Choices (i) austerity and (ii) jejune are our correct answers.

The only contextual clues occur after the comma. The old man is sometimes inappropriately “juvenile,” so let’s start with the second blank, which describes his “nature.” A good prediction would be “childish.” Choice (E) jejune, “childish” or “immature,” matches this prediction precisely and is thus correct. Choice (D) jovial, which means “happy” or “jolly,” is incorrect because it connotes happiness, not immaturity. Choice (F) inquisitive, or “curious,” might describe a trait associated with children, but it does not explicitly mean “childish,” so we can eliminate it.

For the first blank, we now know that the old man’s clothes and furnishings contrast with his immature nature, and so we can predict an answer that means “maturity” or “seriousness.” Choice (A) austerity, meaning “somberness,” matches our prediction and is the correct response. Choice (B) obsolescence, meaning “the quality of being outdated or “old-fashioned,” might be tempting because of the man’s age, but it does not provide a strong enough contrast to the man’s immature behavior, so (B) can be rejected. Choice (C) poverty does not provide a contrast with the man’s immature nature and thus is also incorrect.

The answers are choices (C), (E), and (I).

Read long passages like this in their entirety, looking for clues. Then tackle each blank one at a time. We’re told that the governor’s voting record was supportive of heavy industry, which indicates that he typically made decisions in favor of businesses. Because the first blank describes how “pro-business” the governor was, we can predict a simple word like “very” for the first blank. Choice (C) staunchly, meaning “dependably,” is a great match and is correct. Choice (A) desultorily means “lacking in consistency,” which contradicts the governor’s “lengthy” pro-business record. Choice (B) unsustainably is incorrect because nothing in the passage relates to sustainability; this choice is therefore outside the scope of the passage.

The second blank describes the reaction to the governor’s latest move: the creation of a large environmental preserve. Because the preserve is “at the expense of” pro-business interests, its creation is out of character for the governor. Thus, we can predict a word like “surprising.” Choice (E) arresting, or “striking,” is a great match and is the correct response. Choice (D) debilitating is incorrect because the passage does not discuss the potential consequences, good or bad, of the governor’s decision. Choice (F) vitiating, which means “morally corrupting,” is too negatively charged to be correct.

The detour road sign “However” introduces a sentence that expresses skepticism toward the governor’s decision. “Astute,” or shrewd, observers suspect political motivations behind the decision; perhaps the governor doesn’t care about the environment at all and only wants to win some votes. So we might predict a word like “calculated” for the final blank, which describes the governor’s motive. Choice (I) opportunistic matches this prediction and is correct. The governor’s move is indeed opportunistic because it seizes on a chance to sway voters in his favor. Choice (G) ingenuous, which means “honest,” is contrary to what we predicted and is thus incorrect. Choice (H) uncouth, which means “vulgar,” does not make sense in this context and is also incorrect.

Answer choices (B) and (C) are correct.

The key phrase “imprisonment under false treason charges” and keyword “justly” indicate that Dreyfus was likely released from prison. A good prediction would be, “Alfred Dreyfus was justly freed.”

Choice (B) exonerated, or "absolved of guilt," identifies a fair outcome considering Dreyfus’ false imprisonment. It also indicates that Dreyfus was likely released from prison, which matches our prediction. Choice (C) acquitted, or "judged not guilty," also indicates that Dreyfus’ charges were dropped and he was freed. These are the correct answers. Choice (A) abrogated, or "officially revoked," does not describe something that happens to a person; Dreyfus’ guilt may have been abrogated, but Dreyfus himself could not have been, so this choice is incorrect. Choice (D) interred, or "buried," Choice (E) assassinated, or “murdered,” and Choice (F) shunned, or “rejected,” are all incorrect because none of these choices describes a just outcome following false accusations.

Choices (B) and (D) are the correct answers.

The semicolon indicates that the second part of the sentence defines the blank. Since the demonstration lacked organization and actually hurt the activists’ cause, a good prediction for the blank would be “disaster.” Choices (B) debacle and (D) fiasco both mean “disaster,” and are therefore correct.

Choices (A) stalemate and (C) impasse are synonyms, which make them attractive, but both mean “deadlock.”“Deadlock” suggests a lack of production, but not counterproductivity, so these choices are incorrect. Choice (E) obstacle means “roadblock,” and (F) enigma means “mystery.” Neither matches our prediction, nor do any of the other answer choices have a meaning similar to either of them, so both are incorrect.

The correct answers are choices (B) and (C).

To predict the word that belongs in the blank, we can think about the purpose of the farmers’ advertising campaign: to repair the industry’s public image in the face of recent criticism. Therefore, we can predict that the word in the blank should mean something similar to “defend” or “counter criticism of.” Choice (B) exonerate and Choice (C) vindicate both mean to “free from blame,” which matches our prediction, so these are the correct answers.

Choice (A) recriminate means “to make a counteraccusation.” The clues do not indicate that farmers and farms wish to accuse themselves, or anyone else, of wrongdoing. Instead, an advertising campaign that portrays “virtuous ranchers” would be designed to defend the industry. For the same reason, Choice (D) repudiate, which means “refuse to accept,” would run counter to the meaning of the sentence. Choice (E) eradicate means “to eliminate,” which doesn’t match our prediction or fit with the clues in the sentence. Choice (F) adulterate , which means “to weaken by adding inferior elements,” does not match our prediction because the farmers want to strengthen the industry rather than weaken it.

Checking the choices, we see that only 8 is not a factor of 60. So (D) must be correct.

We can pick numbers. Because we are told that all of the answer choices except for one “must be factors of m,” we know that an answer choice that isn't a factor of m will be the correct answer.

Let's choose a value or m that is permissible. We need a multiple of 10 and 12. Let's choose 60. Let's check each of the answer choices to determine whether any of the choices aren't factors of 60.

The correct answers are answer choices (A), (B), (D), and (E).

The easiest way to find expressions that are factors of 12¹⁷ is through prime factorization. The prime factorization of 12 is 2 × 2 × 3. 12¹⁷ simply means there are thirty-four 2s and seventeen 3s, so any choice that does not need something other than that is a factor.

(A) (–2)²(–3)⁴ = 2²× 3⁴. That is two 2s and four 3s, so this is a factor.

(B) 12³ + 12³ = 2 × 12³ = 2(2 × 2 × 3)³ = 2⁷× 3³. Seven 2s and three 3s, so this is a factor.

(C) 4¹⁸ = 2³⁶. Thirty-six 2s is too many because 12¹⁷ only has thirty-four 2s. Eliminate.

(D) 2¹⁶× 3¹⁵. Sixteen 2s and fifteen 3s, so this is a factor.

(E) 3¹⁷× 4¹⁷ = 3¹⁷× 2³⁴. Exactly seventeen 3s and thirty-four 2s. This is a factor.

(F) 12¹⁷ + 12¹⁷ = 2 × 12¹⁷. This is larger than 12¹⁷, so it cannot be a factor. Eliminate.

The correct answer is D.

The average formula is . We can use this formula in the rearranged form Sum of the terms = (Average) × (Number of terms). Since the average of v, w, x, y, and z is j, the sum of the 5 terms v, w, x, y, and z is 5j. Since the average of x, y, and z is k, the sum of the 3 terms x, y, and z is 3k. If we subtract from the sum of v, w, x, y, and z the sum of x, y, and z, we will be left with the sum of v and w. The sum of v and w is 5j − 3k, that is, v + w = 5j − 3k. The average of the 2 terms v and w is .

The correct answer is B.

This is a great illustration of the payoff on Test Day for spending time now to learn how quadratics work. No calculation is required by this question if we can look at the given quadratic and realize that both its roots will be negative, so Quantity B must be greater.

Look at the "+2" in the quadratic expression. What does it signify? It implies that the signs on the second terms of the binomials into which the quadratic expression can be factored must match. Now look at the "+3 p " in the quadratic. What does it mean? It means that the signs will both be positive. So if the second terms of the binomials are positive, the roots themselves — the values of  p  that the quadratic ultimately solves for — will be negative:

The correct answer is C.

If g and h are consecutive multiples of 4, the absolute difference between g  and  h will always be 4, therefore . The quantity in Quantity A is 80.

The correct answer is C.

Let's connect points B and D with a line segment.