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NMAT Quantitative Skills Syllabus
The Quantitative Skills syllabus for NMAT in full: 4 chapters, 22 topics and 64 sub-topics, every one listed below, plus 50 Quantitative Skills flashcards with answers.
Quantitative Skills syllabus: all 4 chapters
Expand any chapter to see its topics and sub-topics.
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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
- Number System
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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
- Linear and Quadratic Equations
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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
- Lines, Angles and Triangles
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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
- Permutations and Combinations
NMAT Quantitative Skills flashcards — 50 questions with answers
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.
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).
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!).
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.
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.
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.
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 (-).
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).
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).
What is the mean proportional (geometric mean) between two numbers a and b?
Mean proportional = square root of (a x b).
What is the formula for the average of the first n natural numbers?
Average = (n + 1) / 2.
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.
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.
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.
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.
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.
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%.
What is the Simple Interest formula?
SI = (P x R x T) / 100, where P = principal, R = rate% per annum, T = time in years.
What is the Compound Interest amount formula (compounded annually)?
A = P x (1 + R/100)^T, and CI = A - P.
For CI compounded n times per year, what is the amount formula?
A = P x (1 + R/(100n))^(nT), where n is the number of compounding periods per year.
Show the other 30 Quantitative Skills flashcards
What is the difference between CI and SI for 2 years at rate R%?
Difference = P x (R/100)^2 for 2 years.
What are the roots of a quadratic ax^2 + bx + c = 0 (quadratic formula)?
x = (-b +/- sqrt(b^2 - 4ac)) / (2a).
For ax^2 + bx + c = 0, what are the sum and product of the roots?
Sum of roots = -b/a; Product of roots = c/a.
What does the discriminant D = b^2 - 4ac tell you about the roots of a quadratic?
D > 0: two distinct real roots; D = 0: two equal (repeated) real roots; D < 0: two complex (non-real) roots.
What is the key rule when multiplying or dividing both sides of an inequality by a negative number?
The inequality sign must be reversed (e.g., -2x > 4 becomes x < -2).
What does |x| < a (a > 0) and |x| > a mean as inequalities?
|x| < a means -a < x < a; |x| > a means x < -a or x > a.
What are the domain and range of a function?
Domain = the set of all permissible input values (x); Range = the set of all resulting output values (y = f(x)).
What does the vertical line test determine?
A graph represents a function if and only if every vertical line intersects it at most once (each input has at most one output).
How do you find the nth term and sum of an Arithmetic Progression?
nth term: a_n = a + (n-1)d. Sum: S_n = (n/2)[2a + (n-1)d] = (n/2)(first term + last term).
How do you find the nth term and sum of a Geometric Progression?
nth term: a_n = a x r^(n-1). Sum: S_n = a(r^n - 1)/(r - 1) for r != 1.
What is the sum of an infinite GP, and when does it converge?
Sum = a/(1 - r), valid only when |r| < 1.
What are the formulas for sum of first n natural numbers, their squares, and their cubes?
Sum = n(n+1)/2; Sum of squares = n(n+1)(2n+1)/6; Sum of cubes = [n(n+1)/2]^2.
State the product rule and power rule of logarithms.
log(mn) = log m + log n; log(m^k) = k x log m.
What is the change of base formula for logarithms?
log_a(b) = log_c(b) / log_c(a), for any valid base c.
How do you rationalize a surd of the form 1/(a + sqrt(b))?
Multiply numerator and denominator by the conjugate (a - sqrt(b)), giving (a - sqrt(b))/(a^2 - b).
State the Pythagorean theorem and the triangle inequality.
Pythagoras: in a right triangle, hypotenuse^2 = sum of squares of the other two sides. Triangle inequality: the sum of any two sides must exceed the third side.
What is the sum of interior angles of a polygon with n sides, and each interior angle of a regular n-gon?
Sum of interior angles = (n - 2) x 180 degrees; each interior angle of a regular polygon = (n - 2) x 180 / n.
State two key circle theorems relating angles.
The angle subtended by an arc at the centre is twice the angle at the circumference; the angle in a semicircle is 90 degrees.
What is the distance formula and midpoint formula in coordinate geometry?
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2); Midpoint = ((x1 + x2)/2, (y1 + y2)/2).
What is the slope of a line through two points, and the condition for two lines to be parallel or perpendicular?
Slope m = (y2 - y1)/(x2 - x1). Parallel: m1 = m2; Perpendicular: m1 x m2 = -1.
What are the area and perimeter (circumference) formulas for a circle?
Area = pi r^2; Circumference = 2 pi r.
What are the area formulas for a triangle, trapezium, and parallelogram?
Triangle = (1/2) x base x height; Trapezium = (1/2) x (sum of parallel sides) x height; Parallelogram = base x height.
What are the volume and total surface area of a sphere of radius r?
Volume = (4/3) pi r^3; Total Surface Area = 4 pi r^2.
What are the volume and curved surface area of a cylinder and a cone?
Cylinder: Volume = pi r^2 h, CSA = 2 pi r h. Cone: Volume = (1/3) pi r^2 h, CSA = pi r l (l = slant height).
State the fundamental trigonometric identity and the values of sin, cos at 0, 30, 45, 60, 90 degrees.
sin^2(x) + cos^2(x) = 1. sin: 0, 1/2, 1/sqrt2, sqrt3/2, 1; cos: 1, sqrt3/2, 1/sqrt2, 1/2, 0 (at 0,30,45,60,90 degrees).
What is the difference between a permutation and a combination, with their formulas?
Permutation (order matters): nPr = n!/(n-r)!. Combination (order doesn't matter): nCr = n!/(r!(n-r)!).
What is the classical (theoretical) probability of an event, and the range of probability values?
P(E) = (favorable outcomes)/(total equally likely outcomes); 0 <= P(E) <= 1, with P(certain) = 1 and P(impossible) = 0.
State the addition rule of probability for two events A and B.
P(A or B) = P(A) + P(B) - P(A and B). For mutually exclusive events, P(A and B) = 0, so P(A or B) = P(A) + P(B).
State the inclusion-exclusion principle for two sets, |A union B|.
|A union B| = |A| + |B| - |A intersection B|.
What is the relationship between speed, distance, and time, and how do you find average speed for equal distances at speeds x and y?
Speed = Distance/Time. For equal distances at speeds x and y, average speed = 2xy/(x+y) (harmonic mean).
NMAT Quantitative Skills FAQ
What is in the NMAT Quantitative Skills syllabus?
NMAT Quantitative Skills is split into 4 chapters: Arithmetic Foundations, Algebra, Geometry and Mensuration and Modern Mathematics. Together they contain 22 topics and 64 sub-topics.
How many chapters are in NMAT Quantitative Skills?
4 chapters, containing 22 topics and 64 sub-topics. The largest chapter is Arithmetic Foundations, with 6 topics.
Are there flashcards for NMAT Quantitative Skills?
Yes — a 50-card Quantitative Skills 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.