NMAT Quantitative Skills Syllabus

Quantitative Skills syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Skills in NMAT, not a summary of it.

1. 1

   Arithmetic Foundations

   6 topics

   • Number System
     • Classification of numbers (natural, integers, rational, irrational)
     • Factors, multiples, HCF and LCM
     • Divisibility rules and remainder concepts
     • Unit digit and last-two-digit determination
   • Percentages
     • Percentage increase and decrease
     • Successive percentage change
     • Application to population and price changes
   • Ratio, Proportion and Variation
     • Compound and componendo-dividendo
     • Direct and inverse variation
     • Partnership and share division
   • Averages, Mixtures and Alligation
     • Weighted average
     • Alligation rule for mixtures
     • Replacement of solutions
   • Profit, Loss and Discount
     • Cost price, marked price and selling price
     • Successive discounts
     • Faulty weights and dishonest dealings
   • Simple and Compound Interest
     • SI vs CI comparison
     • Compounding frequencies
     • Instalments and depreciation
2. 2

   Algebra

   5 topics

   • Linear and Quadratic Equations
     • Roots, nature of roots and discriminant
     • Sum and product of roots
     • Word problems on equations
   • Inequalities and Modulus
     • Linear and quadratic inequalities
     • Absolute value equations
     • Range of expressions
   • Functions and Graphs
     • Domain and range
     • Composite functions
     • Graph interpretation
   • Progressions
     • Arithmetic progression
     • Geometric progression
     • Sum of special series
   • Logarithms and Surds
     • Laws of logarithms
     • Simplification of surds
     • Indices and exponents
3. 3

   Geometry and Mensuration

   6 topics

   • Lines, Angles and Triangles
     • Triangle properties and congruence
     • Similar triangles
     • Pythagorean theorem applications
   • Polygons and Circles
     • Interior and exterior angles
     • Chords, tangents and arcs
     • Cyclic quadrilaterals
   • Coordinate Geometry
     • Distance and section formula
     • Equation of a line and slope
     • Area of triangle from coordinates
   • 2D Mensuration
     • Area and perimeter of plane figures
     • Sector and segment of a circle
   • 3D Mensuration
     • Surface area and volume of solids
     • Cube, cuboid, cylinder, cone and sphere
     • Combination of solids
   • Trigonometry Basics
     • Trigonometric ratios
     • Heights and distances
4. 4

   Modern Mathematics

   5 topics

   • Permutations and Combinations
     • Fundamental counting principle
     • Arrangements with restrictions
     • Selections and grouping
   • Probability
     • Classical probability
     • Addition and multiplication rules
     • Conditional probability
   • Set Theory
     • Venn diagrams for two and three sets
     • Union, intersection and complement
   • Time, Speed and Distance
     • Relative speed
     • Trains, boats and streams
     • Circular motion and races
   • Time and Work
     • Work efficiency and rates
     • Pipes and cisterns
     • Combined work problems

Quantitative Skills flashcards for NMAT

19 of 50 cards from the Quantitative Skills deck — real questions with worked answers.

1. What is the test for divisibility by 8?

   A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

2. State the relationship between HCF and LCM of two numbers a and b.

   HCF(a,b) x LCM(a,b) = a x b (product of the two numbers).

3. How many trailing zeros does n! have?

   The number of trailing zeros = floor(n/5) + floor(n/25) + floor(n/125) + ... (count of the factor 5 in n!).

4. In Number System, how do you find the unit digit of a power (cyclicity of unit digits)?

   Unit digits repeat in cycles: most digits cycle with period 4 (e.g., 2:2,4,8,6; 3:3,9,7,1). Reduce the exponent mod 4 (using 4 if remainder is 0) to find the unit digit.

5. To find percentage change when a value goes from A to B, what is the formula?

   Percentage change = ((B - A) / A) x 100. Positive = increase, negative = decrease.

6. If a quantity is increased by x% and then decreased by x%, what is the net change?

   Net change is a decrease of (x^2/100)%. The final value is always less than the original.

7. What is the successive percentage change formula for two changes of a% and b%?

   Net % change = a + b + (ab/100), using sign conventions for increases (+) and decreases (-).

8. In Ratio and Proportion, what does it mean for a, b, c, d to be in proportion (a:b :: c:d)?

   a/b = c/d, which gives the cross-product rule a x d = b x c (product of extremes = product of means).

9. Define direct, inverse, and joint variation.

   Direct: y = kx (y increases as x increases). Inverse: y = k/x (y decreases as x increases). Joint: y = kxz (y varies with the product of two or more variables).

10. What is the mean proportional (geometric mean) between two numbers a and b?

    Mean proportional = square root of (a x b).

11. What is the formula for the average of the first n natural numbers?

    Average = (n + 1) / 2.

12. State the Rule of Alligation.

    (Quantity of cheaper)/(Quantity of dearer) = (Price of dearer - Mean price)/(Mean price - Price of cheaper). It is the ratio in which two ingredients at different prices are mixed to get a desired mean price.

13. How does adding/removing a value change an average?

    New average shifts toward the added value. New sum = old sum +/- the value; new average = new sum / new count. If a new entry equals the old average, the average is unchanged.

14. In a replacement problem (e.g., removing x litres of pure liquid from a y-litre vessel and refilling with water, done n times), what fraction of pure liquid remains?

    Remaining pure liquid fraction = ((y - x)/y)^n of the original quantity.

15. What is the formula for Profit% and Loss%?

    Profit% = (Profit / Cost Price) x 100; Loss% = (Loss / Cost Price) x 100. Both are calculated on Cost Price.

16. How is Selling Price related to Marked Price and Discount?

    Selling Price = Marked Price x (1 - Discount%/100). Discount is calculated on the Marked Price.

17. How does a dishonest dealer using false weights compute gain%?

    Gain% = (Error / (True value - Error)) x 100, e.g., selling 1000g claimed but giving 900g: gain% = (100/900) x 100 = 11.11%.

18. What is the Simple Interest formula?

    SI = (P x R x T) / 100, where P = principal, R = rate% per annum, T = time in years.

19. What is the Compound Interest amount formula (compounded annually)?

    A = P x (1 + R/100)^T, and CI = A - P.

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