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GMAT sample questions, with every answer explained

Below are 17 GMAT Focus Edition questions covering all 8 question formats across the three sections, at every difficulty level. Try each one, then open the answer: every question comes with a worked solution and an explanation of why each wrong option is wrong, which is where most of the learning is.

They come from TestLumo’s own practice papers, written to match the measured format, length and difficulty of official items. They are not official GMAT questions. GMAC publishes a small set of those on mba.com, and they are worth doing too.

Quantitative Reasoning sample questions

21 questions in 45 minutes, about 2 minutes 9 seconds each, and no calculator. Every question is Problem Solving: a question and five answer choices, one of them correct. GMAC defines the section’s content as arithmetic and algebra, and most items are set in a real-world context, so the work is as much translating words into an equation as solving it.

The wrong answers are not random. Each one below is the result of a specific slip, such as averaging two speeds or stopping one step early, and the explanations name the slip.

Question 1: Problem Solving

Easy · First-Degree Equations

If x is a number such that 5(x − 2) = 3x + 8, what is the value of x?

  1. A. −1
  2. B. 5
  3. C. 9
  4. D. 17
  5. E. 18
Show the answer and explanation

Answer: C. 9

  • A. This comes from writing 2x = 8 − 10 instead of 2x = 8 + 10, moving the −10 across the equals sign without changing its sign.
  • B. This follows from reading 5(x − 2) as 5x − 2, which gives 2x = 10 and x = 5. The 5 must multiply both terms in the bracket.
  • C. Correct. 5x − 10 = 3x + 8 reduces to 2x = 18, so x = 9.
  • D. This treats the right-hand side as 3(x + 8), giving 5x − 10 = 3x + 24 and x = 17. There is no bracket on the right.
  • E. 18 is the value of 2x, the last line before dividing by 2.

How to solve it

Distributing on the left gives 5x − 10 = 3x + 8. Subtracting 3x from both sides gives 2x − 10 = 8, and adding 10 gives 2x = 18, so x = 9.

From GMAT Quantitative Reasoning Practice Test 2

Question 2: Problem Solving

Medium · Applied Problems

Working alone, an older labelling machine can label a full batch of jars in 12 hours, while a newer machine can label the same batch in 4 hours. If the two machines work together at their constant rates, how many hours do they need to label one full batch?

  1. A. 3
  2. B. 4
  3. C. 6
  4. D. 8
  5. E. 16
Show the answer and explanation

Answer: A. 3

  • A. Correct. The combined rate is 1/3 of a batch per hour, so a full batch takes 3 hours.
  • B. 4 hours is the newer machine working on its own. Adding a second machine must bring the time below the faster machine's own time.
  • C. This halves the older machine's 12 hours, as though the second machine were identical to the first rather than three times as fast.
  • D. This averages the two times, (12 + 4)/2. Times cannot be averaged; only rates add.
  • E. This adds the two times. Working together must take less time than either machine alone, not more.

How to solve it

The older machine does 1/12 of a batch per hour and the newer machine 1/4, so together they do 1/12 + 3/12 = 4/12 = 1/3 of a batch per hour. One batch therefore takes 3 hours.

From GMAT Quantitative Reasoning Practice Test 2

Question 3: Problem Solving

Medium · Elementary Combinatorics

Of the 120 members of a cycling club, 74 own a road bicycle and 58 own a mountain bicycle. Twelve of the members own neither a road bicycle nor a mountain bicycle. How many members of the club own both a road bicycle and a mountain bicycle?

  1. A. 12
  2. B. 24
  3. C. 34
  4. D. 50
  5. E. 108
Show the answer and explanation

Answer: B. 24

  • A. This is 74 + 58 − 120, which uses the full membership instead of the 108 who own at least one bicycle. It happens to equal the number who own neither, which makes it doubly tempting.
  • B. Correct. 74 + 58 − 108 = 24 members own both types.
  • C. 34 is the number who own only a mountain bicycle, 58 − 24, not the overlap.
  • D. 50 is the number who own only a road bicycle, 74 − 24, which is the other exclusive group rather than the shared one.
  • E. 108 is the number who own at least one bicycle, an intermediate figure in the calculation.

How to solve it

Since 12 members own neither, 120 − 12 = 108 own at least one. Inclusion-exclusion gives 74 + 58 − both = 108, so both = 132 − 108 = 24.

From GMAT Quantitative Reasoning Practice Test 2

Question 4: Problem Solving

Hard · Properties of Numbers

If n is the smallest positive integer for which 2,520n is the cube of an integer, what is the value of n?

  1. A. 105
  2. B. 525
  3. C. 3,675
  4. D. 11,025
  5. E. 25,725
Show the answer and explanation

Answer: C. 3,675

  • A. This is 3 · 5 · 7, supplying one extra factor of each deficient prime. That makes every exponent even, not a multiple of three.
  • B. This is 3 · 5² · 7, which fixes the 5 but leaves the 7 at an exponent of 2 rather than 3.
  • C. Correct. 3 · 5² · 7² = 3,675 raises every exponent to a multiple of 3, and no smaller multiplier does.
  • D. This is 3² · 5² · 7², squaring every deficient prime including the 3, which already sits at an exponent of 2 and needs only one more factor.
  • E. This is 3 · 5² · 7³, cubing the 7 instead of squaring it and pushing its exponent to 4 in the product.

How to solve it

Factor 2,520 = 2³ · 3² · 5 · 7. A perfect cube needs every exponent to be a multiple of 3. The 2s are already fine; the 3 needs one more factor, the 5 needs two more and the 7 needs two more. So n = 3 · 5² · 7² = 3 · 25 · 49 = 3,675, and 2,520 × 3,675 = 9,261,000 = 210³.

From GMAT Quantitative Reasoning Practice Test 2

Question 5: Problem Solving

Hard · Applied Problems

A cyclist rode from her home to a lake at an average speed of 24 kilometres per hour and returned home along exactly the same route at an average speed of 16 kilometres per hour. What was her average speed, in kilometres per hour, for the whole round trip?

  1. A. 16
  2. B. 19.2
  3. C. 20
  4. D. 24
  5. E. 40
Show the answer and explanation

Answer: B. 19.2

  • A. 16 is the speed on the return leg alone. The outbound leg was faster, so the round-trip average must be higher.
  • B. Correct. Total distance divided by total time gives 96/5 = 19.2 kilometres per hour.
  • C. This averages the two speeds. That is only valid when equal times are spent at each speed, and here the slower leg takes longer, so the true average is below 20.
  • D. 24 is the outbound speed alone, not an average over both legs.
  • E. This adds the two speeds. Speeds add only when two objects move apart simultaneously, not when one object travels two legs in sequence.

How to solve it

Let each leg be d kilometres. The trip takes d/24 + d/16 = 2d/48 + 3d/48 = 5d/48 hours and covers 2d kilometres, so the average speed is 2d ÷ (5d/48) = 96/5 = 19.2 kilometres per hour.

From GMAT Quantitative Reasoning Practice Test 2

Verbal Reasoning sample questions

23 questions in 45 minutes, about 1 minute 57 seconds each, in two formats. Critical Reasoning gives you a short argument and asks you to weaken it, strengthen it, or say what follows from it. Reading Comprehension gives you a passage and several questions about it, so the passage is read once and used three or four times.

Sentence Correction is no longer on the exam, so there are no grammar questions here. For more Critical Reasoning, with every question type and a method for each, see the GMAT Critical Reasoning questions.

Question 6: Critical Reasoning

Easy · Argument Evaluation

The municipal transit authority of Bramfield replaced the diesel buses on its busiest route with electric buses last spring. Ridership on that route rose by eleven percent over the following six months, while ridership across the rest of the network was flat. The authority's director concluded that passengers had been drawn to the route by the quieter and cleaner electric vehicles, and recommended converting the remaining routes as quickly as funds allow.

Which of the following, if true, most seriously weakens the argument above?

  1. A. A large hospital and two office towers opened along the converted route during those six months, adding many commuters.
  2. B. Purchasing the electric buses cost the authority forty percent more than comparable diesel buses.
  3. C. Surveys conducted in several other cities indicate that riders rank service frequency well above vehicle noise when deciding whether to take a bus.
  4. D. The authority's maintenance staff needed three months of additional training before they could service the electric fleet.
  5. E. Ridership on the converted route had declined slightly in each of the three preceding years.
Show the answer and explanation

Answer: A. A large hospital and two office towers opened along the converted route during those six months, adding many commuters.

  • A. Correct. It supplies a rival cause confined to the converted route, which is precisely why the rest of the network did not move.
  • B. Purchase cost bears on whether conversion is affordable, not on whether the vehicles attracted the extra passengers.
  • C. General rankings elsewhere say nothing about this route, where the frequency of service was never changed.
  • D. Training delays affect the cost and pace of conversion but leave the ridership figures entirely untouched.
  • E. A prior decline makes the reversal more striking, so this strengthens the director's case rather than weakening it.

How to solve it

The director treats the electric buses as the only thing that changed on that route. Any other change large enough to add passengers over the same six months breaks the link. New workplaces along the corridor supply exactly such a change, and they also explain why the rest of the network stayed flat.

From GMAT Verbal Reasoning Practice Test 1

Question 7: Critical Reasoning

Medium · Inference

A national audit of prescribing found that general practices in rural districts issue about twenty percent more antibiotic prescriptions per patient than practices in cities do. The rural practices see, on average, older patients, and older patients are more likely to develop the infections for which antibiotics are appropriate. When the audit's authors adjusted their figures for the age of the patient list, the difference between rural and urban practices narrowed but did not disappear.

Which of the following can most properly be inferred from the statements above?

  1. A. Rural general practices must therefore be prescribing antibiotics in many cases where the drugs can do the patient no good at all.
  2. B. Patients registered with rural practices travel further to reach a surgery than urban patients do.
  3. C. When the audit's figures were adjusted for the age of the patient list, the greater part of the difference between rural and urban prescribing rates disappeared.
  4. D. Infections for which antibiotics are appropriate are commoner in rural districts because rural practices prescribe the drugs more freely.
  5. E. Patient age does not by itself account for the whole prescribing gap.
Show the answer and explanation

Answer: E. Patient age does not by itself account for the whole prescribing gap.

  • A. A residual difference is not evidence of inappropriate prescribing; some other legitimate factor may account for it.
  • B. Travel distance is never mentioned and cannot be derived from prescribing rates or from patient ages.
  • C. The audit reports that the gap narrowed, not by how much. Greater part overstates what was actually measured.
  • D. It turns the stated relation around: age raises infection rates, which raises prescribing, not the other way about.
  • E. Correct. The gap narrowed under adjustment but survived it, which is precisely the claim that age is only a partial explanation.

How to solve it

Adjustment narrowed the gap, so age explains part of it; the gap survived adjustment, so age does not explain all of it. That is the whole of what the figures support, and it is what the correct choice says.

From GMAT Verbal Reasoning Practice Test 1

Question 8: Critical Reasoning

Hard · Argument Evaluation

Since a large share of clerical staff began working from home, the amount of office space leased in Calverton's central district has fallen by a fifth. Rents in that district, however, have held steady. A property analyst argues that this shows demand for central offices remains strong, and that the fall in space leased reflects nothing more than firms taking the same space on shorter and more flexible terms.

Which of the following, if true, most seriously weakens the argument above?

  1. A. Landlords in the district have kept advertised rents unchanged while granting each new tenant an unusually long rent-free period.
  2. B. The clerical staff now working from home were employed by firms whose offices lay in several different parts of the central district.
  3. C. Firms in the outer districts have taken more space than central-district firms surrendered.
  4. D. Several large office buildings in the central district are due for completion next year.
  5. E. Leases signed in the central district since the change average three years, against seven before it.
Show the answer and explanation

Answer: A. Landlords in the district have kept advertised rents unchanged while granting each new tenant an unusually long rent-free period.

  • A. Correct. Effective rents have fallen although quoted rents have not, which removes the analyst's only evidence of strong demand.
  • B. The geographic spread of the affected firms does not bear on what rents now reveal about demand.
  • C. Growth elsewhere may mean relocation, but it leaves open whether central demand is strong or weak.
  • D. Future supply may move rents later; it says nothing about what current rents indicate.
  • E. Shorter terms are exactly what the analyst claims, so this supports the argument instead of weakening it.

How to solve it

The analyst reads a steady headline rent as steady demand. Long rent-free periods cut what a tenant actually pays while leaving the advertised figure untouched, so the steadiness is an artefact of how rent is quoted rather than evidence of strength.

From GMAT Verbal Reasoning Practice Test 1

Passage for questions 9 to 11

The catalogue and the country store

Before the general adoption of rural free delivery, a farm household in the American interior bought manufactured goods from a single country store whose proprietor set prices, extended credit and chose the stock. The mail-order house broke that arrangement by substituting a printed catalogue for the shopkeeper's judgement. Its founders understood that the decisive asset was not the warehouse but the list: a catalogue that quoted a fixed price for a named article, and that arrived unbidden at the farmhouse door, converted a captive customer into a comparison shopper. Rural households learned to treat the volume as a document of record, setting one season's quotation against the last.

The change met resistance that was commercial rather than sentimental. Country merchants organised catalogue burnings and persuaded some legislatures to consider taxing parcels, arguing that the distant firms paid nothing towards the roads and schools of the districts they sold into. The argument had force, but it could not survive the arithmetic. A plough that cost eleven dollars at the crossroads could be had for seven from a catalogue, and the difference was larger than any freight charge. What finally displaced the mail-order house was not the country store but the chain store, which reproduced the catalogue's fixed prices and buying power while restoring the advantage of goods a customer could handle before purchase.

Question 9: Reading Comprehension

Easy · Supporting Idea

The passage indicates that country merchants opposed the mail-order houses on which of the following grounds?

  1. A. That the catalogues quoted prices which the distant firms had no real intention of honouring
  2. B. That distant firms paid nothing towards roads and schools in districts they sold into
  3. C. The introduction of the parcel post without any consultation of the rural shopkeepers it affected
  4. D. That a farm household could not judge the quality of goods that it had never handled for itself
  5. E. That the freight charge on a plough exceeded any saving a farm household might have made
Show the answer and explanation

Answer: B. That distant firms paid nothing towards roads and schools in districts they sold into

  • A. The passage treats the quoted prices as genuine; it is their lowness that the merchants could not answer.
  • B. Correct. This is the merchants' stated argument, which the passage calls forceful but insufficient.
  • C. No consultation over the introduction of parcel delivery is mentioned in the passage.
  • D. Handling goods appears only at the end, as an advantage the chain store restored, not as a merchant complaint.
  • E. The passage says the opposite: the price difference on a plough was larger than any freight charge.

How to solve it

The second paragraph reports that merchants argued the distant firms paid nothing towards the roads and schools of the districts into which they sold. That is the ground the passage attributes to them.

From GMAT Verbal Reasoning Practice Test 1

Question 10: Reading Comprehension

Medium · Supporting Idea

According to the passage, the founders of the mail-order houses regarded which asset as the decisive one?

  1. A. A warehouse large enough to hold goods of almost every possible kind
  2. B. An agreement with the postal service that lowered the cost of carrying parcels to distant farm households
  3. C. A printed catalogue quoting a fixed price for each of the articles it named
  4. D. A network of local agents who were authorised to extend credit to farm households on behalf of the firm itself
  5. E. Buying power from ordering goods in very large lots
Show the answer and explanation

Answer: C. A printed catalogue quoting a fixed price for each of the articles it named

  • A. The passage names the warehouse precisely in order to say that it was not the decisive asset.
  • B. Rural free delivery is mentioned as background, but no agreement of this kind is described.
  • C. Correct. This is the list the passage identifies as the decisive asset of the mail-order house.
  • D. Credit belongs to the country store that the catalogue displaced, not to the mail-order house.
  • E. Buying power appears only later, as an attribute the chain store reproduced from the catalogue.

How to solve it

The first paragraph says explicitly that the decisive asset was not the warehouse but the list, and then defines the list as a catalogue quoting a fixed price for a named article.

From GMAT Verbal Reasoning Practice Test 1

Question 11: Reading Comprehension

Hard · Inference

The passage suggests that the chain store succeeded against the mail-order house because the chain store did which of the following?

  1. A. It persuaded legislatures to impose the tax on parcels that country merchants had long wanted
  2. B. It drove the country store out of business well before the catalogue itself could
  3. C. Every article in the mail-order catalogue was offered at a price that no farm household could refuse
  4. D. It extended credit to farm households on terms that the country store could not match
  5. E. It combined the catalogue's fixed pricing with goods that customers could inspect beforehand
Show the answer and explanation

Answer: E. It combined the catalogue's fixed pricing with goods that customers could inspect beforehand

  • A. The proposed parcel tax is attributed to country merchants, and no legislature is said to have passed it.
  • B. The passage has the catalogue undermining the country store first; the chain store then displaced the catalogue.
  • C. The passage claims parity of pricing and buying power, not an irresistible price on every article.
  • D. Credit is associated with the country store, and the chain store's advantage is described in other terms.
  • E. Correct. The final sentence names exactly this combination as what displaced the mail-order house.

How to solve it

The closing sentence credits the chain store with reproducing the catalogue's fixed prices and buying power while restoring something the catalogue had given up: goods the customer could handle before buying. That combination is what the correct choice names.

From GMAT Verbal Reasoning Practice Test 1

Data Insights sample questions

20 questions in 45 minutes, about 2 minutes 15 seconds each, and the only section with an on-screen calculator. It mixes five formats, one of each below.

  • Data Sufficiency asks whether the two statements give you enough information to answer, not what the answer is. The five answer choices are always the same five.
  • Table Analysis gives a table (sortable on the exam) and a set of statements to mark true or false.
  • Graphics Interpretation gives a chart and a sentence with drop-down gaps to complete.
  • Two-Part Analysis asks for two linked answers, one in each column of a shared list of options.
  • Multi-Source Reasoning spreads the information across two or three tabs, and the question needs more than one of them.

Question 12: Data Sufficiency

Easy · Percents

A market research firm surveyed shoppers leaving a supermarket and asked each whether they had used a loyalty card. Every shopper answered either yes or no. How many of the shoppers surveyed answered yes?

  1. (1)Exactly 65 percent of the shoppers surveyed answered yes to the question.
  2. (2)The firm surveyed 240 shoppers as they left the supermarket that day.
  1. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. D. EACH statement ALONE is sufficient.
  5. E. Statements (1) and (2) TOGETHER are NOT sufficient.
Show the answer and explanation

Answer: C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  • A. A share of 65 percent applies to any total, so the number answering yes is not determined.
  • B. Knowing 240 shoppers were surveyed says nothing about how they split between yes and no.
  • C. Correct. Applying 65 percent to 240 shoppers gives exactly 156 yes answers.
  • D. Neither statement stands alone: a proportion needs a base, and a base needs a proportion.
  • E. The pair is sufficient, since 0.65 × 240 leaves no room for a second value.

How to solve it

The count of yes answers is a percentage applied to a total, so both are needed. Statement (1) fixes the share at 65 percent but not the number surveyed, so the count could be 65 out of 100 or 650 out of 1,000. Statement (2) fixes the number surveyed at 240 but not the share. Together, 0.65 × 240 = 156 shoppers answered yes, a single value. The answer is C.

From GMAT Data Insights Practice Test 3

Question 13: Table Analysis

Easy · Applied Problems

A hotel group reports on the six hotels it operates. For each hotel the table gives the number of rooms, the average nightly rate in pounds, the occupancy rate as a percentage, and the number of staff employed. Nightly room revenue is the number of rooms multiplied by the occupancy rate and by the average nightly rate.

HotelRoomsNightly rate (£)Occupancy (%)Staff
Alderbrook120958046
Brantwood801407538
Calverley200709062
Dunsmere601806030
Eldon Court1501107055
Fairwater100858534

For each of the statements below, select Yes if the table shows it to hold and No if it does not.

StatementYesNo
The hotel with the most rooms also earns the highest nightly room revenue.
The hotel employing the fewest staff also has the lowest average nightly rate.
Every hotel with occupancy of at least 80 percent charges less than £100 a night.
Show the answer and explanation

Answers

  • Yes: The hotel with the most rooms also earns the highest nightly room revenue.
  • No: The hotel employing the fewest staff also has the lowest average nightly rate.
  • Yes: Every hotel with occupancy of at least 80 percent charges less than £100 a night.

How to solve it

Nightly room revenue is rooms × occupancy × rate: Alderbrook 120 × 0.80 × £95 = £9,120; Brantwood 80 × 0.75 × £140 = £8,400; Calverley 200 × 0.90 × £70 = £12,600; Dunsmere 60 × 0.60 × £180 = £6,480; Eldon Court 150 × 0.70 × £110 = £11,550; Fairwater 100 × 0.85 × £85 = £7,225. Calverley has both the most rooms, 200, and the highest revenue, £12,600 — Yes. Dunsmere has the fewest staff at 30, but its £180 rate is the highest of the six, not the lowest — No. Occupancy of at least 80 percent covers Alderbrook (£95), Calverley (£70) and Fairwater (£85), all under £100 — Yes.

From GMAT Data Insights Practice Test 3

Question 14: Graphics Interpretation

Medium · Applied Problems

020406080100120140Year-end headcount£0m£2.5m£5m£7.5m£10m£12.5m£15m£17.5mRevenue20192020202120222023
  • Year-end headcount (bars)
  • Annual revenue (line)
Headcount and annual revenue at a consultancy, 2019 to 2023
Data shown in the chart
CategoryYear-end headcount (bars)Annual revenue (line)
201960£7.2m
202072£9.36m
202190£11.7m
2022108£12.42m
2023120£15.6m

The chart plots a consultancy's year-end headcount (bars, left axis) and its annual revenue in millions of pounds (line, right axis). Revenue per employee is revenue divided by year-end headcount.

Using the drop-down menus, complete the statement below so that it is as accurate as the chart allows.

Revenue per employee was lowest in [drop-down 1], and the consultancy's headcount rose over the five years by [drop-down 2] percent.

  • Drop-down 1: 2019 · 2020 · 2021 · 2022 · 2023
  • Drop-down 2: 50 · 60 · 100
Show the answer and explanation

Answers: drop-down 1, 2022; drop-down 2, 100

How to solve it

Revenue per employee is 7.2/60 = £120,000 in 2019, 9.36/72 = £130,000 in 2020, 11.7/90 = £130,000 in 2021, 12.42/108 = £115,000 in 2022 and 15.6/120 = £130,000 in 2023. The minimum is 2022, even though 2022 revenue is higher than any earlier year — headcount grew faster than revenue that year. Headcount went from 60 to 120, an increase of 60 on a base of 60, which is 100 percent; 60 is that increase counted in people rather than as a percentage, and 50 measures it against the 2023 headcount of 120 instead of the 2019 base.

From GMAT Data Insights Practice Test 3

Question 15: Two-Part Analysis

Medium · Simultaneous Equations

A cooperative bottling plant fills two sizes of bottle, a half-litre bottle and a one-and-a-half-litre bottle, from the same tank of juice. On any given run the plant fills only these two sizes, and the tank is emptied exactly. On Monday the plant emptied a 3,000-litre tank and filled 3,600 bottles in total across the two sizes. The plant's supervisor records two figures in the daily log: the number of half-litre bottles filled, and the total volume of juice, in litres, that went into the one-and-a-half-litre bottles. Assume that every bottle was filled exactly to its stated capacity and that no juice was spilled or left in the tank.

In the table, select the number of half-litre bottles filled and the litres that went into the larger bottles. Make only two selections, one in each column.

Litres in the larger bottlesHalf-litre bottles filledOption
1,200
1,800
2,000
2,160
2,400
3,000
Show the answer and explanation

Answers: Litres in the larger bottles, 1,800; Half-litre bottles filled, 2,400

How to solve it

Let h be the half-litre bottles and o the one-and-a-half-litre bottles, so h + o = 3,600 and 0.5h + 1.5o = 3,000. Substituting o = 3,600 − h gives 0.5h + 5,400 − 1.5h = 3,000, so h = 2,400 and o = 1,200. The larger bottles therefore hold 1,200 × 1.5 = 1,800 litres, and the smaller ones 2,400 × 0.5 = 1,200 litres, which together empty the 3,000-litre tank. The distractor 1,200 is the count of large bottles offered where their volume was asked for, 2,000 is two thirds of the 3,000 litres, 2,160 is 0.6 of the 3,600 bottles, and 3,000 is the tank's whole contents rather than the share in the larger bottles.

From GMAT Data Insights Practice Test 3

Question 16: Multi-Source Reasoning

Medium · Applied Problems

On the exam these sources sit behind 3 tabs. All 3 are printed here.

Source 1: Call for proposals

A research council is awarding grants from a fund of £900,000. Proposals are scored on three criteria, each out of 10: novelty, feasibility and impact.

  • A proposal is shortlisted only if it scores at least 7 on every criterion.
  • A proposal is shortlisted only if its three scores total at least 24.
  • Shortlisted proposals are funded in descending order of total score until the fund is exhausted.

Source 2: Proposals

ProposalNoveltyFeasibilityImpactRequested (£)
Aurora989420,000
Borealis877300,000
Cyrus6910380,000
Delta Rise997250,000
Ember788260,000

Source 3: Council note

Any money left in the fund after the shortlisted proposals have been funded is carried forward to the next round. The council does not part-fund proposals, and a proposal that was not shortlisted is not funded whatever the fund's balance.

Taking all three sources into account, which of the following statements about the outcome of this funding round is best supported?

  1. A. All five proposals are shortlisted, but the fund covers only the first three.
  2. B. Cyrus is shortlisted because its feasibility and impact scores are the highest, taking £310,000.
  3. C. Ember is shortlisted, since it scores at least seven on every criterion.
  4. D. £230,000 carries forward, the fund having stretched to only two of the proposals.
  5. E. The whole £900,000 is spent, leaving nothing to carry into the next round.
Show the answer and explanation

Answer: D. £230,000 carries forward, the fund having stretched to only two of the proposals.

  • A. Three of the five fail a shortlisting test, so the fund is never asked to stretch across five proposals.
  • B. Cyrus does lead on two criteria, but its novelty score of 6 falls below the floor of 7 on every criterion.
  • C. Ember passes the first test but its scores total 23, one short of the 24 the second test requires.
  • D. Correct. Aurora and Delta Rise draw £670,000 of the £900,000, leaving £230,000 unspent.
  • E. Only £670,000 is awarded, and the council will not part-fund an unshortlisted proposal to use the rest.

How to solve it

Apply both shortlisting tests. Aurora scores 9, 8, 9 for a total of 26 and is shortlisted. Borealis clears the per-criterion floor but totals only 22, below 24. Cyrus scores 6 on novelty and fails the floor. Delta Rise scores 9, 9, 7 for 25 and is shortlisted. Ember clears the floor but totals 23. So only Aurora and Delta Rise are shortlisted. Funding in descending order, Aurora takes £420,000 and Delta Rise £250,000, a total of £670,000, leaving £230,000 to carry forward. That is choice D.

From GMAT Data Insights Practice Test 3

Question 17: Data Sufficiency

Hard · Statistics

Set K consists of seven distinct positive integers. The largest integer in set K is 30 and the smallest is 4. What is the median of the integers in set K?

  1. (1)The mean of the seven integers in set K is 16.
  2. (2)Exactly three of the integers in set K are greater than 20.
  1. A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
  2. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
  3. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
  4. D. EACH statement ALONE is sufficient.
  5. E. Statements (1) and (2) TOGETHER are NOT sufficient.
Show the answer and explanation

Answer: E. Statements (1) and (2) TOGETHER are NOT sufficient.

  • A. A sum of 112 leaves the middle five values free; 4, 5, 6, 20, 21, 26, 30 and 4, 6, 7, 18, 21, 26, 30 both qualify.
  • B. Knowing three values exceed 20 caps the median at 20 but does not say where below 20 it falls.
  • C. Both counter-examples satisfy the sum and the count above 20, yet give medians of 20 and 18.
  • D. Neither statement determines the fourth-smallest value on its own.
  • E. Correct. Two admissible sets meet every condition and differ in median, so the value is not determined.

How to solve it

With seven values the median is the fourth smallest. Statement (1) fixes the sum at 112, leaving five distinct integers strictly between 4 and 30 that sum to 78; the sets 4, 5, 6, 20, 21, 26, 30 and 4, 6, 7, 18, 21, 26, 30 both work and have medians 20 and 18. Statement (2) places the fifth, sixth and seventh terms above 20 and the fourth at or below 20, but does not fix it. The two sets above satisfy both statements at once — each sums to 112 and has exactly three members above 20 — yet their medians differ, so the answer is E.

From GMAT Data Insights Practice Test 3

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