About Odd Man Out and Series
Two skills are tested here. The first is spotting the rule behind a series, and the second is noticing which of several numbers fails to share a property with the rest. Both come down to looking at differences, ratios and simple number properties before calculating anything.
What you need to understand
- A series rule usually shows itself in the differences between consecutive terms, so write those down first.
- If the differences are constant the series is arithmetic, and if the ratios are constant it is geometric.
- If the differences themselves follow a pattern, such as rising by a fixed amount, the series is quadratic.
- The second differences of a quadratic series are constant.
- For odd man out questions, look for a shared property such as all being squares, all being primes, or all being multiples of a number.
- Only three of the four numbers share the property, so test the simplest property first.
Formulas to remember
How to work through these questions
- Write the differences between consecutive terms before doing anything else.
- If the differences are not constant, write the differences of the differences.
- If the terms grow very quickly, test for a constant ratio instead.
- For odd man out, test the numbers against one property at a time, starting with the simplest.
- Once a rule is found, check it against every term, because a rule fitting three terms may not fit the fourth.
Mistakes that cost marks
- Assuming a series is arithmetic without confirming that the difference really is constant.
- Missing that the differences themselves rise, which is the signature of a quadratic series.
- Testing a complicated property in an odd man out question when a simple one already separates one number from the other three.
- Looking at the first two or three terms and stopping there.
- Confusing the difference between consecutive terms with the terms themselves.
Worked example
One number in the series 4, 6, 10, 21, 24 is wrong. What should that number be?
- Write the differences: 2, 4, 11, 3.
- The pattern should be 2, 4, 6, 8, so the differences rise by 2 each time.
- Working from 10 with a difference of 6 gives 16, and 16 plus 8 gives 24, which matches the final term.
- So the series should read 4, 6, 10, 16, 24, and the term that should replace 21 is 16.
Answer: 16
Practice questions with answers
A few Odd Man Out and Series questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
The series 4, 12, 36, 104, 324 contains one wrong term. Find the number that should take its place.
Answer: Option A — with explanation
The other terms show the rule clearly, and it is broken at the position holding 104.
Following the same rule, the term should be 108.
So the series should read 4, 12, 36, 108, 324.
Common mistakes
- slipped by one the other way: 107
- slipped by one: 109
- kept the incorrect term printed in the series: 104
Question 2
Which of the following does not belong with the others? 35, 211, 21, 126.
Answer: Option C — with explanation
The three other numbers are all multiple of 7s.
211 is not, so it is the odd one out.
Common mistakes
- 35 is a multiple of 7, so it belongs with the group: 35
- 21 is a multiple of 7, so it belongs with the group: 21
- 126 is a multiple of 7, so it belongs with the group: 126
Question 3
Find the missing number: 5 : 30 = 5 : ?
Answer: Option A — with explanation
The first pair shows the rule: 30 / 5 = 6.
Applying the same rule to the second pair, the missing number is 5 x 6 = 30.
Common mistakes
- applied the ratio twice: 180
- added the ratio: 11
- reported three times the correct value: 90
Question 4
In the series 11, 17, 23, 24, 35 one term is incorrect. Which number should replace it?
Answer: Option A — with explanation
The other terms show the rule clearly, and it is broken at the position holding 24.
Following the same rule, the term should be 29.
So the series should read 11, 17, 23, 29, 35.
Common mistakes
- slipped by one the other way: 28
- slipped by one: 30
- kept the incorrect term printed in the series: 24
Question 5
Find the odd one out: 33, 221, 55, 44.
Answer: Option D — with explanation
The three other numbers are all multiple of 11s.
221 is not, so it is the odd one out.
Common mistakes
- 44 is a multiple of 11, so it belongs with the group: 44
- 55 is a multiple of 11, so it belongs with the group: 55
- 33 is a multiple of 11, so it belongs with the group: 33
Frequently asked questions
What is the first thing to do with a number series?
Write down the differences between consecutive terms. Most rules reveal themselves immediately in those differences.
What does a constant ratio look like?
The terms grow quickly, and dividing any term by the one before it always gives the same number, as in 2, 6, 18, 54.
How do I solve an odd man out question?
Test the simplest properties first, such as perfect squares, primes or multiples of a number, and see which single number fails the test that the other three pass.
What if two rules both seem to fit the series?
Then the series is ambiguous. Prefer the rule that explains every term, and among those that do, prefer the simplest.
