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Numerical Reasoning Test 1

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1. Which share had the largest difference between highest and lowest price over the last 12 months?

  • (A) Huver Co.
  • (B) Drebs Ltd
  • (C) Fevs Plc
  • (D) Fauvers
  • (E) Steapars

(C) Fevs Plc - The information that we need is shown in the table Share Prices.

Step 1 Calculate the difference between the maximum and the minimum.

  • Huver Co. = 1,360 – 860 = 500
  • Drebs Ltd= 22 – 11 = 11
  • Fevs Plc = 1,955 – 1,242 = 713
  • Fauvers = 724 – 464 = 260
  • Steapars = 2,630 – 2,216 = 414

Tip: Notice the wording of the question is asking for the share with the largest absolute change in price, NOT the largest percentage change, which would have been Drebs Ltd. If the question had wanted the percentage change it would have used the word percentage

2. What was yesterday's cost difference between 50 shares in Fevs plc and 100 shares in Steapars?

  • (A) €164,726
  • (B) €251,163
  • (C) €172,577
  • (D) €164,045
  • (E) None of these

(D) €164,045 - The information that we need is shown in the table Share Prices.

Step 1 Calculate yesterday's share price for each share:

  • Fevs plc = 1,586 ÷ 0.91 = 1,742.86
  • Steapars = 2,537 ÷ 1.01 = 2,511.88

Step 2 Calculate the cost difference between 50 Fevs and 100 Steapars shares yesterday:

  • 50 x 1,742.86 = 87,143
  • 100 x 2,511.88 = 251,188
  • Difference = 251,188 - 87,143 = 164,045

Tip: Percentage increases and decreases catch out a lot of people. For this question, think about what's happening. The percentage change from yesterday to today in the case of Fevs is a 9% decrease. So that means (today's price) ÷ (yesterday's price) = 0.91 (a 9% decrease). Using algebra we can recast this as yesterday's price = today's price ÷ 0.91

3. Today's Drebs Ltd share price represents a 40% increase on the price one month ago. What was the Drebs Ltd share price a month ago?

  • (A) €22
  • (B) €25.20
  • (C) €12.68
  • (D) €12.90
  • (E) €12.86

(E) €12.86 - The information that we need is shown in the table Share Prices.

Step 1 Drebs Ltd's share price is shown as 18 Euros at today's prices. This is a 40% increase and so represents 1.40 (140%) of the price one month ago.

Step 2 The price one month ago is calculated as follows:
18 ÷ 1.40 = 12.86.

4. What is the annual dividend paid to the holder of 1,550 Drebs Ltd shares?

  • (A) Cannot Say
  • (B) €635
  • (C) €2,232
  • (D) €2,418
  • (E) €2,822

(D) €2,418

Step 1 Calculate total dividend per share
Interim dividend + Final dividend = 44 + 112 = 1.56 Euros

Step 2 Calculate total dividend for 1,550 shares
1,550 x 1.56 = 2,418 Euros

5. If the exchange rate is €1.15 to the £, what is today's value of 250 Drebs Ltd shares (in £s)?

  • (A) £4,500
  • (B) £2,875
  • (C) £2,785
  • (D) £3,931
  • (E) £3,913

(E) £3,913

Step 1 Calculate today's price of 250 Drebs Ltd shares.
250 x 18 Euros = 4,500 Euros

Step 2 Calculate the price in £s
4500 ÷ 1.15 = £3,913

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6. If a driver travels an average of 4,250 miles per month driving along motorways in an Xtam car, what is the predicted annual consumption of fuel (in gallons)?

  • (A) Cannot say
  • (B) 1,500
  • (C) 125
  • (D) 150
  • (E) 1,250

(B) 1,500 - The information that we need is shown in the graph Car Consumption.

Step 1 The Xtam's fuel consumption is shown as 34 miles to the gallon for motorway driving.
So, 4,250 miles ÷ 34 = 125 gallons per month

Step 2 Annual petrol consumption = 125 x 12 = 1,500 gallons

7. A car dealership has £600,000 to spend and wants to buy equal numbers of the Taber and Ursa cars. What is the largest number of each type of car that can be ordered?

  • (A) 27
  • (B) 48
  • (C) 19
  • (D) 21
  • (E) 22

(D) 21 - The information that we need is shown in the table.

Step 1 The cost of the Taber and Ursa cars are £12,500 and £15,250 respectively.

Step 2 Since the numbers of each car purchased must be equal, calculate the combined cost as follows: £12,500 + £15,250 = £27,750.

Step 3 £600,000 ÷ £27,750 = 21.6

8. What is the ratio of the cost of a Taber: Velvo: Xtam?

  • (A) 2:4:5
  • (B) 1:4:6
  • (C) 1:3:5
  • (D) 2:3:5
  • (E) 1:2:3

(C) 1:3:5 - The information that we need is shown in the table.

Step 1 Taber: Velvo: Xtam costs = 12,500 : 37,500 : 62,500

Notice the common denominator here is 12,500. So the ratio can be simplified to the following. 12,500/12,500 : 37,500/12,500: 62,500/12,500 = 1:3:5.

9. A Tink car is taken on a test drive for 90 minutes around the city. If the average speed is 34 miles per hour approximately how much fuel is consumed?

  • (A) 1.5 gallons
  • (B) 2.5 gallons
  • (C) 2 gallons
  • (D) 0.5 gallons
  • (E) 1.75 gallons

(A) 1.5 gallons - The information that we need is shown in the graph Fuel Consumption.

Step 1 The Tink's fuel economy (city driving) = 34 miles to the gallon.

Step 2 Speed = distance / time.
34 miles per hour = distance / 90 mins = distance / 1.5 hours
So distance = 34 x 1.5 = 51 miles

Step 3 Fuel consumed = (51 miles ÷ 34 miles per gallon) = 1.5 gallons

10. A family plans to spend a month driving around Scottish cities where the average cost of a gallon of petrol is £4.75. If the family drive 1,500 city miles in their Velvo, what would be the family's total petrol costs (to the nearest £)?

  • (A) £216.00
  • (B) £203.57
  • (C) £204.00
  • (D) £215.89
  • (E) None of these

(C) £204 - The information that we need is shown in the graph Fuel Consumption.

Step 1 Velvo's fuel consumption (city driving) = 35 miles per gallon 1,500 ÷ 35 = 42.86 gallons required.

Step 2 Cost = 42.86 x £4.75 = £203.57
To the nearest £ = £204.

Tip: The fact that this is done in a month is irrelevant; sometimes the question deliberately contains redundant information.

11. Legal sector spending on IT hardware, IT software and IT consulting are all set to increase by the same amounts in Year 6 as they did from Year 4 to Year 5. Assuming this is the case, what is the total legal sector spend in Year 6 on these three IT areas combined?

  • (A) £75 million
  • (B) £85 million
  • (C) £95 million
  • (D) £105 million
  • (E) £110 million

(E) £110 million - The information that we need is shown in the graph IT spending by the legal sector.

Step 1 Calculate the increases in each IT spending category
IT hardware = 45 (increase of £5 million from Year 4)
IT software = 30 (increase of £5 million from Year 4)
IT consulting = 20 (increase of £5 million from Year 4)

Step 2 Calculate the total for the year after the projected year 5. Since there is an even increase the same increase of £5 million will occur in IT hardware, software and consulting. Total = 45 + 30 + 20 + (3 x 5) = £110 million

12. For years 1 to 3 inclusive, by how much did Make Fit Ltd's income from consultancy services differ from those of Pure Gap plc?

  • (A) £110 more
  • (B) £110,000 less
  • (C) £1,100,000 more
  • (D) £110 less
  • (E) £1,100,000 less

(E) £1,100,000 less - The information that we need is shown in the graph Income for IT consultancy services.

Step 1 Total the income for each company across the three years 1, 2 and 3.
Make Fit Ltd = 290 + 180 + 260 = 730
Pure Gap plc = 230 + 310 + 300 = 840
730 - 840 = -110 (£10,000's)

13. Which of the following statements is false regarding legal sector spending between Year 4 and projected Year 5?

  • (A) IT consulting will increase by £5million.
  • (B) IT consulting will match that of year 2.
  • (C) IT software will exceed IT consulting.
  • (D) Spending on IT hardware will decline.
  • (E) None of these.

(D) Spending on IT hardware will decline. - The information that we need is shown in the graph IT spending by the legal sector.

Step 1 Check in turn whether each statement is true or false:

  • a) The projected spend on IT consulting is projected to increase by £5million. Option A is true.
  • b) The projected spend on IT consulting is £5million, which matches year 2. Option B is true.
  • c) The projected spend on IT software is £30million and for IT consulting it's £20million. Option C is true.
  • d) There are increases projected for IT hardware, for IT software and for consulting. The option for D is false.
  • e) We see that option D is false, so E cannot be the correct answer.

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14. In which year(s) did Make Fit Ltd and Pure Gap plc's combined IT consultancy income exceed £6million?

  • (A) Year 1 and Year 4
  • (B) Only Year 4
  • (C) Year 1 and Year 3
  • (D) Only Year 3
  • (E) Year 3 and Year 4

(B) Only Year 4 - The information that we need is shown in the graph Income for IT consultancy services.

Step 1 Find the total for each of the years shown and see which years exceed £6million.

Year Make Fit Ltd and Pure Gap plc's
combined IT consulting income
Year 1 290 + 230 (£10,000s) = £5.2 million
Year 2 180 + 310 (£10,000s) = £4.9 million
Year 3 260 + 300 (£10,000s) = £5.6 million
Year 4 320 + 290 (£10,000s) = £6.1 million

15. If Pure Gap plc's income from consultancy in year 2 had been twice as big, what fraction would this have been of the combined income for both Pure Gap plc and Make Fit Ltd in year 2?

  • (A) 18/49
  • (B) 31/40
  • (C) 9/4
  • (D) 4/9
  • (E) 18/31

(B) 31/40 - The information that we need is shown in the graph Income for consultancy services.

Step 1 Calculate Pure Gap's increased year 2 income.
Year 2 Pure Gap sales = 2 x 310 = 620.

Step 2 Calculate combined year 2 income.
Pure Gap + Make Fit sales = 620 + 180 = 800.

Step 3 Calculate the fraction
620/800 = 31/40

16. If actual labour costs rise so as to halve their difference from the target, what will be the change in actual Gross Profit?

  • (A) Falls by £4,500
  • (B) Rises by £4,500
  • (C) No overall effect
  • (D) Rises by £9,000
  • (E) Falls by £9,000

(A) Falls by £4,500

Step 1 Halve the labour costs discrepancy against target (target labour costs - actual labour costs)/2 = (175,000 - 166,000)/2 = £4,500.

Step 2 Calculate effect on Gross Profit
If labour costs rise by £4,500, then profit falls by £4,500.

17. IKE Computers aim to grow monthly gross profit by 1.5%. If all costs remain constant, what will the sales turnover need to be in February to hit the target?

  • (A) £242,099
  • (B) £277,987
  • (C) £38,555
  • (D) £274,299
  • (E) £288,000

(B) £277,987

Step 1 Calculate the required gross profit increase. 36,521 x 1.5% = £547.82.
Given that costs are constant, this means the Net Turnover needs to increase
By £547.8 too. So the Net Turnover needs to be £547.8 + £238,521 = £239,068.8.

Step 2 We have worked out the Net Turnover, but the question asks for Sales Turnover
(i.e. before the sales tax of 14.0% is deducted). So Sales Turnover = 239,068.8 ÷ 86.0% = £277,986.98.

18. If IKE Computers had January sales turnover in the ratio of 4:5 for American:UK operations then what was the January sales turnover for American operations in $ (at an exchange rate of 1.6$ to the £)?

  • (A) $557,400
  • (B) $355,008
  • (C) $216,860
  • (D) $216,680
  • (E) $554,700

(B) $355,008

Step 1 Calculate the January sales turnover for American operations based on the UK value.
UK value is 277,350 and the ratio is American:UK = 4:5
So American = 277,350 x 4/5 = 221,880

Step 2 Convert into $
221,880 x 1.6 = $355,008

Tip: the calculation is NOT 4 ÷ (4 + 5) because the table gives the UK value, not the overall total value of UK and America combined.

19. If IKE Computers employed eighty permanent employees in January who were on the same salary, what would have been the effect on labour costs if they had replaced twenty permanent employees with interim staff each on monthly salaries of £3,000?

  • (A) Cannot tell
  • (B) Decrease of £130,000
  • (C) Decrease of £20,750
  • (D) Increase of £2,075
  • (E) Increase of £18,500

(E) Increase of £18,500

Step 1 Calculate the monthly cost of each full-time employee in January
166,000 / 80 = 2,075.

Step 2 Calculate the difference in monthly labour costs
3,000 - 2,075 = 925

Step 3 Calculate the difference of replacing 20 full time employees with interims
925 x 20 = £18,500.

20. If February's gross profit target is a 40% increase on January's, to be followed by a 25% decrease in March, what is March's gross profit target (in £1,000s)?

  • (A) 66,675
  • (B) 666.8
  • (C) 66.7
  • (D) 6.7
  • (E) 666,750

(C) 66.7

Step 1 40% increase on 63,500 is calculated as 63,500 x 1.40 = £88,900

Step 2 Next, a 25% decrease is 88,900 x 0.75 = 66,675 =66.7 (£1,000s)

Tip: there a couple of areas which could trip you up here. Be careful not to muddle target figures with actual figures in the table. And don't miss that the question asks for your answer in £1,000s

21. Which sector represents approximately 19% of the profits from the five sectors shown?

  • (A) Leisure
  • (B) Manufacturing
  • (C) Retail
  • (D) Government
  • (E) Utilities

(E) Utilities The series of calculations is best shown in a table.

Step 1 - calculate sum Step 2 - Total Step 3 - % of total
Leisure 5.2 + 7.4 + 4.6 = 17.2 17.2 22%
Manufacturing 5 + 7.2 + 6.3 = 18.5 18.5 24%
Retail 4.4 + 5.8 + 3.8 = 14 14 18%
Government 4.5 + 5.9 + 3.6 + 14 14 18%
Utilities 3.5 + 5.1 + 6.2 = 14.8 14.8 19%
Total = 78.5

22. If the ratio of profit to turnover for Pacific Rim contracts was 2:15, what was the Government turnover in the Pacific Rim (in £100,000s)?

  • (A) 36
  • (B) 27
  • (C) 270
  • (D) 360
  • (E) 540

(C) 270 - The information that we need is shown in the table Share Prices.

Step 1 Contracts ratio of profit (£3.6million) to turnover = 2:15 Turnover = £3.6 million x 15/2 = £27 million = 270 (in £100,000s)

23. Reyes Heslop had a target for Leisure profits to be a quarter of their total profits. Assuming profits in other areas remain the same, by how much did the Leisure profits miss this target?

  • (A) £1.8 million
  • (B) £2.4 million
  • (C) £2.7 million
  • (D) £3.2 million
  • (E) £3.4 million

(D) £3.2 million

Step 1 Calculate the total Reyes Heslop profits across all areas other than Leisure.
(6.3 + 7.2 + 5.0) + (3.8 + 5.8 + 4.4) + (3.6 + 5.9 + 4.5) + (6.2 + 5.1 + 3.5) = 61.3million.

Step 2 This needs to be ¾ of all profits for the condition to be met. Therefore all profits, across all sectors, would be 61.3 ÷ 75% = 81.7333million

Step 3 Now we look at the difference between actual and target Leisure profits.
Actual = (4.6 + 7.4 + 5.2) = 17.2
Target = (81.7333 - 61.3) = 20.4333
Shortfall = 3.2333 (millions)

Note: the INCORRECT way of doing this question would be to:
Sum profits across all areas, calculate ¼, then see the difference between that figure and 17.2 million. This method would calculate ¼ of the profits including the reduced figure from Leisure. To see this, use the figure you arrive at using this method for Leisure (19.625) and the total profits become 80.93. Which is not 4x 19.625.

24. A competitor wants to takeover Reyes Heslop and offers a price of 8 times current profits. Reyes Heslop shareholders reject this offer and suggest a price that is 20% higher, what is this suggested price?

  • (A) £79 million
  • (B) £63 million
  • (C) £628 million
  • (D) £754 million
  • (E) £502 million

(D) £754 million

Step 1 Calculate the current profits total across all sectors.
4.6 + 7.4 + 5.2 + 6.3 + 7.2 + 5.0 + 3.8 + 5.8 + 4.4 + 3.6 + 5.9 + 4.5 + 6.2 + 5.1 +3.5 = £78.5 million.

Step 2 Takeover offer price = (£78.5 million x 8) = £628 million Suggested offer price = £628 x 120% = £753.6 million

25. If the Worldwide Sales Director of Reyes Heslop Consulting is aiming for a total sales ratio of 3:2 (American: Pacific Rim), by what absolute amount do American profits need to change if Pacific Rim profits remain constant?

  • (A) £5.35 million increase
  • (B) £15.1 million increase
  • (C) £5.35 million decrease
  • (D) £15.1 million decrease
  • (E) None of these

(A) £5.35 million increase

Step 1 Calculate the absolute levels of American: Pacific Rim ratio sales;
£31.4 million (American): £24.5 million (Pacific Rim)

Step 2 Calculate change needed in American sales to reach 3:2 ratio
(£24.5million x 3/2) - £31.4 million = £5.35 million

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26. What is the difference between direct sales and telesales across the five teams combined?

  • (A) £10 million
  • (B) £11 million
  • (C) £12 million
  • (D) £13 million
  • (E) £14 million

(B) £11 million

Step 1 Calculate the total direct sales and telesales across the five teams

Direct Sales Telesales
Team A 17 16
Team B 13 17
Team C 16 18
Team D 15 17
Team E 14 18
TOTAL 75 86

Step 2 Calculate the difference
86 - 75 = £11 million

27. If there are 50 direct sales and 65 telesales employees assigned to each of the Eastern region's teams A–E, what are the average sales per sales employee for the lowest performing team in terms of overall sales (to the nearest £1,000)?

  • (A) Cannot tell from the data
  • (B) £200,000 (direct); £340,000 (telesales)
  • (C) £260,000 (direct); £260,000 (telesales)
  • (D) £340,000 (telesales); £200,000 (direct)
  • (E) £20,000 (direct sales); £30,000 (telesales)

(C) £260,000 (direct); £260,000 (telesales)

Step 1 Obtain the lowest performing team from calculating the overall sales (direct sales and telesales combined)
Team A total = 33
Team B total = 30
Team C total = 34
Team D total = 32
Team E total = 32
So, Team B is the lowest performing team overall

Step 2 Calculate the average sales per direct sales employee 13/50 = 0.26 million

Step 3 Calculate the average sales per telesales sales employee 17/65 = 0.26 million

28. If the Eastern Region's total sales represent 26% of the total for all regions, what are the total sales across all regions (to the nearest £million)?

  • (A) £124 million
  • (B) £142 million
  • (C) £161 million
  • (D) £619 million
  • (E) £620 million

(D) £619 million

Step 1 Calculate the total sales
86 (for telesales) + 75 (for direct sales) = £161 million

Step 2 Calculate the total sales across all regions
£161 million = 26%
100% = 161 x 100/26 = £619.23 million

29. What are the total sales targets for next year across all five teams if the target is set as a 20% and 10% increase in this year's Direct Sales and Telesales respectively?

  • (A) Direct (£75 million); Telesales (£86 million)
  • (B) Direct Sales (£104 million); Telesales (£82 million)
  • (C) Direct (£82 million); Telesales (£104 million)
  • (D) Direct (£95 million); Telesales (£90 million)
  • (E) Direct (£90 million); Telesales (£94.6 million)

(E) Direct (£90 million); Telesales (£94.6 million)

Step 1 Calculate the increase in the direct sales and telesales totals, as follows:

Direct Sales Telesales
17 16
13 17
16 18
15 17
14 18
TOTAL 75 86
75 x 120% = 90 86 x 110% = 94.6

30. If there are 5 direct sales employees and 6 telesales employees in each team, which sub-team has the lowest average sales per sales employee?

  • (A) Direct sales (Team B)
  • (B) Direct sales (Team D)
  • (C) Telesales (Team A)
  • (D) Telesales (Team B)
  • (E) Telesales (Team D)

(A) Direct sales (Team B)

Step 1 Calculate the average sales per direct sales and per telesales rep, as follows:

Team       Direct Sales Telesales Average sales (per direct sales employee) Average sales (per telesales employee)
Team A 17 16 3.4 2.7
Team B 13 17 2.6 2.8
Team C 16 18 3.2 3
Team D 15 17 3 2.8
Team E 14 18 2.8 3