How to Pass Numerical Reasoning (20 page)

BOOK: How to Pass Numerical Reasoning
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Adding decimals: practice drill

Q1

74.8

Q2

249.75

Q3

87.043

Q4

186.91

Q5

0.003

Q6

15.6202

Q7

2.563

Q8

0

Q9

9.2

Q10

–123.26

Subtracting decimals: practice drill

Q1

1.05

Q2

1.19

Q3

6.962

Q4

1.01

Q5

0.001

Q6

3.4

Q7

2.5583

Q8

–9.9171

Q9

12.8078

Q10

–0.009

Multiplying decimals: practice drill

Q1

23.04

Q2

134.2

Q3

6.92

Q4

21

Q5

1.44

Q6

111.55

Q7

1.22221

Q8

3.0804

Q9

0.1014

Q10

0.000003

Dividing decimals: practice drill

Q1

12

Q2

20

Q3

25

Q4

23

Q5

17

Q6

21

Q7

8.25

Q8

0.2

Q9

6.2

Q10

2.3

CHAPTER 3

Rates

Chapter topics

• Terms used in this chapter

• Converting units

• Working with rates

• Work rate problems

• Answers to
Chapter 3

Terms used in this chapter

Rate:
A ratio that establishes the relationship between two or more different quantities measured in different units.

Knowledge of rates is very useful for any commercial activity that requires you to measure productivity. A key measure of industrial performance may be the rate at which a finished part is produced, for example the number of surfboards waxed in a day or the number of barrels of oil extracted per month. Worker productivity may be measured by the completed number of manual tasks, such as the number of birthday cakes iced per hour or the number of violins varnished in a week. While these formulae do not account for quality control, you may apply an additional formula to find out, for example, the number of birthday cakes spoilt per week during the icing process.

Converting units

Before we reintroduce the formulae to work out rates questions, a word or two on units. Rates are a useful method to compare different units, but like units must be measured in comparable terms. For example, you cannot always make a useful comparison between ‘miles per gallon’ and ‘kilometres per gallon’ or between ‘parts produced per worker’ and ‘parts produced per production line’. The following drills aim to hone your quick conversion skills and will remind you of the common units that you are likely to come across in your test. Where it is critical to know conversion rates, the test will typically contain this information. However, sound knowledge of these common equivalents will help you to calculate your answers quickly and save you those valuable seconds.

Time

Time is the unit that is most frequently converted when working with rates. The basic units of time are seconds, minutes and hours, and you will be required to convert units of time easily between the other time units. The following table is a guide to common time units.

Fraction of hour

Number of minutes

1

10
hour

6 minutes

2
/
10
hour

12 minutes

3
/
10
hour

18 minutes

4
/
10
hour

24 minutes

5
/
10
hour

30 minutes

6
/
10
hour

36 minutes

7
/
10
hour

42 minutes

8
/
10
hour

48 minutes

9
/
10
hour

54 minutes

1
/
3
hour

20 minutes

2
/
3
hour

40 minutes

1
/
6
hour

10 minutes

5
/
6
hour

50 minutes

1
/
4
hour

15 minutes

3
/
4
hour

45 minutes

Distance

Distance is another unit that you may be required to convert. The table below gives the common equivalents of metric measures of distance. You will have the opportunity to practise these conversions in the practice drills.

To convert

Equivalents

Calculation

Km to metres

1 km = 1,000 m

Multiply the number of kilometres by 1,000

Km to cm

1 km = 100,000 cm

Multiply the number of kilometres by 100,000

Km to mm

1 km = 1,000,000 mm

Multiply the number of kilometres by 1,000,000

Metres to km

1 m = 0.001 km

Divide the number of metres by 1,000

Metres to cm

1 m = 100 cm

Multiply the number of metres by 100

Metres to mm

1 m = 1,000 mm

Multiply the number of metres by 1,000

Cm to km

1 cm = 0.00001 km

Divide the number of cm by 100,000

Cm to metres

1 cm = 0.01 m

Divide the number of cm by 100

Cm to mm

1 cm = 10 mm

Multiply the number of cm by 10

Mm to km

1 mm = 0.000001 km

Divide the number of mm by 1,000,000

Mm to metres

1 mm = 0.001 m

Divide the number of mm by 1,000

Mm to cm

1 mm = 0.1 cm

Divide the number of mm by 10

Common units

To convert…

Equivalents

Calculation

Years to weeks

1 year = 52 weeks

Multiply the number of years by 52

Weeks to days

1 week = 7 days

Multiply the number of weeks by 7

Weeks to hours

1 week = 168 hours

Multiply the number of weeks by 168

Weeks to minutes

1 week = 10,080 minutes

Multiply the number of weeks by 10,080

Days to hours

1 day = 24 hours

Multiply the number of days by 24

Hours to minutes

1 hour = 60 minutes

Multiply the number of hours by 60

Hours to seconds

1 hour = 3,600 seconds

Multiply the number of hours by 3,600

Minutes to seconds

1 minute = 60 seconds

Multiply the number of minutes by 60

Feet to inches

1 foot = 12 inches

Multiply the number of feet by 12

Miles to km

1 mile = approx. 1.61 km

Multiply the number of miles by 1.61

Km to miles

1 km = approx. 0.62 mile

Multiply the number of km by 0.62

Ounces to grammes

1 oz = 25 grammes

Multiply the number of ounces by 25

Inches to cm

1 inch = 2.5 cm

Multiply the number of inches by 2.5

Pints to millilitres

1 pint = 570 ml

Multiply the number of pints by 570

Farenheit to Celcius

(F – 32) × 0.55

Subtract 32 from the number of degrees F and multiply by 0.55

Celcius to Farenheit

(C × 1.8) + 32

Multiply the number of degrees C by 1.8 and add 32

Rates conversion practice: drill 1: time

Set a stopwatch and aim to complete the following drill in three minutes.

Q1

hours

=

minutes

Q2

hours

=

minutes

Q3

hours

=

minutes

Q4

hours

=

minutes

Q5

hour

=

minutes

Q6

480 minutes

=

hours

Q7

320 minutes

=

hours

Q8

280 minutes

=

hours

Q9

50 minutes

=

hour

Q10

144 minutes

=

hours

Q11

37 minutes

=

seconds

Q12

36 seconds

=

hour

Q13

hour

=

seconds

Q14

hours

=

seconds

Q15

48 minutes

=

hour

Q16

hour

=

seconds

Q17

hour

=

seconds

Q18

20 seconds

=

minute

Q19

hour

=

minutes

Q20

0.2 hour

=

minutes

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