSAT VERBAL**

**Review—The Verbal Plan**

**Pacing and Verbal Strategy**

Your answers should be similar to the following:

I will start on question number 31, so that I begin with analogies.

I will do the verbal questions in the following order:

1.Analogies with words I know

2.Analogies with words I sort of know

3.Synonyms with words I know

4.Synonyms with words I sort of know

5.Analogies with words I don’t know

I need only to eliminate one answer to guess.

No, I cannot eliminate choices that contain words I do not know.

**Analogies**

**Practice Drill 1—Making Sentences**

You can abbreviate your sentences as we have done below, using one letter to stand for each stem word. Your sentences should be similar to these.

1.A chapter is a section of a book.

2.A scale is used to measure weight.

3.Striped means having lines.

4.Rage is a very strong anger.

5.Rehearsal is practice for a performance.

6.A mechanic fixes a car.

7.A traitor betrays a country.

8.Aggravate means to make a problem worse.

9.A trout is a type of fish.

10.A general leads an army.

11.Crime occurs when someone breaks the law.

12.A buckle fastens a belt.

13.Truculent means prone to a fight.

14.A cure gets rid of illness.

15.A poison is something toxic.

16.A pinnacle is the top of a mountain.

17.Perilous means lacking safety.

18.A humanitarian practices philanthropy.

19.Notorious means having a bad reputation.

20.A miser is a person without generosity.

**Practice Drill 2—Basic Analogy Techniques**

1. **C**A chapter is a section of a book.

2. **D**A refrigerator is used to cool.

3. **B**A fish uses a fin to move itself. (Get specific!)

4. **A**A driver operates/steers a car. (Picture it. Get specific!)

5. **E**A clock is used to measure time.

6. **A**An envelope contains/transports a letter. (Watch out for (E); it’s close but not the best.)

7. **A**A librarian is the person in charge of a library.

8. **C**A pen is used to write.

9. **C**A hurricane is a very, very strong breeze.

10. **A**A ball is a three-dimensional circle. (Choice (B) is wrong because the words are reversed.)

11. **D**A shell is on the outside of an egg.

12. **B**A cup is a smaller unit of measure than a quart.

13. **A**A coach leads a team.

14. **C**A bat is a type of flying mammal. (Get specific!)

15. **B**Famished means very hungry.

16. **C**To sterilize means to get rid of germs.

17. **D**A director directs/leads actors.

18. **B**An applicant wants to be hired. An applicant wants someone to hire him or her. (Think about who’s doing what!)

19. **B**Stale is what bread becomes when it gets old.

20. **C**Unbiased means without prejudice.

**Practice Drill 3—Working Backward**

1.Choices (A) or (B) because a castle is surrounded by a moat and a galaxy is a group of stars

2.Choice (B) because a monarchy is ruled by a sovereign (Choice (E) is okay, but do thieves always practice duplicity? Not really—just thievery.)

3.Choice (B) because submissive means lacking defiance

4.Choices (B) or (C) because quarantine means to isolate a patient and elect means to choose a politician

5.Choice (D) because bland means lacking zest

**Practice Drill 4—Judging “Side of the Fence”**

1.D

2.D

3.S

4.D

5.D

6.S

7.D

8.S

9.S

10.D

11.S

12.D

**Practice Drill 5—Using “Side of the Fence”**

1.A

2.A or C

3.A or D

4.A or B

5.C or D

6.B, C, or E

7.A, B, C, or E

8.A or B

9.A, D, or E

10.A, B, or E

**Practice Drill 6—Working Backward as Much as You Can**

1.A tooth is used for chewing.

2.Eliminate

3.An archipelago is a group of islands.

4.Eliminate

5.Eliminate

6.To jest means to try to be humorous.

7.Eliminate

**Review—The Analogies Plan**

Your answers should be similar to the following:

If I know the words, then I make a sentence.

A sentence is good if it’s specific and definitional.

If my sentence eliminates some but not all choices, I can make another, more specific, sentence.

A specific, definitional sentence uses words that are descriptive.

Some questions that can help me make a sentence are as follows:

· What does A/B do?

· What does A/B mean?

· How does A/B work?

· What does A/B look like?

· How is A/B used?

· Where is A/B found?

· How do A and B compare?

· How are A and B associated?

(A and B are the first two words in the analogy.)

If I know the words but can’t make a sentence, then I ask myself the following:

· Are A and B synonyms?

· Do A and B have something in common?

· Are A and B members of the same group?

· What kind of sequence or pattern are A and B in?

· Do A and B rhyme?

· Do A and B have rearranged letters?

And finally, if none of these questions works with A and B (the first two words in the analogy), then I ask myself the following:

· Can I make a definitional sentence with A and C? (C is the third word in the analogy.)

If I know one of the words, then I work backward, which means that I make a sentence with each choice, and then I try using that sentence with the stem words (the first two words in the analogy).

If I sort of know the words, then I use “Side of the Fence.”

I can also work backward.

If I don’t know the words, I circle the question in the test booklet and skip it.

If I have time left, then I go back and work backward as much as I can.

**Practice Drill 7—All Analogies Techniques**

1. **C**Chocolate is a type of candy just as cat is a type of animal.

2. **A**A pound is a unit that measures weight just as decibel is a unit that measure sound.

3. **A**A student is part of a class just as an actor is part of a cast.

4. **C**A composer creates a symphony just as an architect creates (or designs) a building. Note: choice (E) is not as good because while a writer creates a paragraph, a paragraph is not a large, complete work.

5. **E**Many links make up a chain just as many words make up a sentence.

6. **E**A tadpole is a young form of a frog just as a caterpillar is a young form of a butterfly.

7. **E**A cuff is the part of a garment that is at the wrist just as a collar is the part of a garment that is at the neck. Note: buckle in choice (B) is not part of a garment and body in choice (D) is too general.

8. **A**A congregation consists of worshippers just as a galaxy consists of stars. Note: in choice (C) mines don’t always contain gems.

9. **B**Tactile means sensed by touch just as audible means sensed by sound.

10. **B**A conviction is a strong opinion just as reverence is strong admiration.

11. **C**A caricature is an exaggerated drawing just as hyperbole is an exaggerated statement.

12. **B**Deceleration is a decrease in speed just as descent is a decrease in altitude.

13. **D**Something insipid is very dull just as something entertaining is very diverting.

14. **A**Voracious means wanting a lot of food just as greedy means wanting a lot of money.

15. **E**Adroit means skilled in motion just as articulate is skilled in speech. Note: skill in choice (C) is too general.

16. **E**An anesthetic dulls pain just as a muffler dulls noise.

17. **B**Impeccable is far beyond adequate just as inexhaustible is far beyond sufficient.

18. **C**Symmetrical means balanced, and amorphous means unshaped. Note: this is a vertical relationship.

19. **D**Incessant and intermittent are opposites just as timid and brazen are opposites.

20. **C**Penicillin is a type or kind of antibiotic just as coughing is a kind of symptom.

21. **B**A cobbler makes a shoe just as a blacksmith makes a sword.

22. **A**Fortify is a stronger version of protect just as blitz is a stronger version of attack.

23. **B**Someone reprimands a delinquent just as someone recognizes (i.e. acknowledges) a virtuoso.

24. **E**Someone disinfects a surface to make it become pristine just as someone learns something to make it become uncomplicated.

25. **C**Something inconspicuous is easy to overlook just as something unfounded is easy to reject.

26. **E**A student completes his studies to become a graduate just as a novice completes his studies to become a master.

27. **A**A person who is appreciative shows gratitude just as a person who is ashamed shows compunction.

28. **B**An egg is a discrete part of a dozen. A day is a discrete part of a week, which never changes length. Note: choice (E) is wrong because months vary in length.

29. **C**Someone who makes an illogical choice is acting without reason just as someone who makes a hasty choice is acting without prudence.

30. **D**Payment takes care of debt just as a recall takes care of a defect. Note: a cover-up doesn’t take care of a crime for the better; a cover-up hides a crime.

**SYNONYMS**

**Practice Drill 8—Write Your Own Definition**

Possible definitions:

1.Weird

2.Introduction

3.Giving

4.Doing the right thing

5.Change

6.Circle around

7.Optimistic

8.Stick around

9.Help

10.Build

11.Bend down

12.Honest

13.Tease

14.Rough

15.Self-centered

16.Calm

17.Use

18.Full of life

19.Stretch out

20.Help

**Practice Drill 9—Write Another Definition**

Look up these seven words in a dictionary to see how many different meanings they can have.

**Practice Drill 10—Basic Synonym Techniques**

1.**C**

2.**A**

3.**C**

4.**D**

5.**E**

6.**D**

7.**B**

8.**C**

9.**E**

10.**A**

11.**C**

12.**B**

13.**E**

14.**B**

15.**A**

16.**C**

17.**E**

18.**C**

19.**B**

20.**C**

**Practice Drill 11—Making Your Own Context**

Answers will vary. Possible contexts:

1.Common cold; common man

2.Competent to stand trial

3.Abridged dictionary

4.Untimely demise; untimely remark

5.Homogenized milk

6.Juvenile delinquent; delinquent payments

7.Inalienable rights

8.Paltry sum

9.Auspicious beginning; auspicious occasion

10.Prodigal son

**Practice Drill 12—Using Your Own Context**

1.**C**

2.**D**

3.**D**

4.**D**

5.**A**

6.**B**

7.**C**

8.**A**

9.**D**

10.**A**

**Practice Drill 13—All Synonyms Techniques**

1. **B**An atrocity is something terrible that has occurred.

2. **C**To be indulgent is to spoil or fuss over someone. Be careful! To be indulgent does not mean to be spoiled.

3. **E**To reproach means to scold someone or something.

4. **D**If a supply is scant, then there is not enough of it to go around.

5. **A**To annihilate is to destroy.

6. **D**An amendment is a change or addition to something in order to improve it.

7. **C**To emulate is to copy the original as closely as possible. To simulate is to create an artificial copy of the original.

8. **D**The epitome of something is its perfect example or representation.

9. **B**A countenance is a face or facial expression.

10. **C**To commandeer means to take control of something.

11. **A**To be resilient is to have the ability to rebound or be durable.

12. **A**A vagrant is a homeless or wandering person.

13. **D**To evict is to uproot or eject.

14. **C**To proliferate is to create plentifully.

15. **E**To adhere means to literally stick to something or figuratively to obey rules or orders.

16. **A**A discrepancy is a difference or inequality between two or more things.

17. **D**To be incredulous means to be unbelieving.

18. **C**To invoke is to call upon something, usually a higher power.

19. **D**Something that is opulent is luxurious or lavish.

20. **B**An arsenal is a store or supply of commodities or ideas.

21. **D**A virtuoso, usually a performer, is a master at his or her craft.

22. **E**Sage advice is wise advice. A very wise person or guru may also be referred to as a sage (noun).

23. **D**A vista is a view, usually a beautiful one.

24. **A**Surreptitious means clandestine, secret, or hidden.

25. **C**Perturbation is a state of being stressed, anxious, or in distress.

26. **D**Mercurial is often used to describe personality, though it is anything that fluctuates and changes quickly.

27. **E**Acquiesce is to oblige or agree to something.

28. **C**Insubordinate is to be defiant or rebellious.

29. **B**Querulous means to be whining and irritable.

30. **A**Enervate is to lose energy or exhaust.

**READING**

Detailed explanations can be found online in your Student Tools.

**Practice Drill 1—Getting Through the Passage**

You should have brief labels like the following:

Label for 1st paragraph: Norway → Iceland

Label for 2nd paragraph: Iceland → Greenland

Label for 3rd paragraph: lost

Label for 4th paragraph: saw America; landed Greenland

What? A Viking

So what? Found America early

Passage type? History of an event

**Practice Drill 2—Answering a General Question**

1.**D**

2.**D**

**Practice Drill 3—Answering a Specific Question**

1. **C**

2. **A**Lead word: Iceland

3. **B**

4. **E**Lead word: Greenland

5. **C**

**Review—The Reading Plan**

Your answers should be similar to the following:

After I read each paragraph, I label it.

After I read an entire passage, I ask myself What? So what?

I am better at doing these types of passages.

(Answers will vary. You may be better at answering questions related to history passages, science passages, opinion passages, stories, or poems. You may also be better at shorter passages or passages covering topics that you like. Take note of this when you take a practice test.)

The five main types of general questions, and the questions I can ask myself to answer them, are the following:

· Main idea: What was the “What? So what?” for this passage?

· Tone/attitude: How did the author feel about the subject?

· General interpretation: Which answer stays closest to what the author said and how he said it?

· General purpose: Why did the author write this?

· Prediction: How was the passage arranged? What will come next?

To find the answer to a specific question, I can use three clues:

· Paragraph labels

· Line or paragraph reference

· Lead words

If the question says, “In line 22,” then I begin reading at approximately line 17.

On a general question, I eliminate answers that are:

· Too small

· Not mentioned in the passage

· In contradiction to the passage

· Too big

· Too extreme

· Against common sense

On a specific question, I eliminate answers that are:

· Too extreme

· In contradiction to passage details

· Not mentioned in the passage

· Against common sense

When I’ve got it down to two possible answers, I:

· Reread the question

· Look at what makes the two answers different

· Go back to the passage

· Eliminate the answer that is worse

**Practice Drill 4—All Reading Techniques—All Levels**

1. **E**In the second and third paragraphs, the author details continued space exploration since the end of the Space Shuttle program. The final paragraph indicates that there are still more discoveries possible.

2. **A**All of the choices are true, except (A). ISS (the International Space Station) is not a private company that NASA collaborates with.

3. **D**Be sure to look up any vocabulary words you didn’t know and make flash cards for them. The author’s tone is positive. Sanguine means optimistic. Jubilant is too strong, and tenacious is a better description of those involved in space exploration.

4. **C**Remember that for some questions it can be easier to focus on finding four wrong answers rather than to search for the one right answer. The passage never states that the United States lost momentum, nor does the passage contain information about lost jobs or dreams. There is no mention of how much (or little) money the United States has to spend on any space missions. The passage doesn’t say what NASA will use for manned space flights in the future—it only says it is designing and building spacecraft, but not that they are specifically using rockets and boosters. Other companies are using rockets. Note that the five shuttles were a part of the former Space Shuttle program. Since that program has now ended, the fleet of shuttles is no longer being using to take humans into space.

5. **D**Read the sentence and substitute your own word into the sentence. For example, astronauts “get to” the station on Russian Soyuz spacecraft. Choice (D), *arrive at*, is closest in meaning to “get to.”

**Practice Drill 5—All Reading Techniques—All Levels**

1. **B**With its focus on Martial Arts history and the meaning of words, this passage would most likely appear as an entry in an encyclopedia.

2. **A**In the last sentence of the passage, the author states that benefits to all practitioners include increased focused, fitness, and (for some) fun.

3. **E**The sentence states “This is in contrast to Martial Arts that are practiced for military use or law enforcement,” which are styles that usually end in *jutsu*. The word “This” is referring to another type of Martial Arts, ones that are practiced for a different purpose (i.e., the styles that end in *do*).

4. **D**The author mentions *aikido* as a style of Martial Arts that ends in *do*, which the author goes on to explain is a style of Martial Arts that allows practitioners to improve, among other things, their mental focus and physical fitness.

5. **C**The author doesn’t give a complete list of the types of Martial Art styles ending in *do*, only examples. The author never claims that one style is the superior style—each style has advantages and disadvantages. The author does say that armed service members were the ones who brought back these fighting styles to the States after they learned them while deployed.

6. **D**The author is sharing information about a topic in a neutral way.

**Practice Drill 6—All Reading Techniques—Middle and Upper Levels**

1. **D**Remember to answer the question (*why* is the speaker sharing this information?) and not choose an answer about what the speaker is saying. The final three paragraphs explain the purpose of the author’s speech—theatre has an influence on society and can educate its citizens, ultimately for the better. If there were more theatres, more lives could be reached, educated, and improved as a result.

2. **B**The speaker is not a stage manager or a producer. The speaker is also not being aloof or offering a critique of the play. Rather, the speaker is a strong supporter of the arts and feels strongly about what theatre can offer to citizens and their community.

3. **A**Read the sentence and substitute your own word into the sentence. For example, this theatre “shares” or “offers” pure and clean plays. Choice (A), *provides*, is closest in meaning to “shares” or “offers.”

4. **C**The speaker uses the phrase in the fifth paragraph to show the reach that more theatres could have on a community—“how they would educate and elevate!” He isn’t trying to dictate what individuals should do with their money or guarantee attendance numbers at productions. He is indicating the valuable impact the theatre can have on the city because, as a means of education, theatre can better the lives as well as the actions and beliefs of those who attend shows.

5. **D**In the first three paragraphs, the speaker speaks fondly about his experience as an actor in this same play many years ago and how touched he is by the production he just witnessed.

**Practice Drill 7—All Reading Techniques—Middle and Upper Levels**

1. **C**Based on the style, tone, and topic of this passage, it would most likely be found in a scholarly work such as an academic journal.

2. **D**Eulogize means to praise highly. The author is expressing there is no practice like early rising that has been more highly and universally praised. Thus, early rising is a greatly respected practice.

3. **E**Those who labor “at occupations which demand the light of day” are those who have occupations that require physical labor. Farming is a type of physical work but not the only kind that would require daylight.

4. **E**When the author states that “the influence of this custom extends across the ocean, and here, in this democratic land…,” she references a specific place. Throughout the passage, the author references England or London, so “Across the ocean” refers to across the Atlantic Ocean. The only option listed as a country that could be across this ocean and is also democratic is (E), *the United States*.

5. **A**Remember to use other questions to help on trickier questions. Both questions 2 and 6 can help with this question. The correct answer should mention early rising and its importance.

6. **D**The author speaks highly of early rising and regards staying up late (and thus rising later in the day) as lacking good sense. Thus, she would admire those who get up early.

**Practice Drill 8—All Reading Techniques—Middle and Upper Levels**

1. **C**The children are planning to ambush the speaker (their father) who is working. The speaker hears them whispering their plans, knows they are attempting a surprise attack, and waits for them to carry it out. Plotting and planning are the main actions of the children since the trick they are playing on their father is the main action in the poem.

2. **B**The walls, fortress, and dungeon are all figurative, as the action of the poem takes place in the speaker’s study or office space. The speaker uses those images to explain the eternal love he has for his children.

3. **D**The poem is about the love the speaker has for the children. Kisses and hugs best depict the image of love.

4. **A**The speaker is referring to the children when he calls them *banditti*. Since they are planning a raid and are trying to surround him by climbing into his chair, this word most likely means invaders, which makes *bandits* the closest match.

5. **B**The Children’s Hour is the time of night when there “comes a pause in the day’s occupations.” During this time, the children come to play with their father—a time they all enjoy. The poem is not about a story he tells them or a description of an imaginary game the children play.

**Practice Drill 9—All Reading Techniques—Middle and Upper Levels**

1. **B**The “she” in this sentence is referring to Sara, so (D) and (E) should be eliminated. While Sara “was very firm in her belief that she was an ugly little girl,” the author lists specific features Sara possesses that give her “an odd charm of her own” distinct from Isobel, whom Sara does not look like at all. Since the omniscient narrator gives the reader this information about Sara’s looks and compares it to Sara’s own thoughts, the narrator allows the reader to see that Sara’s perception of herself is not entirely accurate.

2. **D**The last sentence of the passage states that Sara later discovers that Miss Minchin says “the same thing to each papa and mamma who brought a child to her school.” Thus, Miss Minchin’s actions towards newcomers is known.

3. **A**Read the sentence and substitute your own word. For example, Sara says she is not “pretty” in the least. Choice (A), *attractive*, is closest in meaning to “pretty.”

4. **D**Read the question carefully. It asks for the narrator’s tone, not a character’s tone. The narrator is simply sharing information and details that relate to the story.

5. **E**A simile is a literary device that compares two unlike things and uses the word like or as to set up the comparison.

6. **B**Sara states in the 4th paragraph that she is not beautiful at all and that, in her opinion, Isobel is beautiful. She gives reasons for why she considers Isobel beautiful and why she herself is not. Thus, Sara uses Isobel as a standard for beauty in order to show how she does not meet the Isobel-standard of beauty.

7. **D**Read the sentences that use the word “story” and substitute your own word. For example, when Sara says in the last sentence of the 4th paragraph, “she is beginning by telling a story,” she means that Miss Minchin is saying something untrue. Each time “story” is used in the passage, it is used to indicate someone is telling a lie.