How many Set Theory questions come in CAT Quant?

About 0.2 questions in a 22-question Quant section, worth roughly 1 marks. Set Theory appeared in 7 of the 24 CAT papers from 2017 to 2025, 8 questions in all, which ranks it 24 of 25 Quant chapters.

Are Set Theory questions in CAT MCQ or TITA?

13% of the Set Theory questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.

What types of Set Theory questions does CAT ask?

CAT keeps returning to 3 question shapes in Set Theory: The largest or smallest possible overlap; A three-set Venn with exact counts; Symmetric difference.

Set Theory for CAT: Formulas, Weightage & Question Types

Venn regions, and the largest or smallest possible overlap.

Set Theory formula sheet

Everything CAT needs from Set Theory, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place. $n$ is the total number of people.

Inclusion–exclusion


Two sets	$n(A \cup B) = n(A)+n(B)-n(A \cap B)$
Three sets	$n(A\cup B\cup C) = \sum n(A) - \sum n(A\cap B) + n(A\cap B\cap C)$
Everyone counted once	$n(A\cup B\cup C) = n$ when nobody is left out

Reading the regions


Exactly one of three	$\sum n(A) - 2\sum n(A\cap B) + 3\,n(A\cap B\cap C)$
Exactly two of three	$\sum n(A\cap B) - 3\,n(A\cap B\cap C)$
At least two	exactly two $+$ all three
Only $A$	$n(A) - n(A\cap B) - n(A\cap C) + n(A\cap B\cap C)$

How far an overlap can slide


Largest possible $n(A\cap B)$	$\min\bigl(n(A),\,n(B)\bigr)$
Smallest possible $n(A\cap B)$	$\max\bigl(0,\ n(A)+n(B)-n\bigr)$
Smallest possible triple overlap	$\max\bigl(0,\ n(A)+n(B)+n(C)-2n\bigr)$
Largest possible triple overlap	the smallest of the three set sizes

Symmetric difference


Definition	$A \,\Delta\, B$ = in one or the other, not both
Equivalently	$(A \cup B) - (A \cap B)$
It is associative	so $(P\Delta Q)\Delta(R\Delta S)$ can be taken in any order
An element survives	exactly when it appears in an odd number of the sets

The 3 Set Theory question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine.

01
The largest or smallest possible overlap
02
A three-set Venn with exact counts
03
Symmetric difference

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Set Theory in CAT: quick answers

How many Set Theory questions come in CAT Quant?: About 0.2 questions in a 22-question Quant section, worth roughly 1 marks. Set Theory appeared in 7 of the 24 CAT papers from 2017 to 2025, 8 questions in all, which ranks it 24 of 25 Quant chapters.
Are Set Theory questions in CAT MCQ or TITA?: 13% of the Set Theory questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Set Theory questions does CAT ask?: CAT keeps returning to 3 question shapes in Set Theory: The largest or smallest possible overlap; A three-set Venn with exact counts; Symmetric difference.

Set Theory for CAT: Formulas, Weightage & Question Types

Set Theory formula sheet

The 3 Set Theory question types CAT repeats

Is Set Theory costing you marks?

Set Theory in CAT: quick answers

More Modern Maths for CAT