SSC CGL Reasoning · Classification

Number Classification

Four numbers or groups are given and three share a property: prime, square, cube, a divisibility rule or a digit pattern. Name the property and find the one that breaks it.

All Classification notes

Why this matters

Sixteen questions in the bank, thirteen of them from the 2025 shifts, 12 EASY and 4 MODERATE. Each one is a single fact about a number, so the time goes on recall: a student who knows the primes under 100, the squares to 30 and the cubes to 20 answers in seconds.

Concept 1 of 4: Finding the odd one out: the order of tests

Every classification question hides one rule. Three options obey it and one does not. You do not need the setter's exact words for the rule; you need a rule that splits the options three against one.

Definition

Read the last line of the stem first. Most ask for the one that does NOT belong, but some 2025 questions ask for the number SIMILAR to a given list, or the group whose members all share a category. Then the answer is the one that keeps the rule.
Test 1, each number alone: even or odd, prime or not, square, cube, a multiple of something, a digit pattern.
Test 2, the link inside each option (a pair, a triad, a cluster): the later pages teach these.
A rule that fits all four options, or only two, is the wrong rule. Drop it and try the next test.
Fast route: start with the option that looks different (the only even number, the only big one) and ask why it is different. If that reason holds for the other three, you are done.

Worked example

Find the odd one out: (a) 35 (b) 63 (c) 77 (d) 92

Practice this conceptself-check · 4 quick reps

Stopping at a rule that fits all four

If every option is even, being even is not the rule. The rule you want splits the options three against one; keep testing until one does.

Answering a different question from the one printed

Some stems ask for the number similar to a given list, or for the group whose members all belong together. There the answer is the option that follows the rule, not the one that breaks it.

Concept 2 of 4: Prime and composite numbers

A prime has exactly two factors, 1 and itself. Most odd one out questions on primes hide one composite number that looks prime, or one prime among composites.

Definition

Primes under 100 (25 of them): 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.
1 is not prime. 2 is the only even prime.
To test a number, divide it by the primes up to its square root. If none divides it, it is prime.
Fast route: a number above 5 that ends in 0, 2, 4, 5, 6 or 8 is composite. A digit sum that is a multiple of 3 means the number is divisible by 3. After that, only 7, 11 and 13 need a real division for numbers up to about 200.
Composites that look prime and catch students: 51, 57, 87, 91, 119, 133, 143, 161, 187, 221.

Prime test

n \text{ is prime if no prime } p \le \sqrt{n} \text{ divides } n

Worked example

Find the odd one out: (a) 59 (b) 71 (c) 87 (d) 97

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 13 Sep 2025, Shift 3 · Q4Easy

Example 2 · Classification · Number Classification

Choose the option that is similar to the following numbers:29,31,47, 101

Counting 1 as a prime

A prime has exactly two different factors. The number 1 has only one, so it is neither prime nor composite.

Trusting an odd last digit

An odd number can still be composite:

91 = 7 \times 13

and

57 = 3 \times 19

. Run the digit-sum test for 3 and divide by 7 before you call a number prime.

Drill 5 more on prime and composite numbers

Concept 3 of 4: Squares, cubes and divisibility tests

If you know the squares and cubes by heart, a number that is not one of them stands out at once. Divisibility tests do the same job for multiples, without a long division.

Definition

Learn the squares from $1^2$ to $30^2$ and the cubes from $1^3$ to $20^3$ .
A square ends in 0, 1, 4, 5, 6 or 9. A number ending in 2, 3, 7 or 8 is never a square.
The last digit of a cube follows the last digit of the number: 2 gives 8, 8 gives 2, 3 gives 7, 7 gives 3, and every other digit gives itself. So the cube root of a four-digit cube ending in 3 ends in 7.
By 3 or 9: the digit sum is a multiple of 3 or 9. By 4: the last two digits form a multiple of 4. By 11: the alternating sum of the digits is 0 or a multiple of 11.
Some numbers are both: 64 is $8^2$ and $4^3$ ; 729 is $27^2$ and $9^3$ . Find what the other three share before you decide.

Last digits and divisibility

n^2 \text{ ends in } 0, 1, 4, 5, 6, 9 \qquad 3 \mid n \text{ when } 3 \mid \text{digit sum} \qquad 11 \mid n \text{ when } 11 \mid \text{alternating digit sum}

Worked example

Find the odd one out: (a) 343 (b) 729 (c) 1000 (d) 1600

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 12 Sep 2025, Shift 2 · Q17Easy

Example 3 · Classification · Number Classification

One number is not like the others: 1331, 2197, 3375, 4096

Calling a number a square because of its last digit

A square must end in 0, 1, 4, 5, 6 or 9, but the reverse is not true: 26 ends in 6 and is not a square. The last digit can only rule a number out.

Missing that a number can be both a square and a cube

64 and 729 are squares and cubes at once. If the other options are cubes, such a number belongs with them; check what the other three share before you mark it.

Drill 4 more on squares, cubes and divisibility tests

Concept 4 of 4: Digit patterns and true statements

Some numbers are grouped by how their digits are written rather than by their value: the same forwards and backwards, digits in a run, odd and even digits in turn. Look at the digits before you calculate anything.

Definition

Palindrome: reads the same both ways (373, 2552).
Digits in a run: each digit one more or one less than the last (3456, 8765), or a fixed step (1357, 8642). The odd one may run the other way.
Odd and even in turn: in a set like 81, 118, 91 the numbers go odd, even, odd. Mark each number O or E and compare the patterns.
True or false statements: when each option is a little sum or division, work each one out. Three are true and one is false.
If a stem says what a strange sign means, use that meaning exactly. If it says nothing, read the sign in its usual sense.

Worked example

Find the odd one out: (a) 2468 (b) 1357 (c) 3579 (d) 4682

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 18 Sep 2025, Shift 3 · Q8Easy

Example 4 · Classification · Number Classification

Identify the odd one out:

Missing a run that goes the other way

5678 and 8765 both have digits in a run, one going up and one going down. When three options run one way, the fourth can be odd only because of its direction.

Drill 4 more on digit patterns and true statements

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (2)

Prime and composite numbers
Prime test
$n \text{ is prime if no prime } p \le \sqrt{n} \text{ divides } n$
Squares, cubes and divisibility tests
Last digits and divisibility
$n^2 \text{ ends in } 0, 1, 4, 5, 6, 9 \qquad 3 \mid n \text{ when } 3 \mid \text{digit sum} \qquad 11 \mid n \text{ when } 11 \mid \text{alternating digit sum}$

Watch out for (7)

Stopping at a rule that fits all four
→ Finding the odd one out: the order of tests
Answering a different question from the one printed
→ Finding the odd one out: the order of tests
Counting 1 as a prime
→ Prime and composite numbers
Trusting an odd last digit
→ Prime and composite numbers
Calling a number a square because of its last digit
→ Squares, cubes and divisibility tests
Missing that a number can be both a square and a cube
→ Squares, cubes and divisibility tests
Missing a run that goes the other way
→ Digit patterns and true statements

Test yourself on Classification

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Classification chapter test Drill all 16 questions