Practice · Executive Assessment · Integrated Reasoning
EA Integrated Reasoning practice questions
20 questions with worked solutions. Graphics interpretation, sortable table analysis, two-part analysis and multi-source reasoning, with a calculator, as on the assessment.
Practise timed: 12 questions · 30 min All Executive Assessment topics
Grants brought in (1) last year, and events and the shop together raised (2) grants.
(1) £300,000 · £450,000 · £600,000 · £750,000
(2) less than · the same as · more than
Show answer
Answer: (1) £450,000; (2) less than
Grants are 30% of £1.5 million: £450,000. Events (15%) and the shop (10%) make 25%, less than the 30% from grants.
From January to June, visitors increased by approximately (1), and visitors fell in (2) of the five month-on-month changes.
(1) 50% · 85% · 117% · 217%
(2) none · one · two · three
Show answer
Answer: (1) 117%; (2) one
65/30 ≈ 2.17, an increase of about 117%; 217% is the ratio mistaken for the increase. Only March to April (45 to 40) is a fall.
The relationship between price and weekly unit sales is (1), and (2) of the eight products sell more than 200 units a week.
(1) strongly positive · close to zero · moderately negative · strongly negative
(2) three · four · five · six
Show answer
Answer: (1) strongly negative; (2) four
The points fall steadily along a line as price rises (the correlation is about −0.99): strongly negative. The products selling more than 200 a week are those at £5, £8, £10 and £12. The £15 product sells exactly 200, which is not more than 200.
Technology accounts for approximately (1) of all employees, and Finance and HR together employ (2) Sales.
(1) 25% · 30% · 36% · 45%
(2) fewer people than · as many people as · more people than
Show answer
Answer: (1) 36%; (2) fewer people than
The total is 210, and 75/210 ≈ 35.7%. Finance and HR have 30 people between them, fewer than the 45 in Sales.
The school whose pass rate improved by the most percentage points was (1), and the number of schools whose pass rate fell was (2).
(1) School A · School B · School C · School D
(2) none · one · two · three
Show answer
Answer: (1) School D; (2) one
Changes: A +6, B −4, C +4, D +8 points. D improved most, and only B fell.
| Product | Price (£) | Units sold | Units returned | Rating |
|---|---|---|---|---|
| Alpha | 40 | 1,200 | 36 | 4.2 |
| Bravo | 25 | 2,100 | 105 | 3.9 |
| Charlie | 60 | 800 | 16 | 4.6 |
| Delta | 35 | 1,500 | 60 | 4.1 |
| Echo | 50 | 900 | 45 | 4.4 |
| Foxtrot | 30 | 1,800 | 36 | 4.0 |
For each statement, select Yes if it is true according to the table and No otherwise.
| Yes | No | Statement |
|---|---|---|
| The product with the most units sold also has the highest revenue (price × units sold). | ||
| The two products with the lowest return rates (units returned ÷ units sold) also have the two highest ratings. | ||
| Total revenue across the six products is at least £300,000. |
Show answer
Answer: 1: No; 2: No; 3: Yes
(1) No: Bravo sells the most (2,100) for £52,500, but Foxtrot earns more, £54,000. (2) No: the lowest return rates are Charlie and Foxtrot (2% each), while the two highest ratings are Charlie (4.6) and Echo (4.4). (3) Yes: revenues are 48,000 + 52,500 + 48,000 + 52,500 + 45,000 + 54,000 = exactly £300,000.
| Region | Target | Actual | Sales reps |
|---|---|---|---|
| North | 500 | 540 | 6 |
| South | 420 | 399 | 5 |
| East | 380 | 410 | 4 |
| West | 610 | 579.5 | 7 |
| Central | 300 | 330 | 3 |
For each statement, select True if the data support it and False otherwise.
| True | False | Statement |
|---|---|---|
| Exactly two regions missed their target. | ||
| The region with the highest actual sales per rep also has the highest ratio of actual sales to target. | ||
| Total actual sales exceeded total target by more than 3%. |
Show answer
Answer: 1: True; 2: True; 3: False
(1) True: South and West. (2) True: Central has the most sales per rep (110 thousand) and the best attainment (110% of target; North 108%, East 107.9%). (3) False: actual sales total 2,258.5 against a target of 2,210, about 2.2% above.
| Hotel | Rooms | Occupancy (%) | Average room rate (£) | Guest rating |
|---|---|---|---|---|
| Harbour | 120 | 82 | 140 | 4.3 |
| Castle | 80 | 90 | 180 | 4.6 |
| Park | 150 | 70 | 110 | 3.9 |
| River | 100 | 88 | 150 | 4.4 |
| Station | 60 | 75 | 95 | 3.7 |
For each statement, select Yes if it is true according to the table and No otherwise.
| Yes | No | Statement |
|---|---|---|
| Castle earns the most per available room (occupancy × average room rate). | ||
| The hotel with the most rooms has the lowest occupancy. | ||
| Every hotel with a guest rating above 4.0 has an occupancy above 85%. |
Show answer
Answer: 1: Yes; 2: Yes; 3: No
(1) Yes: revenue per available room is £114.80, £162, £77, £132 and £71.25. (2) Yes: Park has 150 rooms and 70% occupancy. (3) No: Harbour is rated 4.3 at 82% occupancy.
| Course | Enrolled | Completed | Satisfaction (out of 5) |
|---|---|---|---|
| Statistics | 240 | 180 | 4.1 |
| Finance | 300 | 210 | 4.3 |
| Strategy | 180 | 162 | 4.6 |
| Marketing | 220 | 143 | 3.8 |
| Operations | 160 | 136 | 4.4 |
For each statement, select True if the data support it and False otherwise.
| True | False | Statement |
|---|---|---|
| The course with the highest completion rate also has the highest satisfaction score. | ||
| Fewer students completed Marketing than completed Operations. | ||
| Across all five courses, more than 80% of enrolled students completed. |
Show answer
Answer: 1: True; 2: False; 3: False
(1) True: Strategy has both the highest completion rate (90%) and satisfaction (4.6). (2) False: 143 completed Marketing and 136 Operations. (3) False: 831 of 1,100, about 75.5%.
A tour costs £a for each adult and £c for each child. Three adults and two children pay £136; two adults and five children pay £164. Select the adult price and the child price.
| Adult price | Child price | |
|---|---|---|
| £16 | ||
| £20 | ||
| £24 | ||
| £28 | ||
| £32 | ||
| £36 |
Show answer
Answer: Adult price: £32; Child price: £20
Doubling the first equation and tripling the second: and , so , , and then gives .
Printer X prints 40 pages a minute. Printer Y is 25% slower. Select the number of pages Y prints per minute, and the number of minutes the two printers working together need to print 1,050 pages.
| Pages per minute for Y | Minutes together | |
|---|---|---|
| 15 | ||
| 20 | ||
| 30 | ||
| 35 | ||
| 50 | ||
| 70 |
Show answer
Answer: Pages per minute for Y: 30; Minutes together: 15
Y prints 75% of 40, which is 30 pages a minute. Together they print 70 a minute, and 1,050/70 = 15 minutes.
Four candidates, W, X, Y and Z, are ranked 1 to 4 with no ties. X is ranked above Y; Z is ranked immediately below W; and Y is not ranked last. Select the rank X must have and the rank Y must have.
| X | Y | |
|---|---|---|
| 1st | ||
| 2nd | ||
| 3rd | ||
| 4th |
Show answer
Answer: X: 1st; Y: 2nd
W and Z take two consecutive ranks. If W–Z are 1–2, then X and Y are 3–4 with Y last, which is not allowed. If W–Z are 2–3, then Y must take 4th, also not allowed. So W–Z are 3–4, and X and Y are 1st and 2nd in that order.
A price rises by x% and the new price then falls by x%, ending 4% below where it started. The starting price was £250. Select the value of x and the final price.
| x | Final price | |
|---|---|---|
| 10% | ||
| 20% | ||
| £240 | ||
| £244 | ||
| £250 | ||
| £260 |
Show answer
Answer: x: 20%; Final price: £240
, so and . The final price is 96% of £250: £240.
A box holds 30 counters, each red or blue, with at least 8 of each colour. Select the largest possible number of red counters and the smallest possible number of red counters.
| Largest | Smallest | |
|---|---|---|
| 8 | ||
| 12 | ||
| 15 | ||
| 18 | ||
| 22 | ||
| 30 |
Show answer
Answer: Largest: 22; Smallest: 8
At least 8 must be blue, so red is at most 22; at least 8 must be red. Both limits are attainable.
Brief
We are planning a two-day conference for 180 delegates. Tickets cost £350 each and a sponsor has committed £12,000. Venues charge per delegate per day, subject to a minimum charge for the whole event; catering is charged separately, per delegate per day.
Venue quotes
| Venue | Per delegate per day (£) | Minimum charge (£) |
|---|---|---|
| Hall A | 55 | 18,000 |
| Hall B | 48 | 20,000 |
| Hall C | 62 | 15,000 |
Catering
| Package | Per delegate per day (£) |
|---|---|
| Standard | 30 |
| Premium | 45 |
Which venue would be the cheapest for the conference as planned?
- Hall A
- Hall B
- Hall C
- Halls A and B would cost the same
- It cannot be determined
Show answer
Answer: A. Hall A
180 delegates for 2 days is 360 delegate-days. Hall A: 55 × 360 = £19,800, above its minimum. Hall B: 48 × 360 = £17,280, below its minimum, so it charges £20,000. Hall C: 62 × 360 = £22,320. Hall A is cheapest, even though Hall B has the lowest daily rate.
Brief
We are planning a two-day conference for 180 delegates. Tickets cost £350 each and a sponsor has committed £12,000. Venues charge per delegate per day, subject to a minimum charge for the whole event; catering is charged separately, per delegate per day.
Venue quotes
| Venue | Per delegate per day (£) | Minimum charge (£) |
|---|---|---|
| Hall A | 55 | 18,000 |
| Hall B | 48 | 20,000 |
| Hall C | 62 | 15,000 |
Catering
| Package | Per delegate per day (£) |
|---|---|
| Standard | 30 |
| Premium | 45 |
Using the cheapest venue and standard catering, what would the conference's profit be?
- £32,400
- £44,400
- £49,200
- £55,200
- £63,000
Show answer
Answer: B. £44,400
Income: 180 × £350 + £12,000 = £75,000. Costs: Hall A £19,800 plus standard catering 30 × 360 = £10,800. Profit: £44,400.
Brief
We are planning a two-day conference for 180 delegates. Tickets cost £350 each and a sponsor has committed £12,000. Venues charge per delegate per day, subject to a minimum charge for the whole event; catering is charged separately, per delegate per day.
Venue quotes
| Venue | Per delegate per day (£) | Minimum charge (£) |
|---|---|---|
| Hall A | 55 | 18,000 |
| Hall B | 48 | 20,000 |
| Hall C | 62 | 15,000 |
Catering
| Package | Per delegate per day (£) |
|---|---|
| Standard | 30 |
| Premium | 45 |
For each statement, select Yes if it follows from the information provided and No otherwise.
| Yes | No | Statement |
|---|---|---|
| If only 100 delegates came, Hall B would cost less than Hall C. | ||
| For 180 delegates, premium catering would cost £5,400 more than standard catering. | ||
| Ticket income alone would cover the cost of Hall C with premium catering. |
Show answer
Answer: 1: No; 2: Yes; 3: Yes
(1) No: at 200 delegate-days, both halls fall below their minimums, so Hall B costs £20,000 and Hall C £15,000. (2) Yes: (45 − 30) × 360 = £5,400. (3) Yes: £22,320 + 45 × 360 = £38,520, well below £63,000 of ticket income.
Summary
A software company starts the year with 2,000 subscribers, each paying £30 a month. New sign-ups and cancellations for the first quarter are in the table.
Sign-ups and cancellations
| Month | New sign-ups | Cancellations |
|---|---|---|
| January | 120 | 60 |
| February | 90 | 75 |
| March | 150 | 50 |
Costs
Fixed costs are £40,000 a month. Serving each subscriber costs a further £6 a month.
How many subscribers does the company have at the end of March?
- 2,060
- 2,075
- 2,120
- 2,175
- 2,360
Show answer
Answer: D. 2,175
2,000 + 120 − 60 = 2,060 at the end of January; + 90 − 75 = 2,075 at the end of February; + 150 − 50 = 2,175 at the end of March.
Summary
A software company starts the year with 2,000 subscribers, each paying £30 a month. New sign-ups and cancellations for the first quarter are in the table.
Sign-ups and cancellations
| Month | New sign-ups | Cancellations |
|---|---|---|
| January | 120 | 60 |
| February | 90 | 75 |
| March | 150 | 50 |
Costs
Fixed costs are £40,000 a month. Serving each subscriber costs a further £6 a month.
Taking the number of subscribers at the end of March, what is the company's profit for March?
- £9,800
- £12,200
- £13,050
- £25,250
- £52,200
Show answer
Answer: B. £12,200
Revenue: 2,175 × £30 = £65,250. Costs: £40,000 + 2,175 × £6 = £53,050. Profit: £12,200.
Summary
A software company starts the year with 2,000 subscribers, each paying £30 a month. New sign-ups and cancellations for the first quarter are in the table.
Sign-ups and cancellations
| Month | New sign-ups | Cancellations |
|---|---|---|
| January | 120 | 60 |
| February | 90 | 75 |
| March | 150 | 50 |
Costs
Fixed costs are £40,000 a month. Serving each subscriber costs a further £6 a month.
For each statement, select True if it follows from the information provided and False otherwise.
| True | False | Statement |
|---|---|---|
| The number of subscribers grew in every month of the quarter. | ||
| February's cancellations were 5% of the subscribers at the start of February. | ||
| At £30 a month, the company needs more than 1,700 subscribers to cover its monthly costs. |
Show answer
Answer: 1: True; 2: False; 3: False
(1) True: net changes are +60, +15 and +100. (2) False: 75/2,060 is about 3.6%. (3) False: each subscriber contributes £30 − £6 = £24 towards the £40,000 of fixed costs, so the break-even point is 40,000/24 ≈ 1,667 subscribers.
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