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CMAT Quantitative Techniques & Data Interpretation Syllabus
The Quantitative Techniques & Data Interpretation syllabus for CMAT in full: 5 chapters, 27 topics and 59 sub-topics, every one listed below, plus 50 Quantitative Techniques & Data Interpretation flashcards with answers.
Quantitative Techniques & Data Interpretation syllabus: all 5 chapters
Expand any chapter to see its topics and sub-topics.
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Arithmetic
8 topics- Number System
- Classification of numbers, factors and multiples
- HCF and LCM and their applications
- Divisibility rules and remainders
- Unit digit and last-two-digit problems
- Percentages
- Percentage change, increase and decrease
- Successive percentage change
- Applications in population and depreciation
- Profit, Loss & Discount
- Cost price, selling price and marked price
- Successive discounts and false weights
- Simple & Compound Interest
- SI and CI formulae and conversions
- Compounding at different frequencies
- Installments and present value
- Ratio, Proportion & Variation
- Direct, inverse and joint variation
- Componendo-dividendo and partnership
- Averages, Mixtures & Alligation
- Weighted average
- Rule of alligation and replacement
- Time, Speed & Distance
- Relative speed, trains and boats-streams
- Circular tracks and races
- Time & Work
- Work-rate and efficiency
- Pipes and cisterns
- Number System
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Algebra
5 topics- Linear & Quadratic Equations
- Roots, nature of roots and discriminant
- Sum and product of roots
- Word problems on equations
- Inequalities & Modulus
- Linear and quadratic inequalities
- Absolute value equations
- Functions & Graphs
- Domain, range and composition
- Maxima and minima of expressions
- Progressions
- Arithmetic progression
- Geometric and harmonic progression
- Logarithms, Indices & Surds
- Laws of indices and surds
- Properties of logarithms
- Linear & Quadratic Equations
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Geometry & Mensuration
6 topics- Lines, Angles & Triangles
- Triangle properties and similarity
- Pythagoras theorem applications
- Centroid, incentre and circumcentre
- Polygons & Quadrilaterals
- Interior and exterior angles
- Properties of parallelograms and trapezia
- Circles
- Chords, tangents and secants
- Cyclic quadrilaterals and arcs
- Coordinate Geometry
- Distance, section and midpoint
- Slope and equation of a line
- Mensuration 2D & 3D
- Areas of plane figures
- Surface area and volume of solids
- Trigonometry & Heights and Distances
- Trigonometric ratios and identities
- Angle of elevation and depression
- Lines, Angles & Triangles
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Modern Mathematics
4 topics- Permutations & Combinations
- Counting principles and arrangements
- Selection and circular permutations
- Probability
- Classical and conditional probability
- Addition and multiplication rules
- Set Theory
- Venn diagrams and operations
- Two-set and three-set problems
- Mensuration in Probability Contexts
- Geometric probability basics
- Permutations & Combinations
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Data Interpretation
4 topics- Tabular Data
- Reading and comparing tables
- Missing-value tables
- Graphical DI
- Bar charts and line graphs
- Pie charts and combination graphs
- Caselet & Mixed DI
- Paragraph-based data
- Multiple-source comparisons
- Data Sufficiency
- Single and two-statement evaluation
- Quantitative and logical sufficiency
- Tabular Data
CMAT Quantitative Techniques & Data Interpretation flashcards — 50 questions with answers
What is the divisibility rule for 8?
A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
How do you find the number of trailing zeros in n! (factorial)?
Sum the integer parts of n/5 + n/25 + n/125 + ... (count factors of 5, since 5s are scarcer than 2s).
State the formula relating HCF and LCM of two numbers a and b.
HCF(a,b) × LCM(a,b) = a × b.
If a number is increased by x% and then decreased by x%, what is the net percentage change?
A net decrease of x²/100 percent (always a decrease).
How do you convert a fraction increase to a percentage increase: if a quantity goes from A to B, what is % change?
Percentage change = ((B − A)/A) × 100.
Define Profit Percent and Loss Percent in terms of Cost Price (CP).
Profit% = (Profit/CP) × 100; Loss% = (Loss/CP) × 100. Both are calculated on CP.
A shopkeeper marks goods x% above CP and gives a discount of y%. What is the formula for the net profit/loss percent?
Net% = x − y − (xy/100); positive means profit, negative means loss.
If two articles are sold at the same selling price, one at x% profit and the other at x% loss, what is the overall result?
Always a net loss of x²/100 percent.
State the Simple Interest formula and the Amount formula.
SI = (P × R × T)/100; Amount A = P + SI = P(1 + RT/100).
State the Compound Interest amount formula for annual compounding.
A = P(1 + R/100)^T; CI = A − P.
What is the difference between CI and SI for 2 years at rate R% on principal P?
Difference = P(R/100)².
In a ratio a:b:c, if each term is multiplied by a constant k, what happens to the ratio?
The ratio remains unchanged (a:b:c = ak:bk:ck).
Define direct, inverse, and joint variation.
Direct: y = kx (y∝x); Inverse: y = k/x (y∝1/x); Joint: y = kxz (y varies as the product of two or more variables).
What is the formula for the average speed over equal distances at speeds x and y?
Average speed = 2xy/(x+y), the harmonic mean of the two speeds.
State the alligation rule for finding the ratio of two ingredients to obtain a desired mean value.
Ratio of cheaper:dearer = (Dearer price − Mean price) : (Mean price − Cheaper price).
If the average of n numbers is A and a new number x is added, what is the new average?
New average = (nA + x)/(n + 1).
Convert speed: how do you change km/h to m/s and vice versa?
km/h to m/s: multiply by 5/18. m/s to km/h: multiply by 18/5.
State the formula for the relative speed of two objects moving (a) toward each other and (b) in the same direction.
(a) Opposite directions: sum of speeds; (b) Same direction: difference of speeds.
A train of length L passes a stationary pole and a platform of length P. What distance does it cover in each case?
Pole: distance = L (own length). Platform: distance = L + P.
If A can do a work in 'a' days and B in 'b' days, how long do they take working together?
Together time = ab/(a+b) days (add rates: 1/a + 1/b).
Show the other 30 Quantitative Techniques & Data Interpretation flashcards
State the discriminant of a quadratic ax²+bx+c=0 and what each value indicates.
D = b² − 4ac. D>0: two distinct real roots; D=0: two equal real roots; D<0: no real (complex) roots.
For a quadratic ax²+bx+c=0, state the sum and product of roots.
Sum of roots = −b/a; Product of roots = c/a.
What happens to an inequality when both sides are multiplied or divided by a negative number?
The inequality sign reverses (flips direction).
Solve the modulus inequality |x| < a (a>0) and |x| > a.
|x| < a means −a < x < a; |x| > a means x < −a or x > a.
Define the domain and range of a function.
Domain = set of all permissible input (x) values; Range = set of all resulting output (y) values.
How does the graph of y = f(x) + c and y = f(x + c) transform relative to y = f(x)?
f(x)+c shifts the graph up by c (down if c<0); f(x+c) shifts it left by c (right if c<0).
State the nth term and sum of n terms of an Arithmetic Progression (AP).
nth term: aₙ = a + (n−1)d; Sum: Sₙ = (n/2)[2a + (n−1)d] = (n/2)(a + l).
State the nth term and sum of n terms of a Geometric Progression (GP).
nth term: aₙ = ar^(n−1); Sum (r≠1): Sₙ = a(rⁿ − 1)/(r − 1). Infinite sum (|r|<1): S = a/(1 − r).
State the three fundamental logarithm laws (product, quotient, power).
log(mn) = log m + log n; log(m/n) = log m − log n; log(mᵖ) = p·log m.
State the change of base formula for logarithms.
log_b a = (log_c a)/(log_c b), for any valid base c.
State the laws: aᵐ × aⁿ, aᵐ ÷ aⁿ, and (aᵐ)ⁿ.
aᵐ × aⁿ = a^(m+n); aᵐ ÷ aⁿ = a^(m−n); (aᵐ)ⁿ = a^(mn).
How do you rationalize the denominator of 1/(√a + √b)?
Multiply numerator and denominator by the conjugate (√a − √b): result = (√a − √b)/(a − b).
State the angle sum property of a triangle and the exterior angle theorem.
Sum of interior angles = 180°; an exterior angle equals the sum of the two remote (non-adjacent) interior angles.
State the Pythagoras theorem and its converse.
In a right triangle, hypotenuse² = sum of squares of the other two sides. Converse: if a²+b²=c², the triangle is right-angled at the vertex opposite c.
What is the sum of interior angles of a polygon with n sides, and the sum of its exterior angles?
Interior angle sum = (n − 2) × 180°; exterior angle sum = 360° (for any convex polygon).
State key properties distinguishing a rhombus from a rectangle.
Rhombus: all sides equal, diagonals bisect at right angles. Rectangle: all angles 90°, diagonals equal. A square is both.
State the relationship between the angle subtended by a chord at the centre and at the circumference.
The angle at the centre is twice the angle subtended by the same arc/chord at any point on the remaining circumference.
What is the angle in a semicircle, and what is the property of angles in the same segment?
Angle in a semicircle = 90°; angles in the same segment of a circle are equal.
State the distance formula and the section formula (internal division) in coordinate geometry.
Distance = √[(x₂−x₁)² + (y₂−y₁)²]; Section (ratio m:n): ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)).
State the slope of a line through two points and the condition for two lines to be perpendicular.
Slope m = (y₂−y₁)/(x₂−x₁); two lines are perpendicular when m₁ × m₂ = −1 (parallel when m₁ = m₂).
State the area and circumference formulas for a circle, and area of a sector with angle θ.
Area = πr²; Circumference = 2πr; Sector area = (θ/360°) × πr².
State the surface area and volume of a sphere and a right circular cylinder.
Sphere: SA = 4πr², V = (4/3)πr³. Cylinder: Total SA = 2πr(r+h), V = πr²h.
State the volume and total surface area of a cone (radius r, height h, slant l).
Volume = (1/3)πr²h; Total SA = πr(l + r), where l = √(r² + h²).
State the values of sin, cos, and tan for 0°, 30°, 45°, 60°, 90°.
sin: 0, 1/2, 1/√2, √3/2, 1. cos: 1, √3/2, 1/√2, 1/2, 0. tan: 0, 1/√3, 1, √3, undefined.
State the three Pythagorean trigonometric identities.
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.
In heights and distances, what does the angle of elevation versus angle of depression mean?
Angle of elevation: angle above the horizontal when looking up at an object. Angle of depression: angle below the horizontal when looking down at an object.
State the formulas for permutations nPr and combinations nCr.
nPr = n!/(n−r)! (order matters); nCr = n!/[r!(n−r)!] (order doesn't matter). Note nPr = nCr × r!.
State the classical (theoretical) definition of probability and the range of any probability value.
P(event) = (favourable outcomes)/(total equally likely outcomes); 0 ≤ P ≤ 1, where 0 = impossible and 1 = certain.
State the addition rule of probability for two events A and B.
P(A∪B) = P(A) + P(B) − P(A∩B); for mutually exclusive events P(A∩B)=0, so P(A∪B)=P(A)+P(B).
State the set cardinality formula for two and three sets (inclusion–exclusion).
|A∪B| = |A|+|B|−|A∩B|; |A∪B∪C| = |A|+|B|+|C| − |A∩B| − |B∩C| − |C∩A| + |A∩B∩C|.
CMAT Quantitative Techniques & Data Interpretation FAQ
What is in the CMAT Quantitative Techniques & Data Interpretation syllabus?
CMAT Quantitative Techniques & Data Interpretation is split into 5 chapters: Arithmetic, Algebra, Geometry & Mensuration, Modern Mathematics and Data Interpretation. Together they contain 27 topics and 59 sub-topics.
How many chapters are in CMAT Quantitative Techniques & Data Interpretation?
5 chapters, containing 27 topics and 59 sub-topics. The largest chapter is Arithmetic, with 8 topics.
Are there flashcards for CMAT Quantitative Techniques & Data Interpretation?
Yes — a 50-card Quantitative Techniques & Data Interpretation deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.