# Mathematics

Answers and Explanations to JTP’s Free SHL-style Numerical Reasoning Test

Dear Candidate,

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practice questions found in our online preparation packs for CEB’s SHL-style tests.

In this PDF you will find answers and detailed explanations to the test.

Take your time, carefully read the explanations and make sure you understand them.

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Question #1

What proportion of scores were 50 and below for ISP5?

A. 13.75%

B. 11.2%

C. 9.8%

D. 20%

E. 7.2%

The correct answer is (E).

All we need to do in order to answer this question is to calculate the proportion

of scores that were 50 and below for ISP5 using the following formula:

(# of scores of 50 and below for ISP5 / total # of scores for ISP5) x 100 =

[112 / (112 + 254 + 785 + 389)] x 100 = 7.2%

This means that 7.2% of the scores given to ISP5 were 50 and below.

256 226

89 25

112

398 387

586

892

254

1,056

854

687

452

785

458 470

75 124

389

0

200

400

600

800

1,000

1,200

ISP 1 ISP 2 ISP 3 ISP 4 ISP 5

N o . o f V o te

s Internet Service Providers (ISP) – Satisfactory Survey Scores

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Question #2

Which ISP had the lowest percentage of scores of 86 and above?

A. ISP 1

B. ISP 2

C. ISP 3

D. ISP 4

E. ISP 5

The correct answer is (C).

We need to calculate the percentage of score of 86 and above for each category

according to the following formula:

(# of scores of 86 and above for ISP / total # of scores for ISP) x 100

ISP 1: (458 / 2,168) x 100 = 21.1%

ISP 2: (470 / 1,937) x 100 = 24.3%

ISP 3: (75 / 1,437) x 100 = 5.2%

ISP 4: (124 / 1,493) x 100 = 8.3%

ISP 5: (389 / 1,540) x 100 = 25.3%

We can see that ISP 3 had the lowest percentage of scores of 86 and above.

256 226

89 25

112

398 387

586

892

254

1,056

854

687

452

785

458 470

75 124

389

0

200

400

600

800

1,000

1,200

ISP 1 ISP 2 ISP 3 ISP 4 ISP 5

N o . o f V o te

s Internet Service Providers (ISP) – Satisfactory Survey Scores

www.jobtestprep.co.ukCopyright 4

Question #3

What is the ratio of the number of scores above 50 and below 86 to the total

number of scores in the survey?

A. 2.85:1

B. 1:3.85

C. 1:1.35

D. 3:4

E. None of the above

The correct answer is (C).

In order to answer this question, we need to carefully follow these steps:

1. Sum up the number of scores above 50 and below 86, i.e. the number of

scores in the 51-65 category plus the number of scores in the 66-85

category: 398+387+586+892+254+1,056+854+687+452+785 = 6,351

2. Sum up the number of scores in the remaining categories (50 and below +

86 and above): 256+226+89+25+112+458+470+75+124+389 = 2,224

3. Calculate the total number of scores in the survey by summing up the

results: 6,351+2,224 = 8,575

256 226

89 25

112

398 387

586

892

254

1,056

854

687

452

785

458 470

75 124

389

0

200

400

600

800

1,000

1,200

ISP 1 ISP 2 ISP 3 ISP 4 ISP 5

N o . o f V o te

s Internet Service Providers (ISP) – Satisfactory Survey Scores

www.jobtestprep.co.ukCopyright 5

Question #4

At a certain cafe, three sandwiches, two pastries and four coffees cost the same as

four sandwiches, one pastry, and two coffees. If one pastry plus two coffees cost £4

and two sandwiches plus one coffee cost £9, how much does one pastry cost?

A. ₤1

B. ₤2

C. ₤3

D. ₤4

E. ₤5

The ratio of the number of scores above 50 and below 86 to the total number

of scores in the survey is 6351:8575 .

Since the result is not compatible with any of the options, we might be tempted

to select the “None of the above” option. However, taking a careful look at the

options, we can see that option (C) is in fact equal to our result, since dividing

both sides of the ratio by 6,351 yields the result of 1:1.35.

Note: The same ratio can be expressed in numerous ways. In our case, the ratio

of 6351:8575 can be expressed as 1:1.35, 0.74:1, 3:4.05 etc. Option (D)

presents a ratio which is very close to the required ratio. However, since the

ratio presented in option (C) is closer, this option is more accurate than option

(D) and thus should be selected.

www.jobtestprep.co.ukCopyright 6

The correct answer is (B).

Let S represent the number of sandwiches, P the number of pastries and C the

number of coffees. According to the question, the following is true:

(1) 3S + 2P + 4C = 4S + P + 2C

(2) P + 2C = 4

(3) 2S + C = 9

Equation 1 can also be represented as:

3S + 2(P+2C) = 4S + (P+2C)

Thus:

3S + 2×4 = 4S + 4

3S + 8 = 4S + 4

S = 4

Plugging back into equation 3:

2S + C = 9

2×4 + C = 9

8 + C = 9

C = 1

Plugging back into equation 2:

P + 2C = 4

P + 2×1 = 4

P + 2 = 4

P = 2

Therefore, one pastry costs £2.

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Question #5

Space Laser LTD. Product Range (in millions of Pounds)

Products Total Cost per Unit

Sale Price per Unit

Profit per Unit

Raw Materials Manufacture Calibration

Houston A 13.4 2.4 0.34 35.3 19.16

Houston AA 16.2 2.7 0.75 39.2 19.55

Houston AA+ 17.8 1.5 0.012 42.7 23.388

Ramon 1 24.1 4.5 0.92 63.4 33.88

Ramon 2 35.6 6.9 1.1 82.4 38.8

What is the approximate percentage change in profit per unit when a 12.5% discount

is given for purchasing 150 units of Houston A?

A. 13

B. 16

C. 23

D. 18

E. 14

The correct answer is (C).

When a discount is given, Profit per Unit is reduced but costs remain constant.

The fixed costs are: (sale price – profit) = 35.3 – 19.16 = ₤16.14

The price after discount is: 87.5% x 35.3 = ₤30.8875

The new profit per unit is: 30.8875 – 16.14 = ₤14.7475

Therefore, the percentage change in profit is:

[1 – (new profit/old profit)] x 100 = 1 – (14.7475/19.16) x 100 = 23%

Notice that there is no need to consider 150 units, as a single unit is sufficient

for calculating the loss in profit.

There is a shorter way to solve the question, if you realise the percentage

change correlates with the discount value. Thus, we can calculate the absolute

discount value: 35.3 x 0.125 = ₤4.4125, and divide it by the old profit per unit

value: (4.4125/19.16) x 100 = 23%.

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Question #6

Space Laser LTD. Product Range (in millions of Pounds)

Products Total Cost per Unit

Sale Price per Unit

Profit per Unit

Raw Materials Manufacture Calibration

Houston A 13.4 2.4 0.34 35.3 19.16

Houston AA 16.2 2.7 0.75 39.2 19.55

Houston AA+ 17.8 1.5 0.012 42.7 23.388

Ramon 1 24.1 4.5 0.92 63.4 33.88

Ramon 2 35.6 6.9 1.1 82.4 38.8

What is the minimum number of Ramon 2 units that must be sold in order to equal

the profit made from selling 25 Ramon 1 units, after a 13% increase in Ramon 1’s

profit?

A. 23

B. 24

C. 25

D. 26

E. 27

The correct answer is (C).

After a 13% increase, the profit from selling one unit of Ramon 1 equals:

£33.88m x 1.13 = £38.2844m

Thus, the profit from selling 25 Ramon 1 units equals:

25 x £38.2844m=£957.11m

We know that the profit from selling one unit of Ramon 2 is £38.8m. Therefore,

the minimum number of Ramon 2 units that must be sold in order to equal

957.11 million pounds is: £957.11m/£38.8m = 24.66.

Since it is more than 24 units, it must be counted as 25.

www.jobtestprep.co.ukCopyright 9

Question #7

Space Laser LTD. Product Range (in millions of Pounds)

Products Total Cost per Unit

Sale Price per Unit

Profit per Unit

Raw Materials Manufacture Calibration

Houston A 13.4 2.4 0.34 35.3 19.16

Houston AA 16.2 2.7 0.75 39.2 19.55

Houston AA+ 17.8 1.5 0.012 42.7 23.388

Ramon 1 24.1 4.5 0.92 63.4 33.88

Ramon 2 35.6 6.9 1.1 82.4 38.8

Which product has the highest calibration cost, relative to its total cost?

A. Houston A

B. Houston AA

C. Houston AA+

D. Ramon 1

E. Ramon 2

The correct answer is (B).

In order to answer the question, we need to follow 3 steps:

1. For each product, we need to find the total cost per unit = sale price per

unit – profit per unit.

2. Next, we need to divide the calibration cost of each product by its total

cost.

3. Finally, we need to look for the largest number (which represents the

highest calibration cost relative to total costs).

Houston A: 0.34/(35.3-19.16) = 0.021

Houston AA: 0.75/(39.2-19.55) = 0.038

Houston AA+: 0.012/(42.7-23.388) = 0.0006

Ramon 1: 0.92/(63.4-33.88) = 0.031

Ramon 2: 1.1/(82.4-38.8) = 0.025

Therefore, Houston AA has the highest calibration cost relative to its total cost.

www.jobtestprep.co.ukCopyright 10

Question #8

Marsha is responsible for buying writing supplies for the office. Paper is £20 per box,

pencils are £10 per package and pens are £35 per package. When Marsha goes to

buy the supplies, she discovers that there is a 10% off sale on pens. If Marsha has

£300 to spend on supplies, and she must buy one box of paper for every package of

pencils or pens, and more packages of pencils than packages of pens, what is the

greatest number of packages of pens that Marsha can buy?

A. 0

B. 1

C. 2

D. 3

E. 4

The correct answer is (D).

In order for Marsha to buy the greatest number of pens, she needs to buy the

smallest number of pencils and paper:

1. We know that Marsha has to buy one box of paper for every package of

pens/pencils she buys. Therefore, for her to buy the smallest number of

paper, she needs to buy one package of paper for each package of

pencils/pens (and no more than that).

2. We also know that Marsha has to buy more pencils than pens. Thus, in

order to buy the minimum number of pencils, she has to buy one more

package of pencils than pens.

According to (1), we can say that Marsha has to buy combos of pencils + paper

and pens + paper at a maximum price of £300 .

A pencils + paper combo will cost £30, and a pens + paper combo will cost

£51.50 (Pens are 10% off, so they cost £31.50 instead of £35.).

www.jobtestprep.co.ukCopyright 11

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For more information and tips on CEB’s SHL-style tests, check out these links:

All you Need to Know About CEB’s SHL-style Numerical Tests

Answers to CEB’s SHL Numerical Reasoning Sample Questions

How to Pass SHL-style Numerical Tests?

What to Expect When Taking an SHL-style Test?

How to Choose Which SHL-style Preparation Pack to Buy?

CEB’s SHL Test Results and Scores – Facts and FAQs

CEB’s SHL Management and Graduate Item Bank (MGIB)

Now, we can calculate the maximum number of pens as follows:

0x(pens+paper)+1x(pencils+paper)=0x£51.50+1x£30=£0+£30=£30

1x(pens+paper)+2x(pencils+paper)=1x£51.50+2x£30=£51.50+£60=£111.50

2x(pens+paper)+3x(pencils+paper)=2x£51.50+3x£30=£103+£90=£193

3x(pens+paper)+4x(pencils+paper)=3x£51.50+4x£30=£154.50+£120=£274.50

4x(pens+paper)+5x(pencils+paper)=4x£51.50+5x£30=£206+£150=£356

Since 4 pens (+ paper) and 5 pencils (+ paper) costs more than £300, the

maximum number of pens that can be bought is 3.

Want to practice more?