Z! Prep SAT Quiz For Tutors

Easy Difficulty, Multiple Choice, Word Problem, Algebra

Question 8 Strategy: Translate the expression into algebra using a variable.

Correct Answer: E. 12. The algebra should be set up as: 2n – (n + 5) = 7. Solving this equation for n gives the correct answer of 12.

Incorrect Answer: A. -12. “Subtracted from twice n” does not indicate that the final answer should be negative.

Incorrect Answer: B. -2. The equation was incorrectly set up as: (n + 5) – 2n = 7. “The sum of n and 5 is subtracted from twice n” indicates that it should be (n + 5) that is subtracted.

Incorrect Answer: C. 0. Explanation. The equation was incorrectly set up as 2 – (n + 5) = 7. “Twice n” does not indicate the number 2.

Incorrect Answer: D. 2. The classic algebra mistake can be seen here where a student forgets to distribute the negative sign to both the “n” and the “5”. 2n – (n + 5) = 7 is incorrectly simplified to: 2n – n + 5 = 7 instead of the correct 2n – n – 5 = 7.

Medium Difficulty, Multiple Choice, Word Problem, Geometry

Question 10 Strategy: Draw a straight line distance between start and end, set up a right triangle.

Correct Answer: B. √41. By considering the straight line distance as the hypotenuse of a right triangle, the Pythagorean Theorem can be applied. a2 + b2 = c2 where c is the hypotenuse. In this case, 52 + 42 = c2. So 25 + 16 = c2. By simplification (combining like terms) 41 = c2. To solve a squared variable, the opposite order operation is conducted (which is to square root each side). Therefore, c = +/- √41. As this is a geometry (distance) problem, only the positive root is a reasonable answer.

Incorrect Answer: A. 3. If the Pythagorean Theorem is set up incorrectly, with the distance not as the hypotenuse, 52 = 42 + c2. In this case, 25 – 16 = c2, so 9 = c2 and c = 3.

Incorrect Answer: C. 5. This is the total horizontal distance traveled.

Incorrect Answer: D. √11. When finding the hypotenuse, the two smaller sides must be added. Also, the horizontal distance is 5, but the vertical distance is only 4 (due to doubling back on the path: 5 – 1 = 4).

Incorrect Answer: E. √10. See above.

Easy Difficulty, Sentence Fill-Ins

Question 1 Strategy: Identify the definition in the question, relate to an answer.
Correct Answer: C. “expansive” correctly relates to 'leaving no topic unaddressed'.
Incorrect Answer: A. “fruitful” does not make sense.
Incorrect Answer: B. “polemical” means controversial.
Incorrect Answer: D. “beneficial” does not make sense.
Incorrect Answer: E. “intense” does not make sense.

Medium Difficulty , Sentence Fill-Ins

Question 2 Strategy: Identify positive and negative vocabulary connotation.
Correct Answer: D. “prideful.. lauded” correctly uses a double positive connotation, matching with 'rightfully' and 'indispensable'.
Incorrect Answer: A. “fearful.. hailed” involves a negative then a positive connotation.
Incorrect Answer: B. “exhausted.. promoted” involves a negative then a positive connotation.
Incorrect Answer: C. “exuberant.. sanctified” does not make sense because sanctify has a religious connotation.
Incorrect Answer: E. “irritated.. derided” involves two negative connotations.

Medium Difficulty, Multiple Choice, Word Problems, Geometry

Question 11 Strategy: Find the surface area of the square pyramid, then test the surface areas of the given cylinders and rectangular prisms one by one until a correct match is found.

Correct Answer: B. Cylinder with height of 2π and radius of 9. The surface of the pyramid can be found by adding the areas of the four triangular faces and the square base. Each triangular face (A = ½bh) has an area of ½(13.5)(6π) = 40.5π. As there are four of them, the total triangular surface area is 40.5π x 4 = 162π. The area of the base is 6π x 6π = 36π2. Thus the total surface area = 162π + 36π2. A cylinder has a surface area = 2πrh + 2πr2. For this cylinder, the surface area = 2π(9)(2π) + 2π(9)2 = 36π2 + 162π.

Incorrect Answer: A. Cylinder with height of 3π and radius of 9. The surface area of this cylinder = 2π(9)(3π) + 2π(9)2 = 54π2 + 162π.

Incorrect Answer: C. Cylinder with a height of 2π and a diameter of 12. If the diameter is 12, then the radius is half that, or 6. The surface area of this cylinder = 2π(6)(2π) + 2π(6)2 = 24π2 + 72π.

Incorrect Answer: D. Rectangular prism with edges 9π, 2π, 8. A rectangular prism has a surface area that adds up all six rectangular faces. If the prism has dimensions of length (l), width (w) and height (h), then the surface area = 2lw + 2lh + 2wh. In this case, surface area = 2(9π)(2π) + 2(9π)(8) + 2(2π)(8) = 36π2 + 144π + 32π = 36π2 + 176π.

Incorrect Answer: E. Rectangular prism with edges 6π, 3π, 8. In this case, surface area = 2(6π)(3π) + 2(6π)(8) + 2(3π)(8) = 36π2 + 96π + 48π = 36π2 + 144π..

Hard Difficulty, Sentence Fill-Ins

Question 3 Strategy: Match both vocabulary terms, identifying the synonym and antonym relationship.
Correct Answer: B. “abrogated.. piety” correctly relates abrogate to its synonym repeal.
Incorrect Answer: A. “aided.. philanthropy” does not make sense, because to aid is not to repeal.
Incorrect Answer: C. “subjugated.. mercantilism” does not make sense, because to subjugate is not to repeal.
Incorrect Answer: D. “heralded.. legality” does not make sense, because to herald is not to repeal, but instead means “to announce or proclaim”.

Hard Difficulty, Short Passage

Question 4 Strategy: Look for key words in the passage.
Correct Answer: D. “Bush's ingenuity with science and inventing was not evident in his daily interactions.” This choice accurately references 'solitude,' 'alone,' and 'unyielding and dogmatic.' All of these key words describe poor social skills.
Incorrect Answer: A. “Bush's inventions were not particularly valued by scientists.” It was his social abilities that were lacking, not his technical acuity.
Incorrect Answer: B. “The scientific community's demand upon Bush were too high.” No mention of demand or expectations is ever made.
Incorrect Answer: C. “Bush could not generate multiple solutions to a problem.” This is directly refuted in the text, as a “multitude of solutions” is referenced.
Incorrect Answer: E. “Scientists who worked with Bush found his research lacking.” It was his social abilities that were lacking, not his research skills.

NOTE: Key words are a critical component of “Active Reading,” a crucial SAT study technique.

Hard Difficulty, Multiple Choice, Word Problems, Arithmetic

Question 12 Strategy: Pick numbers that are easy to work with and substitute for n, d, p. Common sense says that 100 must be on the top of the fraction, not the bottom, to multiply the decimal into a percent.

Correct Answer: D. 100(n – p) / n. Pick n = 100, d = 10, p = 100 – 10 = 90. Note that p is a dependent variable that is derived from n and d. Clearly the discount should be 10%. Plug the numbers into the expression to find that 100(100 – 90) / 100 = 100(10)/100 = 10%.

Incorrect Answer: A. (n – d) / 100n. 100 is in the denominator, which will not make this a percent.

Incorrect Answer: B. (n – p) / 100n. 100 is in the denominator, which will not make this a percent.

Incorrect Answer: C. 100(n – d) / n. Plugging in the chosen numbers results in 90%. This is the “percent cost” of the original, not the discount.

Incorrect Answer: E. 100n / (n – p). Plugging in the chosen numbers results in 10000/10. 1000% discount is not reasonable.

Medium Difficulty, Short Passage

Question 5 Strategy: Infer meaning.
Correct Answer: B. “explain the foundation of Bush's inventiveness and versatility.” Solutions to problems came from his “long hours experimenting alone”.
Incorrect Answer: A. “rationalize why Bush could not make his inventions profitable.” His lack of profitability was an issue during his adulthood, not his childhood.
Incorrect Answer: C. “exemplify Bush's lugubrious experimental practices.” Lugubrious means “dismal” or “gloomy,” which does not relate to Bush's experiments.
Incorrect Answer: D. “suggest that Bush was a misanthrope.” While he might indeed have been a misanthrope, the passage does not take quite such a negative tone throughout.
Incorrect Answer: E. “mention the importance of Bush's childhood laboratory.” The laboratory is incidental, not critical to the main idea of the passage, which is Bush's personality and life.

Hard Difficulty, Multiple Choice, WP, Statistics

Question 13 Strategy: Find the total number of voters, then take the proportion of Democrats. Repeat three times, reducing both the total number and the number of Democrats by one each time to represent selection.

Correct Answer: E. 7 / 136. There are 17 total voters, so the first selection should be 7 / 17. One voter has already been picked so the second selection will be 6 / 16. The third selection will be 5 / 15. Multiplying these three numbers and simplifying gives 7 / 136. A useful time-saving measure is to multiply all three fractions using a calculator, and either check the decimal against the answer, or convert the decimal using a calculator function back into a fraction.

Incorrect Answer: A. 3 / 7. Probability must be considered as the “choice” or “selection” as a proportion of the whole. 3 / 7 would indicate three selections over the “selection” number, which does not identify the proportion of the whole that Democrats represent.

Incorrect Answer: B. 7 / 17. This is only the probability of the first voter selected being a Democrat.

Incorrect Answer: C. 5 / 51. See above explanation.

Incorrect Answer: D. 5 / 119. See above explanation.

Hard Difficulty, Multiple Choice, Algebra

Question 14 Strategy: Distribute the exponents. Remember that (xa)b = xab. Simplify the terms by combining like terms, recalling that xnxm = xn+m.

Correct Answer: B. 3. With distribution, (m1/2n1/3)24 (m-3n-4)2 becomes m12n8m-6n-8. Combining the exponents on like terms results in m12-6n8-8. Therefore, m6=729. The sixth root of 729 is three, so m = 3.

Incorrect Answer: A. 2. This would be an incorrect guess.

Incorrect Answer: C. 4. This would be an incorrect guess.

Incorrect Answer: D. 5. This would be an incorrect guess.

Incorrect Answer: E. 6. This is the exponent of m, not the answer.

Medium Difficulty, Dual Passage

Question 7 Strategy: Compare emotional and logical arguments.
Correct Answer: D. “gives an overview of the recent research relating to preschool programs, whereas Passage 2 describes a specific instance.” Passage 1 is analytical, appealing to logic, while Passage 2 is more intuitive and appeals emotionally to the reader.
Incorrect Answer: A. “discusses programs that choose not to include music while Passage 2 is dismissive of those that do not.” Passage 2 is not directly dismissive, and hardly discusses programs other than Secondo.
Incorrect Answer: B. “contends that there are some unanswered questions about preschool intervention while Passage 2 indicates that “best practices” are well documented.” While Passage 1 does contend that there are some unanswered questions, Passage 2 never concerns itself with documentation, instead literally stating an objection to being “achievement oriented”.
Incorrect Answer: C. “is based on research data whereas Passage 2 utilizes only interview and anecdotal analysis.” Passage 2 does indeed use interviews, but also mentions “early childhood literature,” which is research data.
Incorrect Answer: E. “concentrates on one specific type of intervention while Passage 2 gives an overall impression.” This is incorrect, because Passage 1 discusses many types of interventions.

Easy Difficulty, Improving Sentences, Logic and Order

Question 15 Strategy: Watch out for run-on sentences!

Correct Answer: C. “when she was not yet eleven” immediately follows the declaration of a date “1924.” The inclusion of “when” correctly coordinates with the time, giving a logical reference point for the information regarding her age. The underlined clause is associated with the date 1924, not directly with Nathalia Crane, so it makes sense for a specific year to lead into a clause beginning with “when.”

Incorrect Answer: A. “and she was not eleven then” creates a run-on sentence.

Incorrect Answer: B. “having not reached the age of eleven then” is unnecessarily wordy.

Incorrect Answer: D. “and not yet eleven then” creates a run-on sentence.

Incorrect Answer: E. “not yet eleven at the time” is confusing because the clause needs to be associated with the year 1924 (which cannot have an age, as it is a year not a person), and this option associates with Nathalia Crane.

Medium Difficulty, Improving Sentences, Agreement

Question 16 Strategy: Look for parallel parts of speech in a list or comparison.

Correct Answer: C. “and choose a running shoe carefully” keeps the ordered list in agreement. Listing actions, items, or characteristics should follow in a parallel pattern maintaining the same part of speech. A noun, noun, and noun should order in a single list. In this case, “choose” agrees with “consult” because both are verbs. One should consult and choose.

Incorrect Answer: A. “and the choice of a running shoe should be carefully considered” compares / lists “consult” and “the choice,” incorrectly pairing a verb with a noun.

Incorrect Answer: B. “yet one needs to carefully chose one's shoes” adds a contrast between consult and choose that should not exist due to the inclusion of “yet.”

Incorrect Answer: D. “and one should choose a careful running shoe” makes no sense. A shoe cannot be careful.

Incorrect Answer: E. “because one's shoes need to be considered carefully” changes the subject from “one” to “one's shoes.”

Hard Difficulty, Finding Errors, Comparisons

Question 17 Strategy: Look for comparisons between “like” terms.

Correct Answer: D. “than Carmen” needs to be “than Carmen's role” to correctly compare a role to a role.

Incorrect Answer: A. “Few” is the subject of this clause, referring to a small number of people. It is acceptable to use “few” in this way, much as using “one” or “many” is acceptable.

Incorrect Answer: B. “would dispute” is a correct use of the conditional tense.

Incorrect Answer: C. “is” refers to “the leading role” and is correctly singular.

Incorrect Answer: E. “No error”

Hard Difficulty, Finding Errors, Logic and Order

Question 18 Strategy: Recognize “Standard Grammar.”

Correct Answer: D. “or” should actually be “and.” [between … and] [either … or] and [neither … nor] are the three most common in a list of phrases that always match parts.

Incorrect Answer: A. “Nowadays” is an odd expression, surely, but a correct one.

Incorrect Answer: B. “make a decision” is singular, referring to the subject “an exceptional athlete,” which is also singular.

Incorrect Answer: C. “becoming a” parallels “going to” and is appropriately used.

Incorrect Answer: E. “No error”

TIP: The Z! Prep SAT Course covers the full range of “Standard Grammar” expressions and phrases that prove difficult for so many students to master on their own.

Hard Difficulty, Draft Revising, Logic and Order

Question 20 Strategy: Correctly identify contrasting and comparing coordinating conjunctions.

Correct Answer: D. Replace “likewise” with “while sometimes useful,” correctly contrasts information regarding usefulness and issues in advertising.

Incorrect Answer: A. Replace “likewise” with “for example.” Given the context of the previous sentence: “products that can really help,” having “many advertisements .. unsuitable for a given audience” is in no way an example of products that can help.

Incorrect Answer: B. Replace “likewise” with “on the other hand.” This option seeks to compare advertisements and products directly, but they are not comparable terms.

Incorrect Answer: C. Delete “likewise.” This incorrect edit again seeks to compare products and advertisements directly.

Incorrect Answer: E. Delete the whole sentence. If the sentence is deleted, the next sentence “This is especially true for children, a fast-growing market.” would not make sense.

Medium Difficulty, Draft Revising, Sentences

Question 19 Strategy: Understand the use of semi-colons, commas, and coordinating conjunctions to combine two clauses.

Correct Answer: C. “Some viewers think there should be no ads; others think there are just enough.” The use of a semi-colon is appropriate because each clause could stand alone as a simple sentence and both clauses are conceptually related.

Incorrect Answer: A. “Some viewers think there should be no ads and others have said there are just enough.” This option would need a comma before “and” to be correct, as well as require a change of “and” to “but.”

Incorrect Answer: B. “Some viewers think there should be no ads, others have said there are just enough.” This option would need a “but” before “others” to properly display contrast.

Incorrect Answer: D. “Some think there should be no ads, others have said just enough.” Is unclear language, because “just enough” appears to refer to a spoken statement, not the amount of ads. Furthermore, the removal of “viewers” from the sentence deletes key information regarding the subject.

Incorrect Answer: E. “Some think ads should be eliminated; others say there are enough.” This option removes “viewers” from the sentence, and key information regarding the subject should not be removed.

Medium Difficulty, Multiple Choice, Word Problem, Arithmetic

Question 9 Strategy: Set up a ratio using either 5/3 or 5/8. A counting method could also be employed.

Correct Answer: B. 4. This can be set up as a ratio problem. 5 / 3 = x / (16 – x). In this case, x represents the number of seniors and 16 – x represents the number of juniors (as 16 itself is the total of both seniors and juniors, the remainder once seniors are subtracted must be juniors). Alternatively, 5 / 8 = x / 16. In this second case, the 8 represents (5 + 3) = the total number of students in the ratio. In either case, cross multiplication will result in 8x = 80, so x = 10. The difference between 10 seniors and 6 juniors is thus 4.
Alternatively: 5 to 3 scales up to 10 to 6. These add to 16, so they are the correct numbers for the team.

Incorrect Answer: A. 2. A straight subtraction of 5 – 3 would result in the difference of the ratio between juniors and seniors, not the actual difference of the total number in a 16 person group.

Incorrect Answer: C. 6. Should the ratio have been set up correctly and solved for the number of juniors, 16 – x = 10. However, the prompt requests the difference between the number of juniors and seniors.

Incorrect Answer: D. 8. A mistaken addition of 5 + 3 would result in 8. The prompt, however, does not ask for the total number of students in the ratio.

Incorrect Answer: E. 10. Should the ratio have been set up correctly and solved for the number of seniors, x = 10. However, the prompt requests the difference between the number of juniors and seniors.

Medium Difficulty, Long Passage

Question 6 Strategy: Notice the hidden vocabulary question: “cumulative”
Correct Answer: A. “children who attend preschool do better socially and academically and are more likely to be financially stable as adults.” A cumulative effect is one that adds onto itself, resulting in a greater product than the mere sum of its parts.
Incorrect Answer: B. “increased academic success is correlated with lower rates of welfare dependency.” This is but a single effect, not a multiplicative one.
Incorrect Answer: C. “further studies of preschool programs indicate that they are designed to fit the needs of the children they serve.” This option does not consider the effect of such programs.
Incorrect Answer: D. “some impoverished children who attended preschools were also poor as adults.” If true, this evidence would not support the claim.
Incorrect Answer: E. “in a few instances, participation in preschool programs was not shown to decrease the need for grade repetition and special education.” If true, this evidence would not support the claim.