Practice Questions
The figure below is a rectangular solid. AB = 17, AD = 8, and BC = 9. Quantity A: The volume of the rectangular solid Quantity B: 864 Compare the two quantities and select the appropriate answer. A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
Now triangle BCD is a right triangle. We have (BD)2 = (BC)2 + (CD)2. Triangle ABD is a right triangle. We have (AB) 2 = (AD)2 + (BD)2. Using the equation (BD)2 = (BC)2 + (CD)2 that we obtained from right triangle BCD, let's substitute (BC)2 + (CD)2 for (BD)2 in the equation (AB) 2 = (AD) 2 + (BD)2, which is the equation that we obtained from right triangle ABD. Then we have (AB)2 = (AD)2 + (BC)2 + (CD)2. We know that AB = 17, AD = 8, and BC = 9. The only quantity that we do not know in the equation (AB)2 = (AD)2 + (BC)2 + (CD)2 is CD. We can find the length of CD by substituting AB = 17, AD = 8, and BC = 9 in the equation (AB)2 = (AD)2 + (BC)2 + (CD)2. We have 172 = 82 + 92 + (CD)2. Then 289 = 64 + 81 + (CD)2, 289 = 145 + (CD)2, and 144 = (CD)2. Now lengths cannot be negative, so . The volume of any rectangular solid is length times width times height. The volume of this rectangular solid is 12 × 9 × 8 = 108 × 8 = 864. The quantities in both quantities are equal to 864 and choice (C) is correct.
A certain company will issue 4-letter identification codes to all of its employees. The codes will include only the letters A, C, F, H, K, Q and V. If all the letters of each code are distinct, how many such codes are possible? A) 35 B) 70 C) 105 D) 840 E) 1680
The correct answer is (D), 840. This problem will require us to use permutations. To find the number of permutations of a smaller group out of a larger group, we use the formula: where n is the total number and k is the size of the group. So for our calculations, this means that n = 7 and k = 4. The formula gives us the total number of codes, that is, the number of possible groups of 4 multiplied by the number of ways each group can be arranged: Note that the formula ultimately reduces to 7 x 6 x 5 x 4, which we can also think of as having 7 choices for the first letter, 6 for the second (since the letter chosen for the first letter is now unavailable), 5 for the third, 4 for the fourth.
g and h are consecutive multiples of 4. Quantity A: 5(g - h)² Quantity B: 80 Compare the two quantities and select the appropriate answer. A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
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.
In the graphic above, ABC is an equilateral triangle and ADC is an isosceles triangle (AD = CD). If y = 25, what is the value of x? A) 15 B) 25 C) 30 D) 35 E) 60
The correct answer is D. If ABC is an equilateral triangle that means each side is equal and each angle is 60. If ADC is placed inside of it and is an isosceles (where angle D is the one larger angle) we know that two of the angles are equal. If the angles are equal, then x + y = 60. If y = 25 then 25 + x = 60 =>y = 60 - 25 =>x = 35.
Jane's (i)__________ disposition seemed irresistibly to infect those around her, taking wavering hope and turning it into robust optimism. It was as if in her presence, the silver lining of every cloud became (ii)__________. Blank (i): A) sanguinary B) ruddy C) sanguine Blank (ii): D) lacklustre E) tangible F) coruscant
(C) and (F) are correct. Don't be put off by two- and three-blank sentences; sometimes, getting to the correct answers is easier than in a one-blank sentence because there are more context clues. Just start with whichever blank seems easiest and work your way to the others. In this question, we can begin with the first blank, an adjective describing Jane's disposition, which must be strongly optimistic if it "infects" others and makes them optimistic as well. Choice (C) sanguine can mean either "reddish" (in regard to complexion) or "confident" or "optimistic" (in reference to disposition, as is the case here). This second meaning matches our prediction, so (C) is the correct response. Choice (B) ruddy, "healthily red," refers to someone's complexion and is incorrect. While (A) sanguinary may look similar to (C) sanguine, it actually means "bloody" or "bloodthirsty," which is unsupported by the context and is thus incorrect. For the second blank, the context refers to the saying "every cloud has a silver lining," which means that one should always look on the bright side of things or see the best in even bad situations. The key to selecting the correct answer here is in the previous sentence; Jane takes "wavering hope" and turns it into "robust optimism." She makes optimism stronger, and the correct answer will reflect this. Choice (F) coruscant, meaning "gleaming" or "radiating," completes the image of the silver lining growing brighter, so this is the correct choice. Choice (D) lacklustre, meaning "dull," is the opposite of what we want. Choice (E) tangible, "corporeal" or "touchable," makes little sense because the silver lining is figurative, not literal, so (E) can also be eliminated. Choices (C) and (F) are the correct answers.
Our tour guide was obviously more capable than we thought; after the avalanche, he assumed _______ role, leading us quickly out of danger, checking us all for injury, and assuaging our fright. A. an assuming B. a guarded C. a pretentious D. a protective E. a moralizing F. a tutelary
(D) and (F) are correct. Sentence Equivalence questions can be tricky because they may feature a number of traps. The testmaker may include a pair of synonyms among the choices that do not match the clues in the sentence, or include one word that matches the context perfectly, without a second correct choice to go with it. You need to find the TWO choices that BOTH complete the sentence logically and give it similar meanings. This sentence contrasts the behavior of the tour guide before and after the avalanche. Before the avalanche, the tour guide may have appeared incompetent; after the avalanche, he appeared "capable" because he led the group out of danger. We can deduce that he assumed a "sheltering" role, a prediction that is consistent with the sentence's description of the tour guide's behavior. Both (D) protective and (F) tutelary mean "sheltering," so (D) and (F) are the correct answers. Choices (A) assuming and (C) pretentious both mean "arrogant," and (B) guarded refers to "self-protective" behavior; all three are inconsistent with the tour guide's actions and the sentence's description of him as "capable." Choice (E) moralizing means "to attempt to improve someone's morals" or "to reform," which is also not implied by the list of actions performed by the tour guide after the avalanche. The correct answers are (D) and (F).
Chef James must select 3 different items for each dinner he will create. The items are to be chosen from among 5 different vegetarian and 4 different meat selections. If at least one of the selections must be vegetarian, how many different dinners can the chef create? A. 30 B. 40 C. 60 D. 70 E. 80
(E) is correct. A preliminary step in solving word problems is working your way through the information provided and understanding what is being asked. This question asks for the number of different dinners Chef James could make. Since the order of the selections in the dinner doesn't matter, this is a combinations problem. But it involves three possible combination types: Veg, Meat, Meat; Veg, Veg, Meat; or Veg, Veg, Veg. Calculate the possibilities for each type of combination and then add the results to find the total number of different combinations possible. Let V represent vegetarian and M represent meat. Then with V, M, M, he has 5 choices for the vegetarian (he must choose 1) and 4 choices for meat (he must choose 2). So here we multiply 5 x 4C2 which is equal to 30 selections. For V, V, M, he will choose 2 out of 5 for the vegetarian and 4 choices for the meat. For this course he'll need to calculate 5C2 for the veg selection and multiply that by the 4 meat selections. This equals 40 selections. If he goes with V, V, V, the all-vegetarian menu, he will choose a subgroup of 3 from among 5 vegetarian choices. This is simply 5C3 = 5*4*3 / (3*2) = 10 selections. Add this up to get the answer: 80 selections. You could have also gotten to the answer by finding the total number of choices and removing those that are not possible. If there were no Vegetarian limitation, then the total number of meals that you could create would be 9C3 which is equal to 84. The only meals that are not possible are the all-meat meals. Find the number of those by calculating 4C3. That's equal to 4. 84 ﹘ 4 is 80. Points on Test Day!
After a 12-year imprisonment under false treason charges, Alfred Dreyfus was justly ________, effectively putting an end to the French political scandal known as the Dreyfus Affair. Select the two answer choices that, when used to complete the sentence fit the meaning of the sentence as a whole and produce completed sentences that are alike in meaning. A. abrogated B. exonerated C. acquitted D. interred E. assassinated F. shunned
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.
The protest at the capital yesterday was an absolute _______; while the activists had the best of intentions, the demonstration showed a complete lack of organization and was actually counterproductive to their cause. Select the two answer choices that, when used to complete the sentence fit the meaning of the sentence as a whole and produce completed sentences that are alike in meaning. A. stalemate B. debacle C. impasse D. fiasco E. obstacle F. enigma
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 (i)___________ of the old man's garb and home belied a (ii)___________ nature, and many people lamented his tendency to be outright juvenile in somber circumstances. For each blank select one entry from the corresponding choices. Fill all blanks in the way that best completes the text. A. (i) austerity B. (i) obsolescence C. (i) poverty D. (ii) jovial E. (ii) jejune F. (ii) inquisitive
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.
What percent less than the sales of clothing were the sales from sporting goods? A) 4% B) 5% C) 8% D) 12% E) 16%
Correct answer is E). We do not even have to use the total of $24,000,000 in our calculations. We can say that $24,000,000 is T. Then the sales from clothing were 25% of T, which is 0.25T. The sales from sporting goods were 21% of T, which is 0.21T. The percent that the sales from sporting goods is less than the sales from clothing is ((0.25T - 0.21T)/ 0.25T) x 100% We were actually finding the percent that 21% is less than 25%. However, we included the total sales T in our calculation for clarity. We can see that the Ts will cancel in ((0.25T - 0.21T)/ 0.25T) x 100% = 0.04T/0.25T x 100% = 4/25 x 100% = 4 x 4% = 16%
Due to his lengthy industry-friendly record, the governor was thought to be (i)______ pro-business. So it was (ii)______ when he announced the creation of a large environmental preserve at the expense of industry interests. However, his decision was not met with unqualified enthusiasm. Many astute observers noted the politically (iii)_______ motive of using the decision to court independent voters. For each blank select one entry from the corresponding choices. Fill all blanks in the way that best completes the text. A. (i) desultorily B. (i) unsustainably C. (i) staunchly D. (ii) debilitating E. (ii) arresting F. (ii) vitiating G. (iii) ingenuous H. (iii) uncouth I. (iii) opportunistic
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.
A certain bank vault contains 600 safe deposit boxes. A thief possesses a sack containing 700 keys, only 300 of which correspond to the safe deposit boxes, with no duplicates. If the thief randomly selects a box and then a key, what is the probability that the thief will be able to open the box? A) 1⁄1400 B) 1⁄600 C) 1⁄7 D) 1⁄2 E) 6⁄7
The correct answer is . The thief doesn't stand much of a chance. In order for the thief to be able to open the box, he has to select one of the boxes for which there is a key and then he has to select the right key. With so many boxes and keys, no wonder his chances are so slim. First, let's find the probability of selecting one of the boxes for which there's a key. There are 600 boxes, so the possible outcomes are 600. How many desired outcomes are there? Since the thief has keys for only 300 boxes, then there 300 desired outcomes. So that's a probability of of picking one of the boxes with keys. Once he's picked a box, the thief has to pick the right key. Since he has 700 keys, there are 700 possible outcomes. Only 1 key will open the box, though, so there is only 1 desired outcome, for a probability of of selecting the right key. Now the probability of these two events both happening is
A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is "frozen" if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently six spaces behind player B, what is the probability that player B will be frozen after player A rolls? A) 1⁄12 B) 5⁄36 C) 1⁄6 D) 1⁄3 E) 17⁄36
The correct answer is 5/36. This is a weird setup, but let's think about the situation for a second. In this game a player is "frozen" whenever another player lands on the spot where the first player already has her piece. Then the question asks for the probability that player B will be frozen by player A, who's 6 spaces behind. What does it depend on? It depends on whether player A gets a roll of exactly 6 on the dice. So what's the probability of getting 6 on the dice? First, let's figure out the total possible outcomes for the roll. Since there are 6 numbers on each die, the total number of possible rolls will be 6 x 6 or 36. So there are 36 possible rolls. How many of them would allow player A to move exactly 6 spots? Well, any roll that adds up to 6. So we could have 1/5, 2/4 and 3/3. But remember that since there are 2 dice, there are 2 ways to get 1/5 and 2/4 because either die could get the 1 or the 5, etc. So there's 1/5, 5/1, 2/4, 4/2 and 3/3. That's 5 rolls that add up to exactly 6. So 5 out of the 36 possible rolls would allow player A to "freeze" player B, which gives us a probability of 5/36.
p² + 3p + 2 = 0 Quantity A: p Quantity B: 1 Compare the two quantities and select the appropriate answer. A. Quantity A is greater. B. Quantity B is greater. C. The two quantities are equal. D. The relationship cannot be determined from the information given.
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:
One element, which may not justify violence itself but which __________ its use, is the belief that death in a sacred cause is the proper end of life. A) incriminates B) valorizes C) indicts D) abrogates E) rescinds
The correct answer is B. Let us try to understand the meaning of the sentence from the partial information. The sentence talks about an element that doesn't justify violence itself but does something to its use. This element is the belief that death, if for a sacred cause, can be considered a proper end of life. The structure and reasoning of the sentence implies that the element is trying to justify the use of violence. In other words, justify can be a good fill-in for the sentence. Now, let us look at the meaning of the verbs in the options. A. incriminates - to make (someone) appear guilty of a crime or wrongdoing B. valorizes - to give or ascribe value or validity to C. indicts - to formally accuse of or charge with a crime D. abrogates - to abolish by authoritative action E. rescinds - to take away 'Valorizes,' which means to give validity to something, is the correct answer. 'Incriminates,' 'indicts,' and 'abrogates' are opposite to what the context requires. 'Rescinds' does not go with the intended meaning of the sentence.
The average (arithmetic mean) of the numbers v, w, x, y, and z is j, and the average of the numbers x, y, and z is k. What is the average of v and w in terms of j and k ? A. (j - k) / 2 B. (j + k) / 2 C. (5j - 3k) / 3 D. (5j - 3k) / 2 E. (5j - k) / 2
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 .
Conflict between generations may be a problem that has persisted for centuries, but the nature and intensity of the conflict obviously _____ in response to changes in social and economic conditions A. increase B. disappear C. decline D. vary E. wane
The correct answer is D. The detour road sign but tells you that you can expect a change of direction in the sentence. The first half of the sentence describes a problem —conflict between generations— which does something in response to changes in social and economic conditions. The shift in the sentence turns on the words nature and intensity; these are the aspects of the problem that will be affected by change. Try constructing a paraphrase to convey this shifting problem. For example: Conflict between generations persists for centuries, but the nature of the conflict differs in response to changing conditions. You need a word that conveys a shift in intensity and nature. Scan the answer choices to look for a word that resembles your prediction. All of the given choices convey some type of change. DISAPPEAR, DECLINE, and WANE (to get smaller or weaker) all convey a reduction of intensity. Although you know there will be a change in the problem, nothing in the sentence indicates that the problem will decrease. You are looking for a more neutral term. By this logic, you can also eliminate INCREASE, which suggests the problem has worsened. Only VARY provides a neutral expression of change. Conflict between generations might be a problem that has persisted for centuries, but the nature and intensity of the conflict obviously vary in response to changes in social and economic conditions.
Parliament made a __________ return on Monday, when senators chirped and guffawed their way through the first autumnal question period. [ Note: Select 2 answer choices ] A) lugubrious B) rambunctious C) opprobrious D) staid E) unflagging F) ebullient
The correct answers are B and F. The sentence states that the parliament made a certain kind of return on Monday, and the senators were chirpy and guffawed through the question period. The words chirpy (cheery) and guffaw (chuckle/laugh) tell us that the mood in the parliament was lively and light, so the fill-in, which describes the kind of return that the parliament made, must be a positive word that means the environment was "happy" and "exuberant". The word exuberant can be a good fill-in. Now, let us look at the meaning of the adjectives in the options. A. lugubrious - looking or sounding sad and dismal B. rambunctious - uncontrollably exuberant; boisterous C. opprobrious - expressing scorn or criticism D. staid - sedate, respectable, and unadventurous E. unflagging - tireless; persistent F. ebullient - cheerful and full of energy Both 'rambunctious' and 'ebullient' fit in the blank well. The words 'lugubrious' and 'opprobrious' are negative and therefore do not fit in the blank. 'Staid' and 'unflagging' are unrelated to the meaning of the sentence and therefore do not convey the correct meaning.
Which of the following expressions are factors of 1217 Indicate all possible correct answers. A. (-2)² (-3)⁴ B. 12³ + 12³ C. 4¹⁸ D. 2¹⁶ x 2¹⁵ E. 3¹⁷ x 4¹⁷ F. 12¹⁷ + 12¹⁷
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.
In response to recent criticism of inhumane and unhygienic practices throughout the agricultural industry, farmers resolved to commission an advertising campaign portraying virtuous ranchers that would ________ the industry. Select the two answer choices that, when used to complete the sentence fit the meaning of the sentence as a whole and produce completed sentences that are alike in meaning. A. recriminate B. exonerate C. vindicate D. repudiate E. eradicate F. adulterate
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.
Demonstrating the contradictory relationship between the demeanors of the artists and their reception by the media, the artist who was the least ____________ in interviews was also the most sought after. A) curt B) specific C) cordial D) articulate E) evasive
The first clue in the sentence is "contradictory," and this is used in reference to the relationship between demeanor (of the artist) and reception (by the media). Thus, you can conclude an artist with an unpleasant demeanor is paradoxically well received by the media. Since the word "least" comes before the blank, you can predict pleasant or cooperative. Choice (C), cordial, matches. Even if you didn't know what cordial meant, you could still eliminate choices (A), (B), and (E) based on word charge. They all have a negative or neutral charge and the correct answer is a positive word. By narrowing your choices in this way you can guess strategically.
Demonstrating the contradictory relationship between the demeanors of the artists and their reception by the media, the artist who was the least ____________ in interviews was also the most sought after. A) curt B) specific C) cordial D) articulate E) evasive
The first clue in the sentence is "contradictory," and this is used in reference to the relationship between demeanor (of the artist) and reception (by the media). Thus, you can conclude an artist with an unpleasant demeanor is paradoxically well received by the media. Since the word "least" comes before the blank, you can predict pleasant or cooperative. Choice (C), cordial, matches. Even if you didn't know what cordial meant, you could still eliminate choices (A), (B), and (E) based on word charge. They all have a negative or neutral charge and the correct answer is a positive word. By narrowing your choices in this way you can guess strategically.
-x + y + 3z = 5x + y + -3z = 5If z > 0, what is the ratio of x to z? A) 6/3 B) -3 C) 5/6 D) 3 E) 6/5
To determine this we need to determine what x/z equals. We need to eliminate the y variable and we can do this by subtracting out the two y's. Subtracting-x + y + 3z = 5-(x + y + -3z = 5)-2x + 6z = 0 2x = 6z => now we can divide both sides by 2: x = 6z/2 => now we can divide both sides by z: x/z = 6/2 = 3 Now we know that x/z is equal to 3. The correct answer is D.
If (a + 2b)⁄(11b - 2a) = 2, which of the following must be true about the relationship between a and b? a) a is 15 more than b. b) b is 15 more than a. c) a is 1⁄4 of b. d) a is 4 times b. e) a is 3⁄5 of b.
To make this problem easier to manage we need to multiply both sides of the equation by (11b - 2a) to get (a + 2b) = 2 * (11b - 2a). We need to multiply both sides by this to get rid of the fraction and solve for a in terms of b. (a + 2b) = 2 * (11b - 2a)-> a + 2b = 22b - 4a-> 5a = 20b-> a = 4bThus, a is 4 times b. The correct answer is D.
To those wary of insincerity, a grand compliment should be subjected to great ____________. A) scrutiny B) obstruction C) malice D) acclaim E) repetition
"Wary" is the context clue. If you are wary, then you will be cautious about a grand compliment. Predict questioning for the blank. Choice (A) scrutiny works well, and reads well into the sentence. Choice (D) is a trap answer in that it is synonymous with grand compliment but doesn't answer the blank. The person wary of insincerity would not reciprocate praise for the compliment. scrutiny = examination obstruction = blockage malice = evil intent acclaim = praise repetition = do over more than onc
Quantitative Comparison: A. Quantity A is greater. B. Quantity B is greater. C. The quantities are equal. D. The relationship cannot be determined from the information given.
(C) is correct. Start with Column B, as that's a simple division. Column B = 7. Simplify Column A to find that the two columns are equal: "of" means "times," so you can rewrite this expression as 700 sqrt(pi) % / sqrt(pi). The sqrt(pi) cancels out in the numerator and denominator, so you're left with 700%, which equals 7. This question is a great example of the testmaker's tendency to make the two quantities difficult to compare by making them look different. Your solution to this problem? Make them look alike!
If the integer m is a multiple of both 10 and 12, then all of the following must be factors of m EXCEPT A. 15 B. 12 C. 10 D. 8 E. 6
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.
If (2⁄5)(5x + x) = 12, then x = A) 4 B) 5 C) 6 D) 10 E) 12
Answer B) 5 We just need to do the algebra here. (2/5)(5x + x) = 12 => multiply by 5 to get rid of the fractions5(2/5)(5x + x) = 5*12 => 2(5x + x) = 60 => multiply out the 210x + 2x = 60 => sum the x's12x = 60 => divide by 12x = 5