Quantitative Reasoning section
Number Series puzzles with answers
Five numbers and a blank. Look at the gaps first; they almost always give the rule away.
Short answer
A number series puzzle gives five or six numbers and asks for the next one. Each series follows one rule: add or subtract the same amount, multiply, grow the gaps steadily, alternate two operations, interleave two series, or add the two previous numbers. You find the rule from the gaps between neighbors.
These are practice puzzles. The full test has Quantitative Reasoning items like these, generated fresh for every attempt.
Try one
Plate 01 · Easy
Which number comes next?
87, 80, 73, 66, 59, ?
Tap the option you think is right, or show the answer.
Show the answer
The next number is 52 (option 5).
How to solve it
- Find the gap between neighbors: -7, -7, -7, -7.
- Each number is 7 less than the one before.
- So the next number is 59 - 7 = 52.
This is Number Series puzzle #1 (easy). Every puzzle below works the same way: tap an option to check it, or open the answer for a step-by-step solution.
How these puzzles work
Number series make up the Quantitative Reasoning section on IQ Octopus. They test the same skill as the visual sequences (finding a rule and extending it) with numbers instead of shapes. The arithmetic is never hard; the challenge is spotting which kind of rule is in play.
The engine draws from a fixed set of rule families: steady addition or subtraction, doubling or tripling, gaps that grow by a fixed amount, gaps that double, square numbers with an offset, a step that alternates between doubling and adding, doubling plus a constant, two series taking turns, and each number being the sum of the two before it. The number series guide walks through each family with a method.
A method that works on every one
- Write down the gaps between neighboring numbers.
- If the gaps are equal, add the gap. If they grow steadily, find how much they grow by.
- If the gaps grow fast, try multiplying, or doubling plus a constant.
- If the gaps jump around, look at every other number, or at alternating steps.
- Check your rule against every number shown before you choose.
Easy puzzles
Easy series use one steady step: add, subtract or double. Most common rules in this set: steady addition (8), steady subtraction (6), doubling (3).
Medium puzzles
Medium series use gaps that grow, square numbers, or two series taking turns. Most common rules in this set: two interleaved series (8), growing gaps (6), square numbers (3).
Hard puzzles
Hard series add the two previous numbers, double and add a constant, double the gaps, or alternate two operations. Most common rules in this set: sum of the previous two (6), double plus a constant (5), doubling gaps (3), alternating steps (2).
Want them timed? The number series practice test gives you 10 puzzles with 30 seconds each and an instant practice score.