How to Pass Numerical Reasoning (41 page)

Cross-multiply and solve for C:

9C = 5 × 81 = 405

C = 45

There are 45 students studying Chinese.

Q3
Answer
= 720 pixels

Set up a proportion and solve for the width w:

180
w
= 240 × 540 = 129,600

w = 720

Q4
Answer
= $123.75

Set up a proportion and solve for
x
:

4
x
= 5 × $99 = $495

x
= 123.75

The unit is $, so the answer is $123.75.

Q5
Answer
= 6

Find the missing term in the proportion 3 : 9 =
x
: 18

Set up the ratios as fractions and solve for the missing term:

3 × 18 = 9
x
= 54

x
= 6

You can use common sense to solve this more quickly than setting up the equation. You can see that the second term in the second ratio is twice the second term in the first ratio (18 = 2 × 9). So you could multiply the first term in the first ratio by two (3 × 2) and keep the ratios in proportion.

Q6
Answer
= £2.25

Set up the ratios as a proportion and solve for the missing term:

12
x
= 27

x = 2.25

The unit is £, so the answer = £2.25.

Q7
Answer

Set up a proportion with the known values:

60 M = 10S

Divide both sides by 10.

6M = S

Divide both sides by 6.

Q8
Answer
= 4
x
: 1

Set up the ratio as a fraction and reduce the answer to its lowest terms:

Divide both sides by 4
x
.

Q9
Answer
= 20 carers

Let C be the current number of carers and 6C the current number of residents. This satisfies the ratio 1 : 6. In the future there will be 6C + 40 residents and 8 times as many residents as carers, so now you can solve for C: 6C + 40 = 8C

40 = 8C – 6C

40 = 2C

C = 20

There are 20 carers currently.

Q10
Answer
= 40 mountain bikes and 800 road bikes

Let the number of mountain bikes = M and the number of road bikes = 20M. This satisfies the ratio 1 : 20.

M + 20M = Total number of bikes in the race.

If 200 road bikes were to join the race, the total number of road bikes would be 20M + 200.

When 200 road bikes have joined the race, there will be 25 times as many road bikes as mountain bikes:

25M = 20M + 200

Now you can solve for M:

20M + 200 = 25M

200 = 25M – 20M

200 = 5M

M = 40

40 is the constant number of mountain bikes in the race. Recall the ratio, mountain bikes to road bikes = 1 : 20. If there are 40 mountain bikes, you can find the number of road bikes by setting up a proportion:

Cross-multiply and solve for R:

1R = 20 × 40

R = 800

Mountain bikes = 40 and Road bikes = 800.

CHAPTER 6

Data interpretation

N
ow you have had the opportunity to refresh your memory on the bulk of the skills you need to take a numerical reasoning test, in this chapter you have the opportunity to put them all together and use them to reason with data in charts, tables and graphs. This type of question tests not just your ability to perform rapid calculations under time pressure, but also your ability to think logically and identify exactly what the question is asking you. Test-writers will give you traps to fall into and lead you straight to a wrong answer in the choices, so beware of what is being asked of you and take a couple of extra seconds to re-read each question. Make absolutely sure you understand the question before attempting to solve the problem.

In this chapter, unlike in the preceding chapters, the answers are multiple choice. The reason is that typically you will be given a set of answer choices to choose from in numerical reasoning tests. A key skill in successful test-taking is the ability quickly to recognize any outliers in the answers. Eliminate these answers immediately, so that even if you end up guessing the wrong answer, you will at least reduce the probability of guessing from a wider range of incorrect answers.