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SSC CGL Reasoning · Classification

Number Triads and Sets

Each option is a set of three numbers tied together by one rule: equal steps, a fixed ratio, two numbers made from one, or one number made from the other two.

All Classification notes

Why this matters

Twenty-two questions in the bank, 9 EASY, 12 MODERATE and the chapter's only HARD one. Thirteen of them come from the 2024 shifts. A set has more ways to be linked than a pair, so a fixed order of tests saves the most time here.

Concept 1 of 3: Equal steps, equal ratios and growing gaps in a set

Read a set of three like a short series. The numbers may rise by the same amount, grow by the same multiple, or have gaps that follow their own pattern.

Definition

  • Equal steps: the middle number minus the first equals the last minus the middle (11, 17, 23).
  • Equal ratio: each number is the same multiple of the one before (8, 24, 72 is ×3, ×3).
  • Gaps with a pattern: write the two gaps and compare them across options (10 then 20 is 'the second gap is double the first').
  • A number and its powers: n,n2,n3n, n^2, n^3 (4, 16, 64).
  • Test steps first, then ratios, then the gap pattern. These rules use no outside number, so they are the quickest to check.

Steps and ratios in a set a, b, c

b−a=c−bba=cbb - a = c - b \qquad \frac{b}{a} = \frac{c}{b}

Worked example

Find the odd set: (a) 8, 24, 72 (b) 5, 20, 80 (c) 7, 21, 63 (d) 6, 18, 54
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 15 Sep 2025, Shift 3 · Q21Moderate

Example 1 · Classification · Number Triads and Sets

Which group doesn’t match the pattern?

Mixing up equal steps and equal ratios

5, 20, 80 has steps 15 and 60 but ratios 4 and 4. 11, 17, 23 has steps 6 and 6 but no fixed ratio. Test both before you decide which rule the three options share.
Drill 3 more on equal steps, equal ratios and growing gaps in a set

Concept 2 of 3: Two numbers of a triad built from one

In many triads one number is the seed and the other two are made from it in two separate ways. The odd triad breaks just one of the two links, so both have to be checked.

Definition

  • Find the seed. It is usually the first number, but sometimes the last (first = c2−1c^2 - 1 and middle = 5c, where c is the third).
  • Find each link on its own: one is often a small change (2a + 1, 3a, 4a − 1) and the other a power (a2a^2, a3a^3, a3−1a^3 - 1).
  • Fast route: check the easier link in all four options first. If it already leaves one option out, check only the harder link on that one, to make sure.
  • If the easy link holds in all four, the answer is decided by the harder link.

Worked example

Find the odd triad: (a) 3 : 10 : 27 (b) 5 : 16 : 125 (c) 4 : 13 : 64 (d) 6 : 19 : 210
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2023 · Tier I, 20 Jul 2023, Shift 4 · Q12Moderate

Example 2 · Classification · Number Triads and Sets

Three of the following four triads are alike in a certain way as they are formed by performing same mathematical operations among themselves and thus form a group. Which triad does NOT belong to that group?

Checking only one link of a triad

A triad can keep one link and break the other. If the first link holds in every option, the second link decides; skipping it means guessing.
Drill 4 more on two numbers of a triad built from one

Concept 3 of 3: One number of a set made from the other two

Here no single number is the seed. The third number comes from the first two together (their sum, difference or product, then adjusted), or the middle comes from the two ends.

Definition

  • Order of tests: sum, difference, product. Then divide the third number by the sum or the difference: if three options give the same whole number k, the rule is k(a + b) or k(a − b).
  • Product rules are often adjusted: ab + 5, ab − 5.
  • Mixed rules use squares or cubes: a2−ba^2 - b, a2+b2a^2 + b^2.
  • Middle from the ends: test first + third against the middle (equal, double, three times) and twice the first plus the third.
  • A step that gives a fraction in only one option often marks that option as the odd one, since the setter builds the other three to come out whole.
  • Keep the order: a−ba - b and b−ab - a are different rules.

Rules linking a set a, b, c

c=k(a+b)c=k(a−b)c=ab±ka+c=kbc = k(a + b) \qquad c = k(a - b) \qquad c = ab \pm k \qquad a + c = k b

Worked example

Find the odd set: (a) 6, 4, 32 (b) 9, 11, 70 (c) 5, 7, 18 (d) 8, 10, 56
Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 12 Sep 2024, Shift 2 · Q12Moderate

Example 3 · Classification · Number Triads and Sets

Three of the following numbers are alike in a certain way and one is different. Pick the odd one out. (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc., to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

Taking a rule that only two options obey

In 4, 5, 9 and 6, 3, 9 the sum works, but if the other two options fail it, the sum is not the rule. A rule must hold in exactly three options.

Throwing out an option because a step gives a fraction

When a rule divides by 3 and only one option is not a multiple of 3, that option is usually the answer, not a sign the rule is wrong. Check that the other three come out whole.
Drill 12 more on one number of a set made from the other two

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)

Watch out for (4)

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 testDrill all 22 questions