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Test of Numerical Sequences

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These tests assess the ability to solve arithmetical and mathematical problems, becoming a good measure of inductive and abstract reasoning.

Numerical sequences are presented as a series of numbers arranged according to a logical rule. This rule is based on the relationship all numbers have among them, which usually involve performing basic calculation such as addition, subtraction , multiplication and division. Once that this rule or logical relationship is discovered, you can find out the next number of the sequence. In most cases you can find out a mathematical formula that describes how to compute each term of the sequence.

Sometimes sequences of numbers are combined with letters, in this case you should only take into account the position of the letter in the alphabet.

To find the rule of a sequence, there are several practical tips.

  • Sometimes you just look at the numbers and identify the pattern. It is useful to know some basic sequences: sequences of integers, even numbers, odd numbers, multiplication tables, prime numbers, factorials, squares, power of numbers, etc.

  • Note if each term can be obtained by adding, subtracting , multiplying or dividing the previous term by the same number. For example, in the sequence: 3, 6, 12, 24, 48 each term is obtained by multiplying the previous term by 2. The next term is therefore 96.

  • Compute the differences between the terms, which may be constant (above example) or lead us to another less complex sequence. Take for example the sequence: 2, 5, 10, 17, 26. If we calculate the differences between the terms we get a new sequence: 3, 5, 7, 9; which is a sequence in which each term is obtained by adding two to the previous term. So in this sequence the next number is 11, and keeping in mind that the terms of the original sequence are obtained by summing these values, the next number in the original sequence would be: 26 + 11 = 37.

  • Compute the differences of the differences between the terms (second differences). In the previous example, the second difference is 2, 2, 2. In some very complex sequences, it could be a good idea to try with third differences.

  • Sometimes there are two rules behind the sequence or alternating sequences, one in the odd positions and another in the even positions. For example, in the sequence: 1, 5, 2, 7, 3, 9 you can see that there are two alternating sequences: 1, 2, 3 ( in the odd positions ) and 5, 7, 9 (in the even positions), so that the next value will be 4.

  • There are sequences in which a term is obtained by performing arithmetical operations with the previous two or three terms. Consider this sequence: 4, 7, 11 , 18, 29. In this case each term is obtained by adding the previous two terms, so that the next term will be 18 + 29 = 47.

When there are several rules behind the sequence, always choose the simplest rule. The more you practice the easier will be to decode the logic that govern the sequence, although it is important to note how fast the terms of the sequence increase or decrease their values, so you can guess if the operation that relates the terms is the addition, subtraction, multiplication, division or exponentiation, using a constant value or the previous terms of the sequence.

Each questionnaire has 36 questions, which are presented in order of increasing difficulty, and must be resolved in 36 minutes.

If you wish, in the training mode you can see the solution by clicking on the button located on the top right of each question. Sometimes further information about the logic used is provided.

Questionnaires cannot be selected, they will come out continuously and periodically whenever you request a test.

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