1. science
2. mathematics
3. geometry

Sample Cracking the SAT Practice Tests
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explanations from our flagship Cracking series!
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Sample Cracking the SAT Practice Tests
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explanations from our flagship Cracking series!
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ANSWER EXPLANATIONS FOR PREVIOUS PAGE
1.
A
2.
C
Answer this question in bite-sized pieces. The first step is to use your calculator to compute the sum
of the subscriptions: $68.80. The down payment was half that amount, leaving $34.40 to be paid in 4
installments of $8.60 each. If you answered D or E, you may have misread the question.
1
Try Plugging In The Answers. Starting with C, put in
for x:
2
1
⎛ ⎞
2⎜ ⎟
⎝2⎠
=
2
⎛1⎞
⎜⎝ ⎟⎠ + 1
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1
=
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2
1
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2
1
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⎝ 4⎠
2
2
1
2
2
2
2x + 4x = 2x + 2. Subtract 2x from both sides to get 4x = 2. Divide by 4 to get x = .
2
This is an excellent time to turn on your calculator. If 48,000 people live in Town X and each household has 3.2 people, you can determine the number of households: 48,000 ÷ 3.2 = 15,000. And since
each household has 1.2 televisions, you can now determine the number of televisions: 15,000 u 1.2 =
18,000.
3.
C
4.
B
From the statement, you know that flour is necessary to make the cookies. You don’t know that flour
is the only thing necessary to make the cookies. For example, you may also need sugar and eggs. You
cannot conclude A or E, because there may be other reasons for not making the cookies (maybe you
didn’t feel like it, or maybe you were out of sugar). Choice C is not necessarily true because there may
be other things necessary besides flour. Answer choice D contradicts the original statement. Choice B
must be true because you couldn’t have made the cookies without the flour.
5.
B
Start by plugging in what you know into the function given. If f(x) = x 2 – c, and f(–2) = 6, then plug
in –2 for x in the function: f(–2) = (–2)2 – c. Solve and replace f(–2) with 6: 6 = 4 – c; 2 = –c; and
c = –2. If you picked answer choice A, you forgot that (–2)2 is positive 4, and if you picked answer
choice E then you forgot about the minus sign in the original function.
6.
A
First solve for b. If 9b = 81, then b must equal 9. Insert 9 for b into
9 3 3 9 = 3 3 27 = 3 3 = 9
3 | Sample Cracking the SAT Practice Tests
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Sample Cracking the SAT Practice Tests
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4 | Sample Cracking the SAT Practice Tests
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ANSWER EXPLANATIONS FOR PREVIOUS PAGE
1.
A
The clues to prevent household fires and flammable liquids make flammable a good word to recycle for
the blank. A comes closest to this meaning. B, C, and D are unrelated. E means the opposite of the
word needed.
2.
E
The semicolon is a same-direction trigger. Because Mark hates mistakes, he will review his papers
“carefully.” We can immediately eliminate B, C, and D. E means “very carefully.” If you weren’t sure
what A meant, you had to guess. Give yourself a pat on the back if you guessed rather than leaving
the question blank. Even if you got the question wrong, you did the right thing. And in the long run,
that’s how your score goes up.
3.
B
The clue for the first blank is defends and the trigger word is nor. A good word to use for the first blank
will be one that is the opposite of defends, such as “disagrees with.” This eliminates D and E. Now
look at the second blank. According to the first part of the sentence, Jenkins doesn’t do anything positive or negative, so a good word for the blank is “neutrality.” This eliminates A and C.
4.
A
Great thinkers must have “great” insights, so the first blank is a positive word. The clues here are voiced
so often and mere, which indicate something trivial or unimportant. Things that are voiced often can
be called “repetitions,” or some related negative word. The word ironic also suggests that the first and
second blanks contrast in meaning. The only choice that has a positive word followed by a negative
word is A. Remember to use POE to avoid words you don’t know. Because beliefs is not negative, you
can eliminate B, even if you do not know what banal means.
5.
A
The clue is been taught to communicate, and the trigger word but indicates that the skeptics doubt this.
So the skeptics must be arguing that the apes have not really been taught; they may be “mimicking”
(aping!) their trainers. A is the best choice. Even if you don’t know what A, B, or E means, you should
be able to use POE on C and D, and then guess.
6.
C
The clue is technical difficulty and challenging counterpoint, so good words for the blanks are difficult
and complex, which agree with each other. This eliminates B and D, as both contain answers that disagree with each other. You can eliminate A because diminutive means small. Although inscrutable in E
means “difficult to understand,” the word classical does not mean “difficult” or “complex.”
7.
D
Both the first and second blanks are somewhat negative words. E is the only bad guess, since it doesn’t
make much sense to view a situation as political and be perplexed by it. A, B, C, and D are all good
guesses because at least one of the words is somewhat negative. Guessing one of these choices would
have been better than leaving the question blank. If you look closely, you’ll notice that the trigger
since tells you that the two blanks must be similar to each other. Eliminate A, as there is no evidence
for how obscure or “little known” their situations are. B is close, but bellicose means “prone to fighting,” which is not supported by the sentence. Eliminate C, as sanguine means “confident and positive,”
which does not agree with acute and is not negative.
8.
D
The clues in this sentence are ancient ruins of marvelous bygone civilizations and sad. What is sad about
looking at the ruins of ancient civilizations? Seeing that, you can gather that human greatness doesn’t
last. This idea is reinforced by the time trigger—if an ETS sentence completion compares past and
present, it is usually to show a change. Therefore, you can put “doesn’t last” in the blank, and the best
match is transience.
5 | Sample Cracking the SAT Practice Tests
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Print and try these sample questions and review the detailed answer
explanations from our flagship Cracking series!
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explanations from our flagship Cracking series!
ANSWER EXPLANATIONS FOR PREVIOUS PAGE
3.
E
If the area of square A is 16, the length of each side is 4, and the perimeter is 16. You are told that this
2
is 3 of B’s perimeter, which you can calculate:
2
x = 16
3
x = 16 ×
3
= 24
2
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2
x = 24
3
x = 24 ×
3
= 36
2
If the perimeter of C is 36, each side is 9, and the area of C is 92, or 81. If you chose B, you need to
read the question more carefully.
4.
E
According to the ratios given, you know that the mixture contains more wheat than rye; there must be
more than 5 pounds of wheat. So let’s eliminate A and B. Use the Ratio Box.
Corn
Wheat
Rye
Total
3
5
2
10
2.5
2.5
2.5
2.5
7.5
12.5
5
25
Because there is a total of 5 pounds of rye, the multiplier is 2.5. This allows you to solve for 12.5
pounds for the wheat.
5.
C
Because 135q is one of the middle angles of the circle, the triangles must each have a 45q angle, and are
therefore both identical 45°-45°-90° triangles. Remember (or check the front page of the test) that the
ratio of the sides in such a triangle is x : x : 2 x . You know that the diameter of the circle is 12, so the
hypotenuse (which is equal to the radius of the circle) of each triangle is 6. If 6 is the long side, the other
6
. Now you can find the area of one of the triangles and double it. The
side of each triangle must be
2
6
1 6
6
36
1
×
=
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. So ×
area of a triangle is bh , and both the base and height are equal to
2
2
2
2 4
2
have found the area for one of the triangles, so double it to get 18, or C. Another way to solve this is to
use the side of your answer sheet as a ruler and ballpark. If XZ = 12, the hypotenuse of each triangle is
6. Now mark off the length of 6 with your homemade ruler and compare that to a side of one of the
triangles. You can guesstimate that the side is about 4. Using that approximation, calculate that since
the base and height of both triangles is 4, the area of each triangle is
1
× 4 × 4 = 8 . The area of both
2
triangles together is 16, which is closest to 18, or C. ETS wants you to do complicated geometry, but all
you care about is finding the answer.
6.
A
Translate each statement, piece by piece. The first part tells us that “ the product of x and y is 76.”
Since product means multiplication, then the first equation must be xy = 76, so you can eliminate
answers C and D. The second part says that “x is twice the square of y,” which translates to x = 2y2, so
eliminate answers B and E, and A is the only answer left. Notice that only the y needs to be squared,
which is why B is wrong. The second equation for B would be written as “the square of twice y,” which
is not what the problem stated.
7 | Sample Cracking the SAT Practice Tests
Sample Cracking the SAT Practice Tests
Print and try these sample questions and review the detailed answer
explanations from our flagship Cracking series!
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8 | Sample Cracking the SAT Practice Tests
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Print and try these sample questions and review the detailed answer
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9 | Sample Cracking the SAT Practice Tests
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Sample Cracking the SAT Practice Tests
Print and try these sample questions and review the detailed answer
explanations from our flagship Cracking series!
ANSWER EXPLANATIONS FOR PREVIOUS PAGE
1.
C
All versions of the underlined phrase except C are wordy or awkward.
2.
B
If something has been happening for the last two thousand years, it shouldn’t be discussed in the present or future tense. Eliminate A, D, and E for that error. Building technologies continue to change, so it
would be better to use have changed rather than had changed. Had changed implies that the technologies will no longer change.
3.
A
The sentence is correct as it is written. B and E rewrite the verbs in -ing form, not the first choice for a
clear sentence. C eliminates the cause-and-effect relationship present in the original. D adds the word
it, which makes the sentence a run-on.
4.
D
D uses the correct idiom, belief that. Both A and E use an incorrect idiom, belief of. In B, the first is is
unnecessary and makes the sentence awkward. C adds another unnecessary word, which.
5.
A
There is no error in the sentence as it is written.
12. B
Plural nouns must refer to plural nouns. There are two characters so they cannot be an orphan; they
would be orphans.
13. E
There is no error in the sentence as it is written.
14. A
This sentence confuses subject with object. Because the speaker is the subject, me should be changed to I.
15. A
An adverb, completely, is needed to modify the verb exhausted.
16. A
To correct the error in subject-verb agreement, change is to are because benefits is plural.
17.
D
D creates an error in verb parallelism. The verbs in the list, listening and reading, do not agree with she
practiced. It should be practicing.
18. D
This sentence misuses an incorrect comparison modifier. Because more than two jingoists are mentioned (all), change more to the superlative most.
19. E
There is no error in the sentence as it is written.
20. C
The verbal phrase brushing your teeth acts as a singular noun (you could replace this phrase with it),
which requires the singular verb promotes.
10 | Sample Cracking the SAT Practice Tests