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The most
common mathematical sequences in intelligence tests are
variations on these five:
| 1 |
4 |
9 |
16 |
25 |
36 |
Squares |
| 1 |
8 |
27 |
64 |
125 |
216 |
Cubes |
| 1 |
2 |
4 |
8 |
16 |
32 |
Doubles |
| 1 |
2 |
3 |
5 |
7 |
11 |
Primes,
incorrectly including 1
(Schroeder, 17) |
| 1 |
3 |
6 |
10 |
15 |
21 |
"Triangular" numbers in which the n-th entry is the sum
of integers from 1 to n |
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Sequences may be composite,
with even-numbered outer elements following one rule and
odd-numbered inner elements obeying another: |
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Which comes next in this sequence? |
| A |
... |
16 |
| B |
... |
25 |
| C |
... |
64 |
| D |
... |
36 |
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Here's a variation on the
same theme: |
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Which comes next in this sequence? |
| A |
.... |
25 |
| B |
... |
11 |
| C |
... |
10 |
| D |
... |
7 |
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Remember that numbers are
symbols, so they can be metasymbols like anything else: |
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Which comes next in this sequence? |
| A |
... |
8 |
| B |
... |
4 |
| C |
... |
12 |
| D |
... |
10 |
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Simple transformations can
make familiar sequences appear pathologically weird: |
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Which comes next in this sequence? |
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| Questions about primes always have a way
of appearing on IQ tests, especially in sequences and
odd-man-out questions. All you have to remember is that
prime numbers are positive integers that are exactly
divisible only by themselves and 1. The primes under 50 are
are 2, 3, 5, 7, 11, 13, 17, 19, 23 ... 41, 43, 47. Two is
the only even prime. Five is the only prime whose least
significant digit is 5. |
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Permutations and Combinations |
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You
should review permutations and combinations before taking
an IQ test. The difference is that
permutations include all possible arrangements of the
elements, but
combinations include only unique arrangements. For example,
the letters a, b and c have 6 permutations (abc, acb, bac,
bca, cab, cba) but only one combination (abc). You can
refresh your knowledge of permutations and combinations
here.
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References and Authorities |
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M. R.
Schroeder. Number Theory in Science and Communication.
New York: Springer, 1984. |
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N. J. A. Sloane and S. Plouffe.
The
Encyclopedia of Integer Sequences. San Diego,
California: Academic, 1995; online version available
here.
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