Quantitative Aptitude · Number Series, Coding-Decoding and Odd Man Out

Odd Man Out: Numbers for CA Foundation

Updated 1 October 2026 · Fact-checked

Odd man out (numbers) asks you to pick the one number that breaks the pattern shared by the others. Test each number for common properties: prime, square, cube, divisibility, parity or digit sum. The property that three numbers share and one lacks gives the answer.

Understand Odd Man Out: Numbers

In an odd man out question you get four numbers. Three follow one rule. One does not. Your job is to find the rule and name the number that breaks it.

The rule is almost always a simple property of the number. The common ones are: prime or composite, perfect square, perfect cube, divisible by a certain number, even or odd, digit sum, or a relation such as n² + 1 or n³ - 1.

The odd one out is not a matter of opinion. Many sets can be split in more than one way. The exam expects the cleanest rule, where exactly three numbers share a property and one does not. If a rule leaves two numbers on each side, it is not the intended rule.

This is why knowing tables of squares, cubes and primes helps so much. Once you recognise numbers on sight, the pattern shows up in seconds. This topic is part of Paper 3, which is an MCQ paper with 0.25 negative marking, so speed and accuracy both count.

Key formulas to remember

Primes up to 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47; 2 is the only even prime. 1 is neither prime nor composite.
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400; A perfect square never ends in 2, 3, 7 or 8.
Perfect cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000; Learn these ten by heart. A cube ends in the same digit as its root only for roots ending in 0, 1, 4, 5, 6, 9.
Divisibility by 3 and 9: Divisible by 3 if digit sum is divisible by 3; by 9 if digit sum is divisible by 9; Use the digit sum for both digit-sum patterns and divisibility checks.
Divisibility by 4, 8, 11: 4: last two digits divisible by 4. 8: last three digits divisible by 8. 11: (sum of digits at odd places) - (sum at even places) is 0 or a multiple of 11; Apply these to find a number that is not a multiple of the common factor.
Common number-form patterns: n² ± 1, n³ ± 1, n² + n, n(n + 1); If the numbers look 'one off' from squares or cubes, test these forms.

How to solve Odd Man Out: Numbers questions

Use the same routine for every question. It keeps you from guessing and stops you from picking a rule that fits only some numbers.

1Look at the four numbers and note their size, parity (even or odd) and last digits.
2Check the quick family tests first: are three of them primes, squares or cubes?
3If not, test divisibility: are three of them multiples of the same number such as 3, 4, 7, 9 or 11?
4Next, compute the digit sum of each number and see whether three share the same sum or the same divisibility by 3 or 9.
5Try the form tests: is each number of the type n² ± 1, n³ ± 1 or n(n + 1)?
6Confirm that the rule fits exactly three numbers and fails for exactly one. If two fail, discard the rule and try another.
7Mark the number that fails. Quickly recheck it against the rule before moving on.

Quickest way: Scan for family, then divisibility, then digit sum

When to use it: Use this in the exam when you have about 30 to 40 seconds per question and the numbers are two or three digits.

Glance first: do you recognise squares or cubes from your memorised list? If yes, the answer is usually the one that is not on the list.
If all four are small, check primes. You should know primes up to 50 instantly.
For larger numbers, run digit sums. Add the digits of all four; the one that differs in sum or in divisibility by 3 or 9 is a strong candidate.
Check the last digit and parity next. Three even and one odd (or similar) is a valid rule if nothing else fits.
Use option elimination: if a number clearly fits the group of the other three under a rule, cross it out.
If no rule appears in about 40 seconds, skip it and return later. A wrong answer costs 0.25 marks.

Common mistakes in Odd Man Out: Numbers

Calling 1 a prime number.
1 has no factors other than itself, so it seems prime.
Fix: A prime has exactly two distinct factors. 1 has only one, so it is not prime.
Forgetting that 2 is prime and even.
Students assume all primes are odd and reject 2 from the prime group.
Fix: 2 is the only even prime. In a set like 2, 3, 5, 9, the odd one is 9, not 2.
Accepting the first rule that works for two numbers.
Time pressure makes you stop at a partial pattern.
Fix: A valid rule must fit exactly three numbers and fail for one. Count before you answer.
Mixing up squares and cubes of nearby numbers, for example thinking 144 or 216 belongs to the wrong family.
The tables are not memorised well.
Fix: Revise squares up to 20 and cubes up to 10 until you can recall them without calculation.
Making addition errors in digit sums.
Doing the sums in a rush on a three-digit or four-digit number.
Fix: Add digits in pairs that make 9 or 10 first, and recheck the one number you pick as odd.
Choosing a number just because it looks unusual, such as the largest or the only even one.
Looks seem like a pattern but are not a mathematical property.
Fix: Always state the property in words, for example 'three are cubes'. If you cannot, the rule is not solid.

Worked examples

Example 1

Find the odd one out: (A) 17 (B) 23 (C) 29 (D) 39

Show the solution

Check each number for primality.
17 has no divisors other than 1 and 17, so it is prime.
23 is prime. 29 is prime.
39 = 3 × 13, so it is composite.
Three numbers are prime and one is not, so the rule fits exactly three.

Answer: (D) 39

Example 2

Find the odd one out: (A) 27 (B) 64 (C) 125 (D) 150

Show the solution

Test whether each number is a perfect cube.
27 = 3³, 64 = 4³, 125 = 5³.
150 lies between 5³ = 125 and 6³ = 216, so it is not a cube.
The rule 'perfect cube' fits three numbers and fails only for 150.

Answer: (D) 150

Example 3

Find the odd one out: (A) 124 (B) 232 (C) 340 (D) 436

Show the solution

All four are even and all are divisible by 4, so parity and divisibility by 4 do not separate them.
Find the digit sums.
124: 1 + 2 + 4 = 7.
232: 2 + 3 + 2 = 7.
340: 3 + 4 + 0 = 7.
436: 4 + 3 + 6 = 13.
Three numbers have digit sum 7 and one has digit sum 13.

Answer: (D) 436

Exam tips

Memorise squares to 20², cubes to 10³ and primes to 50. Most questions in this topic are solved by recognition alone.
Test the family rules (prime, square, cube) first. They take the least time and are the most common.
When two rules both seem to work, pick the one that fits exactly three numbers. That is the one the question setter meant.
Do not spend more than about 40 seconds on one question. With negative marking of 0.25 per wrong answer, skip and return if you are stuck.
Practise the same numbers under several rules, for example 49 as a square, as 7², and as a multiple of 7. Flexible thinking speeds up your scan.

Practice questions from Number Series, Coding-Decoding and Odd Man Out

Odd Man Out: Numbers: frequently asked questions

What is odd man out in number questions?

You get four numbers where three share a property and one does not. You must identify the one that breaks the pattern. The property is usually prime, square, cube, divisibility or digit sum.

How do I find the odd one out quickly?

Check for primes, squares and cubes first, then divisibility, then digit sums. Stop as soon as you find a rule that fits exactly three numbers. Memorised tables make this much faster.

Is 1 a prime number in odd man out questions?

No. A prime number has exactly two distinct factors, and 1 has only one. So 1 is neither prime nor composite.

What if more than one number seems to be the odd one out?

Look for a rule that fits exactly three numbers and fails for one. Drop any rule that splits the set two and two. If it is still unclear, skip and return after the other questions.