GMAT CAT 4
Garment industry representative: Women's pants are usually sized according to the circumference of the wearer's natural waist - the narrowest part of her torso, located roughly at the height of her navel. For instance, a pair of women's pants tagged size 29 is designed to fit the average woman with a 29-inch natural waist. Consultant: But then the sizing number is not an actual measurement of the pants themselves. If a pair of pants is tagged size 29, then no dimension of the pants themselves will necessarily measure 29 inches. The current sizing system is thus likely to be more confusing for consumers than, say, a system in which sizes are numbered according to the waistband circumference of the pants themselves. Garment industry representative: You are correct that the size number does not necessarily represent an actual dimension of the pants. However, your proposed sizing system would lead to substantially more confusion than the current one. Which of the following, if true, supports the garment industry representative's position and also undermines the consultant's argument? Most consumers are quick to learn the sizing systems of their preferred brands, regardless of how counterintuitive or unusual they may find those systems at first. Many shoppers will measure their favorite pairs of pants at home before a shopping trip, so that they can quickly evaluate the fit of unfamiliar brands of pants without having to try them on. Even when wearing identical brands and styles of pants, some women prefer a tighter fit, while other women with similar bodies prefer a looser fit; moreover, a given woman's preferences often vary unpredictably from style to style within the same brand. Many women find smaller size numbers psychologically appealing and, when choosing among identically sized garments, are more likely to buy those tagged with smaller size numbers. Different styles of women's pants are worn with their waistbands at widely varying heights, some as high as the wearer's natural waist and some as low as the wearer's hipbone.
(1) Identify the Question The prompt asks for a statement that supports one of the two arguments in the passage while undermining the other. This problem thus combines the attributes of a "strengthen" question and a "weaken" question. Fortunately, the basic mindset for strengthening arguments is the same as that for weakening them; the extra challenge, in a problem like this one, lies in keeping track of which argument you must support and which you must undermine. (2) Deconstruct the Argument The garment industry representative describes the currently prevailing sizing system for women's pants -- a system in which pants are sized according to the average wearer's natural waist circumference, rather than according to any actual dimension of the pants themselves. The consultant criticizes this system, claiming that an alternative system based on the measurements of the pants themselves would be less confusing. The garment industry representative argues the opposite; according to the representative, a system based on the actual measurements of the pants would be more confusing, not less so. (3) State the Goal You are to find a statement that supports the representative's position while undermining the consultant's. In other words, the desired statement should represent an advantage of the existing system (based on the wearer's body measurements) and, at the same time, a disadvantage of the consultant's proposed system (based on the measurements of the pants). (4) Work from Wrong to Right (A) If shoppers are quick to learn the sizing systems of their favorite brands, the most likely conclusion is that no sizing system will remain confusing for very long. Rather than supporting one side at the expense of the other, then, this statement renders the entire debate unimportant. (B) This statement supports the notion of a system based on the measurements of the pants, rather than on those of the wearer's body. This choice thus accomplishes the opposite of what is desired: it supports the consultant's argument and undermines the representative's. (C) If this statement is true, then a sizing system based on the wearer's body measurements cannot feasibly account for the range of preferences desired; a system based on the measurements of the pants themselves could possibly do so. This choice thus accomplishes the opposite of what is desired: it supports the consultant's argument and undermines the representative's. (D) This statement provides evidence that many shoppers would be more psychologically pleased by a system based on their waist measurement, as that number (as described) will be smaller than the corresponding number for the waistband of the pants themselves. However, the argument is not concerned with determining which system would be more psychologically appealing to shoppers; it is concerned only with which system would be less confusing to them. This choice gives no evidence that either system is more or less confusing than the other, so it is irrelevant. (E) CORRECT. If this statement is true, then, under a system based on the measurements of the pants themselves (as proposed by the consultant), shoppers would have to know the exact height at which every style of pants was designed to be worn, as well as their own preferred size at each of those heights. That system would thus be much more complicated -- and therefore more confusing -- than the existing system, in which each shopper only needs to know one measurement (her natural waistline).
Point Q lies in the interior of a particular circle. Is point Q the center of the circle? (1) There exist points A, B, and C, all distinct points on the circle's circumference, such that the distances QA, QB, and QC are identical. (2) At least two different diameters of the circle contain point Q.
(1) SUFFICIENT: According to this statement, Q is equidistant from three different points on the boundary of the circle. This can be true if Q is the center of the circle; all three lengths would be radii of the circle. Could it also be true if Q is not the center of the circle? Try to create a situation satisfying this criterion for which Q is not the center of the circle. No matter where the three points are placed, at least one such impossible situation will occur where, according to the statement, the sides are all the same, but the angles are not actually the same. It is impossible, then, to create a situation where statement 1 is true but Q is not the center of the circle. Q is the center of the circle. Statement (1) is sufficient. (2) SUFFICIENT: All diameters of a circle intersect at the circle's center and nowhere else. Therefore, if Q is the point of intersection of two or more of the circle's diameters, then Q must be the center of the circle. The statement is sufficient.
If 8 x > 4 + 6 x, what is the value of the integer x? (1) 6 - 5 x > -13 (2) 3 - 2 x < - x + 4 < 7.2 - 2 x
D We can start by solving the given inequality for x: 8 x > 4 + 6 x 2 x > 4 x > 2 So, the rephrased question is: "If the integer x is greater than 2, what is the value of x?" (1) SUFFICIENT: Let's solve this inequality for x as well: 6 - 5 x > -13 -5 x > -19 x < 3.8 Since we know from the question that x > 2, we can conclude that 2 < x < 3.8. The only integer between 2 and 3.8 is 3. Therefore, x = 3. (2) SUFFICIENT: We can break this inequality into two distinct inequalities. Then, we can solve each inequality for x: 3 - 2 x < - x + 4 3 - 4 < x -1 < x - x + 4 < 7.2 - 2 x x < 7.2 - 4 x < 3.2 So, we end up with -1 < x < 3.2. Since we know from the information given in the question that x > 2, we can conclude that 2 < x < 3.2. The only integer between 2 and 3.2 is 3. Therefore, x = 3. The correct answer is D.
For positive integer k, is the expression (k + 2)(k^2 + 4k + 3) divisible by 4? (1) k is divisible by 8. (2) (k+1)/3 is an odd integer.
A. The quadratic expression k2 + 4k + 3 can be factored to yield (k + 1)(k + 3). Thus, the expression in the question stem can be restated as (k + 1)(k + 2)(k + 3), or the product of three consecutive integers. This product will be divisible by 4 if one of two conditions are met: If k is odd, both k + 1 and k + 3 must be even, and the product (k + 1)(k + 2)(k + 3) would be divisible by 2 twice. Therefore, if k is odd, our product must be divisible by 4. If k is even, both k + 1 and k + 3 must be odd, and the product (k + 1)(k + 2)(k + 3) would be divisible by 4 only if k + 2, the only even integer among the three, were itself divisible by 4. The question might therefore be rephrased "Is k odd, OR is k + 2 divisible by 4?" Note that a 'yes' to either of the conditions would suffice, but to answer 'no' to the question would require a 'no' to both conditions. (1) SUFFICIENT: If k is divisible by 8, it must be both even and divisible by 4. If k is divisible by 4, k + 2 cannot be divisible by 4. Therefore, statement (1) yields a definitive 'no' to both conditions in our rephrased question; k is not odd, and k + 2 is not divisible by 4. (2) INSUFFICIENT: If k + 1 is divisible by 3, k + 1 must be an odd integer, and k an even integer. However, we do not have sufficient information to determine whether k or k + 2 is divisible by 4. The correct answer is A.
If a and b are positive integers such that a < b, is b even? (1) b/2 - a/2 is an integer. (2) 3b/4 - a/2 is an integer.
B For this yes/no question, or goal is to try to find a definitive answer: either b is always even or b is always something other than even (odd or a fraction / decimal). If b is even only some of the time, then that information would be insufficient to answer the question. This is also a theory question; on such questions, we can try numbers or we can use theory. We can also test some numbers initially in order to help ourselves figure out or understand the theory more thoroughly and then use theory to help guide us through the rest of the problem. 1. insuff: test where both even and wen both odd, both yield integers. this makes us pick up on fact that an integer - an integer = an integer and a non-integer minus a non-integer w the same decimal value will also yield an integer. 2. What would need to be true in order for 3 b/4 to be an integer as well? The value of b would have to be some multiple of 4 (in order to "cancel out" the 4 on the bottom of the fraction). try b=4 and a=2, gives you 2. so b can be even. can b be odd? an even value for a will result in an integer for a/2. to make this true 3b/4 must be an int as well. that will never result if b is odd ex. b=5, a=2 = 15/4 -1 -> not an int. this is not possible what about both b and a are odd? If a is odd, then a/2 will be some number ending in 0.5. Can we make 3b/4 also end in 0.5, so that we'll get an integer when subtracting the two? Let's try some odd positive integer possibilities for b: 3 b/4 could equal 3/4, 9/4, 15/4, and so on, or the decimal equivalents 0.75, 2.25, 3.75, and so on. The pattern here alternates between 0.75 and 0.25
The number of new cases of tuberculosis diagnosed in Country X increased dramatically this year. The country's news media have speculated that the sharp increase in new cases is the result of the tuberculosis outbreak that occurred in neighboring Country Y last year. Health officials in Country X have therefore proposed that all visitors from Country Y must submit to a medical examination before entering Country X. Which of the following, if true, most strongly suggests that the proposed medical examinations will NOT help curb the spread of tuberculosis in Country X? Country Z, which also neighbors Country Y, has not experienced an increase in cases of tuberculosis. Current medical technology is not capable of detecting all carriers of tuberculosis. Country X does not have the resources to examine all visitors from Country Y. Tuberculosis is not spread through human contact. Citizens of Country Y will not travel to Country X if the proposal is implemented.
Because of the speculation that the tuberculosis outbreak in Country X was the result of an outbreak of tuberculosis in Country Y, health officials in Country X have proposed requiring all visitors from Country Y to undergo a medical examination. We are asked to find a choice that suggests that this proposal will not have the desired effect of curbing the spread of tuberculosis in Country X. (A) This has no bearing on the situation between Country X and Country Y. (B) This suggests only that the proposal would not prevent ALL cases. But even if the proposal does not prevent all cases, it could help prevent many. (C) This suggests only that the proposal would not catch ALL carriers of the disease from Country Y. But even if the proposal does not prevent all cases, it could help prevent many. (D) CORRECT. This suggests that the visitors from Country Y are not the source of the disease. Thus, testing them would likely do little to curb the spread of the disease. (E) This does not suggest that the proposal will not help curb the spread of the disease. If the visitors from Country Y are indeed carriers, then their refusal to visit Country X will help curb the disease.
Sarah is in a room with 6 other children. If the other children are 2, 4, 5, 8, 10, and 13 years old, is Sarah 7 years old? (1) The age of the fourth oldest child is equal to the average (arithmetic mean) of the seven children's ages. (2) Sarah is not the oldest child in the room.
C The question "Is Sarah 7 years old?" does not need rephrasing. Notice that all of the other children's ages are listed in order and that Sarah's position in this order is unknown. If Sarah actually is 7 years old, she would be the middle child. However, we cannot rephrase the question as "Is Sarah the middle child?" because that would also be true if she were 6, not 7. It's easier to begin with statement 2 because this statement is clearly not sufficient. (2) INSUFFICIENT: Knowing that Sarah is not the oldest does not provide any other information about the position of Sarah's age relative to the other children. Sarah might be any age from 0 to 12. (1) INSUFFICIENT: This statement tells us that the median and average of this set are the same. In a set of 7 children, the fourth oldest child's age is the median value, and we can set this equal to the average. To find the mean, or the average of the ages, we can use the Average Formula: Average = Sum of Ages / 7. Let's call Sarah's age S. The average, then, is: A = (42+S)/7 Determining the median age is more complicated, because we don't know where Sarah fits into the order. We will have to test three different cases: Sarah's age could be (1) equal to the median, (2) less than the median, or (3) greater than the median. Set each possible median equal to the average. Case 1 (S = Median): S = (42 + S)/7 7S = 42 + S 6S = 42 S = 7 Case 2 (S In this case, Sarah must be among the youngest three, which puts the 5-year-old in the median spot. 5 =(42 + S)/7 35 = 42 + S −7 = S Sarah cannot be −7 years old, so we can ignore this case. Case 3 (S>Median): This puts the 8-year-old in the middle spot. 8 = (42 + S)/7 56 = 42 + S 14 = S Sarah could be 7 or 14, so this statement is not sufficient. (Note: if we had happened to try case 3 before case 2, we could have stopped at that point.) (1) AND (2) SUFFICIENT: Statement 1 tells us that Sarah is either 7 or 14 years old. Statement 2 tells us Sarah is not the oldest, so Sarah is not 14. Therefore, Sarah must be 7. The correct answer is C.
*That every worker has a clean criminal record is of some importance to investment banks which is why a stringent background check is a necessary prerequisite for all of their job applicants.* That every worker has a clean criminal record is of some importance to investment banks which is why a stringent background check is a necessary prerequisite for all of their job applicants Clean criminal records of their employees is important to investment banks; hence, a stringent background check are necessary prerequisites for employment Because they consider it important that all of their employees have a clean criminal record, investment banks require each job applicant to undergo a stringent background check It is of some importance that all investment banks' workers have clean criminal records which is why many of them undergo stringent background checks The reason that investment banks require background checks of their applicants is because they require clean criminal records of their employees
C he sentence has several errors of concision. First, the structure "X is of ... importance which is why Y is a ... prerequisite" is awkward and wordy, and can be more concisely written as follows: "Because [X is ... important], [Y is ... necessary]." Second, both "some importance" and "necessary prerequisite" are redundant: if something is "important" it has "some importance"; similarly, a "prerequisite" is by definition "necessary." (A) This choice is incorrect as it repeats the original sentence. (B) The singular verb "is" does not agree with the plural subject "records." In addition, the plural verb "are" does not agree with the singular subject "background check." Finally, the phrase "necessary prerequisite" is redundant. (C) CORRECT. The redundant and passive clause "X is of significant importance to investment banks" is replaced by the more concise and active clause "they [investment banks] consider X important." In addition, the redundant and passive clause "a background check is a necessary prerequisite [of investment banks]" is replaced by the more concise and active "investment banks require background checks." Finally, the entire sentence is rewritten in the concise form "Because X, Y." (D) The phrase "some importance" is redundant and wordy. In addition, the meaning of the sentence has been changed to state that "many" of the employees underwent a background check; the original sentence asserted that the background check was required, and, therefore, was submitted to by all. (E) The structure "the reason X is because Y" is redundant. The proper idiom is either "the reason X is Y" or "Y is because X." In addition, it is not clear whether the pronouns "they" and "their" refer to "investment banks" or "applicants."
If r + s > 2 t, is r > t ? (1) t > s (2) r > s
D (1) SUFFICIENT: We can combine the given inequality r + s > 2t with the first statement by adding the two inequalities: r + s > 2t t > s __ r + s + t > 2t + s r > t (2) SUFFICIENT: We can combine the given inequality r + s > 2t with the second statement by adding the two inequalities: r + s > 2t r > s __ 2r + s > 2t + s 2r > 2t r > t The correct answer is D.
A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn? 4 6 8 10 12 Hide Explanation
Each side of the square must have a length of 10. If each side of the square were to be a length of 6, 7, 8, or most other numbers, there could only be four possible squares drawn in total, because each side, in order to have integer coordinates, would have to be drawn on the x- or y-axis. A length of 10 is different though, because the side of such a square can be the hypotenuse of a Pythagorean triple, meaning the vertices could have integer coordinates without lying on the x- or y-axis. For example, a square could be drawn with the coordinates (0,0), (6,8), (-2, 14) and (-8, 6). (It is tedious and unnecessary to figure out all four coordinates for each square). If we label the square abcd, with a at the origin and the letters representing points in a clockwise direction, we can get the number of possible squares by figuring out the number of unique ways ab can be drawn. a has coordinates (0,0) and b could have the following coordinates, as shown in the picture: There are 12 different ways to draw ab, and so there are 12 ways to draw abcd. The correct answer is E.
In a certain sport, teams receive 3 points for each win, 1 point for each draw, and no points for losses. In a five-team tournament in this sport, in which each of teams G, H, J, K, and L played each other team exactly once, did team L finish the tournament with the highest point total? (1) Team L finished with 8 points. (2) The sum of all five teams' point totals for the tournament was 23 points.
Each team plays each other team once, so there are a total of 10 games played. (If you're not sure about that, count it out! GH, GJ, GK, GL, HJ, HK, HL, JK, JL, KL). Each team plays a total of 4 games. If one team wins, 3 points are awarded (total) for that game. If the teams tie, 2 points are awarded (total) for that game. If one team wins all four of its games, it would earn 12 points. (1) INSUFFICIENT: We know that team L played four games and earned 8 points. The only way to get 8 points in four games is 3 + 3 + 1 + 1, so team L must have won two games, drawn two, and lost none. With this win-loss record, it's possible that team L finished first. For instance, say that all of the other games in the tournament were draws. In that case, team L would have 8 points, the two teams that lost to L would have 0 + 1 + 1 + 1 = 3 points, and the two teams that tied with L would have 1 + 1 + 1 + 1 = 4 points. On the other hand, it's also possible that team L finished second. For instance, team G could have tied team L and beaten all three of the other teams, finishing with 1 + 3 + 3 + 3 = 10 points to team L's 8 points. (2) INSUFFICIENT: This statement contains no information about the distribution of points among the teams, so we can't tell how any individual team fared. (1) AND (2) SUFFICIENT: To recap, there are 10 total games, and one game results in either 2 or 3 total points awarded. Say that x of the games were won by one team, and thus the remaining 10 - x games were ties. Each "won" game will result in 3 points awarded and each "tie" game will result in two points awarded: 3(x) + 2(10 - x) = 23 3x + 20 - 2x = 23 x = 3 Therefore, exactly 3 of the games were won by one team and lost by the other, and the other 7 were ties. Since team L won two games, none of the other teams could have won more than one game. The maximum point total for any of the other teams is 3 + 1 + 1 + 1 = 6 points, two points lower than team L's total. Therefore, team L finished with the highest point total. The correct answer is C.
In the figure above, ABCD is a square, and the two diagonal lines divide it into three regions of equal area. If AB = 3, what is the approximate length of w, the perpendicular distance between the two diagonal lines? screenshots 0.8 1.2 1.4 1.8 2.1
If AB = 3, then the area of square ABCD is 9, so each of the three regions has area 3. Using the 45−45−90 triangle ratios, the diagonal BD of the square has length 3√2. Label the rest of this diagonal: screenshots In the figure, w + 2Q = 3√2, so w = 3√2 - 2Q. To find Q, note that the two triangular regions can be put together to form a square with area 6 (because each of the regions has an area of 3). The area of the square is equal to s2, so s = √6. Using the 45−45−90 triangle ratios again, the diagonal of this smaller square (2Q) would be (√6)(√2) = √12 = 2√3. 2Q = 2√3, so Q = √3. The value of w is thus 3√2 - 2Q = 3√2 - 2√3. Since the approximate value of √2 is 1.4 and the approximate value of √3 is 1.7, this approximates to 3(1.4) - 2(1.7) = 0.8. This question can also be answered using estimation from the outset. The diagram is drawn to scale (problem solving questions are drawn to scale unless otherwise stated, data sufficiency questions are NOT), so the value of w can be estimated visually. The length of AB is 3; in the diagram, w appears to be around one-fourth of that length, so w should be somewhere around 3/4. Answer choice A, 0.8, is the closest value. The second closest answer, 1.2 (answer choice B), would require that w be 40% of the length of AB. Given the diagram, this seems rather unlikely. The correct answer is A.
Set S contains seven distinct integers. The median of set S is the integer m, and all values in set S are equal to or less than 2m. What is the highest possible average (arithmetic mean) of all values in set S ? m 10m/7 10m/7 - 9/7 5m/7 + 3/7 5m Hide Explanation
In all that follows, the numbers in set S are assumed to be in increasing order (so that the 1st value is the lowest and the 7th value is the highest). Also, if we want the highest possible average, then we need to make every member of Set S as large as possible. The median of S is the 4th value in the set. For the median to equal m, the 4th value must equal m. We must choose the highest possible value for every member of the set. The maximum value of any member of the set is 2m, so the 7th value is 2m. Because every member of the set is an integer, the next highest possible value is 2m - 1, which is the 6th value. The 5th value is the next highest possible number, which is 2m - 2. By a similar logic, the 3rd value is m - 1, the 2nd value is m - 2, and the 1st value is m - 3. S = {m - 3, m - 2, m - 1, m, 2m - 2, 2m - 1, 2m} The sum of the elements of the set is 10m - 9. The average of the values in this set is 10m/7 - 9/7. The correct answer is C.
A certain ball team has an equal number of right- and left-handed players. On a certain day, two-thirds of the players were absent from practice. Of the players at practice that day, one-third were left handed. What is the ratio of the number of right-handed players who were not at practice that day to the number of left-handed players who were not at practice? 1/3 2/3 5/7 7/5 3/2 Hide Explanation
Since the problem deals with fractions, it would be best to pick a smart number to represent the number of ball players. The question involves thirds, so the number we pick should be divisible by 3. Let's say that we have 9 right-handed players and 9 left-handed players (remember, the question states that there are equal numbers of righties and lefties). Two-thirds of the players are absent from practice, so that is (2/3)(18) = 12. This leaves 6 players at practice. Of these 6 players, one-third were left-handed. This yields (1/3)(6) = 2 left-handed players at practice and 9 - 2 = 7 left-handed players NOT at practice. Since 2 of the 6 players at practice are lefties, 6 - 2 = 4 players at practice must be righties, leaving 9 - 4 = 5 righties NOT at practice. The question asks us for the ratio of the number of righties not at practice to the number of lefties not at practice. This must be 5 : 7 or 5/7. The correct answer is C.
Analyst: Creative professionals, such as clothing designers, graphic designers, and decorators, often have very poor managerial skills and do not succeed when they try to run their own businesses. In fact, most of these creative types are less skilled in business than is the average white-collar professional who does not work in a creative field. Generally, creative talent and business acumen rarely go hand in hand. If the analyst's argument is taken as true, which of the following statements can properly be concluded? No successful businesspeople are creative. Some creative types are not less skilled at business than is the average white-collar worker who is not creative. Creativity precludes success in business. Any white-collar worker who is not creative is more successful in business than any creative professional. Business is not a creative endeavor.
The analyst presents several points about the business talents of creative professionals. In drawing a conclusion from the analyst's argument, we must be careful to choose a provable claim, whether or not this claim pulls together all the premises. We also must avoid extending the analyst's argument or selecting statements that are too extreme. Finally, we must not allow this process to be clouded by reactions to the content of the argument; whether or not we agree with the premises, we have to find a provable conclusion. (A) This choice takes the passage's claim that creativity and business acumen rarely go hand in hand to an extreme. The analyst does not assert that absolutely no successful people are creative. (B) CORRECT. The passage states that most creative types are less skilled in business than the average white-collar worker who does not work in a creative field. This implies that some creative types are not less skilled than the average white-collar worker who is not creative. (C) This choice again takes the passage's claim that creativity and business acumen rarely go hand in hand to an extreme. Creativity and business acumen are not mutually exclusive. (D) The passage does not say that all white-collar workers are successful, nor does it say that no creative professionals are successful. (E) The passage makes a distinction between creative talent and business acumen. This does not mean that there are no aspects of business that fall under the realm of creativity.
*The president's nominees to federal circuit courts have been judged conservative for their stands on hot-button issues.* But a review of their financial disclosure forms and Senate questionnaires reveals that the nominees are more notable for their close ties to corporate and economic interests, especially the energy and mining industries. Some of them were paid lobbyists for those same interests. Further, *the nominees with industry ties were overwhelmingly appointed to circuit courts regarded as traditional battlegrounds over litigation affecting these industries.* Independent observers who follow the federal bench believe that the extensive corporate involvement among so many of the nominees is unprecedented. In the argument above, the two portions in boldface play which of the following roles? The first is a generalization that the author aims to attack; the second is that attack. The first is a pattern that the author acknowledges as true; the second is the author's conclusion based on that acknowledgment. The first is a phenomenon that the author accepts as true; the second is evidence in support of the author's conclusion. The first is the author's position based on the evidence cited; the second is a pattern presented in support of that position. The first is an exception to a rule introduced in the argument; the second provides the reasoning behind the exception.
The conclusion of the argument is that the nominees "are more notable for their close ties to corporate and economic interests" than for their positions on controversial issues. The first boldfaced statement is a recognition of the fact that the president's nominees have been branded conservative. The second boldfaced statement offers information in support of the assertion that the nominees are more notable for their corporate ties. So we need to find a choice that describes both statements accurately. (A) The author does not seek to attack the assertion made in the first statement. (B) The author does acknowledge the first statement as true. However, the second statement is not the conclusion. (C) CORRECT. The author does accept the first statement as true, and the second statement is indeed given in support of the conclusion. (D) The first statement is not the author's "position" (i.e., conclusion). (E) The first statement is not an exception to a rule, making the description of the second statement false as well.
A city is hosting a Swiss-system chess tournament called Chessmaster. In a Swiss-system tournament, every player plays every other player, and no one is eliminated. At Chessmaster, each player who wins a match receives two points; those who draw a match each receive half a point; those who lose a match each lose one point; and every player can choose to sit out one match (and neither receive nor lose points). Player X has 4 points after 6 matches. From the available options, select a number of wins and a number of combined draws and losses that would result in Player X's score. The answers must be jointly consistent with the outcome. Make only one choice in each column. Wins Draws + Losses Number 0 1 3 4 5
The only way to answer this question is to quickly work out all the possible patterns of 6 rounds that would result in a score of 4 points. Basically, Player X could have won 1, 2, or 3 games (any more than that and the score is too big, while draws alone can't bring the score up to 4 points in only 6 games). Let's consider these three possibilities: 1 Win: With only 1 win, the only way to get up to 4 points would be to draw the next 4 games, and sit the last one out. This will turn out to be the situation that the answer choices fit. 2 Wins: Looking at the answer choices, we can see that 2 isn't an option. However, with 2 wins, the only way to reach 4 points is to draw twice and then lose once (and sit the final round out). 3 Wins: With three wins (adding up to six points), the only way to get down to 4 points is to lose two matches in a row (and sit out the final round). While 3 is an option in the answer choices, we already know that 2 isn't, so this can't be the correct situation.
During the past decade, the labor market in France has not been operating according to free market *principles, but instead stifling functioning through its various government regulations restricting the hiring and firing of workers.* principles, but instead stifling functioning through its various government regulations restricting the hiring and firing of workers principles, instead it has been functioning in a stifled manner as a result of various government regulations that restrict the hiring and firing of workers principles, rather functioning despite being stifled as a result of government regulations that variously restrict worker hiring and firing principles; the hiring and firing of workers is restricted there by various government regulations, its functioning being stifled principles; instead, its functioning has been stifled by various government regulations restricting the hiring and firing of workers
The original sentence is problematic in its use of the possessive pronoun "its." The antecedent to "its" is the "labor market," which incorrectly and illogically suggests that the labor market is somehow possessing or passing government regulations itself. In addition, the original sentence incorrectly uses active rather than passive voice to describe the effects imposed on the "labor market" by government regulations, thus illogically suggesting that the "labor market" itself is stifling functioning, rather than being stifled by other forces. (A) This choice is incorrect as it repeats the original sentence. (B) This choice incorrectly uses a comma to connect two independent clauses, thus creating a run-on sentence. Two independent clauses must be connected either by a conjunction, such as "and" or "but," or by a semicolon. (C) This choice incorrectly uses "stifled" to modify the labor market itself, as opposed to its functioning. Also, "variously restrict" is awkward; various is used more appropriately to modify "government regulations," rather than the manner in which the regulations restrict worker hiring and firing. (D) In order to properly use a semicolon, both the clause before and after the semicolon must be independent clauses or sentences, and the clauses must be closely related in meaning. In this choice, the underlined portion, though grammatically correct, does not stand alone as an effective independent clause. Also, the pronoun "its" lacks a clear antecedent. (E) CORRECT. This answer choice correctly uses the semicolon to connect two independent but closely related clauses. In addition, the pronoun "its" clearly and unambiguously refers to the "labor market."
For any integer k > 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 1000, what is the maximum possible sum of the length of x and the length of y? 5 6 15 16 18
The problem asks us to find the greatest possible value of (length of x + length of y), such that x and y are integers and x + 3y < 1,000 (note that x and y are the numbers themselves, not the lengths of the numbers - lengths are always indicated as "length of x" or "length of y," respectively). Consider the extreme scenarios to determine our possible values for integers x and y based upon our constraint x + 3y < 1,000 and the fact that both x and y have to be greater than 1. If y = 2, then x ≤ 993. If x = 2, then y ≤ 332. Of course, x and y could also be somewhere between these extremes. Since we want the maximum possible sum of the lengths, we want to maximize the length of our x value, since this variable can have the largest possible value (up to 993). The greatest number of factors is calculated by using the smallest prime number, 2, as a factor as many times as possible. 29 = 512 and 210 = 1,024, so our largest possible length for x is 9. If x itself is equal to 512, that leaves 487 as the highest possible value for 3y (since x + 3y < 1,000). The largest possible value for integer y, therefore, is 162 (since 487 / 3 = 162 remainder 1). If y < 162, then we again use the smallest prime number, 2, as a factor as many times as possible for a number less than 162. Since 27 = 128 and 28 = 256, our largest possible length for y is 7. If our largest possible length for x is 9 and our largest possible length for y is 7, our largest sum of the two lengths is 9 + 7 = 16. What if we try to maximize the length of the y value rather than that of the x value? Our maximum y value is 332, and the greatest number of prime factors of a number smaller than 332 is 28 = 256, giving us a length of 8 for y. That leaves us a maximum possible value of 231 for x (since x + 3y < 1,000). The greatest number of prime factors of a number smaller than 231 is 27 = 128, giving us a length of 7 for x. The sum of these lengths is 7 + 8 = 15, which is smaller than the sum of 16 that we obtained when we maximized the x value. Thus 16, not 15, is the maximum value of (length of x + length of y). The correct answer is D.
During the twentieth century, the study of the large-scale structure of the universe evolved from the theoretical to the practical; the field of physical cosmology was made possible *because of both Einstein's theory of relativity and* the better ability to observe extremely distant astronomical objects. because of both Einstein's theory of relativity and by both Einstein's theory of relativity and by Einstein's theory of relativity and also because of Einstein's theory of relativity and also as a result of both Einstein's theory of relativity and
The underlined portion of the sentence introduces two idioms: made possible by and both X and Y. The former idiom is incorrectly presented in the sentence as made possible because of. (A) The choice is incorrect as it repeats the original sentence. (B) CORRECT. This choice uses both idioms correctly: made possible by and both X and Y. (C) This choice corrects the first idiom (made possible by) but introduces a new error by removing both and replacing it with and also, which is redundant. (D) This choice repeats the original idiom error made possible because of. It also introduces a new error by removing both and replacing it with and also, which is redundant. (E) This choice presents the incorrect idiom (made possible as a result of) rather than the correct idiom, made possible by.
According to the writings of *Thorstein Veblen, the economist, the most reliable signal of a truly wealthy individual is his or her ability and willingness* to engage in "conspicuous consumption"—to spend it in a way that is patently absurd or irrational. Thorstein Veblen, the economist, the most reliable signal of a truly wealthy individual is his or her ability and willingness Thorstein Veblen, the economist, the most reliable signal that one is truly wealthy is whether one is capable and willing economist Thorstein Veblen, the most reliable signal of one's true wealth is whether an individual is capable and willing the economist Thorstein Veblen, an individual's true wealth is most reliably signaled by their ability and willingness the economist Thorstein Veblen, the most reliable signal of true wealth is an individual's ability and willingness
This sentence describes an assertion from the writings of the economist Thorstein Veblen: namely, that individual wealth is most reliably signaled by the ability and willingness to engage in "conspicuous consumption," a concept that the sentence then defines. (A) The pronoun it in the phrase spend it in a way should logically refer to wealth or money; however, no such noun exists in the sentence (wealthy is an adjective). (B) The pronoun it in the phrase spend it in a way should logically refer to wealth or money; however, no such noun exists in the sentence (wealthy is an adjective). Whether is also illogical, suggesting that whether someone is willing or is not willing to engage in "conspicuous consumption" is a signal of wealth. Rather, someone must have both the ability and the willingness to do so. Finally, in the parallel structure capable and willing to engage, the idiom willing to + verb is acceptable, but the idiom capable to + verb is not (the sentence should say capable of engaging). (C) The shift from one's to an individual is unacceptable; it illogically suggests that the person possessing the wealth is not necessarily the same person who engages in "conspicuous consumption." Whether is also illogical, suggesting that whether someone is willing or is not willing to engage in "conspicuous consumption" is a signal of wealth. Rather, someone must have both the ability and the willingness to do so. Finally, in the parallel structure capable and willing to engage, the idiom willing to + verb is acceptable, but the idiom capable to + verb is not (the sentence should say capable of engaging). (D) The plural pronoun their cannot refer to the singular noun an individual's. (E) CORRECT. This sentence contains the singular noun wealth, which serves as a logical antecedent for it. Both ability and willingness combine idiomatically with to + verb.
A piece of wire is bent so as to form the boundary of a square with area A. If the wire is then bent into the shape of an equilateral triangle, what will be the area of the triangle thus bounded in terms of A?
screenshots
Kim finds a 1-meter tree branch and marks it off in thirds and fifths. She then breaks the branch along all the markings and removes one piece of every distinct length. What fraction of the original branch remains?
screenshots
Regular hexagon ABCDEF has a perimeter of 36. O is the center of the hexagon and of circle O. Circles A, B, C, D, E, and F have centers at A, B, C, D, E, and F, respectively. If each circle is tangent to the two circles adjacent to it and to circle O, what is the area of the shaded region (inside the hexagon but outside the circles)? screenshots
screenshots
A triangle in the xy-coordinate plane has vertices with coordinates (7, 0), (0, 8), and (20, 10). What is the area of this triangle? 72 80 87 96 100
screenshots It's not immediately possible to use the standard formula A = bh / 2 for the area of this triangle, because none of the triangle's sides is horizontal or vertical. However, if the triangle is circumscribed by a rectangle, as depicted below, the areas of the three surrounding triangles can readily be found and then subtracted from the rectangle's area to yield the desired result. First, the triangle to the lower left has b = 7 and h = 8, so its area is (7)(8) / 2 = 28. Second, the triangle to the lower right has b = 13 and h = 10, so its area is (13)(10) / 2 = 65. Third, the topmost triangle has b = 20 and h = 2, so its area is (20)(2) / 2 = 20. The total area of the surrounding triangles—that is, the triangles that are not part of the desired area—is 28 + 65 + 20 = 113 square units. The total area of the rectangle is 20 x 10 = 200 square units, so the triangle's area is 200 - 113 = 87 square units. The correct answer is C.