SSC CGL Reasoning · Analogy

Number Set Analogy

A number set gives two or three groups of numbers built by the same rule. Find the rule inside each given group, then pick the option group (or the missing number) that follows it.

All Analogy notes

Why this matters

One hundred and eleven questions in the bank, sixty-five EASY, forty-one MODERATE and five HARD, all from the 2023 and 2024 shifts. This is the largest page of the chapter, and the HARD rows are here: the rule can join any two of the three numbers, so a fixed order of trials saves the most time.

Concept 1 of 3: Sets that climb by fixed steps

Before looking for a sum or a product, look along the set. Many sets simply climb or fall by the same steps, or each number is made from the one before it by the same little rule.

Definition

Write the gaps inside each set: (15, 23, 31) climbs +8, +8.
The gaps may differ but must match across the sets: +4 then +6 in every set.
Or each number is made from the one before: double and add 1, multiply by 3 then by 2.
Fast route: if the steps are equal, the middle number is the average of the outer two. Test 'middle $\times$ 2 = first + third' on each option without working out any steps.

Equal steps

2b = a + c

a, b, cthe three numbers of the set, in order

Worked example

(14, 31, 48) and (52, 69, 86). Which set is like them? (a) (20, 37, 55) (b) (33, 50, 67) (c) (41, 58, 76)

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 9 Sep 2024, Shift 2 · Q17Easy

Example 1 · Analogy · Number Set Analogy

Select the triad in which the numbers are related in the same way as are the numbers of the given triads. (16, 33, 67), (19, 39, 79) (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)

Checking only the first step

An option can match the first gap and break the second. SSC builds most wrong options this way, so check both gaps of every option you keep.

Missing a falling set

A set that drops by 22 each time is still a fixed-step set. Write the gaps with their signs, or the pattern looks random.

Drill 27 more on sets that climb by fixed steps

Concept 2 of 3: One number from a sum or difference of the others

In most sets one number is built from the other two. First find which number is the result: usually the largest, but it may stand in the middle. Then try sums and differences of the other two in a fixed order.

Definition

Find the result: the number the rule makes. It is usually the largest; check the middle place too.
Try, in order: a + b, a $-$ b, 2a + b, a + 2b, then the same with a constant added (a + b + 10) or a multiplier outside (3 $\times$ (a $-$ b)).
Test the rule on both given sets before you look at the options.
'NOT related' questions: three options follow the rule and one breaks it; the one that breaks it is the answer.
Missing number questions: use the rule on the incomplete set.

Linear rule inside a set

c = p\,a + q\,b + r

a, bthe two numbers the rule uses
p, q, rsmall whole numbers, the same for every set

Worked example

(17, 9, 52) and (12, 20, 64). Which set is like them? (a) (15, 6, 41) (b) (10, 14, 48) (c) (8, 22, 62)

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 11 Sep 2024, Shift 2 · Q3Moderate

Example 2 · Analogy · Number Set Analogy

Select the set in which the numbers are related in the same way as are the numbers of the following set. (34, 15, 64) (29, 17, 63) (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.)

Looking for the result only in the last place

In (6, 30, 4) the middle number is

3 \times (6 + 4)

. A search that tries only the third place misses it; check the largest number wherever it stands.

Swapping the first two numbers

For a rule such as 2a + b or a

-

b, the order of a and b matters: (5, 9) and (9, 5) give different results. Keep the positions the given sets use.

Drill 40 more on one number from a sum or difference of the others

Concept 3 of 3: One number from a product or quotient of the others

When the result is far bigger than the other two numbers, sums cannot reach it: try their product. When it is smaller, try a quotient. A fixed multiplier or a small constant on top is common.

Definition

Result much bigger: try a $\times$ b, then k $\times$ a $\times$ b, a $\times$ b + k, a $\times$ b $-$ k.
Result smaller: try a $\div$ b, (a $\div$ b) $\times$ k, a $\div$ b + k.
If the result stands in the middle, the product is of the first and third numbers.
Fast route: divide the result by a $\times$ b in each given set. If both give the same k, the rule is k $\times$ a $\times$ b, and you can test the options by the same division.

Product rule

c = k \times a \times b

kthe same multiplier for every set (often 1, 2, 3, 4 or 5)

Worked example

(6, 7, 210) and (4, 9, 180). Which set is like them? (a) (5, 8, 200) (b) (3, 11, 160) (c) (7, 6, 252)

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 18 Sep 2024, Shift 3 · Q3Easy

Example 3 · Analogy · Number Set Analogy

Select the set in which the numbers are related in the same way as are the numbers of the following sets. (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.) (21, 504, 8) (15, 270, 6)

Multiplying the wrong two numbers

When the big number sits in the middle, the rule multiplies the first and the third. Multiplying the first two gives a rule that fits neither given set.

Keeping an option whose quotient is not whole

If the rule divides and an option's division leaves a remainder, that option fails at once. Use this to strike options out before doing any other working.

Drill 41 more on one number from a product or quotient of the others

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)

Sets that climb by fixed steps
Equal steps
$2b = a + c$
One number from a sum or difference of the others
Linear rule inside a set
$c = p\,a + q\,b + r$
One number from a product or quotient of the others
Product rule
$c = k \times a \times b$

Watch out for (6)

Checking only the first step
→ Sets that climb by fixed steps
Missing a falling set
→ Sets that climb by fixed steps
Looking for the result only in the last place
→ One number from a sum or difference of the others
Swapping the first two numbers
→ One number from a sum or difference of the others
Multiplying the wrong two numbers
→ One number from a product or quotient of the others
Keeping an option whose quotient is not whole
→ One number from a product or quotient of the others

Test yourself on Analogy

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