Which numbers should I memorise for a number series test?

The squares from 1 to 15, the cubes from 1 to 10, the powers of 2 up to 1024, and the triangular numbers up to 55. These four lists are the ones that make a difficult-looking row recognisable in a second. After that, speed comes from writing the gaps, not from more memorisation.

Do tricks replace understanding the rule?

No. Tricks narrow the options and speed up the check, but they work best on top of a method. A shortcut that gets you to a wrong rule faster is worse than none, so always confirm the rule against every number shown.

How can answer options help me?

They can sanity-check your rule. If your answer is not among the options, your rule is wrong. On a well-built test, wrong options are made from common slips, such as repeating the last gap instead of growing it, so a tempting option that you did not compute is a hint to recheck.

Is it worth learning squares up to 15?

Yes. Squares to 15 are the list most often needed, and recognising 144, 169, 196 or 225 at once turns a hard-looking row into a simple one. Cubes to 10 and powers of 2 to 1024 are the next most useful.

Number Series Tricks: Shortcuts That Save Time

There are no secret tricks that make hard series easy. There are, though, a few small habits and lists that remove the slow parts: staring, recomputing, and doubting a rule you have not tested. Here are the ones that pay for themselves.

Know four lists by heart

Squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225.
Cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
Powers of 2: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024.
Triangular numbers: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55.

Triangular numbers are the sums 1, 1+2, 1+2+3 and so on, and their gaps are 2, 3, 4, 5, … so 1, 3, 6, 10, 15, 21, ? gives 28. Recognising 64 as both a square and a cube, or 36 as both a square and a triangular number, also explains why two rules sometimes seem to fit one row.

Write the gaps, always

A tiny second row under the numbers costs three seconds and turns half of all series into a one-glance answer. Do it without deciding whether you need it. The habit matters more than the individual case.

Use the size of the answer

Before computing, decide roughly where the answer should land. In a series that is growing slowly, an option three times the last term is nearly always wrong. In a series that doubles, an option only a little above the last term is too small.

This eliminates two options at a glance, and it protects against a slip in your arithmetic.

Use divisibility and last digits

If every shown number is a multiple of 7, as in 7, 14, 28, 56, 112, the answer is a multiple of 7 as well. It is 224, and an option that is not divisible by 7 can be thrown out at once.

Last digits help on steady steps. 17, 23, 29, 35, 41 ends 7, 3, 9, 5, 1; the next ending is 7, and the term is 47. If an option ends in the wrong digit, it cannot be right.

Run the rule backwards

Once you have an answer, undo your rule from the answer back to the first term. If it lands on the numbers shown, you are done. If a single number is off, the rule is wrong, however good the first two terms looked.

A worked case: 3, 7, 15, 31, 63 with the rule double and add 1. Going forward, 63 × 2 + 1 = 127. Going back from 127, take away 1 and halve: 126 / 2 = 63, 62 / 2 = 31, and so on back to 3. The rule is consistent in both directions.

Know when to leave

A series that does not yield within a short time is costing you the next two. Skip it, answer the rest, and return. How long to give each item is covered in the separate piece on time per series. To practise the whole set of habits under a clock, use the JobCannon Number Series test; for the numeracy side that tables and percentages test, see the JobCannon Numerical Reasoning test.

Number Series Tricks That Save Seconds