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Numerical Test 3
Solutions Booklet
Instructions
This numerical reasoning test comprises 30 questions, and you will have 30 minutes in
which to correctly answer as many as you can. Calculators are permitted for this test, and it is
recommended you have some rough paper to work on.
You will have to work quickly and accurately to perform well in this test. If you don't know the
answer to a question, leave it and come back to it if you have time. Each question will have
five possible answers, one of which is correct. You may click Back and Next during the test to
review or skip questions.
You can submit your test at any time. If the time limit is up before you click submit the test will
automatically be submitted with the answers you have selected. It is recommended to keep
working until the time limit is up.
Try to find a time and place where you will not be interrupted during the test. The test will
begin on the next page.
AssessmentDay
Practice Aptitude TestsQ1 What was the 2010 percentage change in the value of the Pacific Rim
holding between October and November (to the nearest percent)?
(A) 41% less
(B) 41% more
(C) 36% less
(D) 34% less
(E) 33% less
Step 1 – Calculate the Oct value
The information that you need is shown in the pie-chart
£37.5 million x 20% = £7.5 million
Step 2 – Calculate the Nov value
The information that you need is shown in the graph
50.0 x £100,000 = £5 million
Step 3 – Calculate the % difference
7.5 - 5.0 = 2.5
100% x 2.5/7.5 = 33.33% less. Or simply divide 5.0 by 7.5 to get 0.6667, which is a 33.3%
reduction.
Thus, the correct answer is (E) 33% less
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prior written permission from AssessmentDay.Q2 What was the ratio of Pacific Rim: Southern Pacific holdings in October
2010?
(A) 3:2
(B) 2:3
(C) 4:5
(D) 5:4
(E) 4:7
The information that you need is shown in the pie-chart
Step 1 - Put these October %’s into a ratio
20%:35% = 20:35
Step 2 – Simplify the ratio, looking at the available answers.
20:35 = 4:7
Thus, the correct answer is (E) 4:7
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prior written permission from AssessmentDay.Q3 In October 2010 which two Pacific Bond fund holdings when combined had
the same value as Southern Pacific holdings?
(A) Northern Pacific and Central Pacific
(B) Central Pacific and Pacific Rim
(C) Pacific Mixed and Pacific Rim
(D) Pacific Mixed and Northern Pacific
(E) Pacific Rim and Northern Pacific
The information that you need is shown in the graph
Step 1 – Look for those holdings that are likely to have a combined value around the 35%
mark:
Northern Pacific + Pacific Mixed = 30%
Pacific Rim + Pacific Mixed = 32%
Northern Pacific + Central Pacific = 33%
Pacific Rim + Northern Pacific = 38%
Central Pacific + Pacific Rim = 35%
Thus, the correct answer is (B) Central Pacific and Pacific Rim
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prior written permission from AssessmentDay.Q4 Which of the following represents the largest amount?
(A) October’s Pacific Mixed holding
(B) Average November value of each of the 5 holdings
(C) November value of holdings in Northern Pacific
(D) 70% of November’s value of holdings in Southern Pacific
(E) Average December value of each of the 5 holdings
Step 1 - In this one it is not obvious which ones are going to be wrong and therefore able to
be discounted, so we must calculate the value of each option:
(A) October’s Pacific Mixed holding = 4.5 million
(B) Average November value of each of the 5 holdings = 7.2 million
(C) November value of holdings in Northern Pacific = 6.14 million
(D) 70% of November’s value of holdings in Southern Pacific = 6.47 million
(E) Average December value of each of the 5 holdings = 7 million
Thus, the correct answer is (B) Average November value of each of the 5 holdings
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prior written permission from AssessmentDay.Q5 In October 2010 what fraction of the total Pacific Bond did the Northern
Pacific and Pacific Mixed fund holdings represent?
(A) 1/5
(B) 1/10
(C) 1/4
(D) 3/10
(E) 2/5
The information that you need is shown in the pie-chart.
Step 1 - Add the Northern Pacific and Pacific Mixed %’s
18% + 12% = 30%
Step 2 – Express this figure as a fraction
30 / 100 = 3/10
Thus, the correct answer is (D) 3/10
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prior written permission from AssessmentDay.Q6 For Weeks 1 and 3, across all 5 stores combined, what was the difference (in
units) between Actual and Target sales volumes?
(A) 10 over target (Week 1); 10 under target (Week 3)
(B) 10 over target (Week 1); 15 under target (Week 3)
(C) 15 over target (Week 1); 10 under target (Week 3)
(D) 15 over target (Week 1); 15 under target (Week 3)
(E) 20 over target (Week 1); 10 under target (Week 3)
Step 1 – Calculate the total Week 1 and Week 3 sales across the 5 Stores
Week 1: 20 + 30 + 25 + 15 + 5 = 95
Week 3: 35 + 40 + 24 + 12 + 9 = 120
Step 2 - Calculate the total Week 1 and Week 3 targets across the 5 Stores
Week 1: 15 + 20 + 20 + 10 + 10 = 75
Week 3: 35 + 35 + 30 + 15 + 15 = 130
Step 3 – Calculate the difference for Weeks 1 and 3
Week 1: 95 – 75 = 20 over target
Week 3: 120 – 130 = 10 under target
Thus, the correct answer is (E) 20 over target (Week 1); 10 under target (Week 3)
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prior written permission from AssessmentDay.Q7 Over the three week period, which Store achieved the highest sales per
sales staff member?
(A) Redcliff
(B) Ather
(C) Wilkington
(D) Trew
(E) Tunston
Step 1 – Calculate each Store’s total sales
Use the Actual sales figures for each of the 3 weeks, as follows:
Redcliff 20 + 20 + 35 = 75
Ather 30 + 40 + 40 = 110
Wilkington 25 + 18 + 24 = 67
Trew 15 + 14 + 12 = 41
Tunston 5 + 6 + 9 = 20
Step 2 – Calculate each Store’s average sales per sales staff member, as follows:
Redcliff 75 / 8 = 9.4
Ather 110 / 9 = 12.2
Wilkington 67 / 5 = 13.4
Trew 41 / 8= 5.1
Tunston 20 / 6 = 3.3
Thus, the correct answer is (C) Wilkington
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prior written permission from AssessmentDay.Q8 Next year staff numbers are to be reduced by 1 at stores with 6 or less staff,
and by 2 staff at all other stores. What will be the average monthly target per
staff member across all 5 stores if the regional target (across the 5 stores) is
£168,000?
(A) £5,000
(B) £6,000
(C) £7,000
(D) £8,000
(E) £9,000
Step 1 – Calculate the new staff numbers
Redcliff 8 – 2 = 6 staff
Ather 9 – 2 = 7 staff
Wilkington 5 – 1 = 4 staff
Trew 8 – 2 = 6 staff
Tunston 6 – 1 = 5 staff
Step 2 – Calculate the average target per staff member
Average = target / total number of staff = 168,000 / 28 = £6,000
Thus, the correct answer is (B) £6,000
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prior written permission from AssessmentDay.Q9 The Western Region’s overall sales (£120,000) were in a ratio of 3:2 to the
Eastern Region’s sales which itself had half the sales of the Northern and
Southern Regions combined. What were the total sales of all 4 Regions?
(A) £180,000
(B) £200,000
(C) £220,000
(D) £240,000
(E) £360,000
Step 1 – Calculate each Region’s sales
Eastern Region’s sales = 2 x 120,000 / 3 = 80,000
Northern + Southern Regions’ sales = 80,000 x 2 = 160,000
Step 2 – Calculate the total sales
120,000 + 80,000 + 160,000 = 360,000
Thus, the correct answer is (E) £360,000
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prior written permission from AssessmentDay.Q10 All sales in the three week period were based on an average £9.50 reduction
in the sales price of the units sold. What was the total saving made by
customers who bought units over the 3 week period (to the nearest £100)?
(A) £3,000
(B) £3,500
(C) £4,000
(D) £4,500
(E) £5,000
Step 1 – Calculate the total sales
We could use the working from Q6 to obtain Week 1 and Week 3 sales totals.
Week 2 sales = 20 + 40 + 18 + 14 + 6 = 98
Total sales = Week 1 + Week 2 + Week 3 = 95 + 98 + 120 = 313
Step 2 – Calculate the amount saved
313 x £9.50 = £2,973.50
Step 3 - (to the nearest £100)
£2,973.50 = £3,000
Thus, the correct answer is (A) £3,000
Tip: when summing numbers from a column or row, be careful not to take numbers from an
adjacent category. It is also a good idea to enter the numbers as you go straight into your
calculator, instead of writing out the sum on your rough paper then performing the calculation.
This will reduce the number of stages in your working and save time and reduce the potential
for input errors.
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prior written permission from AssessmentDay.Q11 Which sector experienced the highest sales for Quarters 1, 2 and 3
combined?
(A) Telecommunications
(B) Utilities
(C) Manufacturing
(D) Financial
(E) Retail
The information that you need is shown in the graph Consultancy income by sector
Step 1 – Calculate each sector’s sales for Quarters 1, 2 and 3 combined
Telecommunications = 30 + 27 + 25 = 82
Utilities = 35 + 20 + 20 = 75
Manufacturing = 21 + 32 + 30 = 83
Financial = 25 + 29 + 30 = 84
Retail = 23 + 30 + 25 = 78
Thus, the correct answer is (D) Financial
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prior written permission from AssessmentDay.Q12 Quarter 4’s income per sector is in the same ratio as Quarter 3, and the
consultancy income from the Financial sector is £33,000. What is the
consultancy income from the Utilities sector?
(A) Can’t tell from the data provided
(B) £12,000
(C) £22,000
(D) £25,000
(E) £45,000
The information that you need is shown in the graph Consultancy income by sector
Step 1 – Find the Quarter 3 ratios
Utilities: Financial = 20:30 = 2:3
Step 2 – Apply this ratio to the Utilities sector
Utilities income = £33,000 x 2/3 = £22,000
Thus, the correct answer is (C) £22,000
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prior written permission from AssessmentDay.Q13 For Quarters 1 and 3 combined, which two Manufacturing sector consultants
had incomes in the ratio 2:3?
(A) Harry and David
(B) Sarah and Jane
(C) Harry and Jane
(D) David and Peter
(E) David and Sarah
The information that you need is shown in the table.
Step 1 – Calculate each Consultant’s combined Quarter 1 and Quarter 3 income, as shown
below:
Consultant Quarter Quarter Combined
1 3
David 4,000 5,000 9,000
Peter 6,000 7,000 13,000
Sarah 6,000 5,500 11,500
Jane 4,000 7,500 11,500
Harry 1,000 5,000 6,000
The only possible 2:3 ratio is between Harry and David (6,000:9,000)
Thus, the correct answer is (A) Harry and David
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prior written permission from AssessmentDay.Q14 The Manufacturing sector income from the five consultants is supplemented
by the work of an associate consultant. What was the associate consultant’s
income from the Manufacturing sector across Quarters 1 to 3?
(A) £3,000
(B) £4,000
(C) £6,000
(D) £8,000
(E) £9,000
The information that you require here is shown in the table.
Step 1 – Calculate the total manufacturing income from the 5 consultants
Q1 Total = 21,000
Q2 Total = 28,000
Q3 Total = 30,000
Total income (Quarters 1 to 3) = 79,000
The information that you require next is shown in the graph.
Step 2 – Calculate the overall consultancy income from the manufacturing sector
21 + 32 + 30 = 83,000
Step 3 – Calculate the supplementary income
83,000 – 79,000 = 4,000
Thus, the correct answer is (B) £4,000
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prior written permission from AssessmentDay.Q15 The total quarterly income target, starting with £115,000 for Quarter 1,
increased by 20% for each subsequent Quarter. In Quarter 3 what was the
difference between actual income and the target?
(A) £8,000 under-performance
(B) £18,400 under-performance
(C) £31,000 over-performance
(D) £31,000 under-performance
(E) £35,600 under-performance
Step 1 – Calculate the target for Quarter 3, based upon the Quarter 2 target
Quarter 2 target = £115,000 x 120% = £138,000
Quarter 3 target = £138,000 x 120% = £165,600
The information that you require next is shown in the graph.
Step 2 – Calculate the difference Quarter 3 income
Quarter 3 income (000’s) = 25 + 20 + 30 + 30 + 25 = 130
Step 3 - calculate the difference in Quarter 3 between income and target
130,000 - 165,600 = 35,600 under-performance
Thus, the correct answer is (E) £35,600 underperformance
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prior written permission from AssessmentDay.Q16 Simon and Jessica have travel allowances of 60p and 44p per mile
respectively. Simon and Jessica each travel on average 25 miles and 30
miles respectively per sales visit. How much travel allowance is claimed in
total by these 2 Sales Managers in August?
(A) £1,050
(B) £1,122
(C) £2,122
(D) £2,172
(E) £2,272
Step 1 – Calculate Simon and Jessica’s total mileage in August
Simon = 60p x 70 x 25 = £1,050
Jessica = 44p x 85 x 30 = £1,122
Step 2 – Calculate Simon and Jessica’s combined travel allowance payment
£1,050 + £1,122 = £2,172
Thus, the correct answer is (D) £2,172
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prior written permission from AssessmentDay.Q17 If the percentage change in sales visits between September and October
(projected) continues for November, what will Jessica and Kim’s number of
complete sales visits be in November?
(A) 71 visits (Jessica); 77 visits (Kim)
(B) 71 visits (Jessica); 78 visits (Kim)
(C) 72 visits (Jessica); 78 visits (Kim)
(D) 72 visits (Jessica); 79 visits (Kim)
(E) 73 visits (Jessica); 79 visits (Kim)
Step 1 – Calculate the % change for Jessica and Kim
Jessica = 81/90 * 100% = 90%, which is a 10% decrease
Kim = 70/62 * 100% = 112.903%, which is a 12.903% increase
Step 2 – Calculate each Sales Manager’s number of visits for November
Jessica = 81 x 90% = 72.9 visits
Kim = 70 x 112.903% = 79.03 visits
Step 3 - This step can catch out people. The question asks for “complete sales visits” and 0.9
is not a complete visit. So, Jessica completed 72 visits. Don’t be tempted to round up.
Thus, the correct answer is (D) 72 visits (Jessica); visits 79 (Kim)
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prior written permission from AssessmentDay.Q18 If the margin of error on October’s projected client visits is +/- 15%, what are
the ranges for each Sales Manager (rounded to the nearest whole visit)?
(A) 90–100 (Simon); 77–85 (Jessica); 66–74 (Kim)
(B) 90– 107 (Simon); 74–87 (Jessica); 64–76 (Kim)
(C) 81–109 (Simon); 73–89 (Jessica); 63–77 (Kim)
(D) 81–109 (Simon); 69–93 (Jessica); 60–81 (Kim)
(E) 76–104 (Simon); 64–89 (Jessica); 56–76 (Kim)
Step 1 - Calculate the 85% and 115% figures for each Sales Manager
Simon (to the nearest whole visit)
95 x 85% = 80.75 = 81
95 x 115% = 109.25 = 109
Note that already we have eliminated 3 of the possible 5 answers.
Step 2 - Jessica:
81 x 85% = 68.85 = 69
81 x 115% = 93.15 = 93
Kim
70 x 85% = 59.5 = 60
70 x 115% = 80.5 = 81
Thus, the correct answer is (D) 81–109 (Simon); 69–93 (Jessica); 60–81 (Kim)
Tip: note the difference between “round to the nearest whole visit” and “give the number of
complete visits”. This is the difference between rounding to the nearest integer (could be up
or down) and ignoring any part-complete events (will always be rounding down).
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prior written permission from AssessmentDay.Q19 Jessica, who travelled 3,500 miles in July, travelled an extra 10 miles per
client visit compared to Simon. What was the total number of miles Simon
travelled in July?
(A) 2,400
(B) 2,600
(C) 2,800
(D) 3,000
(E) 3,200
Step 1 – Let x = Jessica’s average mileage per client visit
July visits = 70 = 3,500 / x
X = 3,500 / 70 = 50 miles per visit
Step 2 – Calculate Simon’s average mileage per client visit
50 – 10 = 40 miles per visit
Step 3 – Calculate the total number of miles Simon travelled in July
40 x 65 = 2,600 miles
Thus, the correct answer is (B) 2,600 miles
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prior written permission from AssessmentDay.Q20 The average order value per client visit is £145, £135 and £125 for Simon,
Jessica and Kim respectively. Which Sales Managers generate the highest
and lowest order values in June?
(A) Kim (most); Jessica (least)
(B) Simon (most); Jessica (least)
(C) Jessica (most); Kim (least)
(D) Jessica (most); Simon (least)
(E) Kim (most); Simon (least)
Step 1 - Calculate each Sales Manager’s client sales for June, as follows:
Simon 50 visits in June 50 x £145 = £7,250
Jessica 45 visits in June 45 x £135 = £6,075
Kim 60 visits in June 60 x £125 = £7,500
Thus, the correct answer is (A) Kim (most); Jessica (least)
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prior written permission from AssessmentDay.Q21 Which subsidiary will pay the lowest amount in dividends (interim and final
dividends combined)?
(A) Subsidiary 1
(B) Subsidiary 2
(C) Subsidiary 3
(D) Subsidiary 4
(E) Subsidiary 5
Step 1 - Calculate the total dividends payable per share for each subsidiary
Subsidiary 1 = 6.2 + 15.8 = 22
Subsidiary 2 = 8.5 + 10.5 = 19
Subsidiary 3 = 9 + 46 = 55
Subsidiary 4 = 15 + 10 = 25
Subsidiary 5 = 11 + 25 = 36
Step 2 – Calculate the total payable for each subsidiary
Subsidiary 1 = 22 cents x 3 million shares = $660,000
Subsidiary 2 = 19 cents x 3.5 million shares = $665,000
Subsidiary 3 = 55 cents x 12 million shares = $6,600,000
Subsidiary 4 = 25 cents x 2.6 million shares = $650,000
Subsidiary 5 = 36 cents x 20 million shares = $7,200,000
Thus, the correct answer is (D) Subsidiary 4
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prior written permission from AssessmentDay.Q22 Which 2 or 3 subsidiaries had combined sales of 1,890.8 million?
(A) Subsidiaries 1 and 5
(B) Subsidiaries 2 and 5
(C) Subsidiaries 1, 2 and 5
(D) Subsidiaries 3 and 5
(E) Subsidiaries 1, 3 and 5
Step 1 - This question is best answered by a process of elimination:
- Review the last number in each Sales figure. The Sales figures for Subsidiary 1 and
Subsidiary 2 end in “4” and the others end in zero.
- Since the total ends in “8” both Subsidiary a and Subsidiary b must be included in the
answer (i.e. “4” + “4” = “8”).
- At this stage you can see that only one of the possible answers includes Subsidiary 1 and
Subsidiary 2. If you wanted to complete the sum to double-check, do so.
- Subsidiary 1 + 2 + 5 = 1,124 + 3,334 + 14,450 = 18,908 (100,000s).
Thus, the correct answer is (C) Subsidiaries 1, 2 and 5
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prior written permission from AssessmentDay.Q23 Over the next year, Subsidiary 5’s Sales are expected to drop by a fifth whilst
its number of staff is expected to increase by 15%. What will be the
percentage change in the Sales per member of staff from Year 1 to the next?
(A) 25%
(B) 26%
(C) 29%
(D) 30%
(E) 44%
Step 1 – Calculate next year’s changes in the Subsidiary 5 data
Sales 14,450 x 4/5 = 11,560
Number of staff = 13,292 x 115% = 15,285.8
Step 2 – Calculate next year’s Sales per member of staff
11,560 / 15,285.66 = 0.756 (in $100,000’s)
Step 3 – Calculate this year’s Sales per member of staff
14,450 / 13,292 = 1.087 (in $100,000’s)
Step 4 – Calculate the % change in the Sales per member of staff
0.756 / 1.087 = 0.6955, which is a 30.4% drop.
Tip: note we must divide 0.756 by 1.087, not the other way round, because the question asks
us to go from Year 1 to next year. The calculation depends on what we take as the reference
point. In full, the calculation is (1.087 – 0.756) / 1.087 = 30.4%.
Thus, the correct answer is (D) 30%
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prior written permission from AssessmentDay.Q24 What is the ratio of Subsidiary 4’s interim dividend per share compared to
Subsidiary 5’s final dividend per share?
(A) 2:3
(B) 5:2
(C) 2:5
(D) 3:5
(E) 5:3
This is a fairly straight-forward one.
Step 1 – Put the figures from the table into a ratio
15:25
Step 2 – Simplify the ratio
3:5
Thus, the correct answer is (D) 3:5
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prior written permission from AssessmentDay.Q25 What is the lowest average payroll per member of staff (across the 5
subsidiaries)?
(A) $23,751
(B) $22,883
(C) $21,519
(D) $20,764
(E) $20,184
Step 1 - Calculate the average payroll for each subsidiary
Subsidiary 1 = $12,700,000 / 555 = $22,883
Subsidiary 2 = $40,900,000 / 1,722 = $23,751
Subsidiary 3 = $28,900,000 / 1,343 = $21,519
Subsidiary 4 = $57,000,000 / 2,824 = $20,184
Subsidiary 5 = $435,500,000 / 13,292 = $32,764
Thus, the lowest and the correct answer is (E) $20,184
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prior written permission from AssessmentDay.Q26 If Profit before tax increases by 15% for Competitor B and decreases by 8%
for Competitor A, what is the difference between Competitor A and Competitor
B’s corporation tax payments (to the nearest £million)?
(A) £10 million
(B) £12 million
(C) £14 million
(D) £16 million
(E) £18 million
Tip: Don’t be caught out by the fact that the question lists Competitor B first, when you might
be expecting to see Competitor A then Competitor B. This is intended to throw those not
paying attention.
Step 1 – Add 15% to Competitor B’s profit before tax
112 x 115% = 128.8
Step 2 – Decrease Competitor A’s profit before tax by 8%
90 x 92% = 82.8
Step 3 - Calculate the difference in corporation tax (at 30%)
(128.8 – 82.8) x 30% = 13.8 = £14 million (to the nearest £million)
Thus, the correct answer is (C) £14 million
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prior written permission from AssessmentDay.Q27 Competitor B and Competitor C choose to declare their Revenues in $ and
Euros respectively. What are these figures? (Use the exchange rates 1£ =
$1.66; 1£ = €1.15).
(A) $1,043 million (Competitor B); €708 million (Competitor C)
(B) $1,049 million (Competitor B); €690 million (Competitor C)
(C) $1,049 million (Competitor B); €720 million (Competitor C)
(D) $720 million (Competitor B); €1,055 million (Competitor C)
(E) Can’t tell from the data provided
Step 1 – Calculate Competitor B revenue in $
632 x 1.66 = $1,049
Step 2 – Calculate Competitor C revenues in Euros
600 x 1.15 x = €690
Thus, the correct answer is (B) $1,049 million (Competitor B); €690 million (Competitor C)
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prior written permission from AssessmentDay.Q28 What would be the difference in Euros if Competitor A used an exchange
rate of 1£ = €1.20, rather than 1£ = €1.15, when calculating its Profit after
tax?
(A) €0.05 million
(B) €1.15 million
(C) €2.05 million
(D) €3.05 million
(E) €3.15 million
Step 1 – Calculate the difference in the exchange rate
1.20 - 1.15 = €0.05
Step 2 – Calculate the difference in Euros
€0.05 x 63 = €3.15 million
Thus, the correct answer is (E) €3.15 million
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prior written permission from AssessmentDay.Q29 What was the average Gross profit across the 3 competitors (to the nearest
£10million)?
(A) £140 million
(B) £141 million
(C) £142 million
(D) £143 million
(E) £144 million
Step 1 – Calculate the total Gross Profit 128 + 148 + 147 = 423
Step 2 – Calculate the average 423 / 3 = 141
Step 3 – To the nearest £10million = £140 million
Thus, the correct answer is (A) £140 million
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prior written permission from AssessmentDay.Q30 Competitor C moves to a country charging 15% corporation tax and
corporation tax falls to 22% for Competitors A and B. What is the total
corporation tax payable for the 3 competitors (based upon the Profit before
tax figures shown)?
(A) £62 million
(B) £46 million
(C) £26 million
(D) £25 million
(E) Can’t tell from data
Step 1 – Calculate the corporation tax payable for each competitor
Competitor A = 90 x 22% = 19.8
Competitor B = 112 x 22% = 24.6
Competitor C = 117 x 15% = 17.6
Step 2 – Calculate the total corporation tax payable
19.8 + 24.6 + 17.6 = £62 million
Thus, the correct answer is (A) £62 million
-- End of Test --
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