How many Averages questions come in CAT Quant?

About 1.3 questions in a 22-question Quant section, worth roughly 4 marks. Averages appeared in 23 of the 24 CAT papers from 2017 to 2025, 32 questions in all, which ranks it 5 of 25 Quant chapters.

Are Averages questions in CAT MCQ or TITA?

38% of the Averages questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.

What types of Averages questions does CAT ask?

CAT keeps returning to 5 question shapes in Averages: Squeeze one value to its limit; Two groups, one combined average; Relations between sums; Overlapping groups — first k and last k; Someone joins, leaves or is replaced.

Averages for CAT: Formulas, Weightage & Question Types

Two groups combined, someone joining or leaving, and squeezing one value to its limit.

Averages formula sheet

Everything CAT needs from Averages, 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 count and $A$ the average.

The only definition


Average	$A = \dfrac{\text{sum}}{n}$
The form you will actually use	$\text{sum} = \text{average} \times \text{count}$
Deviations	the gaps above $A$ and the gaps below $A$ cancel exactly

Adding or removing one value


Add a value $v$ to $n$ items	new average $= \dfrac{nA+v}{n+1}$
The shift	$\dfrac{v-A}{n+1}$ — so the average rises if and only if $v > A$
Remove a value $v$	new average $= \dfrac{nA-v}{n-1}$
Replace $v$ with $w$	the total moves by $w-v$ , the average by $\dfrac{w-v}{n}$

Two groups combined


Weighted average	$A = \dfrac{n_1A_1 + n_2A_2}{n_1+n_2}$
Alligation	$\dfrac{n_1}{n_2} = \dfrac{A_2 - A}{A - A_1}$
In words	the combined average sits closer to the bigger group

Shifting and scaling


Add $k$ to every value	the average goes up by $k$
Multiply every value by $k$	the average is multiplied by $k$
Assumed mean	$A = \text{guess} + \text{average of the deviations from the guess}$

Evenly spaced values


Average of an AP	$\dfrac{\text{first}+\text{last}}{2}$ , which is the middle term
First $n$ natural numbers	$\dfrac{n+1}{2}$
$n$ consecutive integers	the middle one when $n$ is odd

Averages that are not plain averages


Average speed	$\dfrac{\text{total distance}}{\text{total time}}$ — never the average of the speeds
Equal distances at two speeds	the harmonic mean $\dfrac{2xy}{x+y}$
Equal money spent at different rates	the average rate is the harmonic mean, not the arithmetic one
Equal quantity bought at different rates	then it is the arithmetic mean

The 5 Averages question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine. Beyond these, CAT has asked 3 rarer one-off shapes here.

01
Squeeze one value to its limit
02
Two groups, one combined average
03
Relations between sums
04
Overlapping groups — first $k$ and last $k$
05
Someone joins, leaves or is replaced

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Averages in CAT: quick answers

How many Averages questions come in CAT Quant?: About 1.3 questions in a 22-question Quant section, worth roughly 4 marks. Averages appeared in 23 of the 24 CAT papers from 2017 to 2025, 32 questions in all, which ranks it 5 of 25 Quant chapters.
Are Averages questions in CAT MCQ or TITA?: 38% of the Averages questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Averages questions does CAT ask?: CAT keeps returning to 5 question shapes in Averages: Squeeze one value to its limit; Two groups, one combined average; Relations between sums; Overlapping groups — first k and last k; Someone joins, leaves or is replaced.

Averages for CAT: Formulas, Weightage & Question Types

Averages formula sheet

The 5 Averages question types CAT repeats

Is Averages costing you marks?

Averages in CAT: quick answers

More Arithmetic for CAT