SSC CGL Reasoning · Analogy

Number Analogy

A number analogy joins two numbers by a rule and asks you to use the same rule on a third. On this page the rule is one or two plain steps: multiply or divide, add or take away, or multiply and then add.

All Analogy notes

Why this matters

Fifty-nine questions in the bank, forty-eight EASY and eleven MODERATE, forty-three of them from the 2024 shifts. They reward a fixed order of checks: the ratio, then the difference, then a two-step rule. Squares and cubes come on the last page of this chapter.

Concept 1 of 3: Multiply or divide by one number

Divide the larger number of each pair by the smaller. If both pairs give the same answer, that number is the rule, and the missing term is one multiplication or division away.

Definition

Divide the second number by the first (or the first by the second if the second is smaller).
If both pairs give the same whole number or simple fraction, use it on the third number.
A pair can also be a ratio: 39 and 65 are both 13 times something, 3 and 5. The answer pair must be in the same ratio.
Fast route: divisibility tests. A number is divisible by 3 or 9 when its digit sum is, and by 4 when its last two digits are. You may use digits to TEST divisibility even when the printed note forbids building the rule from digits.

One multiplier

\text{second} = k \times \text{first}

kthe same multiplier in every pair (it may be a fraction)

Worked example

23 : 161 :: 34 : ?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 23 Sep 2025, Shift 2 · Q9Moderate

Example 1 · Analogy · Number Analogy

Find the missing number: 21 : 3 :: 574 : ?

Deciding the rule from one pair

3 : 12 could be 'multiply by 4' or 'add 9'. When two pairs are given, the second one decides; when only one is given, test both rules on the options and keep the one that lands on exactly one of them.

Splitting the digits when the note forbids it

When SSC prints the note about whole numbers, a rule such as 'add the digits of 52' is not allowed. A digit sum used only to check divisibility is fine, because the rule itself still works on the whole number.

Drill 20 more on multiply or divide by one number

Concept 2 of 3: Add or take away one number

When the two numbers of a pair are close in size, their ratio is an awkward decimal but their difference is clean. Subtract, and see whether the same difference appears in the other pair.

Definition

Work out second minus first for each pair.
If the difference is the same in both, add it to (or take it from) the third number.
Fast route: with big numbers that are close together, take the difference before trying anything else. With an option pair question, the difference of each option settles it in a few seconds.

One fixed difference

\text{second} = \text{first} + d

dthe same difference in every pair (negative when the second is smaller)

Worked example

147 : 212 :: 389 : ?

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 · Q18Easy

Example 2 · Analogy · Number Analogy

346 is related to 245 by certain logic. Following the same logic, 580 is related to 479. To which of the following is 613 related, following the same logic? (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.)

The same gap in the wrong direction

If the given pair goes down by 56, an option that goes up by 56 has the same gap but the wrong sign. Write the difference as second minus first every time.

Multiplying first out of habit

For 214 and 131 the ratio is about 0.61 and leads nowhere, while the difference, 83, is the whole rule. When the numbers are close, the difference is the first check, not the last.

Drill 10 more on add or take away one number

Concept 3 of 3: Two steps: multiply, then add

When neither the ratio nor the difference is the same in both pairs, the rule usually has two steps: multiply by one number and add another. Comparing the two given pairs with each other finds both numbers at once.

Definition

Try second = a × first + b. The forms (first $-$ c) $\times$ a and (first + c) $\div$ a are the same rule written another way.
Fast route: the change in the second numbers divided by the change in the first numbers is a. Then b is the second number less a times the first.
When it breaks: two pairs always fit some rule of this shape. If a or b comes out as an untidy fraction, the true rule is something else (a square, a product), so move on.
Use a and b on the third number, then check the answer is one of the options.

Multiplier and constant from two pairs

a = \frac{y_2 - y_1}{x_2 - x_1} \qquad b = y_1 - a\,x_1

$x_1, y_1$ the first given pair
$x_2, y_2$ the second given pair

Worked example

13 : 59 :: 20 : 94 :: 31 : ?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 26 Sep 2025, Shift 3 · Q10Easy

Example 3 · Analogy · Number Analogy

Find the missing number: 10 : 21 :: 12 : ?

Accepting an untidy line

Any two pairs fit some rule 'times a, plus b'. If a comes out as

\frac{37}{9}

, that is a sign the real rule is a square or a product, not a reason to use the fraction.

A one-pair question with two answers in mind

With one given pair, such as 15 : 31, both 'double and add 1' and 'add 16' fit. Work out each rule's answer and keep the one that is printed; if both are printed, the question is ambiguous.

Drill 26 more on two steps: multiply, then add

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 (3)

Multiply or divide by one number
One multiplier
$\text{second} = k \times \text{first}$
Add or take away one number
One fixed difference
$\text{second} = \text{first} + d$
Two steps: multiply, then add
Multiplier and constant from two pairs
$a = \frac{y_2 - y_1}{x_2 - x_1} \qquad b = y_1 - a\,x_1$

Watch out for (6)

Deciding the rule from one pair
→ Multiply or divide by one number
Splitting the digits when the note forbids it
→ Multiply or divide by one number
The same gap in the wrong direction
→ Add or take away one number
Multiplying first out of habit
→ Add or take away one number
Accepting an untidy line
→ Two steps: multiply, then add
A one-pair question with two answers in mind
→ Two steps: multiply, then add

Test yourself on Analogy

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 Analogy chapter test Drill all 59 questions