Sat - MC Grawhill part 71 pptx

690 MCGRAW-HILL’S SAT
8. A You are told that: 12v = 3w
Divide by 3: 4v = w
Multiply by 2: 8v = 2w
The question asks for the value of: 2w − 8v
Substitute for 2w: 8v − 8v = 0
Alternatively, you can try finding values for v and w
that work, like 1 and 4, and plug them into 2w − 8v
and into the choices and find the match.
(Chapter 8, Lesson 1: Solving Equations)
9. C 2ΗxΈ + 1 > 5
Subtract 1: 2ΗxΈ > 4
Divide by 2: ΗxΈ > 2
Interpret the absolute value: x > 2 OR x < −2
You are told that x is negative, so x < −2 is the answer.
(Chapter 8, Lesson 6: Inequalities, Absolute Values,
and Plugging In)
10. B −x
2
− 8x − 5
Substitute −2 for x: −(−2)
2
− 8(−2) − 5
Square −2: −(4) − 8(−2) − 5
Simplify: −4 + 16 − 5 = 7
When evaluating −x
2
, don’t forget to square the value
before taking its opposite!
(Chapter 8, Lesson 1: Solving Equations)
11. D

Cross-multiply: 15 ≤ 2m
Divide by 2: 7.5 ≤ m
Since m is greater than or equal to 7.5, (D) is the answer.
(Chapter 8, Lesson 6: Inequalities, Absolute Values,
and Plugging In)
12. B First find the price after the 6% sales tax:
$60.00 × .06 = $3.60 tax
$60.00 + $3.60 = $63.60 price with tax
(A simpler way is just to multiply 60 by 1.06.)
Now find how much change Theo received:
$70.00 − $63.60 = $6.40 change
(Chapter 7, Lesson 5: Percents)
13. A Write an equation for the first sentence.
n − m = r
Because none of the answer choices contain m, solve
for m in terms of r and n: n − m = r
Add m: n = r + m
Subtract r: n − r = m
Now write an expression for what the question asks for:
s + 2m
Substitute for m: s + 2(n − r)
Distribute: s + 2n − 2r
Alternatively, you can substitute numbers for n, m,
and r, making sure they “work,” and get a numerical
answer to the question.
(Chapter 8, Lesson 1: Solving Equations)
52
3m
≤
14. D Two points on line l are (0, 0) and (10, y).

Find the slope of the line:
Cross-multiply: 5y = 30
Divide by 5: y = 6
Since y = 6, the height of the triangle is 6. Find the area:
A =
1
⁄
2
(base)(height)
Substitute 48 for A: 48 =
1
⁄
2
(base)(6)
Simplify: 48 = 3(base)
Divide by 3: 16 = base = x
Now find x + y = 16 + 6 = 22.
(Chapter 10, Lesson 4: Coordinate Geometry)
15. A Ellen travels the first 15 miles at 30 miles per
hour. Find out how much time that takes:
d = (rate)(time)
Plug in known values: 15 = 30t
Divide by 30:
1
⁄
2
hour = t
The rest of the trip, which is (y − 15) miles long, she
travels at an average speed of 40 miles per hour:
d = (rate)(time)

Plug in known values: (y − 15) = 40t
Divide by 40:
Add the two values together to find the total time:
(Chapter 9, Lesson 4: Rate Problems)
16. B Set up the relationship in equation form:
Plug in what you’re given:
Simplify: 8 = 16k
Divide by 16:
1
⁄
2
= k
Write the new equation:
Plug in new values:
(Chapter 11, Lesson 4: Variation)
y =
()
()
==
1
2
8
4
4
16
1
4
2
y
m

n
=
()
()
1
2
2
8
16
1
2
=
()
()
k
y
km
n
=
2
1
2
15
40
+
−y
y
t
−
=

15
40
m
yy
xx
yy
=
−
−
=
−
−
==
21
21
0
10 0 10
3
5
CHAPTER 16 / PRACTICE TEST 2 691
17. D a + b = s
a − b = t
Add straight down: 2a = s + t
Divide by 2:
a + b = s
a − b = t
Subtract straight down: 2b = s − t
Divide by 2:
Find the
product:

(Chapter 8, Lesson 2: Systems)
18. C y = m
4
= n
3
The answer is in terms of y alone, so find m and n in
terms of y: y = m
4
Take the 4th root: y
1/4
= m
y = n
3
Take the cube root: y
1/3
= n
Find the product mn: mn = (y
1/4
)(y
1/3
) = y
1/3 + 1/4
Add exponents: mn = y
7/12
(Chapter 11, Lesson 6: Negative and Fractional
Exponents)
19. A This question deals with similar triangles:
Set up ratio:
Cross-multiply: 6x = 48
Divide by 6: x = 8

Area of big triangle =
1
⁄
2
(base)(height) =
1
⁄
2
(12)(6) = 36
Area of small triangle =
1
⁄
2
(base)(height) =
1
⁄
2
(8)(4) = 16
Shaded area = area of big triangle − area of small
triangle = 36 − 16 = 20
(Chapter 10, Lesson 6: Similar Figures)
(Chapter 10, Lesson 5: Areas and Perimeters)
20. A Set up a Venn diagram to visualize the
information.
6
12
4
=
x
()()=ab

st st s t+
⎛
⎝
⎜
⎞
⎠
⎟
−
⎛
⎝
⎜
⎞
⎠
⎟
=
−
⎛
⎝
⎜
⎞
⎠
⎟
22 4
22
b
st
=
−
2
a

st
=
+
2
Notice that
1
⁄
3
the number of sedans must equal
1
⁄
5
the
number of convertibles. Say the number of convert-
ible sedans is x. If this is
1
⁄
3
the number of sedans, then
there must be 3x sedans in total, and 3x − x = 2x of
these are not convertibles. Similarly, if x is
1
⁄
5
the num-
ber of convertibles, then there must be 5x convertibles
altogether, and 5x − x = 4x of these are not sedans. So
now your diagram can look like this:
So there must be a total of 2x + x + 4x = 7x cars at the
dealership. The only choice that is a multiple of 7 is

(A): 28.
(Chapter 9, Lesson 5: Counting Problems)
Section 4
1. E
Perimeter of a square = 4s
36 = 4s
Divide by 4: 9 = s
Area of a square = (s)
2
Area = (9)
2
= 81
(Chapter 10, Lesson 5: Areas and Perimeters)
2. C
Cross-multiply: b = 10a
Try positive integer values of a to see how many work:
a 123456789
b 10 20 30 40 50 60 70 80 90
There are nine integer pairs that satisfy the equation.
(Chapter 9, Lesson 3: Numerical Reasoning Problems)
3. E The ten bathrooms cost $20 each to clean:
Total cost = $20 × 10 = $200
To clean each bathroom twice would cost:
$200 × 2 = $400
There are 30 offices, and they cost $15 each to clean:
Total cost = $15 × 30 = $450
To clean each office once and each bathroom twice
will cost: $400 + $450 = $850
(Chapter 11, Lesson 5: Data Analysis)
a

b
=
1
10
both
2
3
s
1
3
s
1
5
c
4
5
c
sedans
convertibles
x
sedans convertibles
both
2x 4x
s
s
s
s
6
12
4

x
692 MCGRAW-HILL’S SAT
4. A Remember the “difference of squares” factor-
ing formula: a
2
− b
2
= (a − b)(a + b)
Substitute: 10 = (2)(a + b)
Divide by 2: 5 = a + b
(Chapter 8, Lesson 5: Factoring)
5. A
To find the value of f(14), find all the factors of 14:
1, 2
, 7, 14
There are two prime factors, 2 and 7.
2 + 7 = 9
f(14) = 9
To find the value of f(6), find all the factors of 6:
1, 2
, 3, 6
There are two prime factors, 2 and 3.
2 + 3 = 5
f(6) = 5
f(14) − f(6) = 9 − 5 = 4
(Chapter 11, Lesson 2: Functions)
6. D First write an equation to find the average.
Multiply by 4: a + b + c + d = 80
If you want a to be as large as possible, make b, c, and
d as small as possible. You are told that they are all

different positive integers: a + b + c + d = 80
Let b = 1, c = 2, d = 3: a + 1 + 2 + 3 = 80
Combine like terms: a + 6 = 80
Subtract 6: a = 74
(Chapter 9, Lesson 2: Mean/Median/Mode Problems)
7. B Let the radius of circle A = a and the radius of
circle B = b. It is given that a = 2b. The circumference
of a circle can be found with the equation C = 2πr.
The sum of their circumferences is 36π:
36π=2πa + 2πb
Divide by π: 36 = 2a + 2b
Substitute for a: 36 = 2(2b) + 2b
Simplify: 36 = 4b + 2b
Combine like terms: 36 = 6b
Divide by 6: 6 = b
Solve for a: a = 2(b) = 2(6) = 12
(Chapter 10, Lesson 5: Areas and Perimeters)
abcd+++
=
4
20
8. C This is a visualization problem. The six possi-
ble planes are illustrated below. Notice that the six
faces of the cube “don’t count,” because each of those
contains four edges of the cube.
(Chapter 10, Lesson 7: Volumes and 3-D Geometry)
9. 16 Set up an equation: 2x − 10 = 22
Add 10: 2x = 32
Divide by 2: x = 16
(Chapter 8, Lesson 1: Solving Equations)

10. 36
There are 180° on one side of a line:
2y + y + y + y = 180°
Combine like terms: 5y = 180°
Divide by 5: y = 36°
(Chapter 10, Lesson 1: Lines and Angles)
2y°
y°
y°
y°
CHAPTER 16 / PRACTICE TEST 2 693
15. 25 First calculate how many grams of sucrose
there are in 200 grams of a 10% mixture.
(200 grams)(.10) = 20 grams of sucrose
Since you will be adding x grams of sucrose, the total
weight of sucrose will be 20 + x grams, and the total
weight of the mixture will be 200 + x grams. Since the
fraction that will be sucrose is 20%,
Cross-multiply: (20 + x)(100) = 20(200 + x)
Distribute: 2,000 + 100x = 4,000 + 20x
Subtract 2,000: 100x = 2,000 + 20x
Subtract 20x: 80x = 2,000
Divide by 80: x = 25
(Chapter 7, Lesson 5: Percents)
(Chapter 7, Lesson 4: Ratios and Proportions)
16. 24 First calculate how long the race took.
distance = rate × time
16 = (8)(time)
Divide by 8: 2 hours = time = 120 minutes
Next, find the new rate that is 25% faster:

new rate = (8)(1.25) = 10 mph
Calculate how long the new race would take:
distance = rate × time
16 = (10)(time)
Divide by 10: 1.6 hours = time = 96 minutes
So she can improve her time by (120 − 96) =24 minutes.
(Chapter 9, Lesson 4: Rate Problems)
20
200
20
100
+
+
=
x
x
11. 5 Think simple: What’s the simplest way to turn
8x + 4y into 2x + y? Just divide by 4!
8x + 4y = 20
Divide by 4: 2x + y = 5
(Chapter 8, Lesson 1: Solving Equations)
(Chapter 6, Lesson 4: Simplifying Problems)
12. 12 Just substitute x = 3 and y = 5 into the equa-
tion and solve for m:
3m − 15 = 21
Add 15: 3m = 36
Divide by 3: m = 12
(Chapter 8, Lesson 1: Solving Equations)
(Chapter 11, Lesson 2: Functions)
13. 15 Ratios such as 4:5 can also be written as 4x:5x.

So the number of men m is 4x and the number of
women w is 5x.
Plug those values into the equation w = m + 3
5x = 4x + 3
Subtract 4x: x = 3
Plug 3 in to 5x: w = 5x = 5(3) = 15
(Chapter 7, Lesson 4: Ratios and Proportions)
14. 8 or 12 y =⎟2x − b⎟
Plug in (5, 2): 2 =⎟2(5) − b⎟
Simplify: 2 =⎟10 − b⎟
(10 − b) = 2 or (10 − b) =−2
Subtract 10: −b =−8 or −b =−12
Multiply by −1: b = 8 or b = 12
(Chapter 8, Lesson 6: Inequalities, Absolute Values,
and Plugging In)
694 MCGRAW-HILL’S SAT
17. 52
Break a shape like
this into recogniz-
able four-sided
figures and trian-
gles that are easier
to deal with.
The area of the
rectangle on the
left is 7 × 4 = 28.
The area of the rectangle on the right is 5 × 4 = 20.
The sum of those two areas is 28 + 20 = 48. The
area remaining for the triangle is the difference
78 − 48 = 30. Set up an equation for the area of a

triangle to solve for x:
Area =
1
⁄
2
(base)(height)
30 =
1
⁄
2
(5)(height)
Divide by
1
⁄
2
: 60 = 5(height)
Divide by 5: 12 = height
To find the hypotenuse of
the right triangle, set up
the Pythagorean theorem
and solve:
5
2
+ 12
2
= c
2
25 + 144 = c
2
169 = c

2
c = 13
(Or just notice that it’s a 5-12-13 triangle!)
To find the perimeter of the figure, add up all of the
sides:
13 + 12 + 4 + 5 + 7 + 4 + 7 = 52
(Chapter 10, Lesson 5: Areas and Perimeters)
(Chapter 10, Lesson 3: The Pythagorean Theorem)
18. 225 Set up a three-circle Venn diagram to visual-
ize this information.
Fifty students study two of the three languages, so let’s
say that 50 students study both Spanish and Latin. (It
doesn’t matter which two languages those 50 students
take; the result turns out the same.) This means that
zero students study both Spanish and French, zero
students study both French and Latin, and zero
students study all three languages.
There are 120 Spanish students in all. There are there-
fore 120 − 50 = 70 students who study Spanish alone.
There are 80 French students in all, all of whom study
just French, and there are 75 total Latin students in-
cluding 75 − 50 = 25 students who study only Latin.
This means that there are 70 + 50 + 80 + 25 = 225
sophomores at Hillside High School.
(Chapter 9, Lesson 5: Counting Problems)
Section 5
1. C The clients were forced to seek more reliable
investment advice, so the manager must have man-
aged their funds badly. ineptitude = lack of skill
2. E Vartan is Armenian; he was born in Iran and

educated in Lebanon and is now president of the
American Brown University. He has a lot of worldly
experience. perpetual = lasting forever; authoritative =
showing authority; cosmopolitan = worldly
3. D They didn’t consider it in great detail, so the
reading must have been without great care. verbatim =
word for word; meandering = wandering; tormented =
feeling anguish or pain; cursory = quick and without
care; substantial = of substance, quite large
Spanish French
Latin
50
0
70
80
25
0
0
4
7
7
44
28
5
5
20
c
x
4
7

7
4
28
5
5
20
12
4
13
CHAPTER 16 / PRACTICE TEST 2 695
4. A If the pathogens (infectious agents) spread
more quickly in close quarters, the crowding would be
a problem. This would cause the disease to spread.
propagation = reproduction, increase in number;
squalor = horrible or dirty conditions; circulation =
moving of something around from place to place;
poverty = state of being poor; deterioration = wearing
down; congestion = crowdedness; proximity = close-
ness; resilience = ability to recover from a challenge
5. E The purpose of research is to find answers to
questions of interest. Therefore, the research endeav-
ors (attempts) to determine or understand the mecha-
nisms by which our brains do things. If the data must
be turned into coherent and understandable informa-
tion, it must not have been coherent to begin with, but
rather just a big rush of information. enhance = make
better; attenuate = reduce in amount; dearth = scarcity,
lack; elucidate = make clear; deluge = huge flood
6. D The fruits mentioned in line 10 refer to the
means of acquiring food and shelter, because they are

described as the fruits for maintaining human life.
7. B The question is whether one can get quick re-
turns of interest (make money) from the capital of
knowledge and learning (from one’s education) (lines
13–15).
8. A The pointing of dogs is mentioned as an in-
stinctive tendency to the performance of an action
(lines 1–2).
9. E Inherited tendencies tend to show themselves
in the behavior of an organism. The paragraph men-
tions the calf and the caterpillar as examples of or-
ganisms with instincts that show themselves in later
behavior.
10. D The final paragraph begins with The best life is
the one in which the creative impulses play the largest part
and the possessive impulses the smallest (lines 56–58).
11. D Lines 22–26 say that the food and clothing of
one man is not the food and clothing of another; if the
supply is insufficient, what one man has is obtained at
the expense of some other man. Therefore, food and
clothing exist in finite amounts and can be used up.
12. E This section of the passage discusses matters
such as good-will (line 38), science (line 31), and paint-
ing pictures or writing poems (lines 35–36) as things
that are not denied to someone else when one person
possesses them.
13. E This sentence discusses the possessive im-
pulses (line 49) as distinct from the creative impulses
discussed in the next sentence. The impulse of prop-
erty in lines 51–52 is the desire to possess property.

14. C This statement echoes the point made in lines
71–72 that spiritual possessions cannot be taken in this
way, that is, by force.
15. D Lines 58–59 say This is no new discovery and
go on to cite the Gospel as a prior source expressing
the same opinions as Russell’s.
16. B The author’s main point is that creativity is of
higher value than possessiveness. The invention
mentioned in answer choice (B) was created to make
money for its inventor (a possessive and materialis-
tic motive) but has the side effect of benefitting all of
humankind.
17. A The passage discusses the perspective one
Native American has on the appearance of the new
superstition (line 44). It discusses how some villagers
have taken to the new religion and also mentions one
fellow tribe member’s attempting to convert the main
character.
18. E In saying that men of the same color are like the
ivory keys of one instrument where each represents all
the rest, yet varies from them in pitch and quality of
voice (lines 4–7), the author is saying that people of
the same race possess important differences.
19. D The author describes the preacher as
mouth[ing] most strangely the jangling phrases of a
bigoted creed (lines 11–12), indicating that she consid-
ers him to be an intolerant person. She describes her-
self as having compassion (line 7) and respect (line 10),
but does not attribute these qualities to the preacher.
20. B Lines 13–14 say that our tribe is one large fam-

ily, where every person is related to all the others.
21. C Both the preacher and the author’s mother
have become followers of the new superstition (line 44).
22. C In saying that a pugilist commented upon a re-
cent article of mine, grossly perverting the spirit of my
pen (lines 66–68), the author is saying that the pugilist
distorted the author’s words in a grotesque way.
696 MCGRAW-HILL’S SAT
23. E The author characterizes herself as a wee child
toddling in a wonder world (lines 72–73), indicating
that she is in awe of the world around her. Although
one might expect her to be vengeful in response to the
pugilist (line 66) who grossly pervert[ed] the spirit of
[her] pen (line 68), there is no indication in the para-
graph that she is vengeful.
24. A The author says in lines 68–72 that still I would
not forget that the pale-faced missionary and the aborig-
ine are both God’s creatures, though small indeed in
their own conceptions of Infinite Love. In other
words, the author respects the missionary but believes
he is small-minded.
Section 6
1. D The verb must agree with the plural subject
claims. Choice (D) is most concise and correct.
(Chapter 15, Lesson 1: Subject-Verb Disagreement)
2. A The original sentence is best.
3. B The participial phrase opening the sentence
modifies Sartre himself, not his writing. This being
the case, the phrase dangles.
(Chapter 15, Lesson 7: Dangling and Misplaced

Participles)
4. C Choice (C) best follows the law of parallelism.
(Chapter 15, Lesson 3: Parallelism)
5. A The original sentence is best.
6. B Choice (B) is the most concise, logical, and
complete.
(Chapter 12, Lesson 9: Write Concisely)
7. C The original phrasing contains an incomplete
thought. Choice (C) is by far the most concise and direct.
(Chapter 15, Lesson 15: Coordinating Ideas)
8. E The participle having spread modifies the dis-
ease, not the doctors.
(Chapter 15, Lesson 7: Dangling and Misplaced
Participles)
9. C The original phrasing contains an incomplete
thought. Choice (C) is by far the most concise and direct.
(Chapter 15, Lesson 15: Coordinating Ideas)
10. D The participle singing modifies Anita, not her
hoarseness. Furthermore, the participle is in the
wrong form; it should be in the perfect form having
sung, because only the previous singing could have
contributed to her hoarseness.
(Chapter 15, Lesson 7: Dangling and Misplaced
Participles)
(Chapter 15, Lesson 9: Tricky Tenses)
11. A The original sentence is best.
12. A The word quick is an adjective and can thus
modify only a noun. But since it modifies the verb
turned, the adverb quickly is needed here.
(Chapter 15, Lesson 12: Other Modifier Problems)

13. B This sentence violates the law of parallelism.
If she is known for her initiative, she should also be
known for devoting her own time.
(Chapter 15, Lesson 3: Parallelism)
14. C Since the Medieval era is long past, its begin-
ning is “completed” or, in grammar terms, “perfect.”
So this phrase should be the “perfect” form of the in-
finitive: to have begun.
(Chapter 15, Lesson 9: Tricky Tenses)
15. B The word neither is almost always part of the
phrase neither of . . . or neither A nor B. So choice (B)
should read nor even.
(Chapter 15, Lesson 10: Idiom Errors)
16. D The word less is used to compare only quanti-
ties that can’t be counted. If the quantities are count-
able, as accidents are, the word should be fewer.
(Chapter 15, Lesson 4: Comparison Problems)
17. B To convey the proper sequence of events, the
perfect tense is required: had spent.
(Chapter 15, Lesson 9: Tricky Tenses)
18. A The subject of the verb has is the plural noun
newspapers. (The sentence is “inverted,” because the
subject follows the verb.) The proper form of the verb,
then, is have.
(Chapter 15, Lesson 1: Subject-Verb Disagreement)
(Chapter 15, Lesson 2: Trimming Sentences)
19. B The original sentence has a “comma splice”
that incorrectly joins two sentences with only a
comma. A better phrasing is dream that led.
(Chapter 15, Lesson 15: Coordinating Ideas)

CHAPTER 16 / PRACTICE TEST 2 697
20. C The subject of the verb is the singular noun
movement, so the proper verb form is has led.
(Chapter 15, Lesson 1: Subject-Verb Disagreement)
(Chapter 15, Lesson 2: Trimming Sentences)
21. E The sentence is correct as written.
22. D This is a prepositional phrase, so the pro-
noun is the object of the preposition and should be
in the objective case. The correct phrasing is for
Maria and me.
(Chapter 15, Lesson 6: Pronoun Case)
23. A The word successive means consecutive, so it
does not make sense in this context. The right word is
successful.
(Chapter 15, Lesson 11: Diction Errors)
24. E The sentence is correct as written.
25. C The word underneath means that it is physi-
cally below something else. It should be changed to
under.
(Chapter 15, Lesson 10: Idiom Errors)
26. E The sentence is correct as written.
27. B The subject of the verb were is arrogance,
which is singular. It should instead be was.
(Chapter 15, Lesson 1: Subject-Verb Disagreement)
28. B The sentence mentions there are numerous
strains of the bacteria, which means that more should
instead be most.
(Chapter 15, Lesson 4: Comparison Problems)
29. C The subject company is singular. Therefore,
they should instead be it.

(Chapter 15, Lesson 5: Pronoun-Antecedent
Disagreement)
30. D Choice (D) is most consistent, logical, and
concise.
31. A Choice (A) is most logical.
(Chapter 12, Lesson 7: Write Logically)
32. B The first paragraph ends with the description
of an idea. The second paragraph begins with an
illustration of how students experience this idea in
their daily lives and then goes on to explain how it can
help them get through their brain freezes. Choice (B)
is the best introduction to the paragraph, because it
explains that a student using the phenomenon can
improve his or her studies.
(Chapter 12, Lesson 7: Write Logically)
33. C The sentence begins using the pronoun you,
so that usage should be maintained throughout the
sentence. Choice (D) is incorrect because a person
has only one brain.
(Chapter 15, Lesson 5: Pronoun-Antecedent
Disagreement)
34. E Sentence 11 concludes a discussion of Isaac
Asimov’s “eureka” experience. The additional sen-
tence expands upon that idea, relating it back to the
lives of students.
(Chapter 12, Lesson 7: Write Logically)
35. C Choice (C) is the most concise and logical
revision.
(Chapter 12, Lesson 7: Write Logically)
(Chapter 12, Lesson 9: Write Concisely)

Section 7
1. B Set up a ratio to solve this problem:
Cross-multiply: 4x = 200
Divide by 4: x = 50 cents
(Chapter 7, Lesson 4: Ratios and Proportions)
2. C Solve for b: 2
b
= 8
b = 3
Plug in 3: 3
b
= 3
3
= 27
(Chapter 8, Lesson 3: Working with Exponentials)
3. A The sum of a, b, and 18 is 6 greater than the
sum of a, b, and 12. Since there are three terms in the
group, it follows that the average of a, b, and 18 would
be 6 ÷ 3 = 2 greater than the average of a, b, and 12.
(Chapter 9, Lesson 2: Mean/Median/Mode Problems)
410apples
20 cents
apples
x cents
=
698 MCGRAW-HILL’S SAT
4. B If you have the patience, you can write out a
quick calendar for yourself to track the days:
Or you can use the simple fact that successive Tues-
days (like any other days) are always 7 days apart.

Therefore, if the 1st of the month is a Tuesday, so are
the 8th, the 15th, the 22nd, and the 29th. Therefore, the
30th is a Wednesday and the 31st is a Thursday.
(Chapter 9, Lesson 3: Numerical Reasoning Problems)
5. A From the given information: m = 8n
0 < m + n < 50
Substitute for m: 0 < 8n + n < 50
Combine like terms: 0 < 9n < 50
Divide by 9: 0 < n < 5
5
⁄
9
Since n must be an integer, n can be 1, 2, 3, 4, or 5.
(Chapter 8, Lesson 6: Inequalities, Absolute Values,
and Plugging In)
6. D First find the value of y: y% of 50 is 32.
Simplify:
Cross-multiply: 50y = 3,200
Divide by 50: y = 64
What is 200% of 64?
Interpret: 2.00 × 64 = 128
(Chapter 7, Lesson 5: Percents)
7. B g(x) = x + x
1/2
Plug in 16 for x: g(16) = 16 + 16
1/2
Take square root of 16: g(16) = 16 + 4
Combine like terms: g(16) = 20
(Chapter 11, Lesson 2: Functions)
8. C The slope of the line is −

3
⁄
4
, so use the slope
equation and the coordinates of point A (0, 12) to find
the coordinates of point B (x, 0):
Cross-multiply: 4(−12) =−3(x)
Simplify: −48 =−3x
Divide by −3: 16 = x
The base of the triangle is 16, and its height is 12.
Area =
1
⁄
2
(base)(height)
Substitute: Area =
1
⁄
2
(16)(12)
Simplify: Area = 96
(Chapter 10, Lesson 4: Coordinate Geometry)
m
yy
xx x x
=
−
−
=
−

−
=
−
=−
21
21
012
0
12 3
4
y
100
50 32×=
9. A Find the sum of each repetition of the pattern:
−1 + 1 + 2 = 2
Next, determine how many times the pattern
repeats in the first 25 terms: 25 ÷ 3 = 8 with a
remainder of 1.
Multiply the sum of the pattern by 8 to obtain the sum
of the first 24 terms: 2 × 8 = 16
The 25th term is −1, which makes the sum 16 +−1 = 15.
(Chapter 11, Lesson 1: Sequences)
10. D The ratio of white marbles to blue marbles is
4 to b. The probability of randomly selecting a white
marble from the jar is
1
⁄
4
. This means that one out of
every four marbles in the jar is white and three out of

every four marbles are blue. If there are four white
marbles, then there are 4 × 3 = 12 blue marbles.
(Chapter 7, Lesson 4: Ratios and Proportions)
11. B Area =
1
⁄
2
(base)(height)
Substitute: 10 =
1
⁄
2
(base)(height)
Divide by
1
⁄
2
: 20 = (base)(height)
The base and the height are both integers. Find all the
“factor pairs” of 20: 1, 20; 2, 10; and 4, 5
Plug each pair into the Pythagorean theorem to find
the least possible length of the hypotenuse:
a
2
+ b
2
= c
2
4
2

+ 5
2
= c
2
Combine like terms: 41 = c
2
Take square root:
a
2
+ b
2
= c
2
2
2
+ 10
2
= c
2
Combine like terms: 104 = c
2
Take square root:
a
2
+ b
2
= c
2
1
2

+ 20
2
= c
2
Combine like terms: 401 = c
2
Take square root:
is the shortest possible hypotenuse.
(Chapter 10, Lesson 5: Areas and Perimeters)
(Chapter 10, Lesson 3: The Pythagorean Theorem)
12. B −1 < y < 0
This means that y is a negative decimal fraction.
Answer choices (A), (C), and (E) will all be negative num-
bers. Answer choices (B) and (D) are positive numbers.
When you raise a simple fraction to a positive number
larger than 1, it gets smaller. y
4
< y
2
, which makes (B) the
greatest value. Pick a value like y =−
1
⁄
2
and see.
(Chapter 9, Lesson 3: Numerical Reasoning Problems)
41
401 = c
104 = c
41 = c

Su M T W Th FSa
12 345
91011678 12
16 17 1813 14 15 19
23 24 2520 21 22
30 3127 28 29
26
CHAPTER 16 / PRACTICE TEST 2 699
13. E Any statement of the form “If A is true, then B
is true” is logically equivalent to “If B is not true, then
A is not true.” Try this with some common-sense
examples of such statements. For instance, saying “If
I am under 16 years old, then I am not allowed to drive”
is the same as saying “If I am allowed to drive, then I
must not be under 16 years old.” The statement in (E)
is logically equivalent to the original.
(Chapter 6, Lesson 7: Thinking Logically)
14. E If each bus contained only the minimum
number of students, the buses would accommodate
6 × 30 = 180 students. But since you have 200 students
to accommodate, you have 20 more students to place.
To maximize the number of 40-student buses, place
10 more students in two of the buses. Therefore, a
maximum of two buses can have 40 students.
(Chapter 9, Lesson 3: Numerical Reasoning Problems)
15. D The volume of a cylinder is equal to πr
2
h. Let’s
say that the radius of cylinder A is a and the radius of
cylinder B is b. Since the height of cylinder B is twice

the height of cylinder A, if the height of cylinder A is
h, then the height of cylinder B is 2h. The volume of
A is twice that of B: πa
2
h = 2πb
2
(2h)
Simplify: πa
2
h = 4πb
2
h
Divide by π: a
2
h = 4b
2
h
Divide by h: a
2
= 4b
2
Take the square root of both sides: a = 2b
Divide by b:
(Chapter 10, Lesson 7: Volumes and 3-D Geometry)
16. C The key is to find a pattern among the many
possible solutions. Pick some values for x to see if you
can see a pattern. For instance, if x = 3, then the gar-
den looks like this:
In this case w = 8. But if x = 4, the garden looks like this:
a

b
=
2
1
And here, w = 12. You might notice that the value of
w has increased by 4. Does this pattern continue?
Let’s try x = 5 to check:
Sure enough, w = 16, and it seems that the pattern
continues and w is always a multiple of 4. Only choice
(C), 40, is a multiple of 4, so that must be the correct
answer.
(Chapter 6, Lesson 3: Finding Patterns)
Section 8
1. B A reputable scientist is well known and well
respected. Saying the evidence is at best indicates
that there is not much evidence at all. It must be
flimsy. Reputable scientists would not likely admit that
a phenomenon exists if the evidence is weak. meager =
scanty, deficient; regret = feel bad about an action,
wish it hadn’t happened; paltry = lacking worth
2. D The concept that the Earth is round is now ac-
cepted as an inarguable truth. It can be inferred that it
was at some point a fact that was thought to be wrong.
incontrovertible = cannot be questioned; mellifluous =
smooth flowing; dubious = doubtful
3. B A profound break of a political party or religion
into factions is a schism. (The Latin word schisma =
split.) unanimity = full agreement; schism = division
into factions; caucus = meeting of party members;
commemoration = event that honors something or

someone; prognostication = prediction
4. C As the father of the American public school
system, Horace Mann would pressure or push the
Massachusetts legislature to institute a system for en-
suring or guaranteeing universal access to eduction.
petitioned = requested, lobbied for; vouchsafing = con-
ceding, granting
5. A Since the light from most stars takes millions
of years to reach us, it is plausible to imagine that by
the time we see the light the star might actually no
longer be there. This would make the present exis-
tence of these stars questionable. debatable = dis-
putable; methodical = systematic; indecorous = not
proper; imperious = acting as if one is superior to an-
other; profuse = abundant