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CLAT Quantitative Techniques★ 1–2 Q within Quantitative Techniques

Algebra, Mensuration and Number Basics

A caselet occasionally hides a small equation, a shape or a number-property step. This chapter fixes the light algebra, the handful of area and volume formulas, and the HCF–LCM and divisibility basics CLAT expects — the last building blocks of the quant section.

⏱ 18 min readFoundational difficulty✓ Free · exam-pattern aligned

Timed practiceMCQs from this chapter with instant scoring

FlashcardsFormulas & traps on spaced repetition

CLAT PYQsSolved previous-year questions

By the end of this chapter you'll be able to…

1Solve a one-variable linear equation by isolating the unknown
2Frame a word problem as a single equation and solve it
3Handle consecutive-integer setups with one variable
4Find HCF and LCM and use the HCF × LCM = product relation
5Apply area, perimeter and volume formulas for standard shapes

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Why this chapter matters in CLAT

Most CLAT quant is arithmetic on data, but a caselet will occasionally hide a small equation to solve, a shape to measure, or a number property to apply. None of it is advanced — one-variable equations, a handful of area and volume formulas, and the HCF–LCM basics — but a student who has not kept these fresh loses easy marks. This chapter gathers the last building blocks so nothing in the section catches you unprepared.

Before you start — revise these

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How CLAT Quant Works

These basics support the data caselets that dominate the section.

Algebra, Mensuration and Number Basics — CLAT Quantitative Techniques

Most CLAT quant is arithmetic on data, but a caselet will occasionally hide a small equation to solve, a shape to measure, or a number property to apply. None of it is hard — one-variable equations, a handful of area and volume formulas, and the HCF–LCM basics. This chapter gathers those building blocks so nothing in the section catches you unprepared.

1. Solving a linear equation

Isolate the variable — undo the additions and multiplications around it.

$a x + b = c \Rightarrow x = \frac{c - b}{a}$

$2 x + 5 = 15 \Rightarrow 2 x = 10 \Rightarrow x = 5.$

Do the same thing to both sides. Subtract the constant, then divide by the coefficient.

2. Framing a word problem

Turn the words into one equation in one unknown.

"A father is three times as old as his son; in 12 years he will be twice as old."
- Son $= x$ , father $= 3 x$ . In 12 years: $3 x + 12 = 2 (x + 12)$ .
- $3 x + 12 = 2 x + 24 \Rightarrow x = 12.$ Son is 12, father 36.

Name the unknown, write the relationship as an equation, then solve. Check the answer against the words.

3. Consecutive integers

Consecutive integers are $x, x + 1, x + 2, \dots$ — one variable covers them all.

"Three consecutive integers sum to 72."
- $x + (x + 1) + (x + 2) = 72 \Rightarrow 3 x + 3 = 72 \Rightarrow x = 23.$
- The integers are $23, 24, 25$ ; the largest is 25.

4. HCF and LCM

HCF (highest common factor) — the largest number dividing both.
LCM (least common multiple) — the smallest number both divide into.
HCF of $12$ and $18$ is $6$ ; LCM of $4$ and $6$ is $12$ .

$HCF \times LCM = product of the two numbers$

Handy check: for $12$ and $18$ , HCF $\times$ LCM $= 6 \times 36 = 216 = 12 \times 18.$

5. Area and perimeter

Shape	Area	Perimeter
Rectangle	$l \times b$	$2 (l + b)$
Square	$s^{2}$	$4 s$
Triangle	$\frac{1}{2} \times base \times height$	sum of sides
Circle	$π r^{2}$	$2 π r$ (circumference)

Rectangle $8 \times 5$ : area $= 40$ .
Circle $r = 7$ (take $π = \frac{22}{7}$ ): area $= \frac{22}{7} \times 49 = 154$ .
Square of area $64$ : side $= 8$ , perimeter $= 32$ .

6. Volume

$cuboid = l \times b \times h, cube = s^{3}$

A cube of side $3$ : volume $= 27$ .
A plot with length twice its breadth and perimeter $60$ : $6 b = 60 \Rightarrow b = 10, l = 20$ , area $= 200 m^{2}$ .

7. Exam protocol

For an equation, do the same operation to both sides — subtract, then divide.
For a word problem, name the unknown and write one equation.
Use $x, x + 1, x + 2$ for consecutive integers.
Recall HCF $\times$ LCM = product of the two numbers.
Keep the area, perimeter and volume formulas at your fingertips.
Watch the units — area in square units, volume in cubic units.

Key formulas & results

Everything to memorise for the exam hall, in one card. Screenshot this for revision.

Linear equation

a x + b = c \Rightarrow x = \frac{c - b}{a}

Do the same operation to both sides: subtract the constant, then divide.

HCF and LCM relation

HCF \times LCM = product of the two numbers

A quick check or a way to find one when the other three are known.

Rectangle and square

area = l \times b, perimeter = 2 (l + b); square area = s^{2}

Square is the special case l = b = s.

Circle

area = π r^{2}, circumference = 2 π r

Take \pi = 22/7 when the radius is a multiple of 7.

Volume

cuboid = l \times b \times h, cube = s^{3}

Volume is in cubic units; area is in square units.

CLAT test series

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Algebra, Mensuration and Number Basics shows up in every CLAT paper — sit a timed one and find out where you actually stand.

1–3Qs in paper

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Traps CLAT sets — and how to dodge them

These are the exact option-traps and misreads that cost marks under negative marking.

WATCH OUT

✗ Moving a term across the equals sign without changing its sign.

✓ Do the same operation to both sides. To clear +5 from 2x + 5 = 15, subtract 5 from both sides to get 2x = 10, then divide by 2. Keeping the equation balanced avoids sign slips.

WATCH OUT

✗ Setting up a word problem with the wrong unknown.

✓ Name the smaller or simpler quantity as x and express the rest in terms of it. If the father is three times the son, let the son be x and the father 3x, then write the future-age condition as one equation.

WATCH OUT

✗ Confusing HCF with LCM.

✓ HCF is the largest number that divides both (so it is at most the smaller number); LCM is the smallest number both divide into (so it is at least the larger number). HCF of 12 and 18 is 6; their LCM is 36.

WATCH OUT

✗ Mixing up area and perimeter formulas.

✓ Perimeter is a length around the shape (2(l+b) for a rectangle); area is the space inside (l × b). Perimeter comes in units, area in square units — the units are a built-in check.

WATCH OUT

✗ Forgetting to take the square root when area is given.

✓ If a square has area 64, its side is √64 = 8, and its perimeter is 4 × 8 = 32. Work back from area to side before finding the perimeter.

Exam-pattern practice

PYQ-style questions with full solutions. Work through them as a readiness check — mark yourself honestly and get your gap report at the end.

Readiness check

Are you exam-ready for Algebra, Mensuration and Number Basics?

8 problems from this chapter. Try each one, reveal the worked solution, mark yourself honestly — get your gap report at the end.

8 questions~6 min

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Solve ax + b = c by subtracting b, then dividing by a — same operation both sides
•Name the unknown and write one equation for a word problem
•Use x, x+1, x+2 for consecutive integers
•HCF ≤ smaller number; LCM ≥ larger number; HCF × LCM = product
•Rectangle: area l×b, perimeter 2(l+b); square: area s², perimeter 4s
•Circle: area πr², circumference 2πr; cube volume s³, cuboid l×b×h
•Area is in square units, volume in cubic units — a built-in check

CLAT question blueprint

How this topic is asked, tier by tier — so you can prep to the pattern.

Typical weightage: 2

Question style	Marks each	Typical count	What it tests
Linear equations & word problems	~1 Q
HCF, LCM & number basics	~0–1 Q
Mensuration	~1 Q

Prep strategy

Drill one-variable equations and simple age/number word problems
Revise HCF, LCM and the HCF × LCM = product relation
Memorise area, perimeter and volume for the standard shapes
Use units as a check on which formula applies

Exam-hall strategy

Battle-tested tips from mentors and toppers for this topic under the sectional clock.

Solve equations by doing the same operation to both sides.
For word problems, name the unknown and write one equation.
Use x, x+1, x+2 for consecutive integers.
Recall HCF × LCM = product of the two numbers.
Keep area, perimeter and volume formulas ready to recall.
Check the units — square units for area, cubic for volume.

Beyond the exam

Where this skill shows up in the job you're competing for — and in life.

Everyday measurement

Area and volume formulas price flooring, paint and packaging — the commonest practical geometry.

Scheduling and cycles

LCM finds when repeating events coincide; HCF splits quantities into equal largest groups.

Setting up problems logically

Translating words into an equation is the same disciplined framing lawyers use to model a dispute.

Where else this topic is tested

Prepare once, score in every exam that asks it.

AILET (NLU Delhi)Basic algebra & mensuration

SLAT (Symbiosis)Elementary maths

MH CET LawNumerical ability — basics

LSAT—IndiaNo quant section

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Questions aspirants ask

Pulled from the Q&A community and mentor sessions.

Do the same operation to both sides so the equation stays balanced. For 2x + 5 = 15, subtract 5 from both sides to get 2x = 10, then divide both sides by 2 to get x = 5. Thinking of it as 'moving terms across' is where sign errors creep in — undo operations symmetrically instead.

Name the simplest quantity as x and express everything else in terms of it, then translate the condition into an equation. If a father is three times as old as his son, let the son be x and the father 3x; the phrase 'in 12 years he will be twice as old' becomes 3x + 12 = 2(x + 12). Solve, then read the answer back against the words to check it makes sense.

The HCF (highest common factor) is the largest number that divides both given numbers, so it is at most the smaller of them. The LCM (least common multiple) is the smallest number that both divide into, so it is at least the larger. For 12 and 18, the HCF is 6 and the LCM is 36. A useful check is that HCF × LCM always equals the product of the two numbers.

Use the units as a guide. Perimeter is a distance around a shape and comes in plain units; area is the space inside and comes in square units (l × b for a rectangle, πr² for a circle); volume is space filled and comes in cubic units (s³ for a cube). If your answer's units do not match what the question asks, you have used the wrong formula.

No. CLAT quant is built on data interpretation, and the algebra and mensuration it uses are elementary — one-variable equations, basic area and volume, and simple number properties. There are no quadratics, trigonometry or coordinate geometry. Keeping these basics fresh is enough to secure the occasional non-arithmetic question.