# Numerical Series Tests

Numerical series tests are a type of numerical aptitude test which require you to find the missing number in a sequence. This missing number may be at the beginning or middle but is usually at the end.

Identify the missing number in the series.

 A B C D E 1 4, 8, 16, 32, ? 48 64 40 46 44 A B C D E 2 4, 8, 12, 20, ? 32 34 36 38 40 A B C D E 3 54, 49, ?, 39, 34 47 44 45 46 42 A B C D E 4 ?, 19, 23, 29, 31 12 15 16 17 18

These number sequences can be quite simple like the examples above. However, you will often see more complex questions where it is the interval between the numbers that is the key to the sequence.

Identify the missing number in the series.

 A B C D E 5 3, 6, 11, 18, ? 30 22 27 29 31 A B C D E 6 48, 46, 42, 38, ? 32 30 33 34 35

These numerical series test questions usually consist of four visible numbers plus one missing number. This is because the test designer needs to produce a sequence into which only one number will fit. The need to avoid any ambiguity means that if the number sequence relies on a more complex pattern then there will need to be more visible numbers. For example;

Identify the missing number in the series.

 A B C D E 7 4, 3, 5, 9, 12, 17, ? 32 30 24 26 22 A B C D E 8 5, 6, 7, 8, 10, 11, 14, ?, ? 19 17 15 16 21 A B C D E 9 1, ?, 4, 7, 7, 8, 10, 9, ? 6 3 11 13 12

1. B – The numbers double each time
2. A – Each number is the sum of the previous two numbers
3. B – The numbers decrease by 5 each time
4. D – The numbers are primes (divisible only by 1 and themselves)
5. C – The interval, beginning with 3, increases by 2 each time
6. B – The interval, beginning with 2, increases by 2 and is subtracted each time
7. D – Each number is the sum of the previous and the number 3 places to the left
8. C A – There are 2 simple interleaved sequences 5,7,10,14,19 and 6,8,11,15
9. A D – There are 2 simple interleaved sequences 1,4,7,10,13 and 6,7,8,9

To solve these number sequence questions efficiently, you should first check the relationship between the numbers themselves looking for some simple arithmetic relationship. Then look at the intervals between the numbers and see if there is a relationship there. If not, and particularly if there are more than 4 numbers visible, then there may be two number sequences interleaved. You will occasionally find multiplication, division, or powers used in these sequences, but test designers tend to avoid them as these operations soon lead to large numbers which are difficult to work out without a calculator.

Letter of the Alphabet as Numbers
Another type of number series question which appears in these tests involves the substitution of letters of the alphabet for numbers. For example A=1, B=2 etc. It may seem strange to consider these as number series questions but they do actually work in exactly the same way once you have changed them back into numbers.

Identify the next letter in the series.

 i ii iii iv v 10 B, E, H, K, ? L M N O P i ii iii iv v 11 A, Z, B, Y, ? C X D V H i ii iii iv v 12 T, V, X, Z, ? Y B A W Q

16. iii – There are two letters missing between each one, so N is next.
17. i – There are 2 interleaved sequences A,B,C and Z,Y, so C is next.
18. ii – Miss a letter each time and ‘loop’ back, so B is next.

Because arithmetic operations cannot be performed on letters there is less room for ambiguity in these questions. This means that interleaved sequences can be used with fewer visible letters than in questions that use numbers. Question 17 for example can use 2 interleaved sequences even though only four letters are visible. This would be very difficult to achieve with numbers.

It is implicit in these ‘alphabetic sequence’ questions that the sequence ‘loops’ back around and starts again. See question 18. It is important to recognize this as it is not usually stated explicitly – you are just expected to know it.

If you see more than one of these questions in a test then it is almost certainly worth taking the time to write out the letters of the alphabet with their ordinal numbers underneath. You can then treat these questions in a similar way to number series questions. This can save a lot of time overall and avoid simple mistakes. If you are told that you need to sit a numerical reasoning test as part of the job selection process and you want to prepare for it properly, then you should ask which type of questions it contains. Specifically, is it just numerical series or does it also contain data interpretation, computation or estimation questions.

These sample question papers each contain 22 questions and have a suggested time limit of 20 minutes. The questions are presented in Letter/A4 format for easy printing and self-marking.

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