EA Integrated Reasoning practice questions

Question 1

Grants brought in ____ last year, and events and the shop together raised ____ grants.

Accepted 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.

Question 2

From January to June, visitors increased by approximately ____, and visitors fell in ____ of the five month-on-month changes.

Accepted 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.

Question 3

The relationship between price and weekly unit sales is ____, and ____ of the eight products sell more than 200 units a week.

Accepted 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.

Question 4

Technology accounts for approximately ____ of all employees, and Finance and HR together employ ____ Sales.

Accepted 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.

Question 5

The school whose pass rate improved by the most percentage points was ____, and the number of schools whose pass rate fell was ____.

Accepted Answer

(1) School D; (2) one — Changes: A +6, B −4, C +4, D +8 points. D improved most, and only B fell.

Question 6

For each statement, select Yes if it is true according to the table and No otherwise.

Accepted 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.

Question 7

For each statement, select True if the data support it and False otherwise.

Accepted 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.

Question 8

For each statement, select Yes if it is true according to the table and No otherwise.

Accepted 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.

Question 9

For each statement, select True if the data support it and False otherwise.

Accepted 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%.

Question 10

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.

Accepted Answer

Adult price: £32; Child price: £20 — Doubling the first equation and tripling the second: 6a+4c=272 and 6a+15c=492, so 11c=220, c=£20, and then 3a=136-40 gives a=£32.

Question 11

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.

Accepted 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.

Question 12

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.

Accepted 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.

Question 13

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.

Accepted Answer

x: 20%; Final price: £240 — (1+x)(1-x)=1-x^2=0.96, so x^2=0.04 and x=20%. The final price is 96% of £250: £240.

Question 14

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.

Accepted 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.

Question 15

Which venue would be the cheapest for the conference as planned?

Accepted Answer

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.

Answer

Hall B

Answer

Hall C

Answer

Halls A and B would cost the same

Answer

It cannot be determined

Question 16

Using the cheapest venue and standard catering, what would the conference's profit be?

Accepted Answer

£44,400 — Income: 180 × £350 + £12,000 = £75,000. Costs: Hall A £19,800 plus standard catering 30 × 360 = £10,800. Profit: £44,400.

Answer

£32,400

Answer

£49,200

Answer

£55,200

Answer

£63,000

Question 17

For each statement, select Yes if it follows from the information provided and No otherwise.

Accepted 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.

Question 18

How many subscribers does the company have at the end of March?

Accepted Answer

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.

Answer

2,060

Answer

2,075

Answer

2,120

Answer

2,360

Question 19

Taking the number of subscribers at the end of March, what is the company's profit for March?

Accepted Answer

£12,200 — Revenue: 2,175 × £30 = £65,250. Costs: £40,000 + 2,175 × £6 = £53,050. Profit: £12,200.

Answer

£9,800

Answer

£13,050

Answer

£25,250

Answer

£52,200

Question 20

For each statement, select True if it follows from the information provided and False otherwise.

Accepted 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.

Question 21

Product A first had more active users than product B in ____, and from January to June product B's active users fell by approximately ____.

Accepted Answer

(1) June; (2) 15% — The gap narrows every month (25, 19, 13, 6, 2 thousand) and A is first ahead in June, 60 against 55. Product B fell from 65 to 55 thousand: 10/65 ≈15.4%.

Question 22

Events received ____ of the budget. If the Content budget were increased by £20,000 and nothing else changed, Content's share of the new total would be about ____.

Accepted Answer

(1) £100,000; (2) 24% — Events: 25% of £400,000 = £100,000. Content rises from £80,000 to £100,000 while the total rises to £420,000: 100/420 ≈23.8%, about 24%. Adding 5 percentage points (to 25%) forgets that the total grows too.

Question 23

For each statement, select Yes if it is true according to the table and No otherwise.

Accepted Answer

1: No; 2: Yes; 3: Yes — (1) No: E costs £1,100 and weighs exactly 1.5 kg. (2) Yes: the battery lives sorted are 7, 9, 11, 12, 14, 15, so the median is 11.5, and 12, 14 and 15 are above it. (3) Yes: C has the top rating, 4.7, and costs £1,450 / 15 ≈ £96.7 per hour, below A and E (£100), B (£105.6), D (£114.3) and F (£117.9).

Question 24

For each statement, select True if the data support it and False otherwise.

Accepted Answer

1: True; 2: False; 3: False — (1) True: East grew 20% (9.5 to 11.4); North and Central 10%, South 5%, West fell 4%. (2) False: the total went from £74.5m to £79.9m, about 7.2%. (3) False: per member of staff, East has £11.4m / 30 = £0.38m; Central only £22.0m / 70 ≈ £0.31m.

Question 25

A consultant charges a fixed fee plus an hourly rate. A 10-hour project costs £2,300 and a 25-hour project costs £4,550. Select the fixed fee and the hourly rate.

Accepted Answer

Fixed fee: £800; Hourly rate: £150 — The extra 15 hours cost £4,550 − £2,300 = £2,250, so the rate is £150 an hour. Then the fixed fee is £2,300 − 10 × £150 = £800.

Question 26

Five projects, P, Q, R, S and T, are scheduled one per week for five weeks. Q is in the week immediately after P. S is earlier than T, and T is earlier than P. R is not in week 1. Select the earliest week in which P can be scheduled and the latest week in which T can be scheduled.

Accepted Answer

Earliest week for P: Week 3; Latest week for T: Week 3 — S, T, P, Q must appear in that order with P and Q adjacent, and R goes anywhere except week 1. That leaves three schedules: S R T P Q, S T R P Q and S T P Q R. P is in week 3 or 4, so its earliest week is 3. T is in week 2 or 3, so its latest week is 3. The same option answers both columns.

Question 27

An investor splits £50,000 between a fund returning 6% a year and a bond returning 2% a year, and earns £2,200 in the first year. Select the amount in the fund and the amount in the bond.

Accepted Answer

Fund: £30,000; Bond: £20,000 — With f in the fund: 0.06f+0.02(50,000-f)=2,200, so 0.04f=1,200 and f=£30,000. The bond holds £20,000. Check: £1,800 + £400 = £2,200.

Question 28

What is the planned first-year cost of the Manchester hires, including recruitment fees?

Accepted Answer

£234,000 — Each Manchester graduate costs £35,000 + £4,000 = £39,000; six cost £234,000.

Answer

£210,000

Answer

£228,000

Answer

£240,000

Answer

£252,000

Question 29

By how much does the plan as it stands exceed the budget?

Accepted Answer

£62,000 — London: 8 × £46,000 = £368,000. Manchester: £234,000. Edinburgh: 4 × £40,000 = £160,000. Total £762,000, which is £62,000 over the £700,000 budget.

Answer

£22,000

Answer

£46,000

Answer

£84,000

Answer

£108,000

Question 30

For each statement, select Yes if it follows from the information provided and No otherwise.

Accepted Answer

1: Yes; 2: Yes; 3: No — (1) Yes: each London hire costs £46,000, so two cuts take £762,000 to £670,000; one cut (£716,000) is not enough. (2) Yes: salaries are £336,000 + £210,000 + £144,000 = £690,000. (3) No: £234,000 / £762,000 ≈ 30.7%.

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.

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

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%.

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%.

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.

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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

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

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

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.

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.

Model	Price (£)	Battery (hours)	Weight (kg)	Rating (out of 5)
A	1,200	12	1.3	4.4
B	950	9	1.6	4.1
C	1,450	15	1.2	4.7
D	800	7	2.0	3.8
E	1,100	11	1.5	4.5
F	1,650	14	1.1	4.6

Yes	No	Statement
		Every laptop priced above £1,000 weighs less than 1.5 kg.
		Exactly half of the laptops have a battery life above the median battery life.
		The highest-rated laptop also has the lowest price per hour of battery life.

Region	Sales 2024	Sales 2025	Staff
North	12.0	13.2	40
South	18.0	18.9	55
East	9.5	11.4	30
West	15.0	14.4	48
Central	20.0	22.0	70

True	False	Statement
		East had the largest percentage growth in sales from 2024 to 2025.
		Total sales across the five regions grew by more than 8%.
		In 2025, Central had the highest sales per member of staff.

Yes	No	Statement
		Cutting two London hires brings the plan within budget.
		The planned salaries alone, without recruitment fees, are within the budget.
		Manchester accounts for more than a third of the planned first-year cost.

X	Y
		1st
		2nd
		3rd
		4th

x	Final price
		10%
		20%
		£240
		£244
		£250
		£260

Largest	Smallest
		8
		12
		15
		18
		22
		30

Venue	Per delegate per day (£)	Minimum charge (£)
Hall A	55	18,000
Hall B	48	20,000
Hall C	62	15,000