GMAT original complete printed practice

A seller buys two products for the same cost per unit. The seller sells 60 units of the first product at 25% above cost and 40 units of the second at 10% above cost. The total profit on these 100 units is $1,900. What is the cost per unit?

• ☐ A. $100
• ☐ B. $15.97
• ☐ C. $76
• ☐ D. $108.57
• ☐ E. $190

If $x\ne 0$ and $x\ne 4$, which expression equals $\frac{x^2-16}{x^2-4x}$?

• ☐ A. $\frac{x}{x+4}$
• ☐ B. $\frac{x+4}{x}$
• ☐ C. $\frac{x-4}{x}$
• ☐ D. $1$
• ☐ E. $x+4$

At their constant individual rates, pump A fills an empty tank in 6 hours and pump B fills it in 12 hours. Pump A operates alone for 2 hours. Both pumps then operate together until the tank is full. How long do they operate together?

• ☐ A. 2 hours
• ☐ B. 2 hours 20 minutes
• ☐ C. 2 hours 40 minutes
• ☐ D. 3 hours
• ☐ E. 4 hours

What is the greatest positive integer $d$ such that $d^2$ divides $2^9{3}^6{5}^3$ and $d^3$ divides $2^{12}{3}^9{5}^4$?

• ☐ A. $540$
• ☐ B. $1,080$
• ☐ C. $1,440$
• ☐ D. $2,160$
• ☐ E. $4,320$

How many integers $n$ satisfy $-3<\frac{2n-5}{3}\le 7$?

• ☐ A. $10$
• ☐ B. $12$
• ☐ C. $13$
• ☐ D. $14$
• ☐ E. $15$

A ticket price is increased by 20% and then the increased price is discounted by 25%. The final price is $90. What was the original price?

• ☐ A. $75
• ☐ B. $100
• ☐ C. $112.50
• ☐ D. $120
• ☐ E. $135

Positive integers $a,b,c$ satisfy $a:b=3:5$ and $b:c=4:7$. If $a+b$ is a multiple of 48, what is the least possible value of $a+b+c$?

• ☐ A. $67$
• ☐ B. $134$
• ☐ C. $160$
• ☐ D. $201$
• ☐ E. $268$

The calculated mean of ten observations is 18. One observation was recorded as 42 instead of its correct value, 24. What is the corrected mean?

• ☐ A. $16.2$
• ☐ B. $18$
• ☐ C. $19.8$
• ☐ D. $20.4$
• ☐ E. $24$

An event sold 80 tickets. Adult tickets cost $15 each and student tickets cost $9 each. If ticket revenue was $960 and there were no other ticket types or fees, how many adult tickets were sold?

• ☐ A. $20$
• ☐ B. $30$
• ☐ C. $40$
• ☐ D. $50$
• ☐ E. $60$

What is the sum of all real solutions of $|2x-3|=x+6$?

• ☐ A. $-8$
• ☐ B. $6$
• ☐ C. $8$
• ☐ D. $9$
• ☐ E. $10$

A vehicle travels 60 kilometers at 30 kilometers per hour and returns along the same route at 60 kilometers per hour, with no stops. What is its average speed for the entire trip, in kilometers per hour?

• ☐ A. $20$
• ☐ B. $40$
• ☐ C. $45$
• ☐ D. $50$
• ☐ E. $60$

What is the remainder when $7^{103}+3^{104}$ is divided by 10?

• ☐ A. $0$
• ☐ B. $1$
• ☐ C. $2$
• ☐ D. $3$
• ☐ E. $4$

In an arithmetic sequence with first term $a$ and common difference $d$, the sum of the third and ninth terms is 44, and the sum of the sixth and tenth terms is 60. What is the twelfth term?

• ☐ A. $42$
• ☐ B. $46$
• ☐ C. $50$
• ☐ D. $54$
• ☐ E. $60$

Among 90 employees, 45 belong to committee A, 40 to B, and 35 to C. Exactly 20 belong to both A and B, 15 to both A and C, and 10 to both B and C; these pairwise counts include employees who belong to all three. Five employees belong to all three. How many employees belong to exactly one committee?

• ☐ A. $25$
• ☐ B. $30$
• ☐ C. $40$
• ☐ D. $45$
• ☐ E. $50$

The equation $x^2-kx+18=0$ has two positive integer roots that differ by 3. What is $k$?

• ☐ A. $6$
• ☐ B. $9$
• ☐ C. $11$
• ☐ D. $18$
• ☐ E. $19$

A container holds 100 liters of a uniformly mixed solution that is 20% salt by volume. Twenty liters are removed and replaced with pure water. After thorough mixing, another 20 liters are removed and replaced with pure water. What percent of the final solution is salt?

• ☐ A. $12.8\%$
• ☐ B. $14.4\%$
• ☐ C. $16\%$
• ☐ D. $18\%$
• ☐ E. $20\%$

A bag contains four red, three blue, and two green counters. Two counters are drawn successively at random without replacement. Given that the first counter drawn is not green, what is the probability that the second counter is green?

• ☐ A. $\frac{1}{9}$
• ☐ B. $\frac{2}{9}$
• ☐ C. $\frac{1}{4}$
• ☐ D. $\frac{2}{7}$
• ☐ E. $\frac{1}{3}$

If $\frac{2}{3}(x-4)=10$, what is $x$?

• ☐ A. $11$
• ☐ B. $15$
• ☐ C. $\frac{32}{3}$
• ☐ D. $19$
• ☐ E. $21$

Two disjoint groups together contain 120 observations. The first group has a mean between 60 and 80 inclusive; the second has mean 100. The combined mean is 88. What is the greatest possible number of observations in the first group?

• ☐ A. $36$
• ☐ B. $48$
• ☐ C. $60$
• ☐ D. $72$
• ☐ E. $84$

A sequence starts with $a_1=2$. For each positive integer $n$, $a_{n+1}=\lfloor 3a_n/2\rfloor$, where $\lfloor y\rfloor$ is the greatest integer no larger than $y$. What is $a_7$?

• ☐ A. $13$
• ☐ B. $19$
• ☐ C. $20$
• ☐ D. $22$
• ☐ E. $28$

If $x\ne 0$ and $x+\frac{1}{x}=5$, what is $x^2+\frac{1}{x^2}$?

• ☐ A. $\frac{25}{2}$
• ☐ B. $24$
• ☐ C. $23$
• ☐ D. $25$
• ☐ E. $27$

Read the following original passage.Digital procurement systems are often praised for lowering the paperwork costs of bidding on public contracts. If such costs are a major obstacle for small suppliers, moving applications online should broaden participation. Yet a hypothetical study of four municipalities found that small suppliers submitted fewer bids after online systems were introduced, even though application fees and the time required to prepare standard forms had fallen.An initial interpretation blamed the new systems: they made it easier for large suppliers to enter local markets and underprice smaller rivals. The researchers found, however, that the decline was concentrated in contracts requiring substantial expenditure before any payment could be received. During the same period, the municipalities had combined several small projects into larger contracts, often making payment conditional on acceptance of the completed project. Small suppliers could now prepare an application cheaply but still lack the financing needed to perform the work while awaiting payment. Contracts permitting payments at intermediate milestones continued to attract relatively more small suppliers.The researchers then compared projects with similar size and payment arrangements before and after the systems changed. In these comparisons, small-supplier participation did not consistently decline. This result weakens the claim that digitization itself caused the overall fall in participation; it does not establish that competition from larger suppliers was irrelevant in every case.The researchers therefore distinguish the cost of entering a bidding process from the cost of undertaking a contract. Removing the first barrier can matter, but its effect may remain limited when the second barrier is substantial. They also caution that a count of bids reveals neither whether the winning prices were lower nor whether the completed work was better. Evaluating procurement reform requires examining these outcomes separately rather than treating participation as a complete measure of success.Which statement best expresses the main point of the passage?

• ☐ A. Digital applications can lower entry costs while financing requirements still restrict supplier participation.
• ☐ B. Larger suppliers generally charge less than smaller suppliers on municipal contracts.
• ☐ C. The number of suppliers submitting bids is the most reliable measure of procurement success.
• ☐ D. Milestone payments always eliminate the financing difficulties of small suppliers.
• ☐ E. Online procurement should be delayed until municipalities can prevent outside competition.

Read the following original passage.Digital procurement systems are often praised for lowering the paperwork costs of bidding on public contracts. If such costs are a major obstacle for small suppliers, moving applications online should broaden participation. Yet a hypothetical study of four municipalities found that small suppliers submitted fewer bids after online systems were introduced, even though application fees and the time required to prepare standard forms had fallen.An initial interpretation blamed the new systems: they made it easier for large suppliers to enter local markets and underprice smaller rivals. The researchers found, however, that the decline was concentrated in contracts requiring substantial expenditure before any payment could be received. During the same period, the municipalities had combined several small projects into larger contracts, often making payment conditional on acceptance of the completed project. Small suppliers could now prepare an application cheaply but still lack the financing needed to perform the work while awaiting payment. Contracts permitting payments at intermediate milestones continued to attract relatively more small suppliers.The researchers then compared projects with similar size and payment arrangements before and after the systems changed. In these comparisons, small-supplier participation did not consistently decline. This result weakens the claim that digitization itself caused the overall fall in participation; it does not establish that competition from larger suppliers was irrelevant in every case.The researchers therefore distinguish the cost of entering a bidding process from the cost of undertaking a contract. Removing the first barrier can matter, but its effect may remain limited when the second barrier is substantial. They also caution that a count of bids reveals neither whether the winning prices were lower nor whether the completed work was better. Evaluating procurement reform requires examining these outcomes separately rather than treating participation as a complete measure of success.The comparison of similarly sized projects with similar payment arrangements serves primarily to do which of the following?

• ☐ A. Show that small suppliers had underestimated the paperwork required by online systems.
• ☐ B. Identify the lowest contract prices obtainable through either system.
• ☐ C. Weaken an explanation that attributes the aggregate participation decline to digitization alone.
• ☐ D. Prove that the municipalities selected larger contracts because applications became cheaper.
• ☐ E. Establish that every small supplier preferred milestone payments to final payment.

Read the following original passage.Digital procurement systems are often praised for lowering the paperwork costs of bidding on public contracts. If such costs are a major obstacle for small suppliers, moving applications online should broaden participation. Yet a hypothetical study of four municipalities found that small suppliers submitted fewer bids after online systems were introduced, even though application fees and the time required to prepare standard forms had fallen.An initial interpretation blamed the new systems: they made it easier for large suppliers to enter local markets and underprice smaller rivals. The researchers found, however, that the decline was concentrated in contracts requiring substantial expenditure before any payment could be received. During the same period, the municipalities had combined several small projects into larger contracts, often making payment conditional on acceptance of the completed project. Small suppliers could now prepare an application cheaply but still lack the financing needed to perform the work while awaiting payment. Contracts permitting payments at intermediate milestones continued to attract relatively more small suppliers.The researchers then compared projects with similar size and payment arrangements before and after the systems changed. In these comparisons, small-supplier participation did not consistently decline. This result weakens the claim that digitization itself caused the overall fall in participation; it does not establish that competition from larger suppliers was irrelevant in every case.The researchers therefore distinguish the cost of entering a bidding process from the cost of undertaking a contract. Removing the first barrier can matter, but its effect may remain limited when the second barrier is substantial. They also caution that a count of bids reveals neither whether the winning prices were lower nor whether the completed work was better. Evaluating procurement reform requires examining these outcomes separately rather than treating participation as a complete measure of success.Which inference about the researchers' interpretation is best supported?

• ☐ A. A supplier able to finance any large project would necessarily win more contracts after digitization.
• ☐ B. A lower application fee can coexist with a higher effective barrier to performing the contracts being offered.
• ☐ C. The presence of large competitors would matter only if all contracts required final payment.
• ☐ D. Unchanged participation in matched projects proves that online systems have no effect on any supplier.
• ☐ E. The total value of contracts awarded to small suppliers must have fallen in proportion to their bid count.

Read the following original passage.Digital procurement systems are often praised for lowering the paperwork costs of bidding on public contracts. If such costs are a major obstacle for small suppliers, moving applications online should broaden participation. Yet a hypothetical study of four municipalities found that small suppliers submitted fewer bids after online systems were introduced, even though application fees and the time required to prepare standard forms had fallen.An initial interpretation blamed the new systems: they made it easier for large suppliers to enter local markets and underprice smaller rivals. The researchers found, however, that the decline was concentrated in contracts requiring substantial expenditure before any payment could be received. During the same period, the municipalities had combined several small projects into larger contracts, often making payment conditional on acceptance of the completed project. Small suppliers could now prepare an application cheaply but still lack the financing needed to perform the work while awaiting payment. Contracts permitting payments at intermediate milestones continued to attract relatively more small suppliers.The researchers then compared projects with similar size and payment arrangements before and after the systems changed. In these comparisons, small-supplier participation did not consistently decline. This result weakens the claim that digitization itself caused the overall fall in participation; it does not establish that competition from larger suppliers was irrelevant in every case.The researchers therefore distinguish the cost of entering a bidding process from the cost of undertaking a contract. Removing the first barrier can matter, but its effect may remain limited when the second barrier is substantial. They also caution that a count of bids reveals neither whether the winning prices were lower nor whether the completed work was better. Evaluating procurement reform requires examining these outcomes separately rather than treating participation as a complete measure of success.Which change most directly addresses the financing mechanism identified in the passage, assuming its administrative cost is held constant?

• ☐ A. Make the final acceptance inspection more detailed without changing payment timing.
• ☐ B. Reduce the time needed to upload standard bidding documents.
• ☐ C. Offer payment at completed intermediate stages of a large project instead of only after final acceptance.
• ☐ D. Invite additional large suppliers to submit bids for the same project.
• ☐ E. Publish winning bid prices after all work has been accepted.

Employees at a company could choose to join a new mentoring program. After six months, participants' output had risen more than nonparticipants' output. The director concludes that mentoring caused the additional rise. Which finding, if true, most weakens that conclusion?

• ☐ A. The company used the same output measure for both groups.
• ☐ B. Participants attended more mentoring sessions than the minimum required.
• ☐ C. Most mentors had worked for the company for several years.
• ☐ D. The participants' output had already been rising faster than nonparticipants' output before the program began.
• ☐ E. Some nonparticipants said they would join a later mentoring program.

A library plans to place reserved books in secure pickup lockers to reduce lines at its service desk. The lockers would be accessed with a library card. Which finding, if true, most strengthens the plan's prospects of reducing those lines?

• ☐ A. Most people waiting at the desk are collecting reserved books and already have cards that will open the lockers.
• ☐ B. The average locker pickup takes less time than a desk pickup, but few of the current desk users collect reserved books.
• ☐ C. Most reserved-book collectors already have usable cards, but the proposed lockers would hold only a small fraction of daily reserved pickups.
• ☐ D. Some patrons could use the lockers, but their reserved books must first be checked out at the service desk.
• ☐ E. Most patrons request lockers, but few have usable cards and obtaining a usable card requires a service-desk visit.

A city garage currently closes at 6 p.m. The manager proposes extending paid parking to 9 p.m. and argues that collecting payments during the added hours will increase total daily parking revenue. Charges during the original hours will remain unchanged. The argument requires which assumption?

• ☐ A. The garage will collect as much revenue in each added hour as in each original hour.
• ☐ B. The operating cost of the garage will not increase when hours are extended.
• ☐ C. Some payments collected during the added hours will not be fully offset by reductions in payments during the original hours.
• ☐ D. Every driver who previously parked before 6 p.m. will continue doing so.
• ☐ E. No other garage in the city offers paid parking after 6 p.m.

A records office introduced a new data-entry screen in January. The same clerks worked both months, and errors were measured using the same audit procedure. January's error rate was lower than December's. Which question best tests whether a change in the work, rather than the screen itself, explains that decline?

• ☐ A. Did the new screen display the familiar fields in a different order?
• ☐ B. Were January's records less complex than December's records, independently of the screen change?
• ☐ C. Did the clerks rate the new screen's labels as easier to read?
• ☐ D. Did the audit continue to identify errors using the same definition in both months?
• ☐ E. Did the new screen let clerks view more fields without scrolling?

Read the following original passage.A hypothetical research team used a network of sensors to measure water temperature in an estuary. The records showed higher readings during storms than during calm periods. One analyst suggested that storms brought warmer water into the estuary. Another noted that the sensors' protective cases became wet during storms and asked whether this condition could affect the measurements.To investigate, the team placed sensors with wet and dry cases in water maintained at the same temperature. Wet-case sensors gave higher readings, although the size of the difference changed with water flow. The experiment established that case wetness could introduce an upward error under the tested conditions. It did not show that every storm reading was entirely erroneous, since the estuary's actual water temperature could also change during storms.The team first considered correcting all storm readings by subtracting the average error found in the experiment. That approach would be reliable only if the relevant error remained sufficiently stable across field conditions. The observed dependence on flow gave reason to doubt this assumption. Further comparisons against independent temperature measurements, made over a range of flow conditions, were therefore needed before a correction could be justified.These findings illustrate a distinction between identifying a source of measurement error and recovering the quantity originally measured. The former may be possible with a controlled comparison; the latter can require information about conditions at each observation. The existing records still preserve useful information about when sensor readings changed and how those readings varied across locations. Their value is consequently reduced in a specific respect rather than eliminated. The team proposes retaining the original records, documenting the suspected error, and limiting claims about absolute temperature until the correction method has been validated.The passage is chiefly concerned with which distinction?

• ☐ A. The difference between comparing sensor networks and studying a single sensor.
• ☐ B. The difference between making temperature observations and measuring water flow.
• ☐ C. The difference between finding a possible source of error and justifiably correcting affected measurements.
• ☐ D. The difference between explaining storms and forecasting their arrival.
• ☐ E. The difference between preserving original records and sharing them with other researchers.

Read the following original passage.A hypothetical research team used a network of sensors to measure water temperature in an estuary. The records showed higher readings during storms than during calm periods. One analyst suggested that storms brought warmer water into the estuary. Another noted that the sensors' protective cases became wet during storms and asked whether this condition could affect the measurements.To investigate, the team placed sensors with wet and dry cases in water maintained at the same temperature. Wet-case sensors gave higher readings, although the size of the difference changed with water flow. The experiment established that case wetness could introduce an upward error under the tested conditions. It did not show that every storm reading was entirely erroneous, since the estuary's actual water temperature could also change during storms.The team first considered correcting all storm readings by subtracting the average error found in the experiment. That approach would be reliable only if the relevant error remained sufficiently stable across field conditions. The observed dependence on flow gave reason to doubt this assumption. Further comparisons against independent temperature measurements, made over a range of flow conditions, were therefore needed before a correction could be justified.These findings illustrate a distinction between identifying a source of measurement error and recovering the quantity originally measured. The former may be possible with a controlled comparison; the latter can require information about conditions at each observation. The existing records still preserve useful information about when sensor readings changed and how those readings varied across locations. Their value is consequently reduced in a specific respect rather than eliminated. The team proposes retaining the original records, documenting the suspected error, and limiting claims about absolute temperature until the correction method has been validated.What is the primary purpose of describing sensors with wet and dry cases placed in water at the same temperature?

• ☐ A. To demonstrate a method for determining the temperature of every past storm.
• ☐ B. To provide controlled evidence that case wetness can affect readings independently of water temperature.
• ☐ C. To show that wet-case sensors always differ from dry-case sensors by a fixed amount.
• ☐ D. To explain why all measurements made during calm weather should be discarded.
• ☐ E. To establish that storms cannot change the estuary's actual water temperature.

Read the following original passage.A hypothetical research team used a network of sensors to measure water temperature in an estuary. The records showed higher readings during storms than during calm periods. One analyst suggested that storms brought warmer water into the estuary. Another noted that the sensors' protective cases became wet during storms and asked whether this condition could affect the measurements.To investigate, the team placed sensors with wet and dry cases in water maintained at the same temperature. Wet-case sensors gave higher readings, although the size of the difference changed with water flow. The experiment established that case wetness could introduce an upward error under the tested conditions. It did not show that every storm reading was entirely erroneous, since the estuary's actual water temperature could also change during storms.The team first considered correcting all storm readings by subtracting the average error found in the experiment. That approach would be reliable only if the relevant error remained sufficiently stable across field conditions. The observed dependence on flow gave reason to doubt this assumption. Further comparisons against independent temperature measurements, made over a range of flow conditions, were therefore needed before a correction could be justified.These findings illustrate a distinction between identifying a source of measurement error and recovering the quantity originally measured. The former may be possible with a controlled comparison; the latter can require information about conditions at each observation. The existing records still preserve useful information about when sensor readings changed and how those readings varied across locations. Their value is consequently reduced in a specific respect rather than eliminated. The team proposes retaining the original records, documenting the suspected error, and limiting claims about absolute temperature until the correction method has been validated.Suppose the flow conditions at each past observation are unknown. Which conclusion follows most directly from the passage?

• ☐ A. No information in the old records can be useful for any purpose.
• ☐ B. The controlled comparison proves that all past storm temperatures were lower than reported.
• ☐ C. The exact true temperature at each past observation cannot be recovered merely by knowing the experiment's average wet-case error.
• ☐ D. Wet-case effects must cancel when readings from all locations are averaged.
• ☐ E. The old records become accurate once the storm observations are removed.

Read the following original passage.A hypothetical research team used a network of sensors to measure water temperature in an estuary. The records showed higher readings during storms than during calm periods. One analyst suggested that storms brought warmer water into the estuary. Another noted that the sensors' protective cases became wet during storms and asked whether this condition could affect the measurements.To investigate, the team placed sensors with wet and dry cases in water maintained at the same temperature. Wet-case sensors gave higher readings, although the size of the difference changed with water flow. The experiment established that case wetness could introduce an upward error under the tested conditions. It did not show that every storm reading was entirely erroneous, since the estuary's actual water temperature could also change during storms.The team first considered correcting all storm readings by subtracting the average error found in the experiment. That approach would be reliable only if the relevant error remained sufficiently stable across field conditions. The observed dependence on flow gave reason to doubt this assumption. Further comparisons against independent temperature measurements, made over a range of flow conditions, were therefore needed before a correction could be justified.These findings illustrate a distinction between identifying a source of measurement error and recovering the quantity originally measured. The former may be possible with a controlled comparison; the latter can require information about conditions at each observation. The existing records still preserve useful information about when sensor readings changed and how those readings varied across locations. Their value is consequently reduced in a specific respect rather than eliminated. The team proposes retaining the original records, documenting the suspected error, and limiting claims about absolute temperature until the correction method has been validated.Which description best captures the author's attitude toward the existing sensor records?

• ☐ A. Qualified confidence in their limited uses, with caution about unvalidated temperature corrections.
• ☐ B. Support for immediately applying the average laboratory correction while further comparisons refine its precision.
• ☐ C. Confidence in the original absolute readings, with reservations about whether laboratory case wetness occurs in the field.
• ☐ D. Interest in the records chiefly as evidence of collection methods, with little reliance on their reported storm timing.
• ☐ E. Preference for replacing the existing records with new measurements rather than preserving the original observations.

A distributor's shipment error rate fell from 2% last year to 1% this year. The manager concludes that the number of incorrect shipments must therefore have fallen. The reasoning is flawed because it fails to consider that

• ☐ A. a decrease of one percentage point in the error rate is necessarily a decrease of one percent in the number of errors.
• ☐ B. the total number of shipments may have increased enough to offset the lower error rate.
• ☐ C. the proportional decrease in the error rate cannot be calculated without knowing the number of shipments.
• ☐ D. a rise in the number of incorrect shipments necessarily implies a rise in the percentage that are incorrect.
• ☐ E. halving the error rate guarantees that the error count falls by half even when the shipment volume changes.

A shop sells only standard and premium notebooks. Premium notebooks cost more than standard notebooks. Between two months, the price of each type fell, yet the average price paid per notebook rose. Which fact best explains this result?

• ☐ A. Fewer notebooks of either type were sold in the second month.
• ☐ B. The shop paid less to purchase each premium notebook in the second month.
• ☐ C. A substantially larger share of the notebooks sold in the second month were premium notebooks.
• ☐ D. The shop advertised the new lower standard-notebook price prominently.
• ☐ E. The average of the two posted notebook prices fell by a smaller percentage than the standard-notebook price alone.

A town plans to replace all its streetlights with lamps that provide the same light output but save $10,000 in electricity each year. It predicts lower annual operating costs after installation. Purchase and installation costs are excluded from this comparison; other operating costs remain unchanged except for any change described below. Which fact most seriously undermines the prediction?

• ☐ A. Installation would require a one-time $15,000 payment.
• ☐ B. Annual insurance costs would increase by $3,000.
• ☐ C. Annual replacement supplies would cost $6,000 more than before.
• ☐ D. Annual maintenance costs would increase by $12,000.
• ☐ E. Routine inspections would add $4,000 to the annual operating costs.

Some critics claim that automation necessarily reduces a region's total employment because automated production requires fewer workers. In one region, production employment fell after automation, but employment in related maintenance and design services grew by more than the production decline. That region therefore challenges the critics' general claim. The two bold statements play which roles?

• ☐ A. The first states a claim challenged by the argument; the second supplies evidence used to challenge it.
• ☐ B. The first supplies evidence for the argument's conclusion; the second states that conclusion.
• ☐ C. The first is the author's recommendation; the second is a reason for adopting it.
• ☐ D. The first and second are two explanations the author treats as equally supported.
• ☐ E. The first states a condition accepted by the author; the second shows that the condition was not met.

Every donated artwork accepted by a museum has a provenance file. Every work with a provenance file appears in the museum's catalog. Some cataloged works are not donated. Which statement must be true?

• ☐ A. Every cataloged work has a provenance file.
• ☐ B. Every donated work appears in the museum's catalog.
• ☐ C. Some accepted donated artworks lack provenance files.
• ☐ D. Every accepted donated artwork appears in the museum's catalog.
• ☐ E. No work that is not donated can have a provenance file.

Read the following original passage.Consider a hypothetical rail network in which companies publish schedules using their stations' local clocks. Each clock keeps accurate local time, yet a passenger changing trains must translate between two timetable references. As connections become more frequent, even a reliable departure time at each station leaves travelers and dispatchers with extra coordination work. The problem arises from the relation between schedules, rather than from a defect in any one clock.An operator might respond by adding a waiting interval before each connecting train departs. On an isolated line, generous intervals can absorb small uncertainties at little cost. At a busy interchange, however, those intervals occupy platforms and rolling stock needed by other services. More protection for one connection can therefore reduce the number of connections the network can offer.A shared timetable reference addresses a different part of the problem. Companies agree on a common way to express scheduled times while retaining their own routes and departure decisions. A dispatcher can then compare arrival and departure entries directly, without repeatedly converting between local references. The agreement need not make trains faster or clocks more precise. It makes information from separate services immediately usable together.The value of this arrangement depends on how services interact. A line whose passengers rarely transfer may gain little from changing its timetable convention. A company at a junction can gain substantially, particularly when neighboring companies also adopt the reference. Adoption thus creates reciprocal advantages: each participant makes its schedule easier for others to use and benefits from their participation. The example shows how a modest shared rule can expand a network's practical capacity even when the capabilities of its individual members remain unchanged.Which statement best expresses the passage's central explanation?

• ☐ A. More precise station clocks allow rail companies to reduce the number of connections they offer.
• ☐ B. Longer waiting intervals chiefly improve a rail network by increasing the speed of individual journeys.
• ☐ C. A shared timetable reference can improve coordination among linked services without improving each service's physical capabilities.
• ☐ D. A common timetable is valuable chiefly because it transfers route decisions from companies to a central dispatcher.
• ☐ E. Differences in timetable conventions matter mainly on isolated lines rather than at busy interchanges.

Read the following original passage.Consider a hypothetical rail network in which companies publish schedules using their stations' local clocks. Each clock keeps accurate local time, yet a passenger changing trains must translate between two timetable references. As connections become more frequent, even a reliable departure time at each station leaves travelers and dispatchers with extra coordination work. The problem arises from the relation between schedules, rather than from a defect in any one clock.An operator might respond by adding a waiting interval before each connecting train departs. On an isolated line, generous intervals can absorb small uncertainties at little cost. At a busy interchange, however, those intervals occupy platforms and rolling stock needed by other services. More protection for one connection can therefore reduce the number of connections the network can offer.A shared timetable reference addresses a different part of the problem. Companies agree on a common way to express scheduled times while retaining their own routes and departure decisions. A dispatcher can then compare arrival and departure entries directly, without repeatedly converting between local references. The agreement need not make trains faster or clocks more precise. It makes information from separate services immediately usable together.The value of this arrangement depends on how services interact. A line whose passengers rarely transfer may gain little from changing its timetable convention. A company at a junction can gain substantially, particularly when neighboring companies also adopt the reference. Adoption thus creates reciprocal advantages: each participant makes its schedule easier for others to use and benefits from their participation. The example shows how a modest shared rule can expand a network's practical capacity even when the capabilities of its individual members remain unchanged.Which inference is most strongly supported by the passage?

• ☐ A. An operator with an accurate local clock can still benefit from adopting the common reference when its passengers transfer to neighboring services.
• ☐ B. The main benefit of adopting a common reference is that connecting trains wait longer before leaving.
• ☐ C. An isolated line is likely to gain more from the convention than a company operating at a junction.
• ☐ D. Companies must surrender their departure decisions before schedules using the common reference can be compared.
• ☐ E. A common reference chiefly shortens the time a train spends traveling between two stations.

Read the following original passage.Consider a hypothetical rail network in which companies publish schedules using their stations' local clocks. Each clock keeps accurate local time, yet a passenger changing trains must translate between two timetable references. As connections become more frequent, even a reliable departure time at each station leaves travelers and dispatchers with extra coordination work. The problem arises from the relation between schedules, rather than from a defect in any one clock.An operator might respond by adding a waiting interval before each connecting train departs. On an isolated line, generous intervals can absorb small uncertainties at little cost. At a busy interchange, however, those intervals occupy platforms and rolling stock needed by other services. More protection for one connection can therefore reduce the number of connections the network can offer.A shared timetable reference addresses a different part of the problem. Companies agree on a common way to express scheduled times while retaining their own routes and departure decisions. A dispatcher can then compare arrival and departure entries directly, without repeatedly converting between local references. The agreement need not make trains faster or clocks more precise. It makes information from separate services immediately usable together.The value of this arrangement depends on how services interact. A line whose passengers rarely transfer may gain little from changing its timetable convention. A company at a junction can gain substantially, particularly when neighboring companies also adopt the reference. Adoption thus creates reciprocal advantages: each participant makes its schedule easier for others to use and benefits from their participation. The example shows how a modest shared rule can expand a network's practical capacity even when the capabilities of its individual members remain unchanged.According to the passage, why can longer waiting intervals be costly at a busy interchange?

• ☐ A. They require station clocks to adopt a less precise way of keeping local time.
• ☐ B. They occupy platforms and rolling stock that other services could use.
• ☐ C. They prevent companies from selecting their own departure times.
• ☐ D. They increase the number of local-time conversions needed for each timetable entry.
• ☐ E. They require neighboring companies to publish fewer details about their routes.

Read the following original passage.Consider a hypothetical rail network in which companies publish schedules using their stations' local clocks. Each clock keeps accurate local time, yet a passenger changing trains must translate between two timetable references. As connections become more frequent, even a reliable departure time at each station leaves travelers and dispatchers with extra coordination work. The problem arises from the relation between schedules, rather than from a defect in any one clock.An operator might respond by adding a waiting interval before each connecting train departs. On an isolated line, generous intervals can absorb small uncertainties at little cost. At a busy interchange, however, those intervals occupy platforms and rolling stock needed by other services. More protection for one connection can therefore reduce the number of connections the network can offer.A shared timetable reference addresses a different part of the problem. Companies agree on a common way to express scheduled times while retaining their own routes and departure decisions. A dispatcher can then compare arrival and departure entries directly, without repeatedly converting between local references. The agreement need not make trains faster or clocks more precise. It makes information from separate services immediately usable together.The value of this arrangement depends on how services interact. A line whose passengers rarely transfer may gain little from changing its timetable convention. A company at a junction can gain substantially, particularly when neighboring companies also adopt the reference. Adoption thus creates reciprocal advantages: each participant makes its schedule easier for others to use and benefits from their participation. The example shows how a modest shared rule can expand a network's practical capacity even when the capabilities of its individual members remain unchanged.What is the main role of the third paragraph in the passage's reasoning?

• ☐ A. It traces the coordination problem to inaccurate clocks and proposes a technical repair.
• ☐ B. It explains how a shared convention makes schedules comparable while leaving individual operating decisions intact.
• ☐ C. It describes a central authority that replaces the decisions of separate companies.
• ☐ D. It compares the financial expense of a new convention with the expense of longer waiting intervals.
• ☐ E. It presents measurements showing how much faster trains became after every company adopted the convention.

For comparable parcels, delivery service X reports 96% on-time delivery and service Y reports 92%. Their fees are identical. A manager concludes that choosing X will reduce the probability that the company's next parcel arrives late. Which assumption does the conclusion require?

• ☐ A. Both services delivered the same total number of parcels when their rates were measured.
• ☐ B. Late delivery is more costly to the company than a higher delivery fee would be.
• ☐ C. The reported difference is relevant to the kind of parcel and route the company will use.
• ☐ D. Neither service has ever delivered every parcel on time during a week.
• ☐ E. Service X operates in more cities than service Y.

A retailer received an average customer rating of 4.6 out of 5 for a new product, compared with 4.0 for its earlier model. The retailer concludes that customers generally find the new product better. Which fact, if true, most weakens the conclusion?

• ☐ A. The new-product survey had substantially fewer respondents than the earlier-model survey.
• ☐ B. Customers who returned the new product were excluded from its rating survey, but returners were included in the earlier model's survey.
• ☐ C. Both surveys used the same five-point scale with the same descriptions for each rating.
• ☐ D. Among buyers who rated both models, the new product also received a higher average rating.
• ☐ E. Both surveys asked buyers to rate several features before giving an overall rating.

A retailer sells every unit at the same positive price, with no other revenue. What is the total sales revenue?(1) Exactly 80 units were sold.(2) The price per unit was $25.Decide whether the statements provide enough information to answer the question. Evaluate each statement separately before combining them.

• ☐ A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• ☐ B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• ☐ C. Both statements together are sufficient, but neither statement alone is sufficient.
• ☐ D. Each statement alone is sufficient.
• ☐ E. The two statements together are not sufficient.

Source 1: Original policy. A shipment contains exactly 100 identical units. Divide it between at most two routes, using integer allocations that do not exceed the listed capacities. All units must arrive by day 4. Use only routes with historical on-time rates of at least 95%. Total charges, including one fixed fee for each used route, must not exceed $2,400. There are no other charges, discounts, or routes.Source 2: Route quotes. Days and charges below are the stipulated planning values; an on-time rate describes past shipments, not a delivery guarantee. Source 3: Approved amendment. The deadline is changed to day 5. Every other requirement and every route quote remains unchanged.For each statement, decide whether it is supported by the supplied information. Select exactly one response for each row.1. Using only route A can satisfy the original policy.2. Allocating 20 units to A and 80 to B satisfies every requirement of the original policy.3. Using only route C can satisfy the amended policy.

• ☐ A. Row 1: Yes
• ☐ B. Row 1: No
• ☐ C. Row 2: Yes
• ☐ D. Row 2: No
• ☐ E. Row 3: Yes
• ☐ F. Row 3: No

The chart gives exact quarterly shipment counts for two divisions. Complete both statements. Blank 1: From Q2 to Q3, West shipments increased by . Blank 2: In Q4, the ratio of East shipments to West shipments was . Select exactly one choice for each blank.

• ☐ A. Blank 1: 20%
• ☐ B. Blank 1: 40%
• ☐ C. Blank 1: 50%
• ☐ D. Blank 2: $3/4$
• ☐ E. Blank 2: $4/3$
• ☐ F. Blank 2: $3/2$

A service team consists of 12 employees, each working one full shift. Each senior employee handles 8 requests, and each junior employee handles 5 requests. The team handles exactly 81 requests, with no overlap or unfinished work. Find the senior count in Column 1 and the junior count in Column 2.Select exactly one response for Column 1 and exactly one for Column 2. The two selections must satisfy the conditions together; a value may be selected in both columns.

• ☐ A. Column 1: Senior count: 3
• ☐ B. Column 1: Senior count: 4
• ☐ C. Column 1: Senior count: 5
• ☐ D. Column 1: Senior count: 7
• ☐ E. Column 1: Senior count: 9
• ☐ F. Column 2: Junior count: 3
• ☐ G. Column 2: Junior count: 4
• ☐ H. Column 2: Junior count: 5
• ☐ I. Column 2: Junior count: 7
• ☐ J. Column 2: Junior count: 9

The numbers $x$ and $y$ are positive integers. What is $x$?(1) $x+y=12$.(2) $x-y=4$.Decide whether the statements provide enough information to answer the question. Evaluate each statement separately before combining them.

• ☐ A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• ☐ B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• ☐ C. Both statements together are sufficient, but neither statement alone is sufficient.
• ☐ D. Each statement alone is sufficient.
• ☐ E. The two statements together are not sufficient.

The table records one complete reporting period. Each completed case is among the cases received in its region. No case belongs to more than one region. Completion rate means completed divided by received. For each statement, decide whether it is supported by the supplied information. Select exactly one response for each row.1. The pooled completion rate for all regions is lower than the unweighted mean of the eight regional completion rates.2. Every region receiving at least 200 cases had a completion rate of at least 80%.3. Every region with mean hours per completed case of at least 10 had a completion rate of at least 80%.

• ☐ A. Row 1: Yes
• ☐ B. Row 1: No
• ☐ C. Row 2: Yes
• ☐ D. Row 2: No
• ☐ E. Row 3: Yes
• ☐ F. Row 3: No

Source 1: Original policy. A shipment contains exactly 100 identical units. Divide it between at most two routes, using integer allocations that do not exceed the listed capacities. All units must arrive by day 4. Use only routes with historical on-time rates of at least 95%. Total charges, including one fixed fee for each used route, must not exceed $2,400. There are no other charges, discounts, or routes.Source 2: Route quotes. Days and charges below are the stipulated planning values; an on-time rate describes past shipments, not a delivery guarantee. Source 3: Approved amendment. The deadline is changed to day 5. Every other requirement and every route quote remains unchanged.For each statement, decide whether it is supported by the supplied information. Select exactly one response for each row.1. No allocation can satisfy the original policy.2. If only B's capacity were increased to 100, using B alone could satisfy the original policy.3. The historical rate for C establishes that at least 99 of the 100 units in this shipment will arrive on time.

• ☐ A. Row 1: Yes
• ☐ B. Row 1: No
• ☐ C. Row 2: Yes
• ☐ D. Row 2: No
• ☐ E. Row 3: Yes
• ☐ F. Row 3: No

A program admits an applicant only if the applicant has both a current license and at least two years of experience. Only admitted applicants may receive the special award. Every award recipient must also have a supervisor recommendation. Recommendations do not guarantee an award, and some admitted applicants receive no award. In Column 1, select a condition that every award recipient must meet. In Column 2, select a case that cannot occur under these rules.Select exactly one response for Column 1 and exactly one for Column 2. The two selections must satisfy the conditions together; a value may be selected in both columns.

• ☐ A. Column 1: Necessary award condition: Has a current license.
• ☐ B. Column 1: Necessary award condition: Has at least four years of experience.
• ☐ C. Column 1: Necessary award condition: Is admitted without a current license.
• ☐ D. Column 1: Necessary award condition: Is admitted but receives no award.
• ☐ E. Column 1: Necessary award condition: Has a recommendation but receives no award.
• ☐ F. Column 2: Impossible case: Has a current license.
• ☐ G. Column 2: Impossible case: Has at least four years of experience.
• ☐ H. Column 2: Impossible case: Is admitted without a current license.
• ☐ I. Column 2: Impossible case: Is admitted but receives no award.
• ☐ J. Column 2: Impossible case: Has a recommendation but receives no award.

Five real numbers have arithmetic mean $m$. What is $m$?(1) Their sum is 75.(2) Their deviations from 15 sum to zero.Decide whether the statements provide enough information to answer the question. Evaluate each statement separately before combining them.

• ☐ A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• ☐ B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• ☐ C. Both statements together are sufficient, but neither statement alone is sufficient.
• ☐ D. Each statement alone is sufficient.
• ☐ E. The two statements together are not sufficient.

Each point represents one of eight employees, using exact training hours and assessment scores. The vertical scale begins at 40; no point is omitted or superimposed. Blank 1: Among employees with at least 8 training hours, scored at least 80. Blank 2: The displayed relationship . Select exactly one choice for each blank.

• ☐ A. Blank 1: 25%
• ☐ B. Blank 1: 50%
• ☐ C. Blank 1: 75%
• ☐ D. Blank 2: establishes that training caused higher scores
• ☐ E. Blank 2: is consistent with a positive association but does not establish causation
• ☐ F. Blank 2: shows no association between hours and scores

The table records one complete reporting period. Each completed case is among the cases received in its region. No case belongs to more than one region. Completion rate means completed divided by received. For each statement, decide whether it is supported by the supplied information. Select exactly one response for each row.1. The three regions receiving the most cases together completed more than half of all completed cases.2. B and E have equal completion rates, and no region has a higher completion rate.3. G completed fewer cases than H.

• ☐ A. Row 1: Yes
• ☐ B. Row 1: No
• ☐ C. Row 2: Yes
• ☐ D. Row 2: No
• ☐ E. Row 3: Yes
• ☐ F. Row 3: No

Source 1: Original policy. A shipment contains exactly 100 identical units. Divide it between at most two routes, using integer allocations that do not exceed the listed capacities. All units must arrive by day 4. Use only routes with historical on-time rates of at least 95%. Total charges, including one fixed fee for each used route, must not exceed $2,400. There are no other charges, discounts, or routes.Source 2: Route quotes. Days and charges below are the stipulated planning values; an on-time rate describes past shipments, not a delivery guarantee. Source 3: Approved amendment. The deadline is changed to day 5. Every other requirement and every route quote remains unchanged.For each statement, decide whether it is supported by the supplied information. Select exactly one response for each row.1. Using C alone under the amendment costs $740 less than the least-cost allocation that meets all original requirements except the budget limit.2. Allocating 40 units to C and 60 to B satisfies every amended requirement.3. The amendment makes route D eligible.

• ☐ A. Row 1: Yes
• ☐ B. Row 1: No
• ☐ C. Row 2: Yes
• ☐ D. Row 2: No
• ☐ E. Row 3: Yes
• ☐ F. Row 3: No

The real numbers $x,y$ are positive. Is $x/y>2$?(1) $x>10$.(2) $y<5$.Decide whether the statements provide enough information to answer the question. Evaluate each statement separately before combining them.

• ☐ A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• ☐ B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• ☐ C. Both statements together are sufficient, but neither statement alone is sufficient.
• ☐ D. Each statement alone is sufficient.
• ☐ E. The two statements together are not sufficient.

A fund distributes exactly $360 between project X and project Y, with no remainder. Project X receives twice as much as Y. Select the allocation to X in Column 1 and the allocation to Y in Column 2.Select exactly one response for Column 1 and exactly one for Column 2. The two selections must satisfy the conditions together; a value may be selected in both columns.

• ☐ A. Column 1: X allocation: $90
• ☐ B. Column 1: X allocation: $120
• ☐ C. Column 1: X allocation: $180
• ☐ D. Column 1: X allocation: $240
• ☐ E. Column 1: X allocation: $270
• ☐ F. Column 2: Y allocation: $90
• ☐ G. Column 2: Y allocation: $120
• ☐ H. Column 2: Y allocation: $180
• ☐ I. Column 2: Y allocation: $240
• ☐ J. Column 2: Y allocation: $270

Quotes apply to an order of exactly 100 identical units. Total charge is 100 times the unit price plus the listed shipping fee. A supplier is eligible only if its total charge is at most $1,000, delivery takes at most 4 days, and its historical defective-unit rate is at most 1.5%. These are the only eligibility conditions; equality at any cutoff is allowed. For each statement, decide whether it is supported by the supplied information. Select exactly one response for each row.1. Exactly three suppliers are eligible.2. H is eligible because its total charge is lower than the total charge of every eligible supplier.3. C has the shortest delivery time among the eligible suppliers.

• ☐ A. Row 1: Yes
• ☐ B. Row 1: No
• ☐ C. Row 2: Yes
• ☐ D. Row 2: No
• ☐ E. Row 3: Yes
• ☐ F. Row 3: No

The graph gives the exact cumulative number of orders completed since opening. Counts increase linearly within each plotted interval. Blank 1: The number completed from hour 5 to hour 9 is times the number completed from hour 0 to hour 2. Blank 2: The mean completion rate over the full nine hours is orders per hour. Select exactly one choice for each blank.

• ☐ A. Blank 1: $1/2$
• ☐ B. Blank 1: $1$
• ☐ C. Blank 1: $2$
• ☐ D. Blank 2: $14/3$
• ☐ E. Blank 2: $6$
• ☐ F. Blank 2: $7$

The real number $x$ is not zero. Is $x>1$?(1) $x+1/x=5$.(2) $x>0.5$.Decide whether the statements provide enough information to answer the question. Evaluate each statement separately before combining them.

• ☐ A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• ☐ B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• ☐ C. Both statements together are sufficient, but neither statement alone is sufficient.
• ☐ D. Each statement alone is sufficient.
• ☐ E. The two statements together are not sufficient.

A library introduced reservation reminders and then observed fewer uncollected reservations. Its director attributes the entire decline to the reminders. In Column 1, select the finding that most strongly supports a causal contribution from reminders. In Column 2, select the finding that most directly limits attributing the entire before-and-after decline to reminders alone. Treat each finding as true and otherwise use only the information supplied.Select exactly one response for Column 1 and exactly one for Column 2. The two selections must satisfy the stated roles; the same candidate may be used in both columns if warranted.

• ☐ A. Column 1: Strengthens: During the same period, a new fee was also introduced for leaving reservations uncollected.
• ☐ B. Column 1: Strengthens: In a randomized test with identical fees and pickup rules, users sent reminders left fewer reservations uncollected than users sent none.
• ☐ C. Column 1: Strengthens: Surveyed users who collected their books often said that a reminder helped them remember the pickup.
• ☐ D. Column 1: Strengthens: The total number of reservations increased during the period even though the number left uncollected fell.
• ☐ E. Column 1: Strengthens: The time allowed for collecting a reservation was unchanged when reminders were introduced.
• ☐ F. Column 2: Limits: During the same period, a new fee was also introduced for leaving reservations uncollected.
• ☐ G. Column 2: Limits: In a randomized test with identical fees and pickup rules, users sent reminders left fewer reservations uncollected than users sent none.
• ☐ H. Column 2: Limits: Surveyed users who collected their books often said that a reminder helped them remember the pickup.
• ☐ I. Column 2: Limits: The total number of reservations increased during the period even though the number left uncollected fell.
• ☐ J. Column 2: Limits: The time allowed for collecting a reservation was unchanged when reminders were introduced.

Quotes apply to an order of exactly 100 identical units. Total charge is 100 times the unit price plus the listed shipping fee. A supplier is eligible only if its total charge is at most $1,000, delivery takes at most 4 days, and its historical defective-unit rate is at most 1.5%. These are the only eligibility conditions; equality at any cutoff is allowed. For each statement, decide whether it is supported by the supplied information. Select exactly one response for each row.1. Every supplier offering delivery within 3 days has a defective-unit rate of at most 1.5%.2. Every supplier charging at most $1,000 in total meets the defective-unit cutoff.3. At least one supplier with no shipping fee is eligible.

• ☐ A. Row 1: Yes
• ☐ B. Row 1: No
• ☐ C. Row 2: Yes
• ☐ D. Row 2: No
• ☐ E. Row 3: Yes
• ☐ F. Row 3: No

The positive integers $a,b$ describe two batch sizes. What is $a+b$?(1) $a+b=3(a-b)$.(2) $ab$ is a multiple of 8.Decide whether the statements provide enough information to answer the question. Evaluate each statement separately before combining them.

• ☐ A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• ☐ B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• ☐ C. Both statements together are sufficient, but neither statement alone is sufficient.
• ☐ D. Each statement alone is sufficient.
• ☐ E. The two statements together are not sufficient.