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Numerical Critical Reasoning
Test 2
Solutions Booklet
Instructions
This numerical reasoning test comprises 20 questions, and you will have 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. The test does not
have an overall time limit however each question does has a time limit. The first question
relating to each table or graph has 90 seconds, and subsequent questions relating to the
same table or graph have 75 seconds.
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 approximate turnover of Downshire Foods in 2010 (in £millions)?
Answer £2m
STEP 1 Look at the table above. Turnover : Capital in 2010 = 1.4:1
1.4 Turnover x £1,452,650 Capital = £2,033,710
STEP 2 This is £m = £2.03m = £2m (zero decimal places)
TIP Make a note of the Ratio and that for every £1 of Capital there is £1.4 in Turnover.
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prior written permission from AssessmentDay.Q2 Between which two years did Downshire Food's pre-tax profit as a percentage of
capital increase the most?
Answer 2010 - 2011
STEP 1 You need to work out the pre-tax profit as a percentage of capital for each year.
Pre-tax Profit 2007 / Capital 2007 = £185,700 / £979,500 = 0.19 = 19%
2007 2008 2009 2010 2011
Capital (£) 979,500 1,096,300 1,273,800 1,452,650 1,500,321
Ratio
1.4:1 1.2:1 1.3:1 1.4:1 1.5:1
(Turnover:Capital)
Pre-tax Profit (£) 185,700 220,675 262,500 266,100 392,100
Pre-tax profit as a
19% 20% 21% 18% 26%
%age of Capital
STEP 2 You now need to decide which years showed the biggest increase.
2007 – 2008 = 1% increase
2008 – 2009 = 1% increase
2009 – 2010 = 3% decrease
2010 – 2011 = 8% increase
STEP 3 Therefore, the answer is between 2010 and 2011
TIP Jotting down a quick table in rough will help you see the answer more quickly. You
don’t even need to work out the actual difference as it is clear to see which one has
the biggest increase…this will also save time.
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prior written permission from AssessmentDay.Q3 What was the pre-tax profit of Downshire Foods as a percentage of turnover in 2008?
Answer 17%
STEP 1 Work out the Turnover in 2008 as you did in Question 1.
1.2 Turnover: 1 Capital = 1.2 x £1,096300 = £1,315,560
STEP 2 Pre-tax profit divided by Turnover x 100 =
£220,675 / £1,315,560 = 0.168 = 17%
STEP 3 So the answer is 17%
TIP Make sure you calculate the Turnover for 2008 first.
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prior written permission from AssessmentDay.Q4 Which indicator for Downshire Foods showed a decrease in 2009 compared to the
previous year?
Answer Pre-tax profit as a percentage of turnover
STEP 1 If you haven’t already, it would be good to complete the solutions table for
2008 and 2009.
2007 2008 2009 2010 2011
1,500,32
Capital (£) 979,500 1,096,300 1,273,800 1,452,650 1
Ratio
(Turnover:Capital) 1.4:1 1.2:1 1.3:1 1.4:1 1.5:1
Pre-tax Profit (£) 185,700 220,675 262,500 266,100 392,100
Pre-tax profit as a
%age of Capital 19% 20% 21% 18% 26%
Turnover 1.2 x 1096300 1.3 x 1273800
= =
1,315,560 1,655,940
Pre-tax profit as a 17% 16%
%age of Turnover
STEP 2 You are now comparing 2008 to 2009 to see what went up and what went
down:
Pre-tax profit as a percentage of turnover went down
Pre-tax as a percentage of capital went up
Turnover in £'s increased
Capital in £'s increased
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prior written permission from AssessmentDay.STEP 3 only Indicator to decrease between those years was Pre-tax profit as a percentage of
turnover
TIP Look at the answers before you start working out. This way you only work out what
you need to and this saves time. For example you can instantly discount Capital and
Turnover as correct just by looking at the table.
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prior written permission from AssessmentDay.Q5 Which force has the most officers?
Answer Devon & Cornwall
STEP 1 You need to sum Total Male Ranks to Total Female Ranks per force.
Avon & Somerset Male + Avon & Somerset Female =
1,545 + 495 = 2,040
STEP 2 Repeat for all Forces and note them down.
The Force with the most officers is therefore Devon & Cornwall
TIP You don’t need to add up the separate columns as this has been totalled for you.
So it is simply adding Total Males to Total Females.
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prior written permission from AssessmentDay.Q6 What is the ratio of Male Sergeants to Female Sergeants across all Forces?
Answer 6 Males : 1 Female
STEP 1 Sum all the Males Sergeants = 2646
STEP 2 Sum all the Female Sergeants = 463
STEP 3 Male : Female
2646 Males : 463 Females
2646 Males / 463 = 1 Female
5.71 Males : 1 Female
Therefore the answer is 6 Males to every Female.
TIP When calculating ratios, you must make sure you check what the question is
asking you. In this case how many Males to Females means you want to know
Male: Female.
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prior written permission from AssessmentDay.Q7 Approximately what proportion of all Sergeants work in Cleveland?
Answer 8%
STEP 1 Male Sergeants in Cleveland = 212
Female Sergeants in Cleveland = 25
Total Sergeants in Cleveland = 212 + 25 = 237
STEP 2 2646 Male Sergeants overall
463 Female Sergeants overall
Total Sergeants = 2646 + 463 = 3109
STEP 3 Total Sergeants in Cleveland / Total Sergeants =
237 / 3109 = 0.076 = 8%
TIP Remember to round up or down correctly. Also, if you have your numbers from the
previous question you can use these to save time.
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prior written permission from AssessmentDay.Q8 Among Police Officers in Bedfordshire, what percentage were women?
Answer 27%
STEP 1 Look up Total Males in Bedfordshire =
869 Males
STEP 2 Look up Total Females in Bedfordshire =
315 Females
STEP 3 Total Ranks in Bedfordshire = 869 + 315 = 1184
STEP 4 Females in Bedfordshire / Total Ranks in Bedfordshire = 315 / 1184 =
0.266 = 26.6% = 27%
TIP Make sure you look up the correct line in the table as it is easy to get the Forces
mixed up.
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prior written permission from AssessmentDay.Q9 What was the percentage change in Mango Price from July 2011 to August 2011?
Answer -1.92
STEP 1 July Price = £598.03
August Price = £586.54
STEP 2 We can see from the graph that there was a drop in price therefore we
should expect a negative number.
August – July = £586.54 - £598.03 = -£11.49
STEP 3 (X% of July) + July = August
(X% of £598.03) + £598.03 = £586.54
(X% of £598.03) = -£11.49
X% = -£11.49 / £598.03 = -1.92%
TIP Step 3 is walking you through the calculation. The quickest way to calculate this is to
simply put Difference/July into your calculator.
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prior written permission from AssessmentDay.Q10 If the change in price from Dec 2011 to Jan 2012 is 0.21% what is the price in Jan
2012?
Answer £607.96
STEP 1 The change is positive therefore we expect an increase in Price
(0.21% of December 2011) + December 2011 = January 2012
STEP 2 (0.21% x 606.69) + 606.69 = 1.27 + 606.69 = £607.96
TIP Make sure you calculate 0.21% which is 0.0021 NOT 21%
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prior written permission from AssessmentDay.Q11 If the monthly percentage change for September was the same as in August, what
would the price of Mangos have been in September 2011?
Answer £575.27
STEP 1 The percentage change in August is the percentage change from July to August.
The percentage change in September is the percentage change from August to
September.
We already worked out the percentage change from July to August in Q9 = -
1.92%
STEP 2 Now 586.54 x 0.980787 = 575.27
£575.27
TIP Try to keep your working neat and clear so you can reuse answers you have
already worked out!
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prior written permission from AssessmentDay.Q12 Between which two months was there the largest change in the price of Mangos?
Answer August and September 2011
STEP 1 You need to work out the difference in price from month to month:
June – July = 598.03 – 608.33 = -10.3
July – August = 586.54 – 598.03 = -11.49
August – September = 599.11 – 586.54 = 12.57
September – October = 606.83 – 599.11 = 7.72
October to November = 605.79 – 606.83 = 1.04
November to December = 606.69 – 605.79 = 0.9
December to January = Cannot say
STEP 2 Ignoring whether it was a positive or negative change, you need to decide which
months saw the biggest change.
Therefore, August to September showed the biggest change in price
TIP Even though it is an option, you cannot work out what January 2012 price is
without making assumptions. So there is no way to calculate this so this option
can be eliminated.
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prior written permission from AssessmentDay.Q13 What percentages of patients were treated with a Crown?
Answer 51%
STEP 1 No of treatments are 54. But there were only 51 patients as some had more than
one treatment.
26 / 51 = 0.5098 = 51%
TIP Make sure you read the notes so you don’t assume there were 54 patients.
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prior written permission from AssessmentDay.Q14 Of those that had Partial FDPs, what %age had implants (closest answer)?
Answer 55%
STEP 1 21 people had FDPs. 11 of these had implants.
STEP 2 11/21 x 100 = 0.524 = 52%. Therefore the closest answer is 55%.
TIP Remember to look carefully at the answer options as you are asked to select the
closest answer.
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prior written permission from AssessmentDay.Q15 What is the greatest number of treatments one patient has had?
Answer 3
STEP 1 51 patients. However there were 54 treatments completed. We are told that 2
people had multiple treatments.
TIP Each person had 1 treatment = 51 treatments. Therefore, there are 3 left which
2 people shared….one must have had one extra treatment and the other must
have had 2 extra.
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prior written permission from AssessmentDay.Q16 On average, how many implants did each patient have?
Answer 2
STEP 1 97 implants. 51 patients in total.
STEP 2 Therefore, 97 implants / 51 patients = 1.91 implants each = on average 2
implants each.
TIP Make sure you round up or down correctly.
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prior written permission from AssessmentDay.Q17 Given that the customers’ gardens are all square, which shed(s) will fit in Simmons'
garden?
Answer None
STEP 1 Find out the dimensions of Simmons’ garden. We are told that it is square and that it
has an area of 2.4m². So square root 2.4 = 1.549m.
STEP 2 Look at table showing the dimensions of each shed. We notice that although the area
of the Somerest Modular shed is less than 2.4m², all of the sheds have at least one
side which is longer than 1.579m. So none of the sheds will fit in Simmons’ garden.
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prior written permission from AssessmentDay.Q18 What is the Somerset Shed’s measurement in feet (Length by Width)?
Answer 4’ by 6’
STEP 1 4 feet = 1.22m
Therefore, 1m = 4/1.22 = 3.28 Feet
Shed Length (m) Width (m) Base
1.25m = 3.28 x 1.25 = 1.82m = 3.28 x 1.82 = 4’ by 6’
Somerset Modular 4.1’ 5.97’
STEP 3 Therefore, rounded up the correct answer is 4’ by 6’
TIP Make sure you get the Length and Width the correct way round!
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prior written permission from AssessmentDay.Q19 What is the lowest total price Tailor will have to pay for a shed installation which will fit
in his garden?
Answer £271.97
STEP 1 Tailor’s space = 3.8m²
STEP 2 Using your workings from Question 17, you can see that all the sheds will fit in the
space. The cheapest is Apex, at £189.99.
Somerset Modular = 2.23m²<3.8m² which will fit in the space
Apex = 2.13m²<3.8m² which will fit in the space
Overlap = 3.14m²<3.8m² which will fit in the space
STEP 3 A DIY Timber base kit is also required. The smallest base that will fit and is also the
cheapest is Kit B at £71.99.
STEP 4 Lastly, add the cost of Treatment Spray to reach the final cheapest price of £271.97
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prior written permission from AssessmentDay.Q20 What is the percentage discount for the Overlap shed?
Answer 30-40%
STEP 1 Original Price = £321.99
Current Price = £197.95
STEP 2 £328.99 - £197.95 = £131.04
£131.04 / £328.99 = 40%
STEP 3 The correct answer is therefore 30-40%
TIP A quicker way is to calculate 197.95 / 321.99 = 0.615 which is a 38.5% reduction.
-- End of Test --
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