Read How to Pass Numerical Reasoning Online
Authors: Heidi Smith
Getting to the right answer
When you are asked to calculate an exact answer, calculate it. The question will give you an indication of the level of precision that is expected from you, for example, ‘Give the answer to 3 decimal places’. If you are asked for this level of precision, usually you will have a calculator to assist you.
If you are given a range of answers to choose from, do a quick estimate of the correct answer first. Then eliminate all out-of-range answers or the ‘outliers’. This technique reduces the likelihood of choosing incorrectly under pressure and gives you a narrower range of answers from which to choose the correct answer. Your estimate may be accurate enough to choose the correct answer without completing any additional calculations. This will save you time and allow you to spend more time on difficult questions. Once you have eliminated some answers from the multiple-choice range, you can substitute in possible correct answers to the question and effectively solve the question using the answer as the starting point.
Translating the language
Part of the difficulty of aptitude tests is in understanding exactly what is being asked of you. Before you set off to answer a question, be absolutely sure that you understand what you are being asked to do. Think carefully whether you have enough information to translate the question into an equation, or whether you need to complete an interim step to provide you with enough information to answer the question. If you are working with graphs and charts, read the labels accompanying the diagrams to make sure you understand whether you are being given percentages or actual values. Read the axis label in case the axes are given in different values. Typically, once you have translated the words, the maths becomes much easier.
Calculators
Many aptitude tests disallow the use of calculators, so you may as well get into the habit of doing mental arithmetic without it. If you are of the GCSE generation, maths without a calculator may seem impossible: after all, calculators are a key tool in maths learning today. However, all the examples and practice questions in this book have been designed so that you can work out the correct answer without the use of the calculator. Think of it as a positive. Think of it this way: if you can’t use a calculator in the test, the maths can’t be that hard, can it? If you set about the practice questions and drills with your calculator, you will be wasting your test preparation time and practice material. By all means, check your answers afterwards with your calculator, but get into the habit of sitting down to take the test without it.
Test timings
Where timings are applied to the practice questions in this workbook, do try to stick to the time allocated. One of the skills tested in aptitude tests is your ability to work quickly and accurately under pressure. However, sometimes you do not have to finish all the questions in order to do well in a test, but of those you do answer, you must answer those questions correctly. If you find that at first you are taking longer to complete the questions than the allocated time, work out which aspect of the problem is taking the extra time. For example, are you wasting time reworking simple calculations or are you having difficulty in working out exactly what is being asked in the question? Once you have identified the problem, you can go back to the relevant section of this book to find suggestions to help overcome the difficulty.
What else can you do to prepare?
If you find that you draw a complete blank with some of the mental arithmetic questions, particularly the timed questions, find other ways to exercise your grey matter even when you are not in study mode. Add up the bill in your head as you are grocery shopping. Work out the value of discounts offered in junk e-mail. Work out whether the deal on your current credit card is better or worse than the last one. Work out dates backwards. For example, if today is Saturday 3 August, what was the date last Tuesday? If my birthday is 6 April 1972 and today is Monday, on what day was I born? On the bus on the way to work, work out roughly how many words there must be on the front page of your neighbour’s newspaper, based on your estimate of the number of words per line and the number of lines per page. Play sudoko, all levels. In other words, become proficient at estimating everyday calculations. Think proactively about numbers and mental arithmetic. It will pay off enormously in the test.
Getting started
This introduction has explained the purpose of this workbook and has recommended a method to use it. Now roll up your sleeves and go straight on to
Chapter 1
.
• Terms used in this chapter
• Multiplication tables
• Dividing and multiplying numbers
• Prime numbers
• Multiples
• Working with large numbers
• Working with signed numbers
• Averages
• Answers to
Chapter 1
Arithmetic mean:
The amount obtained by adding two or more numbers and dividing by the number of terms.
Average:
See Mode, Median and Arithmetic mean.
Dividend:
The number to be divided.
Divisor:
The number by which another is divided.
Factor:
The positive integers by which an integer is evenly divisible.
Find the product
of …:
Multiply two or more numbers together.
Integer:
A whole number without decimal or fraction parts.
Lowest common multiple:
The least quantity that is a multiple of two or more given values.
Mean:
See Arithmetic mean.
Median:
The middle number in a range of numbers when the set is arranged in ascending or descending order.
Mode:
The most popular value in a set of numbers.
Multiple:
A number that divides into another without a remainder.
Prime factor:
The factors of an integer that are prime numbers.
Prime number:
A number divisible only by itself and 1.
Test-writers assume that you remember the fundamentals you learnt in school and that you can apply that knowledge and understanding to the problems in the tests. The purpose of this chapter is to remind you of the basics and to provide you with the opportunity to practise them before your test. The skills you will learn in this chapter are the fundamentals you can apply to solving many of the problems in an aptitude test, so it is worth learning the basics thoroughly. You must be able to do simple calculations very quickly, without expending any unnecessary brainpower – keep this in reserve for the tricky questions later on. This chapter reviews the basics and includes a number of practice drills to ease you back into numerical shape. Remember, no calculators …
‘Rote learning’ as a teaching method has fallen out of favour in recent years. There are good reasons for this in some academic areas but it doesn’t apply to multiplication tables. You learnt the times-tables when you first went to school, but can you recite the tables as quickly now? Recite them to yourself quickly, over and over again, when you’re out for a run, when you’re washing up, when you’re cleaning your teeth, when you’re stirring your baked beans – any time when you have a spare 10 seconds thinking time. Six times, seven times and eight times are the easiest to forget, so drill these more often than the twos and fives. Make sure that you can respond to any multiplication question without pausing even for half a second. If you know the multiplication tables inside out, you will save yourself valuable seconds in your test and avoid needless mistakes in your calculations.
Multiplication tables: practice drill 1
Practise these drills and aim to complete each set within 15 seconds. (Remember, the answers are at the end of the chapter.)
Drill 1 | Drill 2 | Drill 3 | Drill 4 | Drill 5 | |
1 | 3 × 7 = | 8 × 3 = | 9 × 3 = | 7 × 5 = | 7 × 15 = |
2 | 6 × 5 = | 11 × 6 = | 9 × 2 = | 6 × 3 = | 11 × 11 = |
3 | 8 × 9 = | 13 × 2 = | 7 × 7 = | 4 × 7 = | 4 × 12 = |
4 | 3 × 3 = | 11 × 13 = | 12 × 7 = | 3 × 4 = | 8 × 10 = |
5 | 9 × 12 = | 13 × 9 = | 6 × 8 = | 8 × 15 = | 13 × 4 = |
6 | 2 × 4 = | 6 × 14 = | 6 × 7 = | 8 × 8 = | 11 × 2 = |
7 | 8 × 5 = | 3 × 15 = | 13 × 5 = | 2 × 6 = | 7 × 12 = |
8 | 13 × 3 = | 9 × 8 = | 13 × 4 = | 7 × 6 = | 9 × 15 = |
9 | 6 × 7 = | 4 × 5 = | 8 × 8 = | 4 × 12 = | 9 × 9 = |
10 | 2 × 7 = | 6 × 3 = | 7 × 13 = | 5 × 14 = | 3 × 8 = |
11 | 7 × 12 = | 12 × 4 = | 6 × 15 = | 3 × 11 = | 3 × 3 = |
12 | 2 × 12 = | 11 × 7 = | 9 × 8 = | 9 × 6 = | 3 × 8 = |
Multiplication tables: practice drill 2
Drill 1 | Drill 2 | Drill 3 | Drill 4 | Drill 5 | |
1 | 8 × 9 = | 4 × 5 = | 3 × 6 = | 6 × 11 = | 11 × 11 = |
2 | 13 × 13 = | 9 × 3 = | 9 × 5 = | 5 × 3 = | 3 × 7 = |
3 | 11 × 14 = | 13 × 4 = | 7 × 3 = | 5 × 6 = | 6 × 8 = |
4 | 9 × 6 = | 6 × 8 = | 5 × 9 = | 8 × 5 = | 12 × 4 = |
5 | 11 × 5 = | 7 × 7 = | 11 × 15 = | 14 × 14 = | 5 × 5 = |
6 | 4 × 3 = | 11 × 10 = | 6 × 7 = | 12 × 3 = | 8 × 14 = |
7 | 7 × 8 = | 8 × 9 = | 3 × 11 = | 14 × 4 = | 9 × 7 = |
8 | 9 × 6 = | 5 × 13 = | 8 × 4 = | 13 × 3 = | 12 × 15 = |
9 | 12 × 5 = | 3 × 14 = | 9 × 6 = | 7 × 6 = | 3 × 3 = |
10 | 13 × 14 = | 2 × 12 = | 12 × 4 = | 8 × 7 = | 4 × 2 = |
11 | 4 × 9 = | 4 × 6 = | 8 × 2 = | 3 × 8 = | 14 × 8 = |
12 | 2 × 5 = | 9 × 5 = | 3 × 13 = | 11 × 12 = | 6 × 10 = |