Numerical Reasoning Test3 Solutions

Numerical Reasoning

Sample Practice Test Solutions Booklet

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Q1

Of all pregnancies during 2001, what percentage was from women aged 30 and over? 12.8%

14.5%

32.8%

42.6%

For 2001, the number of pregnancies in women aged 30 and over is: 30 to 40 = 20,000 Over 40 = 20,000 Sum = 40,000. And the number of pregnancies from all women was: Others = 8,000 18-20 = 14,000 20-25 = 26,000 25-30 = 34,000 30-40 = 20,000 40+ = 20,000 Sum = 122,000. So the percentage is simply 40,000 ÷ 121,000 = 32.79% (and to save time you can obviously just work out 40 ÷ 121 without the thousands).

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Q2

During which period did the number of pregnancies in the Over 40s increase the most? 2000 – 2001

2001 – 2002

2002 – 2003

2003 – 2004

By studying the graph for Over 40s, we can quickly see that between 2001 and 2002 pregnancies increased by two markers on the scale, whereas all the other years either stayed steady or increased by only one scale mark. We don’t need to actually work out the numerical values to see this, although it is 4,000 for the period 2001-2002.

Q3

The number of pregnancies for 25-30 year olds was projected to rise by 9% every year between 2001 and 2003. If this had been the case, approximately how many more pregnancies would have occurred in 2003 for the 25-30 age bracket?

690

395

1,114

1,160

In 2001 we see that pregnancies for 25-30 year olds is 34,000. For an increase of 9% each year, this would mean in 2002 there would have been 34,000 x 1.09 = 37,060. In 2003 there would have been 37,060 x 1.09 = 40,395.4. This compares with the actual figure of 40,000. So the difference is 395. It is good practice at this point to check that we have indeed calculated the projected figure to be higher than the actual, as suggested in the question. If we had not, we know we have made an error.

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Q4

What was the overall profit as a percent of revenue for 2002? 4.28%

5.25%

6.51%

8.96%

Overall Revenue in 2002 = £60,800,000. Overall Costs = £12.3 x number of sales so £12.3 x 4,500,000 = £55,350,000. Now overall profit is costs deducted from revenue so £60,800,000 - £55,350,000 = £5,450,000. We’re not quite done yet as the question asks for profit as a percentage of revenue, which is 5,450,000 ÷ 60,800,000 = 8.96%.

Q5

What was the Cash Balance as a percentage of total costs for 2001? 3.5%

3.6%

3.7%

3.8%

Cash Balance in 2001 = £2.0 million. Total costs = £12.4 x 4,600,000 = £57.04 million. So Cash balance as percent of total costs is 2.0 ÷ 57.04 = 3.51%. It is slightly faster to leave the data in millions for this calculation, as long as you don’t confuse yourself.

Q6

Which year saw the largest percentage increase in number of sales over the previous year? 2000

2001

2002

2003

Work out the percentage increase from year to year: 2000: 4300 ÷ 4100 = 104.9% 2001: 4600 ÷ 4300 = 107.0% - This is the largest. 2002: 4500 ÷ 4600 = 97.8% 2003: 4700 ÷ 4500 = 104.4%

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Q7

For the two factories combined, what was the excess production of jeans in April that were not sold? 500

1,000

1,500

2,000

You have to first work out that the letters at the bottom of the graph represent Feb, March, April, May, June, Jul. So in April, production from Factory A = 5,000. Production from Factory B = 1500; total production = 6,500 pairs of jeans. Total sales of both men’s and women’s = 3,500 + 2,500 = 6,000 pairs of jeans. So excess production = 500.

Q8

The jeans that are produced but not sold each month are stored for when sales exceed production. From the period February to July inclusive, what was the net number of jeans put into storage? 500

1,000

1,500

2,000

For each month, the production minus sales (i.e. the number of pairs of jeans put to storage) is: F: 6500 – 6000 = 500 M: 6000-6500 = -500 (i.e. 500 were taken out of storage) A: 6500-600 = 500 M: 6500-600 = 500 J: 7000-6500 = 500 J: 7000-7000 = 0 The net number is then 500 – 500 + 500 + 500 + 500 + 0 = 1,500.

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Q9

What proportion of employees in Company B hold either an Honors Degree or a Masters Degree? 16%

78%

94%

Cannot say

It is not possible to tell from the data whether a particular employee holds just an Honors Degree and not a Masters Degree, or vice versa, or both. Therefore it is not possible to determine. Don’t be fooled into thinking you can add up 16% and 78% of 1,100.

Q10

How many more employees hold A-levels in Company C than in Company D? 320

425

615

785

In Company D there are 25,600 employees, of which we are told 90% have A-levels. In Company C there are 24,700 employees, of which we are told 95% have A-levels. So Company D (25,600 x 90%) = 23,040 and Company C (24,700 x 95%) = 23,465. This is a difference of 425 employees. And we can take comfort in the fact that we have worked out the answer to be a positive number (i.e. we have got the companies the right way round).

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Q11

What company has the highest ratio of employees who hold Masters Degrees to employees who hold A-levels? Company A

Company B

Company C

Company D

We have to work out this ratio for each company. Company A: 23:99 = 23.23 – This company has the highest ratio. Company B: 16:96 = 16.67 Company C: 12:95 = 12.63 Company D: 18:90 = 20.00

Q12

For all four companies combined, what is the average percentage of employees who are Honor Degree qualified? 58.9%

63.1%

67.2%

72.4%

First work out how many from each company hold an Honors Degree. Company A: 680 x 85% = 578 Company B: 1,100 x 78% = 858 Company C: 24,700 x 64% = 15,808 Company D: 25,600 x 61% = 15,616 This totals (578 + 858 + 15808 + 15616) = 32,860. And we can find the total number of all employees for these four companies as (680 + 1100 + 24,700 + 25,600) = 52,080. So the combined average is 32,860 ÷ 52,080 = 63.095%

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Q13

If in 1998 inflation was 2.6%, what was it in 2003? 2.53%

2.56%

2.58%

2.62%

Starting with 2.6%, for each year multiply by the ‘percentage change’ to arrive at the subsequent year. So 2.6% x 99.7% x 99.4% x 99.4% x 99.1% x 99.7% = 2.53%

Q14

Between 1997 and 2007, how many times did inflation not vary from the previous year? 1

2

3

Cannot say

Count how many times the graph is at 0%, since this is the ‘Annual percent change’. Once in 2004 and once in 2007.

Q15

Between 1999 and 2007, what year experienced the largest proportional increase in inflation? 2003

2004

2005

2006

There was only one year between 1999 and 2007 in which the inflation increased: 2006, which we can see because this is the only year between 1999 and 2007 that experienced a positive change.

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- End of Sample Numerical Reasoning Practice Test -

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