CMAT Quantitative Techniques & Data Interpretation Syllabus

Quantitative Techniques & Data Interpretation syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Techniques & Data Interpretation in CMAT, not a summary of it.

1. 1

   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
2. 2

   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
3. 3

   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
4. 4

   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
5. 5

   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

Quantitative Techniques & Data Interpretation flashcards for CMAT

24 of 50 cards from the Quantitative Techniques & Data Interpretation deck — real questions with worked answers.

1. 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.

2. 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).

3. State the formula relating HCF and LCM of two numbers a and b.

   HCF(a,b) × LCM(a,b) = a × b.

4. 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).

5. 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.

6. 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.

7. 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.

8. 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.

9. State the Simple Interest formula and the Amount formula.

   SI = (P × R × T)/100; Amount A = P + SI = P(1 + RT/100).

10. State the Compound Interest amount formula for annual compounding.

    A = P(1 + R/100)^T; CI = A − P.

11. What is the difference between CI and SI for 2 years at rate R% on principal P?

    Difference = P(R/100)².

12. 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).

13. 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).

14. 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.

15. 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).

16. 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).

17. 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.

18. 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.

19. 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.

20. 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).

21. 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.

22. For a quadratic ax²+bx+c=0, state the sum and product of roots.

    Sum of roots = −b/a; Product of roots = c/a.

23. What happens to an inequality when both sides are multiplied or divided by a negative number?

    The inequality sign reverses (flips direction).

24. 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.

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