Numerical Reasoning Test 1
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(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.
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
(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:
Step 2 Calculate the cost difference between 50 Fevs and 100 Steapars
shares yesterday:
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
(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.
(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
(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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(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
(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
(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.
(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
(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.
(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
(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)
(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:
(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 |
(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
(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.
(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.
(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.
(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.
(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
(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 |
(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)
(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.
(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
(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
(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
(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
(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
(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 |
(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 |