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Official GMAT Questions | Two-Part Analysis | Hard Set 2

Two Part Analysis | Official Practice Questions | 10 Hard
Teaching Mode
Q1 Hard Finding the one sentence that states a conditional probability, rather than a plain unconditional one
A statistician reached the following conclusions about games between university soccer teams: Overall, a team playing on its home field has a 45% chance of a win, a 25% chance of a loss, and a 30% chance of a draw (a tied outcome). In the games where one or more goals are scored, the team that scores the first goal has a 55% chance of scoring it in the game's first half and a 45% chance of scoring it later in the game. When that team is the home team (that is, a team playing on its home field), there is a 40% chance that the other team will score no goals at all, and therefore a 60% chance that it will score one or more goals.

Select for X and for Y two different outcomes such that the information provided explicitly includes the statistician's estimates of the probability that if X occurs, so will Y. Make only two selections, one in each column.
XY
The home team scores at least two goals in the game.
The home team scores the first goal.
A goal is scored in the first half of the game.
A goal is scored in the second half of the game.
The team opposing the home team scores at least one goal.

Answer Key and Working

X: The home team scores the first goal. Y: The team opposing the home team scores at least one goal.
  1. Step 1, before picking any option, lay out every single number the passage actually gives, since this question is really a hunt for one very specific sentence hidden among several unrelated statistics. Statistic one, an overall home field record of 45 percent win, 25 percent loss, 30 percent draw, describing the outcome of a game in general, not tied to any other event. Statistic two, among games where at least one goal is scored, whichever team scores that first goal does so in the first half 55 percent of the time and in the second half 45 percent of the time, describing WHEN the first goal happens, not linking it to any separate later event. Statistic three, when the team that scored first happens to be the home team, there is a 40 percent chance the other team scores no goals at all, and therefore, as the passage itself states, a 60 percent chance the other team scores one or more goals.
  2. Step 2, understand precisely what the question is asking for, since the phrase "the probability that if X occurs, so will Y" is asking for a genuine conditional probability, a statement of the form, given that X has already happened, here is the chance Y also happens. This is different from an unconditional statistic like the 45 percent win rate, which is not conditioned on any other event occurring first.
  3. Step 3, scan the three statistics from Step 1 and check each one for this exact conditional structure. Statistic one is a flat, unconditional breakdown of game outcomes, it is not phrased as "given some event X, here is the chance of some different event Y," so it does not fit. Statistic two describes two timing outcomes (first half or second half) for the very same single event, namely the first goal being scored, it is not describing one event making a second, different event more or less likely, so it also does not fit.
  4. Step 4, statistic three is different from the other two in a crucial way, since it explicitly begins with a condition, "when that team is the home team," and then gives a probability for a separate, distinct outcome, namely how many goals the OTHER team goes on to score. This is precisely the conditional structure the question wants, X has occurred (the home team scored the first goal) and now here is the probability of Y occurring (the opposing team scores at least one goal).
  5. Step 5, translate statistic three carefully into the exact X and Y wording used in the answer choices. The condition X is "the home team scores the first goal," matching the option "The home team scores the first goal" precisely. The outcome Y is "the other team will score one or more goals," which matches the option "The team opposing the home team scores at least one goal" precisely, since these two phrases describe the identical event using different but equivalent wording.
  6. Step 6, double check by rereading the sentence with the chosen X and Y substituted in. "When the home team scores the first goal, there is a 60 percent chance that the team opposing the home team scores one or more goals." This is exactly what the passage states, word for word in meaning, confirming this pairing is correct.
  7. Step 7, work through why each remaining option fails to fit either blank. "The home team scores at least two goals in the game" is never linked to any other event by a stated probability anywhere in the passage, none of the three statistics mention a second goal by the home team at all, so this option cannot be paired with anything. "A goal is scored in the first half of the game" and "a goal is scored in the second half of the game" both belong to statistic two, which, as established in Step 3, describes two alternative timings for the SAME event rather than a condition producing a separate outcome, so neither of these can serve as the Y that follows from some stated X, nor can either serve as an X that produces some stated Y elsewhere in the passage.
  8. Step 8, watch the trap of assuming that because statistic two mentions two different percentages (55 percent and 45 percent) it must represent a conditional relationship the same way statistic three does. The key difference is that statistic three names a condition using the word "when," attached to a completely different downstream outcome (how many goals the OTHER team scores), whereas statistic two is simply reporting two mutually exclusive timings for one and the same first goal, with no second, separate event being predicted at all. Recognizing this structural difference, rather than being distracted by the presence of percentages in both places, is what pins down the correct pair.
Final answers: X: The home team scores the first goal. Y: The team opposing the home team scores at least one goal.
Q2 Hard Rearranging the percent change formula to express a Fall 1999 value and a Spring 2004 ratio algebraically
Over a period of 5 academic years from Fall 1999 through Spring 2004, the number of faculty at a certain college increased despite a decrease in student enrollment from 5,500 students in Fall 1999.

In the given expressions, F and S represent the percent change in the number of faculty and students, respectively, over the 5 academic years, and R represents the number of students per faculty member in Fall 1999. The percent change in a quantity X is calculated using the formula
XNew minus XOldXOld (100)
Select the expression that represents the number of faculty in Fall 1999, and select the expression that represents the number of students per faculty member in Spring 2004. Make only two selections, one in each column.
Number of faculty in Fall 1999Students per faculty member in Spring 2004
5,500 R
5,500R
1R
(100+S100+F) R
(100 minus S100+F) 1R
(100+F100 minus S) 1R

Answer Key and Working

Number of faculty in Fall 1999: 5,500 divided by R. Students per faculty member in Spring 2004: R times (100 plus S), all divided by (100 plus F).
  1. Step 1, before touching any algebra, pin down in plain words exactly what every letter in this problem stands for, since mixing up the variables is the single easiest way to get a percent change problem like this wrong. R is defined as the number of students per faculty member in Fall 1999, meaning R equals total Fall 1999 students divided by total Fall 1999 faculty. F is the percent change in the number of faculty from Fall 1999 to Spring 2004. S is the percent change in the number of students over that same period. We are also told directly that Fall 1999 had 5,500 students.
  2. Step 2, use the definition of R from Step 1 to solve for Fall 1999 faculty, since that is exactly what the first blank is asking for. Since R equals students divided by faculty for Fall 1999, rearranging gives faculty equals students divided by R. Substituting the known Fall 1999 student count of 5,500 gives Fall 1999 faculty equals 5,500 divided by R.
  3. Step 3, before working out Spring 2004 values, rebuild the percent change formula from the ground up so that every later algebraic step is fully justified rather than just memorized. Percent change of a quantity X equals (X new minus X old) divided by X old, all multiplied by 100. Rearranging this formula to solve for X new in terms of X old and the percent change, multiply both sides by X old to get X new minus X old equals (percent change divided by 100) times X old, then add X old to both sides to get X new equals X old times (1 plus percent change divided by 100), which can be written more cleanly as X new equals X old times (100 plus percent change) divided by 100.
  4. Step 4, apply this rearranged formula from Step 3 to students first. Students in Spring 2004 equals students in Fall 1999 times (100 plus S) divided by 100, which is 5,500 times (100 plus S) divided by 100.
  5. Step 5, apply the same rearranged formula to faculty. Faculty in Spring 2004 equals faculty in Fall 1999 times (100 plus F) divided by 100. Using the Fall 1999 faculty value found in Step 2 (5,500 divided by R), this becomes (5,500 divided by R) times (100 plus F) divided by 100.
  6. Step 6, now compute students per faculty member in Spring 2004, which is exactly Spring 2004 students divided by Spring 2004 faculty, since that ratio is precisely what "students per faculty member" means (mirroring exactly how R itself was defined for Fall 1999 back in Step 1). Divide the Step 4 result by the Step 5 result.
  7. Step 7, carry out this division carefully, term by term, to avoid losing track of any piece. The numerator is 5,500 times (100 plus S) divided by 100. The denominator is (5,500 divided by R) times (100 plus F) divided by 100. Dividing the numerator by the denominator, the shared factor of 5,500 cancels completely (it appears in both the numerator and the denominator), and the shared factor of divided by 100 also cancels completely (it too appears in both), leaving simply (100 plus S) divided by (100 plus F), multiplied by R, since dividing by (5,500 divided by R) is the same as multiplying by (R divided by 5,500), and after the 5,500 terms cancel we are left with just R remaining as a multiplier.
  8. Step 8, write out the final simplified result clearly. Students per faculty member in Spring 2004 equals R times (100 plus S), all divided by (100 plus F). This matches the option written as R multiplied by the fraction with numerator (100 plus S) and denominator (100 plus F).
  9. Step 9, work through why each of the remaining options fails to represent either quantity correctly. "5,500 R" for Fall 1999 faculty would only be correct if R were faculty divided by students rather than students divided by faculty, but Step 1 established R specifically as students per faculty member, so faculty must equal students divided by R, not students multiplied by R, ruling this option out. "1 divided by R" is simply the reciprocal of R itself and represents faculty per student in Fall 1999 rather than the actual headcount of faculty, since it never incorporates the 5,500 student figure at all, so it cannot represent an actual faculty count.
  10. Step 10, continue checking the remaining Spring 2004 options. The option with (100 minus S) divided by (100 plus F), multiplied by 1 divided by R, incorrectly uses a minus sign in front of S and also uses the reciprocal of R rather than R itself; since S is already a signed percent change (it will itself be a negative number, given that enrollment decreased), the formula from Step 3 always uses a plain "100 plus" the percent change, never a manually inserted minus sign, so building in an extra minus sign here double counts the direction of the change. The option with (100 plus F) divided by (100 minus S), multiplied by 1 divided by R, has the numerator and denominator of the F and S terms flipped relative to the correct derivation in Step 7, and also incorrectly uses 1 divided by R instead of R, compounding two separate errors at once.
  11. Step 11, watch the trap of assuming that because student enrollment decreased, the formula must be adjusted with a subtraction sign somewhere to reflect that decrease. The percent change formula defined in the passage already produces a negative value for S automatically when a quantity decreases, precisely because X new is smaller than X old in that case, making (X new minus X old) negative. This means the general formula, X new equals X old times (100 plus percent change) divided by 100, requires no separate adjustment for decreases, since a negative S already correctly shrinks the (100 plus S) term below 100 on its own.
Final answers: Number of faculty in Fall 1999: 5,500 divided by R. Students per faculty member in Spring 2004: R times (100 plus S), all divided by (100 plus F).
Q3 Hard Equating cost per unit of usable energy across two fuels sharing the same efficiency percentage
When fully burned, natural gas produces approximately 1,000 BTU of heat per cubic foot of fuel, and propane produces about 2,500 BTU of heat per cubic foot of fuel. For a furnace in which either natural gas or propane may be burned as fuel, the efficiency of a given fuel is the usable heat energy produced when the fuel is burned in the furnace, expressed as a percentage of the total heat energy produced when the fuel is burned.

Kaiser will purchase a furnace whose efficiency with respect to either natural gas burned alone or propane burned alone is 90%. In the table select for natural gas cost per cubic foot and for propane cost per cubic foot the values that are jointly consistent with the information given for which the fuel cost per BTU of usable heat energy produced by this furnace would be approximately the same for each fuel burned alone. Make only two selections, one in each column.
Natural gas cost per cubic footPropane cost per cubic foot
0.0035
0.0070
0.0110
0.0175
0.0350

Answer Key and Working

Natural gas cost per cubic foot: 0.0070. Propane cost per cubic foot: 0.0175.
  1. Step 1, before comparing costs, build a clear picture of what "efficiency" means here from the ground up. The passage defines efficiency as the usable heat energy actually produced, expressed as a percentage of the total heat energy the fuel is capable of producing when burned. In plain terms, if a fuel produces some total amount of heat when burned, only a percentage of that total heat actually becomes usable heat in the furnace, and efficiency is exactly that percentage.
  2. Step 2, compute the usable heat each fuel actually delivers per cubic foot in Kaiser's specific furnace, which has a 90 percent efficiency for both fuels. For natural gas, total heat per cubic foot is 1,000 BTU, so usable heat equals 1,000 multiplied by 0.90, which is 900 usable BTU per cubic foot. For propane, total heat per cubic foot is 2,500 BTU, so usable heat equals 2,500 multiplied by 0.90, which is 2,250 usable BTU per cubic foot.
  3. Step 3, understand exactly what quantity the question wants us to equalize between the two fuels, since this determines the entire approach. The question asks for the fuel cost per BTU of usable heat energy to be approximately the same for each fuel. Cost per usable BTU is calculated simply as cost per cubic foot of fuel divided by usable BTU per cubic foot of that same fuel, using the usable BTU figures computed in Step 2.
  4. Step 4, set the two fuels' cost per usable BTU equal to each other, since that is precisely the condition the question is asking us to satisfy. Using cost(gas) and cost(propane) as the unknown cost per cubic foot values we need to find, the requirement becomes cost(gas) divided by 900 equals cost(propane) divided by 2,250.
  5. Step 5, solve this equation for the ratio between the two costs, since the answer choices give us specific candidate cost values rather than the usable BTU figures directly, so we need a clean relationship between cost(gas) and cost(propane) to test against the table. Cross multiplying the equation from Step 4 gives cost(propane) multiplied by 900 equals cost(gas) multiplied by 2,250, and dividing both sides by 900 gives cost(propane) equals cost(gas) multiplied by (2,250 divided by 900).
  6. Step 6, simplify the ratio (2,250 divided by 900) using simple arithmetic, since a clean numerical multiplier is much easier to test against the answer choices than a raw fraction. Dividing both 2,250 and 900 by 900 gives 2,250 divided by 900 equals 2.5. So the required relationship is cost(propane) equals cost(gas) multiplied by 2.5.
  7. Step 7, test each candidate value from the shared list (0.0035, 0.0070, 0.0110, 0.0175, 0.0350) as the natural gas cost, and check whether multiplying it by 2.5 lands exactly on another value in that same list, since that would identify the correct propane cost. Testing 0.0035 as gas cost, 0.0035 multiplied by 2.5 equals 0.00875, which does not appear anywhere in the list.
  8. Step 8, testing 0.0070 as gas cost, 0.0070 multiplied by 2.5 equals 0.0175 exactly, and 0.0175 IS one of the five listed candidate values. This is a match, giving the pair gas cost equals 0.0070 and propane cost equals 0.0175.
  9. Step 9, for completeness and to confirm this pairing is uniquely correct, test the remaining candidates as the gas cost as well. Testing 0.0110 as gas cost, 0.0110 multiplied by 2.5 equals 0.0275, which does not appear in the list. Testing 0.0175 as gas cost, 0.0175 multiplied by 2.5 equals 0.04375, which does not appear in the list. Testing 0.0350 as gas cost, 0.0350 multiplied by 2.5 equals 0.0875, which does not appear in the list.
  10. Step 10, having tested all five candidates as the gas cost, only 0.0070 produces a propane cost (0.0175) that also appears in the given list of five values, confirming gas cost equals 0.0070 and propane cost equals 0.0175 is the unique jointly consistent pair.
  11. Step 11, watch the trap of assuming the 90 percent efficiency figure must somehow directly enter the final cost ratio calculation, making the problem feel more complicated than it actually is. Since BOTH fuels share the exact same 90 percent efficiency in this particular furnace, that percentage appears as an identical multiplier on both sides of the equation in Step 4, and it cancels out completely during the cross multiplication in Step 5, leaving a ratio (2.5) that depends purely on the raw BTU per cubic foot figures given at the very start of the passage (2,500 divided by 1,000), not on the efficiency at all. If the two fuels had DIFFERENT efficiencies in this furnace, the efficiency would not cancel and would need to be incorporated directly into the ratio, but that is not the situation described here.
Final answers: Natural gas cost per cubic foot: 0.0070. Propane cost per cubic foot: 0.0175.
Q4 Hard Finding a one directional implication between two statements about a company's workforce
A certain company defines its annual labor turnover rate as the number of employees who left the company during the year divided by the average of the number of employees on the first day of the year and the number of employees on the last day of that year. Last year, the company had a labor turnover rate of exactly 25%.

Assuming that the information above is true, select for Statement 1 and for Statement 2 the statements such that if Statement 1 is true, then Statement 2 must be true, but it could be the case that Statement 2 is true and Statement 1 is false. Make only two selections, one in each column.
Statement 1Statement 2
Last year, more people left the company than began work at the company.
Exactly 25% of the employees working at the company on the first day of last year left the company last year.
More than 25% of the employees working at the company on the first day of last year left the company last year.
All and only those who were employees at the company on the first day of last year were employees on the last day of last year.
Last year, the number of employees on the first day of the year was equal to the number of employees on the last day of the year.

Answer Key and Working

Statement 1: All and only those who were employees at the company on the first day of last year were employees on the last day of last year. Statement 2: Last year, the number of employees on the first day of the year was equal to the number of employees on the last day of the year.
  1. Step 1, before evaluating the answer options, rebuild the given turnover formula in plain, concrete terms from the ground up. Turnover rate equals the number of employees who left during the year, divided by the average of the headcount on the first day of the year and the headcount on the last day of the year. Last year this rate was exactly 25 percent, meaning some nonzero number of employees actually left, since a turnover rate of 25 percent could not occur if zero employees left.
  2. Step 2, understand precisely what kind of relationship the question wants between Statement 1 and Statement 2, since this determines exactly how we test each candidate pair. We need Statement 1 to be a SUFFICIENT condition for Statement 2, meaning whenever Statement 1 is true, Statement 2 is automatically guaranteed to be true as well, but the reverse must fail, meaning Statement 2 could be true even in some situation where Statement 1 is false. This is a strictly one directional relationship, not a two way equivalence.
  3. Step 3, test the candidate "All and only those who were employees at the company on the first day of last year were employees on the last day of last year" as a possible Statement 1. Translate this into plain language, it says the group of people employed on day one and the group of people employed on the last day are literally the exact same set of individuals, with nobody added and nobody removed from that group over the course of the year (even though the turnover formula tells us SOME departures happened, this statement is specifically about the group composition at the two single-day snapshots, not about whether any comings and goings happened during the year in between).
  4. Step 4, if this candidate Statement 1 is true, work out what must logically follow about the headcounts. If the exact same set of individuals makes up the workforce on day one and on the last day, then simply by counting how many people are in that identical set, the headcount on day one must equal the headcount on the last day, since counting the same group of people twice always gives the same number both times. This directly and unavoidably produces "the number of employees on the first day equaled the number of employees on the last day," which is exactly the wording of the candidate being tested as Statement 2.
  5. Step 5, now test the necessary reverse direction, checking whether Statement 2 being true would force Statement 1 to also be true, since a genuine one directional (rather than two directional) relationship requires this reverse direction to fail. Suppose the headcount on day one equals the headcount on the last day (Statement 2 is true). Does this force the exact same individuals to be present both times (Statement 1)? Not necessarily, since the company could have had some employees leave and have hired an equal number of brand new employees to replace them over the course of the year, keeping the TOTAL headcount unchanged from day one to the last day, while the actual set of individual people present has genuinely changed. This shows Statement 2 can be true while Statement 1 is false, confirming the required one directional relationship.
  6. Step 6, having confirmed both directions in Steps 4 and 5, this pairing, Statement 1 equals "same exact people both days" and Statement 2 equals "same headcount both days," satisfies the question's requirement precisely, since Statement 1 forces Statement 2 but Statement 2 does not force Statement 1.
  7. Step 7, work through why each of the remaining candidates fails to fit either role as well as this pair does. "Last year, more people left the company than began work at the company" describes a scenario where departures exceed new hires, which would actually cause the LAST day headcount to be SMALLER than the first day headcount, not equal to it, so pairing this with the "equal headcounts" statement would be directly contradictory rather than supportive, ruling it out as either Statement 1 or Statement 2 in this particular pairing.
  8. Step 8, continue checking the remaining candidates. "Exactly 25% of the employees working at the company on the first day of last year left the company last year" and "More than 25% of the employees working at the company on the first day of last year left the company last year" both describe the SIZE of the departing group as a fraction of the day one headcount, but neither of these statements, by itself, forces any specific conclusion about whether the population of remaining plus newly hired employees results in an unchanged total headcount, since the number of NEW hires during the year is left completely unspecified by these statements; a company could lose exactly 25 percent of its day one staff and then hire back more, fewer, or exactly the same number of new staff, so these statements do not reliably force the headcount equality the way the correct Statement 1 does.
  9. Step 9, watch the trap of assuming the specific 25 percent turnover figure given in the passage must directly appear inside the correct Statement 1 or Statement 2, since the 25 percent number is simply background information establishing that turnover was nonzero, and the actual logical relationship being tested (about population continuity forcing headcount equality) does not require referencing that specific percentage at all. The two answer options that reference "25%" directly are tempting distractors precisely because they echo a number from the passage, but they describe departure SIZE rather than the population continuity relationship the question is actually asking about.
Final answers: Statement 1: All and only those who were employees at the company on the first day of last year were employees on the last day of last year. Statement 2: Last year, the number of employees on the first day of the year was equal to the number of employees on the last day of the year.
Q5 Hard Building the true range from two separate rounding rules, then finding the tightest containing interval from a list
Lee is planning a trip and estimates that, rounded to the nearest 5 kilometers (km), the length of the trip will be 560 km and that, rounded to the nearest one quarter hour, the driving time for the trip will be 7 hours. If these estimates are correct, then Lee's average driving speed during the trip will be between x kilometers per hour and y kilometers per hour, where x is less than y.

From the values given in the table, select for x and for y the values that complete the statement in such a way that the interval between the selected values includes all possible average speeds for Lee's trip and y minus x is minimal. Make only two selections, one in each column.
XY
73
76
79
82
85

Answer Key and Working

X: 76. Y: 82.
  1. Step 1, before doing any arithmetic, understand exactly what "rounded to the nearest 5 km" means for the true, unrounded distance, since this defines the entire range we need to work with. If a value rounds to 560 when rounded to the nearest 5, the true value must be within 2.5 (half of 5) of 560 in either direction, but capped so it does not round up to the NEXT multiple of 5. This gives a true distance L satisfying 557.5 is less than or equal to L, and L is strictly less than 562.5 (using strictly less than at the top end since a distance of exactly 562.5 would round to 565, not 560, by standard rounding convention).
  2. Step 2, apply the exact same rounding logic to the driving time, which is rounded to the nearest one quarter hour (15 minutes) to give 7 hours. Half of one quarter hour is one eighth of an hour, which as a decimal is 0.125 hours. So the true time T satisfies 7 minus 0.125 is less than or equal to T, and T is strictly less than 7 plus 0.125, which is 6.875 is less than or equal to T, and T is strictly less than 7.125.
  3. Step 3, recall the basic relationship between speed, distance, and time, since this is the only formula needed to finish the problem. Average speed equals distance divided by time. To find the full range of possible speeds, we need to find both the smallest possible speed and the largest possible speed that could result from any valid combination of L (from Step 1) and T (from Step 2).
  4. Step 4, work out which combination of L and T produces the SMALLEST possible speed, since speed equals distance divided by time, the smallest speed comes from using the smallest possible distance together with the largest possible time (a shorter trip taking a longer time gives the slowest average speed). Using the smallest L (557.5) and the largest T (just under 7.125, treated as 7.125 for the purposes of finding the boundary of the range), minimum speed equals 557.5 divided by 7.125, which equals approximately 78.25 kilometers per hour.
  5. Step 5, work out which combination produces the LARGEST possible speed, using the same logic in reverse, the largest speed comes from the largest possible distance together with the smallest possible time (a longer trip taking a shorter time gives the fastest average speed). Using the largest L (just under 562.5, treated as 562.5 for the boundary) and the smallest T (6.875), maximum speed equals 562.5 divided by 6.875, which equals approximately 81.82 kilometers per hour.
  6. Step 6, having established from Steps 4 and 5 that every possible true average speed falls somewhere between approximately 78.25 and approximately 81.82 kilometers per hour, translate this into the requirement for x and y. Since the interval from x to y must FULLY CONTAIN every possible speed in this range, x must be less than or equal to 78.25 (so that no possible speed falls below x), and y must be greater than or equal to 81.82 (so that no possible speed falls above y). Additionally, the question asks for y minus x to be as small as possible, meaning we want the tightest possible interval from the given list that still fully contains the true range.
  7. Step 7, scan the five candidate values (73, 76, 79, 82, 85) for the value to use as x, remembering x must be less than or equal to 78.25. Checking each candidate, 73 qualifies (73 is less than 78.25), 76 qualifies (76 is less than 78.25), but 79 does NOT qualify, since 79 is greater than 78.25, meaning if x were 79, the true minimum speed of approximately 78.25 would fall below x, leaving it outside the interval, which is not allowed. Among the qualifying candidates (73 and 76), the largest one gives the tightest, smallest possible interval, so x equals 76.
  8. Step 8, scan the same five candidates for the value to use as y, remembering y must be greater than or equal to 81.82. Checking each candidate, 82 qualifies (82 is greater than 81.82), and 85 also qualifies, but 79 does NOT qualify, since 79 is less than 81.82, meaning if y were 79, the true maximum speed of approximately 81.82 would fall above y, leaving it outside the interval, which is not allowed. Among the qualifying candidates (82 and 85), the smallest one gives the tightest, smallest possible interval, so y equals 82.
  9. Step 9, confirm the final pairing, x equals 76 and y equals 82, giving an interval width of 82 minus 76, which equals 6, and verify this interval of 76 to 82 fully contains the true range of approximately 78.25 to 81.82 found in Steps 4 and 5, since 76 is less than 78.25 and 82 is greater than 81.82, confirming this interval is valid and, from the choices given, as tight as possible.
  10. Step 10, watch the trap of choosing whichever listed number happens to be numerically closest to the computed boundary, rather than rounding outward to fully contain the range. The value 79 is numerically closer to the true minimum speed of 78.25 than 76 is, which can make 79 look tempting for x, but 79 is actually slightly GREATER than 78.25, meaning any true speed between 78.25 and 79 would fall outside an interval starting at 79, violating the requirement that the interval include every possible speed. Since the interval must contain the ENTIRE true range with no exceptions, x must always be rounded down to the nearest qualifying candidate, and y must always be rounded up to the nearest qualifying candidate, rather than rounding either one to the nearest listed value in an ordinary sense.
Final answers: X: 76. Y: 82.
Q6 Hard Distinguishing average from median in a skewed distribution to complete a conditional statement
Companies A and B are part of the same industry and are located in the same city. For Company A, the average (arithmetic mean) salary of its employees, in United Arab Emirates dirhams (AED), is 10,000 AED higher than that for Company B. However, more than half of the employees at Company A have salaries below the average for Company B.

Statement: If the average salary at Company B is (blank 1), then the median salary at Company A is (blank 2).

Select for 1 and for 2 the options that complete the statement so that it most accurately reflects the information provided. Make only two selections, one in each column.
12
greater than 100,000 AED
less than 100,000 AED
equal to 110,000 AED
between 100,000 and 110,000 AED
greater than 110,000 AED

Answer Key and Working

1: less than 100,000 AED. 2: less than 100,000 AED.
  1. Step 1, before touching the answer choices, carefully rebuild the two facts given about Company A's salary distribution from the ground up, since this question hinges entirely on correctly distinguishing an average from a median. Fact one, Company A's average salary is 10,000 AED higher than Company B's average salary. Fact two, more than half of Company A's employees earn below the average salary at Company B specifically (not below Company A's own average, but below Company B's average).
  2. Step 2, recall, from the ground up, what a median actually represents, since this is the concept the question is really testing. The median of a group of salaries is the middle value when all the salaries are lined up in order, meaning that at least half of the salaries lie at or below the median, and at least half lie at or above it. Equivalently, if we know that MORE than half of a group's salaries fall below some particular reference number, then that reference number must be above the median of that group, since the median is defined as the point where the split is exactly half and half, and having more than half below some number pushes that number above the true middle point.
  3. Step 3, apply this median logic directly to Fact two from Step 1. Since more than half of Company A's employees earn below Company B's average salary, Company B's average salary must lie above Company A's median salary. Written as an inequality, median(A) is less than average(B). This is a completely general relationship that holds true regardless of what the actual numeric value of average(B) happens to be, it is a structural relationship between the two numbers, not tied to any specific dollar figure.
  4. Step 4, now use this general relationship from Step 3 to test each candidate description of average(B) offered in blank 1, checking whether picking that description lets us DEFINITIVELY pin down median(A) using only the fact that median(A) is less than average(B). Test the candidate "less than 100,000 AED" for blank 1. If average(B) is less than 100,000 AED, and we know from Step 3 that median(A) is less than average(B), then by simple transitivity, median(A) must also be less than 100,000 AED, since median(A) is below a number that is itself below 100,000.
  5. Step 5, this transitivity chain in Step 4 gives a clean, fully determined answer for blank 2, namely "less than 100,000 AED," matching exactly the same phrase used for average(B) in blank 1. This works because the SAME threshold value (100,000 AED) serves as the shared upper bound for both average(B) and, by extension, median(A).
  6. Step 6, work through why testing any of the other four candidates as blank 1 fails to produce an equally definite conclusion about median(A). Test "greater than 100,000 AED" for blank 1. If average(B) is greater than 100,000 AED, all we can conclude from Step 3 is that median(A) is less than average(B), which is some number greater than 100,000, but median(A) itself could be anywhere below that unspecified larger number, including values well below 100,000, well above 100,000, or anywhere in between; there is no single specific description among the answer choices that median(A) is FORCED into, so this candidate does not produce a valid, uniquely determined blank 2.
  7. Step 7, similarly test "equal to 110,000 AED" for blank 1. If average(B) equals exactly 110,000 AED, we only know median(A) is less than 110,000 AED, meaning median(A) could be 109,999, or 50,000, or any other value below 110,000; this range is far too wide to match any single one of the specific answer choices for blank 2 exactly, so no valid pairing emerges from this candidate either.
  8. Step 8, similarly test "between 100,000 and 110,000 AED" and "greater than 110,000 AED" for blank 1. In both cases, all we can conclude is that median(A) is less than whatever value or range is given, but since these ranges do not share a common, exactly matching upper threshold with any of the five specific blank 2 options, no forced, uniquely correct pairing exists for either of these candidates. Only the "less than 100,000 AED" candidate, from Step 4, produces an airtight, uniquely determined conclusion, precisely because its own upper bound (100,000) becomes, by direct transitivity, the exact same upper bound that must also apply to median(A).
  9. Step 9, watch the trap of assuming that because Company A's AVERAGE salary is 10,000 AED higher than Company B's, Company A's MEDIAN salary must also be higher than Company B's average. Average and median can diverge sharply whenever a distribution is skewed by a small number of extreme values. Here, it is entirely possible for a handful of very high earning employees at Company A to pull the company's average salary up substantially, while the bulk of Company A's employees still earn comparatively modest salaries, keeping Company A's median salary low, even lower than Company B's average. This is exactly the scenario Fact two directly confirms is happening, so the intuitive assumption that "a higher average means a higher median too" must be set aside here.
Final answers: 1: less than 100,000 AED. 2: less than 100,000 AED.
Q7 Hard Reading an 'all of those that include also include' statement as a strict subset relationship
A certain mail order company sells T shirts, buttons, stickers, and current and past issues of its magazine. Each order placed to the company consists of one or more items and, for each order, the company packages all of the items in the order together. Any employee who packages an order, packages the entirety of that order. Among the orders placed to the company today:
  • None includes both a T shirt and a magazine.
  • All of those that include a past issue of the magazine also include the current issue of the magazine.
  • Most of those that include a magazine also include a sticker.
  • None of those that include a button also include a sticker.
Statement: For the orders placed to the company today, if one employee were to package all of the orders that include a (blank 1), that employee would also package all of the orders that include a (blank 2).

Select for 1 and for 2 the two different options that complete the statement so that it is most accurate based on the information provided. Make only two selections, one in each column.
12
Button
Current issue of the magazine
Past issue of the magazine
Sticker
T shirt

Answer Key and Working

1: Current issue of the magazine. 2: Past issue of the magazine.
  1. Step 1, before evaluating any answer choice, translate each of the four bulleted rules into simple, concrete group language, since this question is fundamentally about which group of orders is fully contained inside which other group of orders. Rule one, no order contains both a T shirt and a magazine, meaning the group of T shirt orders and the group of magazine orders never overlap at all. Rule two, every order containing a past issue also contains the current issue, meaning the group of past issue orders sits entirely inside the group of current issue orders, with no exceptions. Rule three, most orders containing a magazine also contain a sticker, meaning a majority, but not necessarily all, of magazine orders also have a sticker. Rule four, no order containing a button also contains a sticker, meaning the button group and the sticker group never overlap at all.
  2. Step 2, understand precisely what the question is asking for, since the phrasing determines which of the four rules is actually relevant. The statement to complete says that packaging every order containing item 1 would automatically mean packaging every order containing item 2 as well. This can only be guaranteed with certainty if the group of orders containing item 2 is ENTIRELY CONTAINED within the group of orders containing item 1, since only then would covering every item 1 order also, without exception, cover every item 2 order.
  3. Step 3, scan the four rules from Step 1 for one that describes exactly this kind of full containment (a strict subset) relationship between two specific, nameable items rather than a majority relationship or a total exclusion relationship. Rule one describes total exclusion (T shirts and magazines never coexist in the same order), not containment, so it does not fit. Rule three describes a majority relationship (MOST magazine orders have a sticker, but not ALL), which is weaker than full containment and cannot guarantee that packaging every magazine order would cover every sticker order, since some sticker orders might not include a magazine at all, and even among magazine orders, a few might lack a sticker, so this rule does not fit either. Rule four, like rule one, describes total exclusion (buttons and stickers never coexist), not containment.
  4. Step 4, rule two is different from the other three in exactly the way needed, since it states, without any exception or qualifier like "most," that EVERY SINGLE order containing a past issue of the magazine also contains the current issue of the magazine. This is precisely a full containment relationship, the group of past issue orders is a strict subset of the group of current issue orders, with zero exceptions.
  5. Step 5, translate rule two directly into the blanks. If an employee packages every order that contains the current issue of the magazine (blank 1), that employee automatically packages every order in the past issue group too, because rule two guarantees every past issue order is ALSO a current issue order, meaning there is no past issue order sitting outside the current issue group that could be missed. So blank 1 is "Current issue of the magazine" and blank 2 is "Past issue of the magazine."
  6. Step 6, double check the direction is correct by testing it in reverse, since subset relationships only work in one direction and reversing the blanks would create an invalid statement. If an employee packaged every order containing a PAST issue instead (reversing blank 1 and blank 2), would that guarantee covering every CURRENT issue order? No, because plenty of orders could contain the current issue magazine without also containing any past issue at all (a customer buying only the newest issue, for example), meaning some current issue orders would be left unpackaged. This confirms the direction found in Step 5, current issue first, past issue second, is the only valid direction.
  7. Step 7, work through why the remaining three options (Button, Sticker, T shirt) fail to fit either blank, tying back to the exclusion relationships identified in Step 1. Since buttons and stickers never appear in the same order (rule four), and T shirts and magazines never appear in the same order (rule one), none of these three items can be placed into a full containment relationship with any other single item the way current issue and past issue can, since containment requires one group to sit entirely inside another, not to avoid the other entirely.
  8. Step 8, watch the trap of being drawn toward rule three (the "most" magazine orders also have a sticker) simply because it also involves the magazine and feels similar in flavor to rule two. The crucial difference is the word "most" versus "all", a "most" relationship still permits a minority of exceptions, meaning it is fundamentally weaker than the strict, exception free containment guarantee needed to be certain that packaging every order of one type would, without fail, also cover every order of the other type. Only a rule phrased with "all" or "every," like rule two, provides the certainty this particular statement requires.
Final answers: 1: Current issue of the magazine. 2: Past issue of the magazine.
Q8 Hard Choosing the connective word that correctly paraphrases a necessary condition versus an unconditional guarantee
Ethics board member: All actions that are permissible under the code of ethics are also legal in all of the jurisdictions in which our company operates. Furthermore, regardless of whether it has been determined if an action is legal, it is always permissible to ask the ethics board to review the action for conformity to the code of ethics.

Statements: Without exception, an action is permissible under the code of ethics (blank 1) it is legal in all of the jurisdictions in which the company operates. Furthermore, one is permitted to ask the ethics board to review an action for conformity to the code of ethics (blank 2) the legality of the action has been established.

Select for 1 and for 2 the two different options that complete the statements so that they most accurately paraphrase the Ethics board member's assertions. Make only two selections, one in each column.
12
if
only if
unless
whether or not
or

Answer Key and Working

1: only if. 2: whether or not.
  1. Step 1, before choosing any connective word, translate the ethics board member's two separate assertions into the plain logical structure they are actually built from, since precise translation is the entire task here. Assertion one, "all actions that are permissible under the code of ethics are also legal in all of the jurisdictions in which our company operates," is a one directional rule that says being permissible always leads to being legal. Using an arrow to represent "leads to," this is permissible leads to legal. Crucially, the passage never states the reverse, it never claims that every legal action is automatically permissible.
  2. Step 2, translate assertion two the same careful way. "Regardless of whether it has been determined if an action is legal, it is always permissible to ask the ethics board to review the action" says that the permission to REQUEST a review holds no matter what, completely independent of whether the action's legal status has been figured out yet, whether it turns out to be legal, illegal, or simply undetermined. This is an unconditional guarantee, not a conditional relationship at all.
  3. Step 3, work out which connective word correctly expresses "permissible leads to legal" (from Step 1) for blank 1, using the plain, ground level meaning of each candidate. The phrase "only if" specifically means the sentence coming before it can only be true if the sentence coming after it is also true, which is exactly permissible leads to legal, since it says you cannot have permissibility WITHOUT legality, matching the one directional relationship precisely with no implied reverse.
  4. Step 4, work out which connective word correctly expresses "holds no matter what the legal status is" (from Step 2) for blank 2. The phrase "whether or not" is specifically used to say something is true regardless of which of two possibilities occurs, matching exactly the passage's own wording, "regardless of whether it has been determined," which describes an outcome that does not depend at all on the legal determination going one way or the other.
  5. Step 5, assemble the two completed sentences and read them back against the original passage to confirm the translation captures the same meaning. "An action is permissible under the code of ethics only if it is legal" matches "all permissible actions are legal" precisely. "One is permitted to ask for review whether or not the legality of the action has been established" matches "regardless of whether it has been determined if an action is legal, it is always permissible to ask for review" precisely.
  6. Step 6, work through why each of the remaining candidates fails to fit either blank. Using plain "if" for blank 1 would create the sentence "an action is permissible if it is legal," which actually reverses the direction of the original claim, implying legal leads to permissible, a claim the passage never makes (the passage only ever says permissible actions are legal, not that every legal action is automatically permissible). "Unless" for blank 1 would introduce a negation not supported by the passage at all, since the passage states a positive, unconditional forward relationship rather than an exception based one. "Or" does not express any conditional or necessary condition relationship whatsoever, it is simply a word for listing alternatives, and does not fit the logical structure of either sentence.
  7. Step 7, similarly check why the remaining candidates fail for blank 2. "Only if" for blank 2 would create a necessary condition relationship (permission to ask for review requires legality to already be established), which directly contradicts the passage's explicit statement that review permission holds "regardless of" legal determination, meaning it holds even BEFORE legality is known. "If" alone and "unless" both introduce some kind of conditional dependency on the legal determination, but the passage explicitly rules out any such dependency by using the word "regardless."
  8. Step 8, watch the trap of assuming that because assertion one uses the word "also" (permissible actions are "also" legal), a plain "if" might seem like the more natural, conversational translation. However, "if" and "only if" express logically opposite directions of implication, and only "only if" correctly preserves the one way relationship (permissible leads to legal, not legal leads to permissible) that the ethics board member actually asserts, making the seemingly more natural "if" a subtle but important logical error here.
Final answers: 1: only if. 2: whether or not.
Q9 Hard Expressing a rule and its contrapositive using the same necessary condition phrase
Linguist: Plosives and fricatives are two classes of consonants. A voicing contrast is a distinction between two consonants that are identical except that one is voiced and the other is unvoiced. In language family X, languages with voicing contrasts in their fricatives always have voicing contrasts in their plosives. This means that in that family, any given language has a voicing contrast in its fricatives (first blank) it has a voicing contrast in its plosives. In other words, a given language in that family lacks any voicing contrasts in its plosives (second blank) it lacks any such contrasts in its fricatives.

Select for First blank the word or phrase that most logically completes the statement with the first blank. And select for Second blank the word or phrase that most logically completes the statement with the second blank. Make only two selections, one in each column.
First blankSecond blank
and
if
only if
or
unless

Answer Key and Working

First blank: only if. Second blank: only if.
  1. Step 1, before filling in either blank, restate the linguist's core given fact in the plainest possible terms, building it up piece by piece. A voicing contrast is defined as a pair of otherwise identical consonants where one is voiced and the other is not. The given fact about language family X is, languages that have a voicing contrast among their fricatives ALWAYS also have a voicing contrast among their plosives, with no exceptions. Using an arrow to mean "always leads to," this is has fricative contrast leads to has plosive contrast.
  2. Step 2, translate the first blank's sentence using this relationship. The sentence reads, a given language has a voicing contrast in its fricatives (first blank) it has a voicing contrast in its plosives. We need a connective word that correctly expresses "has fricative contrast leads to has plosive contrast," meaning having the fricative contrast requires, and cannot happen without, having the plosive contrast as well.
  3. Step 3, test "only if" for the first blank using its precise, ground level meaning, "only if" means the statement before it is true only under the condition that the statement after it is also true, in other words, you cannot have the first thing without the second thing. Applying this, "has a fricative contrast only if it has a plosive contrast" means exactly, you cannot have the fricative contrast without also having the plosive contrast, which matches the given fact from Step 1 precisely.
  4. Step 4, now work out the second blank, which describes something slightly different, the LOGICAL CONTRAPOSITIVE of the original relationship rather than the original relationship itself. The contrapositive of "has fricative contrast leads to has plosive contrast" is "lacks plosive contrast leads to lacks fricative contrast," since the contrapositive of any true "leads to" statement is formed by reversing the order of the two conditions and negating each one, and a genuine "leads to" relationship and its contrapositive are always logically equivalent to one another (both are simply two different ways of stating the exact same underlying fact).
  5. Step 5, translate the second blank's sentence using this contrapositive relationship. The sentence reads, a given language lacks any voicing contrasts in its plosives (second blank) it lacks any such contrasts in its fricatives. We need a connective expressing "lacks plosive contrast leads to lacks fricative contrast," meaning lacking the plosive contrast requires, and cannot happen without, also lacking the fricative contrast.
  6. Step 6, test "only if" for the second blank as well, using the exact same reasoning as Step 3. "Lacks a plosive contrast only if it lacks a fricative contrast" means, you cannot lack the plosive contrast without also lacking the fricative contrast, which matches the contrapositive relationship from Step 4 precisely. So both blanks are correctly filled using the identical phrase, "only if," even though the two sentences describe what looks like two different scenarios (one about having contrasts, one about lacking them), because the two sentences are actually logically equivalent restatements of the same single underlying fact from the passage.
  7. Step 7, work through why the remaining connective options fail to fit either blank correctly. Plain "if" would reverse the intended direction in both sentences, turning "has fricative contrast if it has plosive contrast" into a claim that having the plosive contrast guarantees having the fricative contrast, which is the opposite direction from what the passage actually states (the passage only guarantees the flow FROM fricative contrast TO plosive contrast, not the reverse). "And" simply joins two clauses together without expressing any conditional relationship between them at all, failing to capture any directional dependency. "Or" presents the two clauses as alternatives rather than as one clause depending logically on the other. "Unless" introduces a negation based exception structure that does not match either the original relationship or its contrapositive, both of which are straightforward necessary condition relationships rather than exception clauses.
  8. Step 8, watch the trap of assuming the two blanks must use two DIFFERENT words simply because the two sentences describe superficially different situations, one about consonants having contrasts and one about consonants lacking contrasts. Since the second sentence is explicitly built as the logical contrapositive of the first (as shown in Step 4), and a true statement and its contrapositive always carry the identical necessary condition structure, both blanks are correctly filled with the very same phrase, "only if," reflecting that they are really just two equivalent expressions of one single underlying logical fact about language family X.
Final answers: First blank: only if. Second blank: only if.
Q10 Hard Drawing inferences from a stated relative-likelihood relationship without overstating what it actually guarantees
In a study conducted over several years, seabird and domesticated cat populations on a geographically isolated island changed from year to year. Researchers found that over the course of the study, the relationship (R) between seabirds and domesticated cats was such that the island's seabird population was three times as likely to decrease from the previous year if the island's domesticated cat population increased (even if slightly) during the same year. The researchers are about to begin a second, follow up study with the same duration as the first study. Based on recent trends, the researchers made the following projections: R will hold and the island's domesticated cat population will decrease during more years of the second study than it did in their first study.

Assuming that the information above is true, select for Can be inferred as true the statement that can be most reasonably inferred as true from the information provided, and select for Can be inferred as false the statement that can be most reasonably inferred as false from the information provided. Make only two selections, one in each column.
Can be inferred as trueCan be inferred as false
If the researchers' projections are accurate, the island's seabird population is likely to increase during more years of the second study than it did in the first.
During the first study, most years had an increase in the island's domesticated cat population.
If the researchers' projections are accurate, the island's seabird population is likely to increase during most of the years of the second study.
During the first study, the island's seabird population decreased only when the island's domesticated cat population increased.
During the first study, most years during which the island's seabird population decreased were years during which the island's domesticated cat population increased.

Answer Key and Working

Can be inferred as true: If the researchers' projections are accurate, the island's seabird population is likely to increase during more years of the second study than it did in the first. Can be inferred as false: During the first study, the island's seabird population decreased only when the island's domesticated cat population increased.
  1. Step 1, before evaluating any answer choice, restate the relationship R in the most literal, ground level terms possible, since overstating or understating this relationship is exactly what the wrong answer choices are designed to tempt you into doing. R says, in a year when the cat population increases, the seabird population is three times as likely to decrease that same year, compared to a year when the cat population does not increase. This is a statement about RELATIVE likelihood, a cat increase makes a seabird decrease three times more probable than it otherwise would be, it is not a statement that a seabird decrease can ONLY happen alongside a cat increase, and it is not a statement about exactly how often cat increases happen in the first place.
  2. Step 2, translate the projection for the second study into the same concrete terms. The projection states two things, R will continue to hold in the second study exactly as it did in the first, and the cat population will decrease during MORE years of the second study than it did during the first study. Since R links seabird declines to cat INCREASES specifically, and the cat population is projected to decrease during more years (meaning it will increase during correspondingly FEWER years, since a year not spent decreasing is a year the population either increased or stayed flat, and fewer non-decrease years means fewer opportunities for the specific increase trigger described in R), there will be fewer years in the second study containing the specific trigger (a cat increase) that R says raises the odds of a seabird decline.
  3. Step 3, reason through what this reduction in trigger years implies for the seabird population across the whole second study. With fewer years featuring the cat increase trigger, and since that specific trigger is what elevates seabird decline risk under R, we would expect relatively fewer years of elevated seabird decline risk in the second study compared to the first study. Fewer years of elevated decline risk translates naturally into more years where the seabird population is likely to increase (or at least not experience the tripled decline risk), when comparing the second study to the first study as a whole.
  4. Step 4, this reasoning directly supports the option "If the researchers' projections are accurate, the island's seabird population is likely to increase during more years of the second study than it did in the first," since this is a comparative claim (more years in study two than in study one), which is exactly the type of conclusion the reduced trigger frequency in Step 3 supports, without requiring us to know any exact fractions or majorities, only a relative comparison between the two studies.
  5. Step 5, now work through the option designed to be inferred as FALSE, "During the first study, the island's seabird population decreased only when the island's domesticated cat population increased." The word "only" here makes an extremely strong, absolute claim, that a seabird decline literally cannot happen unless a cat increase happens in that same year. But recall from Step 1 that R only tells us a cat increase makes a seabird decline three times MORE LIKELY, not that a seabird decline is impossible without a cat increase; R leaves room for seabird declines to happen in non cat increase years too, simply less often (specifically, at one third the rate).
  6. Step 6, since R explicitly allows for seabird declines to occur even without a cat population increase (just at a lower rate), the claim that declines happened "only" alongside cat increases directly overstates and misrepresents what R establishes, making this the statement we can most reasonably infer as FALSE from the given information.
  7. Step 7, work through why the remaining two options fail to be as well supported as the two selected answers. "During the first study, most years had an increase in the island's domesticated cat population" makes a claim about how OFTEN cat increases happened during the first study specifically, a majority or minority frequency that the passage never actually states or implies anywhere, R only describes the relative RATE of seabird decline conditional on a cat increase happening, it says nothing about how commonly cat increases themselves occurred, so this frequency claim is entirely unsupported speculation.
  8. Step 8, similarly, "If the researchers' projections are accurate, the island's seabird population is likely to increase during most of the years of the second study" looks tempting because it echoes the correct true statement's language about the seabird population increasing, but it makes a much STRONGER claim, specifically that MORE THAN HALF of the second study's years will show an increase. The information given only supports a relative, comparative statement (more increase years than in the first study), not an absolute majority claim about the second study taken on its own, since we are never told what fraction of years had increases in the first study to begin with, so we cannot conclude anything about reaching a majority in the second study either.
  9. Step 9, watch the trap of upgrading a comparative claim ("more than before") into an absolute claim ("more than half," or "only," or "most"), which is exactly the mechanism connecting the two incorrect distractors in Steps 7 and 8 and the one incorrect distractor in Step 5 to the two correctly supported answers. The passage's numeric claim (three times as likely) is itself a comparative, relative statement, and the safest, most defensible inferences drawn from a comparative premise are themselves comparative conclusions, not absolute ones about majorities, exclusivity, or exact frequencies that were never actually stated.
Final answers: Can be inferred as true: the island's seabird population is likely to increase during more years of the second study than it did in the first. Can be inferred as false: during the first study, the seabird population decreased only when the cat population increased.
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