Sequences — odd one out
Every number is shown and one of them breaks the pattern the rest follow; find it.
What this practises
In these questions every number is shown, and nothing is left out. All but one of them share something, and one does not. You are not finding the next number: you are finding the one that breaks the pattern.
This practises naming what a group of numbers have in common, which is the kind of reasoning this section is about. The questions are at the Building level, the middle of the three levels used across this section. Don't worry if you can't see the pattern straight away: there are only a few things to try.
How to go about it
- Try comparing the numbers. Are they multiples of the same number? Are they square numbers?
- If the numbers are in order, write the gap between each pair of neighbours.
- Name what all the others share, then find the one that does not.
Ask yourself: does what I named hold for every other number?
Worked example: multiples
18, 30, 36, 44, 54, 66
Here 18, 30, 36, 54 and 66 are all multiples of 6. The number 44 is not: 6 × 7 = 42 and 6 × 8 = 48, so 44 falls between two multiples. So 44 is the number that breaks the pattern.
Worked example: squares
16, 25, 49, 50, 81
The numbers 16, 25, 49 and 81 are squares (4 × 4, 5 × 5, 7 × 7 and 9 × 9). The number 50 is not a square, so 50 is the odd one out.
Worked example: a run
11, 17, 23, 29, 36, 41
The gaps should all be 6, but 29 to 36 is 7 and 36 to 41 is 5. The number 36 is one above its place, so 36 is the odd one out.
How to attack this question type
- 1
Try the small tests first: is each number a multiple of the same small number, such as 3 or 7, and is it a square? If exactly one number fails a test that all the others pass, that number is your answer.
- 2
Do not pick the number that looks biggest or smallest. The odd one out breaks the property, and it is often about the same size as the rest.
- 3
If the numbers are in a run, write the gaps. One number will sit slightly off the steady step.
Practice · untimed
One of these numbers does not belong with the others.
11, 18, 23, 29, 35
Which is it?
More in Numerical Reasoning
Number sequences
Find the missing term by working out the rule that generates the sequence.
Ratio and proportion
Share a quantity in a given ratio, or scale one quantity against another.
Rates and work
Scale a rate — workers, speed, cost per unit — up or down to a new quantity.
Age problems
Relate two ages now and at another time, then solve for one of them.
Sequences — missing number
Pairs or a small grid follow one rule; work the rule out and fill in the hidden number.
Sequences — find the rule
A run of numbers was built by one rule; choose the written rule that fits every step.