Cracking the SAT

Part VII

SAT Practice Tests and Explanations

Chapter 26

Answers and Explanations for Practice Test 4

  1.  B  Although all three parts of 3x + 9y + 12 are divisible by 3, the expression 3(x + 3y + 4) is not among the answers, so your best bet is to try each of the answers. A is out, because if 3 is factored out of the expression, The last number should be a 4, not a 9. Putting brackets around only part of the expression, such as (3x + 9y), does not change the value of the entire expression. Since (3x + 9y) +12 = 3(x + 3y) + 12, B is correct. You’re done! There is no need to try out any further answer choices.

  2.  C  Take this word problem in bite-sized pieces. We want to find the total cost of the order of 12 boxes of books. First multiply the total number of boxes by the price of 1 box: 12 × $4.95 = $59.40. There is a $7.00 service fee for the order, so $59.40 + $7.00 = $66.40.

  3.  B  On this question you can use Plugging In The Answers. The numbers in the answer choices replace the f(x) portion of the equation, so you can just write out the rest of it, , next to each to see if it can be true. Starting with C, if , then = 3x – 2, and x = . Since C works, eliminate A—we know it’s not true. You can also eliminate D and E because we are looking for the smallest number that works for f(x). Now let’s try B: If 0 = , then 0 = 3x – 2, and x = . is bigger than , so cross out C. B is correct.

  4.  B  To find out how many cars the 9th graders washed, take the Funds Raised and divide by the Price per item in the row for the 9th graders. , answer B.

  5.  A  First find the number of cookies sold by 10th graders, again dividing Funds Raised by Price per item. . Now find the number of cookies sold by 12th graders: . Now subtract to find out how many more cookies the 10th graders sold: 180 – 120 = 60, answer A.

  6.  C  This is a multiplication problem, so to find C we need to find out what digit times 6 results in a product that ends in 8. The multiples of 6 that end in 8 are 18 and 48. If C is 3, then 6 × 3 is 18, and we carry the 1. The C in answer 94C8 also must be 3: 6 × 7 = 42, plus the 1 we carried, is 43. This gets a 3 into the C spot, (using 8 as a multiplier does not lead to an 8 in the C spot in the product). Now we need to find the value of D. Since we are carrying the 4 from the last multiplication, 6 × D must result in a product of 0. Only 6 × 5 = 30 fits, so D = 5. Finally, find the sum of C+ D: 3 + 5 = 8, answer C.

  7.  A  Arc RST is half the circumference of the circle. Finding the radius is key to any circle question. The question states that the area of the shaded portion of the circle is 25π and is of the circle, so we know that the whole circle has an area of 9(25π) or 225π. Now we can use the area formula to get the radius: πr2 = 225π, so r = 15. The formula for the circumference of a circle is 2πr, so the circumference of the whole circle is 30π, and since arc RST is half the circumference, its length is 15π, answer A.

  8.  B  Here is a chance to use Plugging In The Answers. Start with the middle value in C and see which makes the equation true: It is not possible for x to be 0, because 02 – |0| ≠ –6. The larger values don’t equal –6 either: D gives 0 while E gives positive 6. B is correct: (–2)2 – |−10| = 4 – 10 = –6.

  9.  40 Divide both sides of the equation by three to find that (y – 2) = 8. There’s no need to find y, since we need only to find five times the value of (y – 2). Multiply both sides of the equation to find that 5(y – 2) = 40.

10.       or .666 or .667

Out of the 12 tomatoes, we know 4 are rotten, but the question asks for the probability of choosing a not rotten tomato. If 4 tomatoes are rotten, 8 must not be rotten so the probability is . You could grid in the fraction as is, reduced to , or transform it into a decimal.

11.  3,072 Because the t in represents the number of months, we cannot use the 2 years time frame given in the question in place of t. The colony has been growing for 24 months, which is evenly divisible by the 3 in the fractional exponent. The equation is much easier now that the fractional exponent is gone. .

12.  15 We can’t find the value of y without first finding the value of x. A straight line is 180°, so 5x + x = 180, and 6x = 180. Divide both sides by 6 to find that x = 30. Vertical angles are equal, so 2y = x, or 2y = 30, so y = 15.

13.  0 or 5 Translate this word problem into math: . Simplify to 2x2 = 10x, then x2 = 5x, and finally x = 5. There is another possibility: If x is replaced by 0 in the equation at any stage, it creates a true equation. .

14.  10 Here is another translation problem. The first sentence can be translated to b = c + 9, the second sentence as c = a + 4, the third sentence as d = a + 3. The question at the end is really asking for the value of bd. Plug in a value for a in the third equation and it will give the value of d that we need. If a = 2, then d = 2 + 3 = 5. Use the same value for a in the second equation to find a value for c: c = 2 + 4, so c = 6. Plug this into the first equation to get the b value we need in order to find bd. b = 6 + 9 = 15, so bd = 15 – 5 = 10.

15.       or .9

This is a rate question, so we can use the formula . Putting the information for Jeanine’s trip to work into this form gives 40 = . Isolate t to find that t = so t = . Coming from work, Jeanine drives faster, so the rate is different, but the mileage is the same: 50 = , so t =, and t = . Add the two together:

16.  15 A line that is tangent to a circle forms a 90° angle with a radius or diameter. Radius and line form the legs of right triangle ABC, and the hypotenuse is . We know that AC = 10, and that AB = , or one-half of AC, so AB = 5. When the hypotenuse is twice the length of the shortest side, we have a 30-60-90 triangle. The ratio of this special right triangle (as shown in the front of every math section on the SAT) is x : x : 2x, where x is the length of the side opposite the 30° angle. So BC = 5 × = 5 × 3 = 15.

17.       or 9.5

Use an average pie every time the question uses the word average. In this case we end up with the following average pies that use the information in the question:

We need an average pie for the first six numbers. The six numbers’ average is 15, so the total of those six numbers is 15 × 6 = 90. The last six have an average of 4, so the total of those six numbers is 4 × 6 = 24. Now take the two totals and add them together for the final mention of the wordaverage. The total for all 12 numbers is 114, so to find the average, divide 114 by 12, which gives 9.5. You could also reduce the fraction , since numerator and denominator are both divisible by 6, to .

18.       or 2.4

Write the information from the question onto the figure given:

CD = 6, so AB = 6 because ABCD is a rectangle. Since the area of the rectangle is 120, we can find the length by using what we know in the area formula. Area = lw, so 120 = l(6), and 20 = l. Side AD = 20, and we know that AE = 12, so ED must equal 8. Now we have enough information to find the length of . The perpendicular means that triangle ABD and triangle EFD are similar, so their sides are in proportion to each other: , so 20 × EF = 48, and EF = 2.4 or .

  1.  D  The words their offspring indicate that the instinct must be about how these fish care for their young. The word “parental” is a good word for the second blank, which is pretty close to the second words in D (nurturing) and E (maternal), but not A, B, or C. Because the fish lack this instinct, we need a negative word for the first blank, which describes how the fish treat their offspring. Only spurn and devour are negative, and the second word in A does not fit; only the words in D match the meanings of both blanks.

  2.  E  The trigger and indicates that two similar ideas are connected, so the first blank must mean something like stop production. Only E, recall, works well in the blank. But wait! Don’t just bubble in E right away; make sure that the second word works too, because a word for the blank that is too narrow might eliminate the correct answer. The second blank describes the useless inventory which they could not distribute. The company must have had “a lot of” inventory, and an abundance is indeed a match.

  3.  B  The word yet indicates a relationship that is opposite or unexpected. Every previous attempt to get rid of the mayor failed, and these attempts are the impeachment efforts. The continuous failure should stop the critics from trying any more, but the yet means that we need the opposite of stop, something like “continued.” A, foundered, is a synonym for failed. B, persevered, means “persisted, maintained, or continued steadfastly,” a good match. C and D mean the opposite of continued. D, condensed, does not relate at all to the sentence. B is correct.

  4.  A  The word whether tells us that Jerome has a decision to make. He needs to “figure out” whether one thing or another is the truth. Eliminate C and D; these are not close to “figure out.” There is some tough vocab in the answers: A, ascertaining, means “finding out definitely” which is the closest match. In B, exonerate means “to free from blame.” In E, importuning means “begging.”

  5.  B  The trigger Even though tells us that the sentence contains an opposite relationship between the way Lodge’s opponents felt about one aspect of Lodge and the way they felt about another aspect. We get a better clue for the second blank in the sentence: The phrase eloquence and persuasiveness indicates positive qualities in a speaker. Eliminate A, D, and E, which all have negative words in both blanks. We need a negative word for only the first blank, and “opposed” fits well with opponents. We can get rid of only C and D, but that leaves just B as a good match for both blanks.

  6.  E  This question is asking “Why does the author mention the Patent Office?” Eliminate A; it doesn’t mention anything about not issuing patents to outside influences. B is out because slaves are not discussed in this part of the passage. C is the opposite of what we are looking for, which is that others did make contributions, but could not be acknowledged. D is not correct; the people were purposely left off the patent. E is the best paraphrase of the information in the passage.

  7.  B  B is correct because the author of Passage 1 believes that others (including Greene) contributed to the development of Whitney’s cotton gin. Choice A is quite appealing, but the author of Passage 1 did not actually make such a statement, so it must be eliminated. Both C and E contradict what the Passage 1 author states. The comparison in D is not made.

  8.  B  B is correct because the author of Passage 2 referred to earlier models (such as the roller gin) as inept. Both A and E contradict what the Passage 2 author stated. There is no support for C or D.

  9.  C  An inference question on the SAT still needs to be proved by evidence you can find in the passage. In this case, we need to find evidence in both passages for an answer to be correct. A and E are out because roller gins is only in Passage 1. Eliminate D because it is not mentioned in either passage. Eliminate B because only Passage 1 mentions slaves. Only C is represented in both passages.

10.  A  We need to find out what the author did before the teacher arrived. At the end of the first paragraph we read that the author’s state of mind for weeks was anger and bitterness, replaced by a feeling of languor, or laziness. This is best paraphrased by resentment and inactivity in A. There is no indication that the author was unloved, as in B. C may be tempting, but the author states that she did not knowwhat marvel or surprise was in store for her, but that does not mean that she did not expect anything good ever to occur in her life. There is no evidence for D in the passage. The passage indicates that she was sentimental and tender in the description of the familiar leaves and blossoms, so E is out.

11.  C  This is a Vocab In Context (VIC) question, so you should treat it like a sentence completion. Go back to the passage, cross out the word described, and fill in your own word based on the context of the passage. In this case, a good phrase for the blank is “came after.” The only answer choice that is close to “came after” is followed, in C. Choice A is tempting, because it is a definition for succeeded, but does not fit this context. Whenever a VIC question asks you about a commonly known word, such as succeeded, the primary meaning of the word is almost always a trap. B may be tempting because of the two distinct moods described, but split does not fit as a replacement for succeeded in the sentence.

12.  D  We need to find out how the author felt, so go to the passage and read the section of the passage near the analogy to find evidence of her feelings. In lines 13–20 she feels shut in, tense and anxious and has no way of knowing how to find her way. Choice A may be tempting becausescared is a good match, but sinking is not mentioned in the analogy. There is no evidence for anger in B. The word adventurous in C is too positive a spin of the author’s description. D is correct because lost fits the situation of having no way of knowing one’s position. E is incorrect because this part of the passage describes a time before the teacher came.

13.  C  This question is really asking, “What does finger play tell us about the author?” The phrase describes the author’s desire to imitate her teacher’s movements, but in lines 32–33 she describes that she didn’t know she was spelling a word. There is no mention of words in A. The author is just learning that words exist: The word grammar is not mentioned in the passage so eliminate B. C is a good paraphrase of the description in the passage. The author did not yet understand that she was using language, so D is out. E is too extreme.

14.  A  The sentence that depicts the author breaking the doll states that the author became impatient at her repeated attempts, and then describes breaking the doll. In A, frustration matches the feeling of impatience. There is no evidence in the passage for any of the other answers. E may seem close, but enraged is a different emotion from impatience. The word frustration is a much closer match.

15.  C  When the SAT gives quotes to match to the question, be sure to read the quotes in context and not just rely on how they sound. When Keller realized the significance of the spelled out W-A-T-E-R, she came to understand the mystery of language. The quote in C describes her feeling when this happened.

16.  C  The experience in lines 28–34 is imitation without knowing. Later in the passage lines 57–61 describes the moment that the author really understood what language was. The answer that best matches “imitation” and “understanding” is memorization and comprehension in C.

17.  D  The passage states that the author was keenly delighted when she broke the doll. Eliminate A, C and E because none of those answers have a first word that is close to delighted. After the author’s breakthrough in language, she feels repentance and sorrow. This matches the second word in D, regret. B is out because disgust is too strong.

18.  B  The question is asking “What’s the narrator’s view on language?” The lead word language turns up in line 59, and is part of a description of how the author finally connected words to the sensations and objects around her. The passage states that when the mystery of language was revealed to her, it awakened her soul and made her eager to learn about her environment. The author definitely feels that language has affected her in a positive way, so eliminate A: The word impractical is the opposite of the author’s feelings. B is correct because she had a new interest in theworld around her when she realized that each thing had a name. The passage is about the authors awakening to understanding language, not a mystery, as in C. Eliminate D because only is extreme. E is the opposite of what is stated in the passage.

19.  D  This question is asking about the primary purpose of the passage. What is the author’s goal in writing the passage? A is a detail, not the primary reason for the passage. While the classification is described as a bold step, the main idea of the passage is not to encourage bolderclassifications, so B is out. The ignorance mentioned in C is contradicted by the passage, which describes a lot of knowledge about the life forms. D is correct. The concept of abundance of undiscovered life forms is supported from the blurb at the top (not an unusual occurrence) and is supported throughout the passage in phrases such as glutted with new species. The new phylum is the Naniloricus mysticus. There is no approval as in E.

20.  C  The first paragraph describes, in part, how the new animal appears; the phrase ambulatory pineapple is a good way to summarize that description. Thus, C is the answer.

21.  E  Lines 14–15 describe how the Naniloricus mysticus is anatomically distinct enough to be its own group. Only E, physical characteristics matches anatomically.

22.  B  Choice B is correct because the author states that the phylum to which Nanaloricus mysticus is assigned is now a larger group, since about thirty other species have been discovered. The remaining choices find no support in the passage.

23.  E  The word inferred tells you that the author did not directly state the right answer but gave you enough information to draw a conclusion. On inference questions, look for an answer that you can definitely support with evidence in the passage. Only E is supported by the passage, because the myth is that scientists get excited about new species: The reality is that museums are glutted with too many new species. A goes against common sense. There is no evidence for evolving as in B. C is true, but not mentioned in the passage. D is the opposite of what is stated in the passage.

24.  A  The question is provided in the context of the author’s statement that scientists don’t have time to describe more than a small fraction of the new species pouring in each year, indicating a rapid pace of new discoveries. Thus, A is correct. The remaining answers are not supported and, in the case of C, too strong.

  1.  B  The word whether indicates a choice between two options, but the sentence as written is unclear about what the second option would be. Since tremendous destruction is caused, the common whether … or not construction is not appropriate. Changing the word to when, as in B, clarifies the sentence. C changes the meaning of the entire sentence; D and E are both passive and awkward.

  2.  D  The adverb where is only used for specific, physical locations. It cannot be used with Lincoln’s … life. The film is about Lincoln’s life, as seen in D. Any additional words between are unnecessary and cause other errors.

  3.  A  The sentence is correct as written. The list of actions is in parallel form. B and D are not parallel, C changes the meaning and E is wordy.

  4.  E  The sentence as written is incomplete. It lacks a verb in the portion of the sentence after the semicolon, which must be able to stand on its own as a sentence. B indicates that the grass walked—not possible! C creates an unclear, incomplete sentence. The comma in D sets off an incomplete thought. Only E replaces the ing words from the original with verbs that make the sentence complete.

  5.  E  In the sentence as written ringing is not parallel to the verbs declared and sent. In B the verb ring is in the present tense. In C being makes the sentence too wordy. D becomes unclear, and had rung is the incorrect tense. Only E uses the correct tense rang without adding any other errors.

  6.  C  The sentence as written is choppy and the adverb clearly should modify a verb. B contains a subject-verb agreement error between was and promises. C is correct because clearly modifies the verb be. In D it is unclear what clearly is supposed to be modifying.

  7.  A  The sentence is correct as written. There is an ambiguous pronoun it in B, and the rest of the answers rearrange the elements of the sentence in ways that make the sentence unclear.

  8.  A  The sentence is correct as written. B is wordy, C is not parallel to the other parts of the sentence. D uses being, which usually makes a sentence unnecessarily passive and wordy, as it does here. E creates an incomplete sentence.

  9.  C  Any ing construction, such as building is not as active as ETS prefers, so you can probably cross off A, B, and E right away. While what follows despite, in D, is a contrast; it should not be the vocalists themselves, but an opposite action to strive that should be set up as the contrast. B also contrasts strive with vocalists, and are building is not parallel with the verbs in the rest of the sentence. C is correct because but is the correct conjunction, build is parallel to strive, and the sentence is more active. The repeated use of or is inappropriate in D. E sets up vocalists as the contrast and uses building rather than the active build.

10.  D  The lack of punctuation between wartime and furthermore creates a run-on sentence. Each part could stand on its own as a sentence, so they should be joined by a semicolon, as in D. B and C use it’s which means it is rather than the necessary possessive pronoun its. A comma is not strong enough to link two complete sentences, so E creates a comma splice.

11.  B  The sentence as written contains a subject-verb error. The subject of the sentence is Wendy. The other people mentioned in that part of the sentence, John and Michael, are enclosed by the two commas in a phrase that is non-essential to the sentence. B uses the correct verb flies without adding any errors to the sentence. C uses the wrong verb tense. In D besides should link the children and Peter Pan, and flying creates an incomplete sentence. E uses flies, but creates a plural subject by listing all three children.

12.  A  The preposition for in A creates an idiom error. The correct idiom is jealous of.

13.  D  The word no creates a double negative and disrupts the parallel structure in the list of what was not packed.

14.  C  There is an agreement problem in the sentence: The plural some does not agree with the singular the other, which should be the others.

15.  C  There is a parallelism error. The phrase in C should be in the same form as designers of shoes so designers of purses would be the parallel way to phrase C.

16.  E  There is no error in this sentence.

17.  C  The action of adding spices is singular, which is not in agreement with the plural verb make. The verb should be makes.

18.  E  There is no error in this sentence.

19.  A  There is an idiom error in A, which should read should have. This may be a tricky question because in speech, the contraction should’ve often sounds like should of.

20.  C  There is an agreement problem with the pronouns in C. The pronoun she is a subject pronoun while him is an object pronoun. Because “they” were the perfect couple, both pronouns should be subject pronouns, as “they” is.

21.  E  There is no error in this sentence.

22.  C  The sentence is discussing a future time next week. The verb in C is incorrect because has spent is in a tense for an action that happened in the past and is continuing into the present. It should be will have spent.

23.  B  There is a parallelism error in the sentence because of the pronoun they. To be parallel with be and have, B should simply read provide.

24.  D  There is a pronoun agreement between the singular it and they in D. A country is singular.

25.  D  The use of having in D creates an idiom as well as a parallelism error. The construction should be “To x is to y.” D should be to have.

26.  A  When referring to people, the pronoun which is incorrect; A should be who.

27.  A  When the eitheror construction is used, we need a singular verb, because we are referring only to Jack or Ashlee but not both. The plural verb are in A should be is.

28.  B  There is a subject-verb agreement problem between the singular the Weimaraner and the plural verb have in B.

29.  A  The adverb where should be used only for physical locations. The sentence refers to time, so A should be when it.

30.  B  A paragraph break would best be added between sentences 4 and 5 because sentences 1–4 describe the sanctuary itself, while sentences 5–12 describe the birds that are treated at the sanctuary.

31.  A  The word besides means “furthermore,” while beside refers to a physical location next to or near something. This second meaning fits with the context while the first does not, so A is correct.

32.  E  A contains an ambiguous pronoun it. The contrasting relationship indicated by and yet in B does not fit the context of the sentence. C is unclear. The lack of tries makes D too absolute. E concisely combines the two sentences and retains the original meaning.

33.  B  Go to the passage and see what happens when each pair of sentences is switched. B is the best option, because as is, the pronoun this in sentence 9 does not refer to anything in sentence 8, but if sentences 9 and 10 are switched, this would refer to the situation of the caged birds. Sentence 9 also explains why the birds are in cages. The rest of the pairs of sentences are in proper chronological order.

34.  C  Answer C best combines the sentences because it uses even though to link the idea of the birds that had been shot to the legality of shooting birds. The conjunction despite does not fit the relationship between the phrases. In B shot by cars makes little sense. There is an incomplete sentence after the semicolon in D. E contains an ambiguous pronoun it.

35.  A  Of the sentences listed, all provide essential information in the passage as it is written except sentence 10. Its information is redundant with that in sentence 11. As mentioned in the explanation for question 33, the unsupported this in sentence 9 is a problem, and switching 9 with 10 fixed that error. However, placing sentence 9 after 11 would fix the issue in 9, and make sentence 10 completely unnecessary.

  1.  C  Translate the words into math: 7 × n = 84, and we want to know the value of 4n. 7n = 84, so n = 12, and 4n = 48, answer C.

  2.  E  Out of the initial 16 gallons, 4 are removed, so 12 gallons remain. The fraction can be reduced to , which is 75%, answer E.

  3.  D  We can use PITA for this question. First use C, 0.33, for t. If we must add t to each of the four values, we will have 4t. 4 × 0.33 = 1.32. When 1.32 is added to the sum in the question of 2.74, the total is 4.06, which is less than the 4.22 we were looking for. Eliminate A, B, and C and try a larger number. In D, 0.37 × 4 = 1.48, and 1.48 + 2.74 = 4.22, just what we were looking for.

  4.  B  Because the triangle is equilateral, and each of the three sides is cut in half, all of the short segments in the triangle are equal. This means that all four triangles within the larger triangle are equilateral and congruent. Since one of the four triangles is shaded, the shaded area is of the area of the larger triangle. × 24 = 6, answer B.

  5.  E  Only s is equal to a number without a variable, so plug that into the equations in the question. The value of s is negative. The variable r is positive, because r = −, and when − takes the place of s, the negative signs cancel out: and r = 4. Because r is positive, q is negative:q = − becomes q = −. Finally, because q is negative, p is positive: p = −, then and p = 4.

  6.  C  First find the value of x: 27 divided by 3 is 7, with 2 left over, so x = 2. 2x = 4 so divide 23 by 4: 4 goes into 23 evenly 5 times and there are 3 left over, so the answer is C, 3.

  7.  A  This is a great Plugging In question. Make d = 2, so the first 10 hours cost $2.00, and e = 3, so service costs $3.00 an hour. Pick a number above 10 for h to make your math easier: If h = 20, it can be split into two parts: The first 10 hours cost $2.00, and the second 10 hours cost 10 × $3.00 = $30.00. Altogether that’s $32.00, the number we’re looking for in the answers. Plug in the values for d, e, and h. The expression in A becomes 2 + 3(20 – 10) = 2 + 3(10) = 32. A works, but always check all the answers just in case: B gives 602, C gives 80, D gives –480, and E gives 640. A is correct.

  8.  E  In the graph, y is always positive. E is correct because absolute value is always positive. One way to answer this question is to plug in points from the graph into the equations in the answers. Using point (1, 2), A works because 2 = 2(1). Eliminate B because 2 does not equal 11; also, because of x2, this is a parabola, not a line. Although the point works in C, 2x2 indicates a parabola, so eliminate C. Eliminate D because 2 does not equal 1 – 2. In E 2 = 2 does work. Now try the other point from the graph just on equations A and E. A is out because 2 does not equal –2.

  9.  256 To solve this equation, get by itself. = 16, so square both sides: ()2 = 162, so x = 256.

10.  1 or 9 List the numbers described: All the odd integers from 0 to 10 are 1, 3, 5, 7, 9. Of these numbers, 3, 5, and 7 are prime, leaving only 1 or 9.

11.  2  Because the two triangles have the same area and each have a base with length 5, their heights must be equal as well. For a triangle, Area = bh. The bottom triangle has a height of 5 because the base is on the x-axis and the tip is at –5. This means that t = 7 – 5 = 2.

12.      52, 59, or 66

One way to solve this problem is to plug in numbers for j until you get a result that is between 50 and 70. Another way is to list the multiples of 7 that are close to the range given, such as 49, 56, and 63, and add 3 to each one, which gives 52, 59, and 66 respectively. Any one of these three numbers will get you the credit for the question. You need to come up with only one possible value.

13.  148 Use Fred’s Theorem: A line crossing two parallel lines creates big angles and small angles. The big angle that matches y is split by a line perpendicular to d and e. The big angle is 58 + 90 = 148, which is also the value for y. Another way to solve this is to find the third angle of the triangle: 180 – 90 – 58 = 32. The 32° angle and the y° angle make up a straight line, so 180 – 32 = 148.

14.  15 We need to find the cost of a single share of stock x. Of the nine people, 5 bought a share each, so if cost = c, then that is 5c. There are also 3 people who each bought of a share, so that’s 3(c). There is one more person, who bought of a share. Since the club spent $114, we can create the equation . This simplifies to . Multiply both sides by to get c by itself, and c = 114() = 15.

15.  4  First simplify the equation 4xn2 = 4x+1 • n, to 4xn = 4x+1, then plug in. If x = 2, then 42 • n = 42+1. Since 16n = 43, then 16n = 64 and n = 4.

16.  12  Plug in the value we are given for x into the function. . Now we can solve for all possible values of a as the question asks: , and the fraction can be further simplified: . Since a2 + 12 = –7a can be rearranged into a quadratic equation, we can find two possible values for a: a2 + 7a + 12 = 0, so (a + 3)(a + 4) = 0, and a can either be –3 or –4. The answer is 12 because we need the product of the possible answers and (–3)(–4) = 12.

17.  118  Based on the numbers for the 1996–1997 academic year and the percents shown in the graph, the 500 students are broken down into the following groups:

In the 1997–1998 school year, there were 20 more students, for a total of 520. The percent of students studying Japanese is now 10% of this, so there are 52 Japanese students and the same number of Spanish, Latin and German students as in the previous year. The number of French students (f) is the only unknown now: 520 = (52 + 200 + 100 + 50) + f , and 520 = 402 + f, so f = 118.

18.  20  This is a pattern question in disguise: Write it out, and be methodical! For the four spaces for digits, the first can be only 1, the second could be any digit 0 through 9, the third can be only 0 through 5, and the last digit can be any digit 0 through 9. When the last two spaces have the highest possible digits, showing :59, if the hour is 5 or below, the total is less than 19. This includes the hour of 12, because the hour does not count as 12, it is 1 + 2 = 3. In the next hour, the digits in 6:59 add to 20. In the next hour, the digits in 7:59 add up to 21. If the middle digit is one less, 7:49 adds up to 20. If instead the last digit was one less, 7:58 also adds up to 20. In the 8 o’clock hour, we have, 8:39, 8:48, 8:49, 8:57, 8:58, and 8:59. In the 9 o’clock hour we have 9:29, 9:38, 9:39, 9:47, 9:48, 9:49, 9:56, 9:57, 9:58, and 9:59. There will be none in the 10 or 11 o’clock hours because their hour digits add up to 1 and 2 respectively and are too small. Count up the times that work: There are a total of 20 times during the 12 hours that add up to 20 or more.

  1.  E  Of the 6 shelves of the bookcase, one shelf has 20 books and the rest have 30 books each. 20 + 5(30) = 20 + 150 = 170, answer E.

  2.  C  The question gives the value for c, so we know that b = = 6. Since a + b = 14, then a + 6 = 14 and a = 8, answer C.

  3.  B  For $15, Karim could buy 5 packs of either type of card. Baseball cards are 10 to a pack: 5 × 10 = 50 baseball cards. Basketball cards are 12 to a pack: 5 × 12 = 60. The difference between 50 and 60 is 10, answer B.

  4.  A  Translate this problem into math and solve. The number of trucks times the number of cartons times the number of boxes within the carton is equal to the total number of boxes: 5k × 60 = 900. Now solve for k: 5k = 15, so k = 3. You could also use PITA (Plugging In The Answers).

  5.  D  To solve this problem, use percent translation. The first part of the sentence translates to p = 700, and p = 2000. Now use the value for p and translate the last part of the question: × 2,000 = 800, answer D.

  6.  D  Use Bite-Sized Pieces with a wordy question like this. To paraphrase, the question states that total cost = (food cost × number of people) + (hourly cost × number of hours). We are given the total cost of the food, so we don’t need to use the number of people we are given. We are also told the hourly cost in the question, but need to find the difference in cost for a two-hour and a four-hour party: 200 + (50 × 2) = 300 and 200 + (50 × 4) = 400, so there is a difference in cost of $100.

  7.  B  We’ve got some quadratic equations here. The expression a2 – b2 can be factored into (a + b)(ab). The question tells us that ab = 7, so we can replace that quantity in the factored equation: (a + b) × 7 = 119, so a + b = 17. We need to find the value of a, and we can use simultaneous equations. If we stack and add the equations, the b-values cancel out:

so a = 12, as seen in B.

  8.  D  The exponent outside the parentheses must be distributed to every part within. Remember MADSPM: An exponent outside the Parentheses is Multiplied by the exponents within. We end up with . This is not in the answers as is, but , which does match D.

  9.  C  We need to have all the quantities in the same form of measure, so convert both into inches. Brian jumped 14 ft., 9 in., which is (12 × 14) + 9 = 177. Mike jumped 2 feet further, which is 30 inches further: 177 + 30 = 207. Look at the answers—all of them mention the distance of 17 feet: 17 × 12 = 204 inches, which is 3 inches less than the total of 207. Mike therefore jumped 17 feet, 3 inches, as in C.

10.  C  Plug in the values from the chart! Use the pair (–3, –7) from the top of the chart and eliminate answers that are not true: A becomes –7 = –3 – 4, which is true. Keep it. B becomes –7 = –3 – 2, so since –7 does not equal –5, eliminate it. Keep C: –7 = 2(–3) – 1 is true. Get rid of D, which becomes –7 = 2(–3) + 2: –7 does not equal –4. Get rid of E: –7 = 3(–3) – 3. –7 does not equal –9. Now use another pair just to test A and C. Using (–1, –3), A gives –3 = –1 – 4, which is not true, so eliminate it, leaving only C. The values (–1, –3) work: –3 = 2(–1) – 1.

11.  D  Plug in on geometry if there are variables in the equation. In the figure, the angle marked a° looks bigger than 90° so make a = 150. The value of c should be something different, such as c = 140. Now we have information to figure out two of the angles of the triangle in which we findb. There are 180° in a straight line, so the angle on the left is 180 – 150 = 30 and the angle on the right is 180 – 140 = 40. There are 180° in a triangle, so 180 = b + 30 + 40, and b = 110, which is our target number. After replacing a and c in the answers with 150 and 140, respectively, only D equals 110. A gives 10; B gives –110; C gives 200; E gives 70.

12.  C  Each of the three expressions in parentheses could create a value that makes the equation equal 0. Check to make sure that the three parentheses each have a distinct value for m before you bubble anything in. In the first parentheses, if 10m + 8 = 0, then 10m = –8, and m = −. In the second parentheses, if 16m + 4 = 0, then 16m = –4, and m = −. Check the third parentheses: If 2m = 0, then m = 0. Those are three distinct values, so C is correct.

13.  B  This is a pattern question, so write it out: If the red marble lands in section 1, the possible red-blue pairs are 1 and 2, 1 and 3, 1 and 4, and 1 and 5. That’s 4 possibilities. If the red marble lands in section 2, the possible red-blue pairs are 2 and 1, 2 and 3, 2 and 4, and 2 and 5. We count all four pairs, because though it seems like 1 and 2 is the same as 2 and 1, in both cases we dropped the red marble first, and red and blue is a different arrangement than blue and red. If the red marble lands in 3, the possibilities are 3 and 1, 3 and 2, 3 and 4, and 3 and 5: another 4 possibilities. A red marble in section 4 will give 4 possibilities, and in section 5 will also give 4 possibilities. 4 + 4 + 4 + 4 + 4 = 20, answer B.

14.  B  Draw a figure if one is described in the question but not shown. In this case, we know a square lies in a circle, and the way we draw these shapes depends on what is in each of the statements above the answers. Since the question wants to know what must be true, try to draw a figure to disprove each statement. Statement I can be disproved with a drawing such as

Eliminate A, C, and E because they all contain I. B and D both contain II, so it must be true. Check out statement III. The circle above disproves III, so get rid of D. Only B can be correct. Skipping statement II saves time: To prove it true you’d need to make the biggest possible square inside the circle, such as

The diameter of the circle is the same as the diagonal of the square. If the diameter were 10, then the radius would be 5, and the area of the circle would be 25π. To find the area of the square, we can use the diagonal as the hypotenuse of a 45-45-90 triangle. The legs and hypotenuse have a ratio of x : x : x. In this case, the value of 10 = x. Solve for x to find the side of the square: . The area of the square is . This is less than 25π, which is a little over 75.

15.  E  To answer this question, list some cubes of integers and see whether any of the digits in the statements turn up: 23 = 8, so we know that statement III is true. Eliminate A, B, and C because none of them contain III. Both of the remaining answers contain I, so it must be true. We need to check only statement II. List cubes until a 6 comes up in the unit’s digit or until the unit’s digit begins repeating: 33 = 27, 43 = 64, 53 = 125, 63 = 216 so II is true. Pick E.

16.  A  Plug in! Come up with a list of three consecutive even integers, and divide by 6 to determine the remainder: 2 + 4 + 6 = 12. When 12 is divided by 6, the remainder is 0. If you are not sure, you can try with a different set of consecutive even integers: 10 + 12+ 14 = 36, and 36 is evenly divided by 6. The remainder will always be 0, answer A.

17.  E  The phrase in terms of means that this is a Plugging In question. The figure above the question is not drawn to scale, so redraw or add to the figure based on information in the question. Because and are tangent to the circle, they form a 90° angle with a radius or diameter of the circle. Draw in diameter and mark the right angles. Draw the diagonal of the rectangle . The question states that ∠COE = 120° so ∠COB = 60°. We have a 30-60-90 triangle, COB, in which is the radius of the circle and the shortest side of the triangle. Time to plug in! If r = 5, the sides of this special right triangle are 5 : 5 : 10. So CO = 10, which is half the length of CF, which must equal 20. Now plug in r = 5 in the answers: A results in 10π; B results in 10; C gives 10; D gives 20π. Only E has a result of 20.

18.  E  Convert the equation into the y = mx + b format: 5y = –2x + 10. Simplified, this is . The slope in this equation is −. A line that is perpendicular will have a slope that is the negative reciprocal of this, or . Right away you can eliminate B and C because their slopes are negative. Use points in the graph to find the slope of each answer. Eliminate A; it has points at (1, 0) and (2, 5), for a slope of 5—too steep. Eliminate D, because its points, (1, 0) and (6, 2), give a slope of , the reciprocal of what we want. E is correct; its points, (1, 0) and (3, 5), give a slope of .

19.  D  The term direct proportion means that once you square x, the ratio between x2 and y should be the same for all pairs in the table. Use your test booklet as scratch paper and write the value for x2 for each pair to check the ratios. In A, 22 = 4, for a ratio of 1 : 4. This does not match the 9 : 6 ratio of the next pair, so eliminate A. The first ratio in B is 1 : 2, but the second is 16 : 8, so eliminate B. In C the first ratio is 4 : 3, but the second is 16 : 9, so eliminate C. Only D is a match: 1 : 3, 4 : 12, and 9 : 27 are all equivalent ratios.

20.  C  Out of the 300 mice, if 75% are male, 25% must be female, so translate: × 300 = 75 females. Eliminate D and E, because there are no more than 75 females of any sort. Because 20% of the mice are albino, and 25% of the mice are female, both groups are small enough not to overlap at all. There are 80% non-albino mice, so × 300 = 240 non-albino mice, so all 75 females could be non-albinos.

  1.  A  In this sentence, the clue is takes extra care to avoid hitting squirrels. A good word to use for the blank would be “hit.” You can probably eliminate B and C pretty easily, but the rest of the words may be less familiar. Maltreat comes closest to the harm caused by hitting. Placate means “to allay the anger of” and entreat means “to plead.”

  2.  A  The first blank describes what is done to bacteria by antibiotics. A good word for the first blank is “killed.” Eliminate B and E since the first words do not come close to “killed.” The trigger but indicates that the second blank should indicate that the antibiotics are less “able to kill.” The word effective in A is a good match, while profitable and weak do not fit the sentence.

  3.  D  The clue lack of propriety indicates that Amy was doing improper things. You can see the root prop is shared by these two words. Even without looking at that word, you know that rumors are typically bad things, so this would negatively impact how the bookstore would feel about hiring Amy. A good phrase for the blank is “took back.” Only D rescinded matches this meaning. A is incorrect as fortified means “strengthened.” B is incorrect as cogitated means “pondered.” C is incorrect as tempered means “softened.” E is incorrect as regulated means “controlled.”

  4.  C  The clue in this sentence is surreptitiously embezzled a considerable sum of money, and the trigger word is although, which means the blank must be the opposite of surreptitious or sneaky. If you put “not sneaky” or “honest” in the blank, the best match is forthright. E evasive is a synonym for sneaky, so it’s the opposite of what we’re looking for.

  5.  E  The questionable tactics led to the supervisor’s stepping down. Thus, the workers were probably unhappy about the tactics, so “unhappiness” is a good word for the first blank. Eliminate A and B because they are positive words. The second blank is about how the workers felt until he stepped down. Their unhappiness probably lasted the whole time the supervisor was there, so it probably did not “end” until he left. Of the three answers left, only subside matches “end.”

  6.  C  The phrase respected for, along with Just as and also, indicates that the words in the blank are both positive. The relationship between the blanks is an opposite, however, because in the first blank she is praised for how she does her job, the clue ability to know when indicates that circumstances differ at certain times. A, B, and E all have similar relationships. D has an opposite relationship, but overlook is negative. C is correct because initiative is a positive description of taking action and to delegate is to give responsibility to someone else.

  7.  A  The semicolon trigger is like an equal sign between the two parts of the sentence. The second part of the sentence has the clue can be lethal, but also has the trigger however, which indicates an opposite meaning from the first part. A good phrase for the blank is “not lethal.” The best match is A, innocuous. Eliminate B because virulent means “harmful,” the opposite of what we are looking for. C is incorrect: The word efficacious means “effective.” D is incorrect: The word capricious means “impulsive.” E, artificial, has nothing to do with whether something is lethal.

  8.  B  The sentence describes the work with a pair of opposites linked by the trigger but: functional but lacking elegance. The blanks are also opposites, linked by the too much … not enough construction. Recycle “functional” and “elegant” for the blanks. There is no mention of money in the sentence, so A, financial, and E, lucrative, should be eliminated. In B, utilitarian . . aesthetic is a good match. In C, pragmatic means “practical” which would be good as a first blank word, but is not a match for “elegant.” Eliminate D because pedestrian means “everyday,” and is not a synonym for “functional.”

  9.  D  The passage is informational: It states a problem and potential cause (global warming, excess of carbon dioxide), describes a response (plant trees), gives a reason for that particular response (consume carbon dioxide), provides a reason that the response is not completely successful (other harmful pollutants) and concludes that trees are not enough to fix all the pollution. This even-handed treatment of different sides of the issue is best described as objective. The other answers are too positive or negative.

10.  B  The author states that, while trees can remove carbon dioxide, they cannot remove certain other pollutants and thus cannot provide an effective solution to air pollution. Thus, B is correct. The remaining answers are not supported and, in the case of D, too strong.

11.  B  Although the question says inferred, you need to find the answer that is backed up by what is stated in the passage. There is no evidence of a doctoral degree, so eliminate A. B is supported in lines 10–11, in which the drug that Elion inventedmade the first organ transplant possible.In C, greatest is extreme. There is no evidence in the passage for D or E.

12.  C  This is an EXCEPT question, so it will probably be time consuming to answer. You need to know which statement is not true, so you need to go back to the passage and find where each answer is discussed. Remember: You’re looking for something that is not mentioned, so you can eliminate answer choices that are mentioned. The passage mentions A in lines 8–10: she developed treatments for several … diseases. B is in the date given in line 10: 1957. D is in lines 5–6: a few women had become notable scientists, and E is in line 8: Elion never completed a doctoral degree but she developed numerous medical innovations.

13.  A  A main purpose question asks “Why did the author write this?” A is correct. The purpose of the passage as a whole can be found by looking at the main ideas of each paragraph: The first paragraph discusses Johnson’s personality (complicated). The second discusses his achievement. The third paragraph begins with the word Yet, which connects his dreams to Johnson’s achievements, and the sentence also discusses Johnson’s flaws of personality. We have a theme here: achievements and personality. Only A mentions these two aspects in personality and performance. This is not a straightforward, chronological history so B is incorrect. C and E are incorrect because they are extreme. D refers to a detail of the passage, not the passage as a whole.

14.  B  Go back to the passage and read a little bit above or below the quote to find why the author included it. Line 1 of the passage mentions McNamara, who describes Johnson as complicated. After the quote, the passage states that this appropriately describes both the man and the administration. From answering other questions, you may see that man and the administration fits with the personality and accomplishments theme of the passage, which is also seen in B in Johnson’s presidency and character. A and C are incorrect because the passage starts with a quote: There is no argument or view yet. D is incorrect because no objection is raised. E is incorrect because no authority is needed: The blurb does more to provide authority with its mention of noted historian.

15.  C  C is correct because Johnson both brought the liberal consensus to its fullest expression since World War II (lines 9–10) (success) and suffered so many setbacks and had tragic flaws (lines 7 and 12) (imperfect). Johnson was not described as simple (A), impulsive (B), cooperative (C), or reflective (E).

16.  B  Why did the author use the quote? The phrase As one civil rights leader noted tells you that the quote is an illustration of the author’s previous statement the author, which is that Johnson accomplished more that anyone else could even imagine. The quote supports the author’s contention that Johnson did a lot for civil rights. This is best paraphrased in B. The quote praises Johnson, and does not point out flaws, so A is incorrect. In C, prove is extreme. D is negative, and not supported by the passage. There are no failings mentioned in the quote, and kind is too mild for the praise in the quote.

17.  E  The word achieved should lead you to the second paragraph, which details the achievements. The phrase above all in line 17 indicates the most remarkable of these, which is civil rights as in E. The rest of the answers are not supported by the passage.

18.  E  This question is asking “Why did Johnson fail as President?” The answer is in the final paragraph, between tragedy in line 52 and presidency in line 55. The passage states that both his personality and his political assumptions proved inadequate. E is correct because it mentions both personality and beliefs which is similar in meaning to assumptions. A is too specific a detail and does not mention personality or beliefs. B is incorrect because there is no mention of Roosevelt in the context of Johnson’s failures. C is a result of Johnson’s failure, not the cause of it. D is too specific: It is only one example of Johnson’s overall inadequate political assumptions.

19.  C  Look in the passage around the mention of illness to figure out what it is. Lines 27–28 mention that egomania is an occupational disease, and the illness refers back to disease. You need to find a word in the answers that is close to egomania. There is no mention of fantasies as mentioned in A until later in the passage, out of context of the discussion of illness. B is too literal, and there is no mention of heart disease. C is correct because self-centeredness is close in meaning to egomania. There is no evidence for inner conflicts or societal racism in the context of that paragraph.

20.  B  Go back to the passage, find the word eclipse, and cross it out. Then read the sentence and come up with your own word. The paragraph is talking about Johnson’s belief that he alone could fix everything, emulate or copy the actions of his mentors, and then eclipse or “do even better than” them since only he could fill the role. B surpass fits the context of the sentence best. C may be tempting as darken describes a physical eclipse, but the word is used figuratively in the passage. D is close, but doesn’t indicate a “better” quality, as one can dominate by force.

21.  A  Go back to the passage and find out what Johnson’s desire to help others did. The lead word help others should take you to lines 42–43 helping others … he could most directly satisfy his own ego. Eliminate any answers that do not mention this. Only A mentions self-esteem, a synonym for ego, and bolster or “boost” is a positive word that fits with satisfy.

22.  C  The lead word in this question is Doris Kearns, and her name appears twice. In line 35, Johnson is sharing his Fantasizing with her, and in lines 50–51 he is sharing another personal feeling with her. The correct answer should mention sharing feelings. A is incorrect because most is too extreme; Johnson could have had personal thoughts that the passage doesn’t mention that are even more personal than the ones mentioned. There is no evidence in the passage for B. C is correct because a confidant is someone to confide in, and the use of at times makes it the opposite of extreme. On the SAT wishy-washy is a good thing. There is no evidence for D. E is not necessarily true; there is no evidence of recording.

23.  B  The lead word in this question is ironic, which takes you to irony in line 55. The irony described is that Johnson’s work for consensus led only to a fragmented nation. This is best paraphrased in B. There is no evidence in the passage for any of the other answers.

24.  D  The author criticizes Johnson’s personality, but mentions his many accomplishments. In the final paragraph the author mentions tragedy and that Johnson did more than anyone else for unity, but things turned out exactly the opposite of what he intended. D is correct because measured sympathy means that the author has a small or limited amount of sympathy. The list of ironies in the final paragraph makes it seem that the author recognizes the effort Johnson put into his presidency, and feels a little sorry that things turned out badly for Johnson. The author is not objective ordetached: He does criticize, so A is out. In B disappointment is a little personal. C and E are extreme.

  1.  C  The trigger because tells us that buying more books causes Jamal’s efforts to hit a snag, so he must be trying to “slow” his spending habits. Eliminate A, B, and E because their words for the first blank do not agree with “slow.” A good word for the second blank is something like “excuse” since he thinks buying books is worth going against his efforts. Only C, curb … justify matches for both blanks.

  2.  A  There are two clues: a CD player … in the 1950s and a cellular phone … in ancient Rome. These make “out of place in time” a good phrase for the blank. A is correct: The root chron refers to time, and ana indicates an opposite or negative. B may be tempting because antiquated means old, but this doesn’t reflect the out-of-place element of the clues.

  3.  C  The clue not through sudden inspiration is linked by the trigger but rather to the description of a gradual investigative approach. A good word for the blank is “eliminates” since eventually only one explanation remains. Only C, exhausts has this meaning.

  4.  C  The clues stood in awe and twirled with effortless grace make something like either “awesome” “graceful” good words for the blank. Eliminate A, B, D, and E because these are negative and we need something more positive, such as lithe which means “flexible and agile,” similar to “graceful” and good qualities for dancers.

  5.  D  There is a time trigger in this sentence, indicated by After and now. The clue experiencing a mild renaissance means that the work is more popular now than before, so “drop” is a good word for the blank. Only D, ebb, which means “a decline,” matches. A is incorrect becauseblandishment means “flattering actions or speech.” B is incorrect because disparity means “an inequality.” C is incorrect because transgression means “a bad deed.” E is incorrect because elevation is the opposite of “drop.”

  6.  B  The clue for the first blank is the contractor was truly sorry, so “sorrow” is a good word to describe his voice. Eliminate D and E because gratification and jubilance are positive, happy emotions. The clue for the second blank is hoping for and needs to relate to being sorry for causing inconvenience. A word like “forgiveness” works for the second blank. In the answers that are left, only C clemency fits. The second word in the answers we eliminated both mean “correcting or making better,” which may be tempting, but remember that their first words are the opposite of what we need.

  7.  A  A question that asks what can be inferred needs to be supported by evidence in the passage, so go back and see what the author’s reference to “music controversies” tells us. The passage states that In those days there weren’t any major music controversies. So we can infer that eventually there were some. This is reflected best in A. There is no evidence in the passage for the rest of the answers. C may be tempting because ignorance is mentioned in the passage, but is not an answer to this question. D may be true, but is not mentioned in the passage at all.

  8.  D  We need to answer the question, “What does it’s all jazz mean?” The passage states that the narrator was willing to have some unknown performers participate because It’s all jazz—differences didn’t matter. This is best paraphrased in D. Eliminate A because it lacks common sense. B is not supported by the passage. C is extreme: The word all is easy to prove false. There is no evidence for E, although ignorant may be tempting because the word ignorance is mentioned in the passage; this does not answer the question asked.

  9.  A  Go back to the passage to see what it says about the lead words bop musicians to find out how bop musicians differ from other jazz musicians. In lines 28–29, the passage states that the author thought “be-bop” musicians were superior folks, better educated, more civilized. This is best paraphrased in A: better educated and more polite. B is not stated in the passage. C is not supported. D is incorrect because jazz musicians were also influenced by swing music. There is no evidence of the better understanding mentioned in E.

10.  C  The author’s attitude toward be-bop in Passage 1 is negative. In lines 31–32, he states that he found it boring. And the more I heard it and understood it, the less I liked it. Only C uninteresting reflects boring. Eliminate A: There is no evidence in the passage of inferior imitation. B is contradicted by the passage: The author understood it, he just didn’t like it. D reverses the chronology of emotions. E is too positive.

11.  D  Go back to the passage and summarize what Gillespie means by lines 33–34. Gillespie is responding to the author’s criticism of be-bop. The passage states that he said It’s not a question of … better or worse, it just keeps movin’, indicating that young musicians should experiment with the instruments, so that music keeps changing. A is incorrect because to perfect jazz is not mentioned (or possible!). B is incorrect because the quote is not about fame. C contradicts the statement that it’s not about being better or worse. E is not mentioned in lines 33–34. Only D reflects thisexperimentation and change without contradicting the passage.

12.  C  To answer this question go back to the passage to find the specific reason that the author uses the phrase. The paragraph is about the differences between be-bop and swing music. This contrast is best captured in C. A and B are too specific in their focus on musicians; the comparison is about the characteristics of the music in general. D is tempting because these musicians are mentioned in Passage 2, but not in this comparison of musical styles. E is much too specific.

13.  E  You need to go back to the passage and find out what Groovin’ High is used as an example of. Groovin’ High appears in line 65, and the phrase for instance indicates that this is an example of what is mention right before for instance, namely that it was based on changes of some early songs. A and D are incorrect because the swing piece is Whispering (line 66) while Groovin’ High is a bop piece. Eliminate B because it is not about solo works. There is no evidence of rejected in C. Only E summarizes what is stated in the passage in lines 62–66.

14.  D  In lines 67–70, the author of Passage 2 expresses the opinion that bee-bop was not necessarily better, just different. While the author of Passage 1 would agree that bee-bop was not better, he found it worse than just different: it was boring. Thus, the author of Passage 1 would express partial disagreement.

15.  B  The best answer is B. This is a Vocab In Context (VIC) question, so you should work it like a sentence completion. Go back to the passage, cross out the word interpreters, and fill in your own word based on the context of the passage. In this case, a good word to put in the blank is “players.” The only answer choice that is close to “players” is performers, in B. Choice A is tempting, because it seems to describe musicians, but someone can compose without playing. C is also tempting, because it refers to a more common meaning of the word interpreters, but that is not the meaning that is used in the passage. Remember: When a VIC question asks you about a commonly known word, such as interpreters, the primary meaning of the word is almost always a trap. Eliminate it! D and E are wrong, because these words don’t match players.

16.  D  Go back to the passage and see what lines 67–70 say about bop. The passage says that the author is not convinced that bop is better, it’s just different in that it is more harmonically advanced. This is best paraphrased in D, more harmonically sophisticated. A and B are mentioned in the passage, but not in lines 67–70. C is not true, although McShann is mentioned elsewhere in the passage. E is incorrect because it is not true at all, and more important, there is no evidence in the passage to support it.

17.  B  To find out why the author of Passage 2 makes this statement, go back to the passage. The word whereas in line 72 indicates a contrast between the statement you need to find out about and the information before whereas. The gist is that there were few bop musicians but there were many jazz musicians working in older idioms (lines 72–73) because bop was more difficult to do well (lines 69–70). This is best paraphrased in B. A is incorrect because public appreciation is not the point of the contrast. C is incorrect because it does not mention the musicians. D contradicts the passage, which states that bop was more complicated. E is true, but not the point of the contrast.

18.  E  Go back to the passages and find out what is similar in their mentions of Dizzy Gillespie. Passage 1 mentions him as an example of a be-bop musician and supporter. Passage 2 also mentions Gillespie’s influence in be-bop, stating in the first paragraph that he was part of when be-bop was born. A is incorrect; there is no personal affection. B is incorrect because most influential is extreme. C and D are incorrect because explore the significance and argue his importance are too strong and do not reflect the point of the passages.

19.  C  Another question about the two passages together, but this time you need to find out what is different between them. Passage 1 is about a personal experience of a specific concert that took place in 1940 or 1941. Passage 2 is more generally about the history of music and how it changed over a period of time: early 1940s … in 1945 be-bop was born … the period from 1945 to 1955. This is best paraphrased in C. A is incorrect because the passages are both historical, not about the future. B is incorrect because there is no ambivalence. There is no musical theory in Passage 2, so D is incorrect. There is no emotional argument in Passage 1, so eliminate E.

  1.  C  The slope of any horizontal line is 0, so right away you should know that the answer is C. Remember: Slope is , and there is no rise when the y-value doesn’t change. The slope formula gives

  2.  D  This is a great question for PITA. The question gives the number of adult and child tickets sold, and we know the total price is $800. The answer choices list a price for each kind of ticket, so start with C and find a(100) + c(50): C gives 7(100) + 3(50) = 850, which is too big. It’s hard to determine which direction will give a lower total cost. A and B turn out to be too big, but D is just right: 6(100) + 4(50) = $800.

  3.  B  To solve this rate problem, set up two equivalent fractions: We know that 38 out of every 10,000 are defective and want to find how many defective chips there would be out of 1,000,000: . You could cross-multiply or see that 1,000,000 has two more zeros than 10,000, so n should have two more zeros after 38 to become 3,800, as in answer B.

  4.  B  The lowest number that both 8 and 10 are factors of is 40. Convert the fractions to a denominator of 40: . There is no factor that 9 and 40 have in common, so the fraction cannot be reduced. The number in place of a in is 9. Be careful! E has the value of b.

  5.  E  The numbers in the answer choices mean this is a great PITA question: We can try out the numbers in the answers as the price of Juanita’s fifth item. First break the wordy question into bite-sized pieces—there is a lot of information to sort through. The cost of the four known items is 6 + 11 + 14 + 19 = $50. We want to find the price that, when added to $50 and then multiplied by 1.05 (for the total cost and 5% tax), should result in $63. Start with C. $6 + $50 = $56; $56 × 1.05 = $58.80—too small, so eliminate A, B, and C. Now try D: $8 + $50 = $58; $58 × 1.05 = $60.90—too small, so eliminate D. Only E is left: $10 + $50 = $60; $60 × 1.05 = $63.00.

  6.  E  Plug in the number given for a in the expression to find the value: –2 + (–2)2 – (–2)3 + (–2)4 – (–2)5. Remember PEMDAS, the order of operations: The first thing to do here is deal with the Exponents, then we can take care of the Addition and Subtraction: –2 + 4 – (–8) + 16 – (–32), which simplifies to –2 + 4 + 8 + 16 + 32 = 58, answer E.

  7.  A  The top graph is of the countries’ populations, and the bottom graph is of the countries’ areas. Find the population density, , for each country by taking its number from the top graph and dividing that by its number from the bottom graph:

The highest value among the countries is that of Ecuador, answer A.

  8.  A  Plug in the number of bananas sold on Tuesday into the equation in place of n in order to find the value of p, the price per banana: 60 = , so 60p = 12 and p = 0.2. Since the price is in dollars, that’s $0.20, as seen in A.

  9.  C  The revenue is the cost of television × number of televisions sold. We need the information from the graph only for the television that costs $3,500 and for the television that costs $1,000 in order to determine how much more revenue the $3,500 television produced. There were 150 of the $3,500 televisions sold, for a revenue of $525,000. There were 250 of the $1,000 televisions sold, for a revenue of $250,000. The difference between the two is $525,000 – $250,000 = $275, 000, as seen in C.

10.  C  The 5 equal lengths that make up the two sides of the largest triangle tell us that we are dealing with 5 similar triangles. The largest triangle has sides 15 : 25 : 30, and the sides of all 5 triangles will have an equivalent ratio. Reduced, the ratio is 3 : 5 : 6, which happens to be the dimensions of the smallest triangle. We want to find the length of BD, the base of a triangle with sides of 6 and 10. This is twice as big as the smallest triangle, so the base BD must be 6 × 2 =12, answer C.

11.  D  Label the figure with any information provided by the question. We know that YD = 4 and DZ = 3. First focus on triangle ADZ. Because we have an angle of 30° and a right angle symbol, we are working with a 30-60-90 triangle. The length of AD is the hypotenuse of the triangle and one of the dimensions we need to find the area of rectangle ABCD. The ratio of sides in triangle ADZ is x : x : 2x, where x is the length of the side opposite the 30° angle and 2x is the hypotenuse So AD = 2x = 6. To find the other dimension of the rectangle, look at triangle CYD. This too is a 30-60-90 triangle, ∠CDY = 30° because it forms a straight line with the 90° of the rectangle and the 60° from triangle ADZ. The question states that DY = 4, and this is opposite the 60° angle. Using the ratio, 4 = x, and , and the hypotenuse, CD, must be . Now we have enough information to find the area of the rectangle: . Multiply the top and bottom of the fraction by to get 16, as seen in answer D.

12.  A  Let’s start with the fact that Amy’s flight is before Dave’s, which means she must be flying on Wednesday or Thursday. Her flight is after the flight to London, which means it has to be Thursday, and the flight to London is on Wednesday. Eliminate C, D, and E. We also know that she is not flying to London, because the flight to London is the day before her flight, so she must be flying to either Seattle or St. Louis. Since Dave is not flying to Seattle, that means that Amy must be flying to Seattle, answer choice A.

13.  D  The answer choices are split between those that are oriented like the original graph of y = x2 and those that are flipped upside down. In the equation y = –(x + 3)2 – 4, the negative sign flips the graph upside down, so eliminate the right-side up ones in A and B. Any number inside the parentheses added to x moves the graph to the left. Eliminate C because it has moved to the right. Any number outside the parentheses moves the graph up or down: When the number is subtracted from the expression in parentheses, the graph moves down, which makes D correct; E is the result that would happen if 4 were added instead of subtracted.

14.  A  Start with the second equation, xy = 1. The only way for this to equal 1 would be if y = 0 or x = 1. The problem states that x and y are both greater than zero, which means that it must be that x = 1. Plugging that into the first equation gives us , so = 1, and y = 2.

15.  A  Come up with a list of numbers that fits the description in the question. We know the smallest, largest, and middle numbers out of 7 spots:

13, __, __, 24, __, __, 37

Because the mode is 18, there must be more than one 18 in the list, and there is only one place they would fit:

13, 18, 18, 24, __, __, 37

The last piece of information we have is that the mean, or average, is 23. Since there are 7 numbers, the total sum is 7 × 23 = 161. The numbers we already know from the list add up to 13 + 18 + 18 + 24 + 37 = 110. The last two integers must equal 51 when added together, so only 25 and 26 fit in the two spaces left in our list. Now add 8 and 43 to the list and evaluate statements I, II, and III. The mode will not change: 18 still occurs the most, so III is not true. Eliminate C, D, and E for containing III. The numbers 8 and 43 are lower and higher, respectively, than anything on the original list, so the median stays the same, so II is not true. Eliminate B because it contains II, leaving only A.

16.  D  Whenever a question describes a geometric figure but doesn’t show it, draw it out. The center is at (4, 3), and the circle passes through the origin. The key to any circle is knowing the radius, which in this case is a line between the center at (4, 3) and the origin, as shown in the following diagram:

This makes it clear that the radius is the hypotenuse of a right triangle that has legs of 3 and 4. You can use the Pythagorean theorem or remember that 3:4:5 is a Pythagorean triplet. Since the radius has length 5, Area = πr2 = π52 = 25π, answer D.

  1.  C  As written, the sentence is incomplete: Having is not a verb. B is passive, which we don’t want. C is correct because it is a complete sentence and is active. D lacks a verb and so is a sentence fragment. E is choppy and awkward.

  2.  A  There is no error in the sentence as written. The words begins and ends are in parallel form. The word that is unnecessary in B. C contains an agreement problem between have begun and ending. D creates an incomplete sentence because the ing words do not function as verbs. E contains an agreement problem between are begun and ended.

  3.  B  The sentence as written contains a fragment: The phrase to produce should simply be produce as it is in B. C is wordy and unclear. D contains an agreement problem between the past tense was and the present tense in the rest of the sentence. The ing word in E creates a sentence fragment.

  4.  E  The verb construction has … spoken indicates an action that is no longer continuing, which does not make sense in relation to speaking English fluently. In B, while being is unnecessarily wordy. The ing word moving in C indicates something currently happening, while now lets you know that the moving happened in the past. D contains the redundant word years. Only E correctly places moved in the past tense, and speaks fluently in the present.

  5.  B  There is an idiom error in the sentence as written. The correct idiom is considered to be, as in B. The meaning of the sentence changes in C, and D and E use ing words that do not fit with the rest of the sentence.

  6.  E  There is a comparison error between compositions of Mozart and Beethoven, the person. B is awkward because the comparison is not in parallel form. C compares compositions to Beethoven. D is wordier than it needs to be, though it does make a proper comparison. E is the most concise proper comparison.

  7.  D  There is a pronoun error in the sentence as written: The subject pronoun he should be the object pronoun him. If we take Artemis out of the sentence, it is clearer that Constance would flee the country with him, as in D. B uses the incorrect pronoun. C and E are passive and confusing due to the ing word being.

  8.  B  The sentence as written contains a pronoun error. This time we have the object pronoun whom when we need the subject pronoun who. This correction is seen in B. C and E are incorrect because the pronoun that should not be used for people. D uses the subject pronoun.

  9.  A  The sentence is correct as written. The verb learn is parallel with the other verbs in the list, wear and maintain. None of the other answers is parallel.

10.  D  The sentence has a verb tense error, because runs indicates the simple present tense, which does not fit with the continuous action of over 100 years. In B the construction has ran is incorrect. C and E contain misplaced modifiers. D is correct because it uses the correct construction has run without introducing any new errors.

11.  A  The sentence is correct as it stands. The descriptive phrase is set off from the present tense part of the sentence by a pair of commas and uses consistent past tense verbs within it to describe the history of the Institute discussed in the sentence. B and C require the use of was beforenamed. D contains agreement problems between was opened and had been. E has a misplaced modifier.

12.  D  The sentence as written contains a comma splice. We need a transition at the end of the underlined portion. B uses the opposite direction transition, nevertheless, when we need a same direction transition. C changes the meaning of the sentence. D is correct because it uses the same direction transition since without introducing any other errors. E is unclear and changes the meaning of the sentence.

13.  E  There is a parallelism error between to kill and otherwise selling in the sentence as written. B uses the plural pronoun they that should refer to the singular friend. The plural verb have does not agree with my friend. D uses the simple past tense when we need the past perfect for raised. E contains the correct had raised and the construction to sell is parallel to to kill.

14.  E  The sentence as written contains a comparison error between the gifts and Brian. B contains the same error and adds a subject-verb agreement error. C creates an improper comparison between the gifts and the shop. D has a subject-verb error between the singular selection and the plural verb are. E is correct because that of refers to The selection and Joanne’s … Shop is parallel to Brian’s shop.