More How to Win at Aptitude Tests
Abstract Reasoning – These tests measure problem solving ability in a context-free environment and are largely based on non-verbal and non-numerical questions.
Spatial Reasoning – These tests measure the ability to perform operations such as rotation or combining different features of two- and three-dimensional objects in one’s head.
Mechanical Reasoning – These tests measure the ability to work out how different mechanical operations and physical principles affect objects.
Perceptual Ability – These tests measure the ability to take in and manipulate verbal, numerical and other textual information.
For each test you will also see a classification system which will tell you how that particular test is used, how long it is likely to be, and other relevant information, such as the level of difficulty. The format used is as follows:
Test 1 Name
Type of test: Speed, power or both.
Typical length: The typical number of questions in the test.
Typical time allowed: How long one is typically allowed to complete such a test.
Used for: The type of job it tends to be used for. These are classified as:
Basic, such as clerical, or jobs with occasional requirements for this ability, but mostly at a simple or basic level.
Intermediate, such as supervisory or junior management jobs which require more frequent or complex use of this ability.
Higher, such as professional, middle and senior management, or specialist types of work which require frequent use of this ability in high-level problem solving situations.
Frequency of use: Whether the test is in common use or is used less often. We have focussed on those types of tests that are in common use.
Remember that this information is only a guide. The actual tests you may face are likely to vary in how closely they match those given in this book.
At the end of each test, or each set of similar tests, you will find hints and tips that provide suggestions for how to prepare for and approach that particular type of test.
In Chapter 8, there is more detailed information on exactly what to do to prepare yourself for the testing session and what happens afterwards.
The answers to all of the tests, plus an explanation where appropriate, are in Appendix I at the end of this book.
Finally, in Chapter 7 we go through an example of a Personality Test. Full scoring instructions are given with the test, but remember – with personality tests there are no right or wrong answers. Only you will know what is right!
2 Numerical Tests
Numerical ability tests fall into one of two camps – outright mathematical ability requiring you to carry out mathematical calculations, and numerical problem-solving ability requiring you to work out what mathematical calculations you should apply, rather than just telling you. This second type is referred to as numerical reasoning and tends to have more of a power than speed design.
In the case of mathematical ability, the type of calculation you are expected to perform will usually be made clear to you. Our first set of five tests looks at mathematical ability.
Note that the numbers involved are not too complex – it would be beyond most people to calculate 2654 ÷ 13 in their head! Also, note that you are not given a set of answers from which to choose. The rationale behind this is that if you can work out the correct answer then you can simply write it down, and if you can’t work out the answer then guessing won’t help much.
Tests 1–5 concentrate on basic mathematical computation or calculation. Try them, they will act as a useful warm up for the numerical tests later on which are to do with applying mathematical ability to real world problems.
Numerical Test 1 (Addition)
Type of test: Speed
Typical length: 25–35 questions
Typical time allowed: 20–30 minutes
Used for: Basic level
Frequency of use: Common
In this test your task is simply to calculate the correct answer. Give yourself 20 minutes.
1 7 + 45 =
2 15 + 21 =
3 9 + 57 =
4 215 + 37 =
5 12 + 6 =
6 154 + 45 =
7 39 + 22 =
8 17 + 89 =
9 25 + 98 =
10 21 + 75 =
11 54 + 4 =
12 14 + 25 =
13 102 + 14 =
14 19 + 16 =
15 17 + 7 =
16 22 + 9 =
17 5 + 18 =
18 8 + 14 =
19 3 + 19 =
20 45 + 5 =
21 165 + 14 =
22 48 + 5 =
23 112 + 54 =
24 97 + 81 =
25 25 + 52 =
26 44 + 57 =
27 8 + 46 =
28 13 + 67 =
29 19 + 28 =
30 20 + 15 =
Numerical Test 2 (Subtraction)
Type of test:Speed
Typical length: 25–35 questions
Typical time allowed: 20–30 minutes
Used for: Basic level
Frequency of use: Common
In this test your task is simply to calculate the correct answer. Give yourself 20 minutes.
1 12 − 107 =
2 54 − 58 =
3 8 − 96 =
4 23 − 101 =
5 65 − 135 =
6 79 − 65 =
7 24 − 47 =
8 29 − 21 =
9 13 − 29 =
10 168 − 64 =
11 9 − 35 =
12 185 − 18 =
13 36 − 57 =
14 48 − 67 =
15 57 − 24 =
16 59 − 32 =
17 24 − 152 =
18 65 − 144 =
19 72 − 33 =
20 12 − 225 =
21 9 − 49 =
22 208 − 26 =
23 26 − 53 =
24 7 − 118 =
25 38 − 52 =
26 61 − 34 =
27 109 − 81 =
28 42 − 22 =
29 48 − 18 =
30 153 − 62 =
Numerical Test 3 (Division)
Type of test: Speed
Typical length: 25–35 questions
Typical time allowed: 20–30 minutes
Used for: Basic level
Frequency of use: Common
In this test your task is simply to calculate the correct answer. Give yourself 30 minutes.
1 21 ÷ 7 =
2 15 ÷ 3 =
3 66 ÷ 11 =
4 111 ÷ 37 =
5 45 ÷ 9 =
6 64 ÷ 16 =
7 39 ÷ 13 =
8 36 ÷ 12 =
9 25 ÷ 25 =
10 190 ÷ 19 =
11 80 ÷ 4 =
12 75 ÷ 25 =
13 78 ÷ 13 =
14 110 ÷ 10 =
15 122 ÷ 2 =
16 95 ÷ 5 =
17 70 ÷ 7 =
18 54 ÷ 27 =
19 16 ÷ 4 =
20 63 ÷ 7 =
21 170 ÷ 10 =
22 10 ÷ 1 =
23 74 ÷ 2 =
24 60 ÷ 3 =
25 125 ÷ 25 =
26 250 ÷ 5 =
27 300 ÷ 60 =
28 390 ÷ 13 =
29 99 ÷ 9 =
30 160 ÷ 20 =
Numerical Test 4 (Multiplication)
Type of test: Speed
Typical length: 25–35 questions
Typical time allowed: 20–30 minutes
Used for: Basic level
Frequency of use: Common
In this test your task is simply to calculate the correct answer. Give yourself 25 minutes.
1 12 × 6 =
2 17 × 5 =
3 5 × 16 =
4 69 × 3 =
5 17 × 7 =
6 6 × 15 =
7 2 × 127 =
8 8 × 9 =
9 15 × 15 =
10 65 × 4 =
11 9 × 32 =
12 32 × 10 =
13 44 × 3 =
14 17 × 54 =
15 13 × 5 =
16 6 × 120 =
17 19 × 8 =
18 4 × 45 =
19 6 × 50 =
20 7 × 35 =
21 12 × 9 =
22 21 × 4 =
23 9 × 13 =
24 25 × 10 =
25 4 × 37 =
26 13 × 7 =
27 28 × 5 =
28 45 × 9 =
29 120 × 5 =
30 55 × 5 =
Numerical Test 5 (Combination)
Type of test: Speed/Power
Typical length: 25–35 questions
Typical time allowed: 20–35 minutes
Used for: Basic level
Frequency of use: Common
In this test your task is simply to calculate the correct answer. Give yourself 35 minutes.
1 5 × 6 + 11 =
2 6 + 12 − 8 =
3 1 × 5 ÷ 5 =
4 25 × 10 ÷ 25 =
5 4 + 7 × 4 =
6 23 × 10 − 150 =
7 22 + 20 × 3 =
8 9 × 30 ÷ 27 =
9 8 × 45 ÷ 10 =
10 16 × 25 × 2 =
11 66 − 8 × 5 =
12 15 − 5 ÷ 2 =
13 4 × 7 − 5 =
14 6 × 4 + 120 =
15 25 ÷ 5 × 10 =
16 5 × 44 ÷ 22 =
17 14 + 50 × 2 =
18 20 + 28 ÷ 12 =
19 35 + 7 ÷ 5 =
20 50 − 7 × 10 =
21 3 + 39 × 5 =
22 6 × 5 + 170 =
23 48 ÷ 12 − 2 =
24 3 + 15 × 2 =
25 16 × 3 + 25 =
26 10 + 8 ÷ 9 =
27 5 − 5 × 27 =
28 2 × 6 × 5 =
29 1 × 10 + 117 =
30 36 ÷ 9 × 6 =
Numerical Test 6 (Combination – Percentages and Fractions, Series, Equations)
This test brings together everything you have done so far, and asks you to apply it to more real world problems. The test that follows involves dealing with number series, percentages, fractions, decimals and equations. This test begins to introduce you to some numerical problem solving – it provides you with a range of possible answers from which you need to select the correct one. In some cases you can identify what the correct answer must be without having to do any actual calculation. Remember that fractions, decimals, algebra and percentages are all just the application of basic addition, subtraction, multiplication and division.
Because the answers in this type of test are sometimes given, you may not have to work out possible solutions from scratch. It is quite possible to simply insert one answer option after another (especially in the case of algebraic equations) until you find the correct one, or until you have exhausted them all without finding the correct one.
Type of test: Speed/Power
Typical length: 25–40 questions
Typical time allowed: 25–40 minutes
Used for: Intermediate/higher level
Frequency of use: Common
Answer the following questions, choosing the correct answer, if you think there is one, from the set of five response options below. You have 35 minutes.
1 Which number comes next in the following series?
1 4 7 10 13 16
a) 17
b) 19
c) 21
d) 25
e) none of these
2 What is p in this equation?
2 + 3p = 14
a) 2
b) 3
c) 4
d) 6
e) none of these
3 0.2 × 5 =
a) ½
b) 0.75
c) 1
d) 1½
e) none of these
4 ¼ × ½ =
a) 1⁄16
b) 1⁄8
c) 1
d) 2
e) none of these
5 15% of 200 =
a) 15
b) 30
c) 45
d) 60
e) none of these
6 Which number comes next in this series?
0 1 3 6 10 15
a) 19
b) 21
c) 26
d) 32
e) none of these
7 3x + 2y = 14
If x is 4 then what is y?
a) −6
b) 1
c) 7
d) 12
e) none of these
8 0.3⁄0.2 + 1.5 =
a) 1
b) 1.6
c) 2.5
d) 3
e) none of these
9 Which number replaces z in this equation?
3⁄4 - z⁄12 = ¼
a) 1
b) 2
c) 4
d) 6
e) none of these
10 50% of 200⁄100 =
a) 0
b) 1
c) 2
d) 50
e) none of these
11 Which number comes next in this series?
0 1 −1 2 −2 3
a) −4
b) −3
c) 4
d) 5
e) none of these
12 What is m?
m⁄4 = m − 6
a) −2
b) 2
c) 4
d) 8
e) none of these
13 What number replaces k in this equation?
(k × 0.4) + k = 2.8
a) 0.5
b) 1
c) 1.5
d) 2
e) none of these
14 4⁄9 X 3⁄6 =
a) 2⁄9
b) 6⁄1
c) 2⁄3
d) 1⁄9
e) none of these
15 20% of 0.1 =
a) 1
b) 0.2
c) 0.02
d) 1.2
e) none of these
16 Which number comes next in this series?
1 1 2 3 5 8
a) 10
b) 12
c) 13
d) 15
e) none of these
17 2y × 2y =
a) y
b) 2y
c) 2y2
d) 4y2
e) none of these
18 Which of the following is exactly divisible by 6.2?
a) 26.2
b) 43.4
c) 60.2
d) 160.2
e) none of these
19 1 = 1⁄9 + 16⁄?
a) 9
b) 16
c) 18
d) 32
e) none of these
20 8 = 20% of:
a) 20
b) 40
c) 16
d) 160
e) none of these
21 Which number comes next in this series?
0 1 2 5 20 25
a) 50
b) 75
c) 125
d) 150
e) none of these
22 If x = z and z = 3 then:
x⁄z + X =
a) 2
b) 3
c) 4
d) 6
e) none of these
23 2.1 × 2.1 − 0.75 =
a) 1.21
b) 2.42
c) 3.66
d) 3.25
e) none of these
24 ¼ + ½ × 3⁄4 =
a) 3⁄8
b) 9⁄16
c) 12⁄6
d) ¼
e) none of these
25 10% of 40% of 200 =
a) 8
b) 20
c) 40
d) 80
e) none of these
26 Which number comes next in this series?
1 1 0 −1 −1 −2
a) −3
b) −4
c) −5
d) 2
e) none of these
27 6p + 4q = 2q + 2p is the same as:
a) 2qp + 2 = 4
b) 4p + 2 q = 0
c) 2qp + 2p = 4q
d) 4q + 2p = 0
e) none of these
28 Which number replaces t in this equation?
1.2⁄t = 1.2 + 3.64 − 4.84
a) 0.21
b) 0
c) 2.2
d) 2
e) none of these
29 3⁄5 of 3⁄8 is:
a) 3⁄15
b) 6⁄15
c) 9⁄8
d) 9⁄40
e) none of these
30 60% of 340 is greater than:
a) 190
b) 220
c) 240
d) 260
e) none of these
Numerical Test 7 (Number Series)
So far we have seen examples of numerical tests that have tended to focus on mathematical ability, with a small amount of problem solving involved. Now we turn our attention to some more difficult numerical ability tests that expressly address problem solving – how well you can identify which mathematical calculations you need to perform in order to reach the correct answer.
It is less important in this type of test to be able to carry out straightforward mathematical calculations – the emphasis is on how you get to that point. Note again that as in Test 6 the actual mathematical calculations involved are sometimes quite simple once you know what they are.
Type of test: Speed/Power
Typical length: 15–25 questions
Typical time allowed: 20–30 minutes
Used for: Intermediate/higher level
Frequency of use: Not that common in this ‘pure’ form but items of this type crop up from time to time.
This test contains a set of number series, arranged in pairs with two numbers in each square. In this test your task is to look at the number in the top left diagonal of the square and work out how it relates to the number in the bottom right diagonal of the same square. There are five squares in each set and they all share the same rule for relating the top number to the bottom number. Occasionally you may come across a version of this test that asks you to identify the odd one out, rather than the next in the sequence. With this type of test, the principle and method of solving the question are identical.
When you have worked out what the rule is, you should be able to work out the missing number. Give yourself 25 minutes.
1
a) 6
b) 7
c) 8
d) 9
2
a) 9
b) 10
c) 12
d) 14
3
a) 5
b) 6
c) 4
d) 3
4
a) 4
b) 5
c) 6
d) 8
5
b) 16
b) 18
c) 19
d) 20
6
a) 24
b) 19
c) 21
d) 25
7
a) 18
b) 20
c) 24
d) 26
8
a) 14
b) 16
c) 17
d) 18
9
a) 10
b) 15
c) 25
d) 50
10
a) 7
b) 8
c) 9
d) 12
11
a) 27
b) 29
c) 33
d) 35
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