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NumericalReasoningTest1-Solutions

Numerical Test 1

Solutions Booklet

Instructions

This is a warm-up test comprising just 12 questions. You will have 15 minutes to answer them. 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 four possible answers, one of which is correct. You may click Back and

Next during the test to review or skip questions.

Try to find a time and place where you will not be interrupted during the test. When you are

ready, turn to the next page and begin.

AssessmentDay

Q1 How many Bernd cars were sold in May?

(A)

(B) 1,000 (C) 5,000 (D) 10,000

The trick to this question is to recognise that the graph gives sales figures cumulatively.

Step 1 - We see from the graph that the cumulative Bernd sales at the end of April are 9,000. We see that the cumulative Bernd sales at the end of May are 10,000.

Step 2 - Therefore during May (10,000 – 9,000 =) 1,000 Bernd cars must have been sold.

Thus the correct answer is (B) 1,000

Q2What were the total sales of Tymko cars for May, June and July combined?

(A) 21,000

(B) 16,000

(D) 6,000

Don’t waste time working out the sales for each month. Since the data is cumulative, we can say combined sales for May, June and July = (cumulative sales for end of July) – (cumulative sales end of April).

Step 1 - (Cumulative sales July) – (Cumulative sales April) = (21,000) – (15,000) = 6,000

Thus the correct answer is (D) 6,000

Q3If the number of Bernd cars sold in July had been equal to the number of Bernd cars sold in June, how many more Bernd cars would have been sold

during July?

(A) 1,000

(B) 1

(D) 2,000

Step 1 - First, find out the number of Bernd cars sold in June. From the cumulative graph we see this is 1,000.

Step 2 - Now, compare this with how many Bernd cars were actually sold in July. We see

from the graph there were no sales 1,000 – 0 = 1,000

Thus the correct answer is (A) 1,000

In Liverpool what was the net effect of live birth and death rates on the population during 2000?

(A)

200 decrease (B) 600 increase (C) 500 increase (D) 300 increase

Step 1 - In Liverpool the population was 500,000 at the start of the year. We are told there were 13.4 births per thousand of the population. So this means there were (500 x 13.4 =) 6,700.

Step 2 - We are told there were 12.4 deaths per thousand of the population, i.e. 500 x 12.4 = 6,200.

Step 3 - The net effect on population is 6,700 – 6,200 = 500.

Thus the correct answer is (C) 500 increase.

Q5How many live births occurred in 2000 in Birmingham and Glasgow combined?

(A) 21,812

(B) 18,210

(D) 32,100

Step 1 - In Birmingham there were 995 x 13.6 = 13,532 births. In Glasgow there were 600 x

13.8 = 8,280 live births. In total that is 13,532 + 8,280 = 21,812

Thus the correct answer is (A) 21,812

Q6Of the cities shown, which had the lowest number of people under the age of

15 at the start of the year 2000?

(A) Birmingham

(B) Glasgow

(D) Leeds

Tip - The question says “of the cities shown”. Without this technically we would have to

respond “cannot say” because we are not told any information about any other cities and

therefore we would not be able to say with any certainty which had the lowest number. As it happens in this question “cannot say” is not an option so we would have been OK, but it’s a catch worth looking out for.

Step 1 - Work through each city shown calculating the number of under 15 year olds. Don’t worry about entering the thousands in your calculator – this just wastes time.

London: don’t bother calculating as it is not a possible answer.

Birmingham: 995 x 0.18 = 179.1

Glasgow: 600 x 0.21 = 126

Liverpool: 500 x 0.22 = 110

Leeds: 450 x 0.23 = 103.5

Thus the correct answer is (D) Leeds

Q7Which of the countries shown experienced the largest percentage increase in public transport spending from 2007 to 2008?

(A) UK

(B) US

(D) Cannot tell

Step 1 - Calculate the percentage increase from 2007 to 2008 for each country. Don’t bother with the billions, the percentage calculation won’t be affected.

UK: 38 ÷ 35 = 8.57% increase

US: 136 ÷ 128 = 6.25% increase

Germany: 46 ÷ 44 = 4.55% increase

Italy: 28 ÷ 26 = 7.69% increase

Thus the correct answer is (A) UK

Tip: we will be using this short-hand method of calculating percentages as it saves time. If

you prefer you can do it the long way. So for example the UK percentage would be as follows.

Step 1: (38-35) ÷ 35 = 0.085714

Step 2: 0.085714 x 100 = 8.5714

Step 3: 8.57% increase

Q8Which of the countries shown had the highest public transport spend per capita in 2008?

(A) UK

(B) US

(D) Cannot say

Step 1 - Simply divide the public transport spend by the population for each country. Again,

use units which simplify the calculation because we are only interested in the relative order of magnitude.

UK: 38 ÷ 60.1 = 0.632

US: 136 ÷ 302.5 = 0.450

Germany: 46 ÷ 84.3 = 0.546

Italy: don’t bother as this is not an option.

Thus the correct answer is (A) UK

Q9In 2007 Italy had a target to spend 8% more on public transport than they did in 2006. By how much were they short of this target?

(A) ￡1 million

(B) ￡1 billion

(D) Cannot tell

Step 1 - In 2006 Italy spent ￡25 billion An increase of 8% is: ￡25 billion x 1.08 = ￡27 billion.

Step 2 - We see from the table that Italy actually spent ￡26 billion. That’s ￡1 billion short of

the target.

Thus the correct answer is (B) ￡1 billion

Q10Visitors arriving from which website were most likely to make a purchase at https://www.wendangku.net/doc/0f17981732.html,?

(A) Website W

(B) Website X

(D) Website Z

Step 1 - For each arrival website, calculate the percentage of visitors who made a purchase out of the number of visitors.

W: 2,876 ÷ 315,380 = 0.912%

X: 284 ÷ 26,850 = 1.06%

Y: 183 ÷ 82,520 = 0.222%

Z: 204 ÷ 12,630 = 1.62%

Thus the correct answer is (D) Website Z

Q11If the average profit made per sale at https://www.wendangku.net/doc/0f17981732.html, was ￡12, approximately how much more profit was made from visitors from Website X than visitors

from Website Y?

(A) ￡1,212

(B) ￡1,852

(D) ￡891

Step 1 - Calculate how many more sales came from Website X than from Website Y.

284 – 183 = 101.

Step 2 - Calculate the profit difference. 101 x ￡12 = ￡1,212

Thus the correct answer is (A) ￡1,212

Q12Assuming all visitors arrived via either website W, X, Y or Z, approximately what percentage of visitors arrived at https://www.wendangku.net/doc/0f17981732.html, from Website Y?

(A) 15.7%

(B) 18.9%

(D) 30.3%

Step 1 - Add up the total number of visitors. 315,380 + 26,850 + 82,520 + 12,630 = 437,380.

Step 2 - Calculate the percentage of them who came from Website Y. 82,520 ÷ 437,380 =

18.87%

Thus the correct answer is (B) 18.9%

-- End of Test --