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XAT Quantitative Ability Syllabus
The Quantitative Ability syllabus for XAT in full: 4 chapters, 21 topics and 43 sub-topics, every one listed below, plus 51 Quantitative Ability flashcards with answers.
Quantitative Ability syllabus: all 4 chapters
Expand any chapter to see its topics and sub-topics.
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Arithmetic
6 topics- Number System
- Factors, multiples, HCF and LCM
- Divisibility, remainders and unit digits
- Bases and number properties
- Percentages, Ratios and Proportion
- Successive percentage change
- Ratio, proportion and variation
- Profit, Loss and Discount
- Marked price and successive discounts
- Partnership and profit sharing
- Interest
- Simple interest
- Compound interest and installments
- Averages, Mixtures and Alligation
- Weighted averages
- Mixture and replacement problems
- Time, Speed, Distance and Work
- Relative speed, trains, boats and streams
- Time and work, pipes and cisterns
- Number System
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Algebra
6 topics- Linear and Quadratic Equations
- Roots, nature and relations
- Equations in two and three variables
- Inequalities and Modulus
- Linear and quadratic inequalities
- Absolute value equations
- Functions and Graphs
- Domain, range and composite functions
- Graph interpretation and transformations
- Progressions
- Arithmetic and geometric progressions
- Sum of special series
- Logarithms and Surds
- Logarithm properties
- Indices and surd simplification
- Maxima, Minima and Polynomials
- Optimisation of expressions
- Factorisation and identities
- Linear and Quadratic Equations
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Geometry and Mensuration
5 topics- Lines, Angles and Triangles
- Triangle properties and congruence
- Similarity and Pythagorean applications
- Circles and Polygons
- Chords, tangents and arcs
- Quadrilaterals and regular polygons
- Coordinate Geometry
- Distance, section and area formulas
- Equation of lines and slopes
- Mensuration
- Area and perimeter of 2D figures
- Surface area and volume of solids
- Trigonometry
- Trigonometric ratios and identities
- Heights and distances
- Lines, Angles and Triangles
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Modern Mathematics
4 topics- Permutations and Combinations
- Arrangements and selections
- Circular and conditional counting
- Probability
- Basic and conditional probability
- Dice, cards and combinatorial events
- Set Theory and Venn Diagrams
- Union, intersection and complements
- Two and three set problems
- Binomial and Counting Principles
- Binomial theorem basics
- Counting with restrictions
- Permutations and Combinations
XAT Quantitative Ability flashcards — 51 questions with answers
What is the test for divisibility by 11?
A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is 0 or a multiple of 11.
How many factors does a number N = p^a · q^b · r^c (p, q, r prime) have, and what is the sum of its factors?
Number of factors = (a+1)(b+1)(c+1). Sum of factors = [(p^(a+1)-1)/(p-1)] · [(q^(b+1)-1)/(q-1)] · [(r^(c+1)-1)/(r-1)].
State the relationship between HCF, LCM and two numbers a and b.
HCF(a,b) × LCM(a,b) = a × b. (Holds only for two numbers.)
How do you find the unit digit of a^n (cyclicity method)?
Unit digits repeat in cycles (max length 4). Find the cycle of the base's unit digit, then take n mod 4 (using 4 when remainder is 0) to pick the corresponding unit digit.
What is the formula for successive percentage change of a% then b%?
Net change = a + b + (ab/100) percent. Use negative signs for decreases.
If a quantity increases by x%, by what % must it decrease to return to the original value?
Required decrease = [x/(100+x)] × 100 percent.
If a:b = p:q and b:c = r:s, what is a:b:c?
a:b:c = p·r : q·r : q·s (scale b's two ratios to a common middle term).
What is the difference between Profit% on Cost Price vs. on Selling Price for the same profit amount?
Profit% on CP = Profit/CP × 100; on SP = Profit/SP × 100. Since SP > CP for a profit, profit% on SP is smaller than profit% on CP.
A shopkeeper marks up by m% and gives discount d%. What is the net profit/loss %?
Net % = m - d - (m·d/100). Positive means profit, negative means loss.
What does selling two items at the same price, one at +x% and one at -x%, yield?
Always a net loss of (x/10)^2 percent, i.e. x²/100 %.
State the simple interest and compound interest formulas.
SI = P·R·T/100. CI amount = P(1 + R/100)^T, so CI = P[(1+R/100)^T − 1].
For 2 years, what is the difference between CI and SI at rate R% on principal P?
Difference = P(R/100)². For 3 years it is P(R/100)²·(3 + R/100).
What is the formula for the average speed over a round trip at speeds u and v?
Average speed = 2uv/(u+v) (harmonic mean of the two speeds, for equal distances).
In alligation, what is the rule for the ratio of two ingredients mixed to get a mean value?
Quantity of cheaper : Quantity of dearer = (Dearer price − Mean) : (Mean − Cheaper price).
If A can do a job in a days and B in b days, how long do they take together?
Together time = ab/(a+b) days; combined rate = 1/a + 1/b per day.
What are the relative speeds for two objects moving in the same vs. opposite directions?
Same direction: relative speed = |u − v|. Opposite directions: relative speed = u + v.
For a quadratic ax² + bx + c = 0, what are the sum and product of roots?
Sum of roots = −b/a; Product of roots = c/a.
What does the discriminant D = b² − 4ac tell you about a quadratic's roots?
D > 0: two distinct real roots; D = 0: two equal real roots; D < 0: two complex conjugate roots. D a perfect square (with rational a,b,c) means rational roots.
What is the rule for the direction of an inequality when multiplying or dividing by a negative number?
The inequality sign reverses (flips) when both sides are multiplied or divided by a negative quantity.
Solve and describe the solution of |x − a| < b (b > 0).
−b < x − a < b, i.e. a − b < x < a + b. (For |x − a| > b: x < a − b or x > a + b.)
Show the other 31 Quantitative Ability flashcards
How do you find the domain restrictions for f(x) = 1/g(x) and f(x) = √(h(x))?
For 1/g(x): exclude values where g(x) = 0. For √(h(x)): require h(x) ≥ 0.
What does it mean for a function to be even or odd?
Even: f(−x) = f(x) (symmetric about y-axis). Odd: f(−x) = −f(x) (symmetric about origin).
State the nth term and sum of an arithmetic progression (AP).
nth term: aₙ = a + (n−1)d. Sum: Sₙ = n/2·[2a + (n−1)d] = n/2·(first + last).
State the nth term and sum of a geometric progression (GP).
nth term: aₙ = a·r^(n−1). Sum: Sₙ = a(rⁿ − 1)/(r − 1) for r ≠ 1. Infinite sum (|r|<1): S∞ = a/(1 − r).
What are the relationships among Arithmetic Mean (AM), Geometric Mean (GM) and Harmonic Mean (HM)?
AM ≥ GM ≥ HM (for positive numbers, equality when all equal); and GM² = AM × HM for two numbers.
State the key logarithm laws: product, quotient, power and change of base.
log(mn) = log m + log n; log(m/n) = log m − log n; log(mⁿ) = n·log m; change of base: log_b a = log_c a / log_c b.
How do you rationalize a denominator of the form 1/(a + √b)?
Multiply numerator and denominator by the conjugate (a − √b), giving (a − √b)/(a² − b).
For a continuous function on a closed interval, where do maxima/minima occur?
At critical points where f'(x) = 0 or f' is undefined, or at the endpoints of the interval. Compare values to find absolute max/min.
What does the second derivative test say about a critical point?
If f'(c)=0 and f''(c) > 0, c is a local minimum; if f''(c) < 0, c is a local maximum; if f''(c)=0 the test is inconclusive.
State the Remainder Theorem and Factor Theorem for polynomials.
Remainder Theorem: dividing P(x) by (x − a) leaves remainder P(a). Factor Theorem: (x − a) is a factor of P(x) iff P(a) = 0.
What is the sum of the interior and exterior angles of any triangle?
Interior angles sum to 180°. Each exterior angle equals the sum of the two remote interior angles; exterior angles sum to 360°.
State the Pythagorean theorem and the three common Pythagorean triples.
In a right triangle, hypotenuse² = sum of squares of the other two sides. Common triples: (3,4,5), (5,12,13), (8,15,17).
What are the conditions for two triangles to be similar, and what follows about their areas?
Similar by AA, SAS, or SSS proportionality. Corresponding sides are in equal ratio k; their areas are in ratio k².
State the formula for the area of a triangle given its three sides (Heron's formula).
Area = √[s(s−a)(s−b)(s−c)], where s = (a+b+c)/2 is the semi-perimeter.
What is the angle subtended by a diameter, and the relation between central and inscribed angles?
Angle in a semicircle (subtended by diameter) is 90°. The central angle is twice the inscribed angle subtending the same arc.
State the sum of interior angles and each interior angle of a regular n-sided polygon.
Sum of interior angles = (n−2)×180°. Each interior angle of a regular polygon = (n−2)×180°/n.
What is the distance formula and the midpoint formula in coordinate geometry?
Distance = √[(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 perpendicular?
Slope m = (y₂−y₁)/(x₂−x₁). Two lines are perpendicular when m₁·m₂ = −1; parallel when m₁ = m₂.
State the section formula for a point dividing a segment in ratio m:n internally.
Point = ((m·x₂ + n·x₁)/(m+n), (m·y₂ + n·y₁)/(m+n)).
State the surface area and volume of a sphere of radius r.
Surface area = 4πr². Volume = (4/3)πr³.
State the curved surface area, total surface area and volume of a cylinder (radius r, height h).
CSA = 2πrh; TSA = 2πr(r+h); Volume = πr²h.
State the volume and total surface area of a cone (radius r, height h, slant l).
Volume = (1/3)πr²h; CSA = πrl; TSA = πr(r+l), where l = √(r²+h²).
What are the values of sin, cos and tan at 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 fundamental Pythagorean trigonometric identities.
sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.
What is the difference between a permutation and a combination, with formulas?
Permutation (order matters): ⁿPᵣ = n!/(n−r)!. Combination (order doesn't matter): ⁿCᵣ = n!/[r!(n−r)!].
How many ways can n distinct objects be arranged in a circle?
(n−1)! arrangements for a circle; if clockwise and counterclockwise are considered identical (e.g. a necklace), it is (n−1)!/2.
State the basic probability formula and the probability of the complement.
P(event) = favorable outcomes / total outcomes. P(not A) = 1 − P(A). P ranges from 0 to 1.
State the addition rule for probability of A or B, and the rule for independent events A and B.
P(A∪B) = P(A) + P(B) − P(A∩B). For independent events, P(A∩B) = P(A)·P(B).
State the inclusion-exclusion formula for two and three sets.
|A∪B| = |A| + |B| − |A∩B|. |A∪B∪C| = |A|+|B|+|C| − |A∩B| − |B∩C| − |A∩C| + |A∩B∩C|.
How many subsets does a set with n elements have, and how many proper subsets?
Total subsets = 2ⁿ; proper subsets (excluding the set itself) = 2ⁿ − 1; non-empty proper subsets = 2ⁿ − 2.
State the Binomial Theorem and the general (r+1)th term of (a + b)ⁿ.
(a+b)ⁿ = Σ_{k=0}^{n} ⁿCₖ a^(n−k) b^k. General term: T_{r+1} = ⁿCᵣ a^(n−r) bʳ. Sum of all coefficients = 2ⁿ (set a=b=1).
XAT Quantitative Ability FAQ
What is in the XAT Quantitative Ability syllabus?
XAT Quantitative Ability is split into 4 chapters: Arithmetic, Algebra, Geometry and Mensuration and Modern Mathematics. Together they contain 21 topics and 43 sub-topics.
How many chapters are in XAT Quantitative Ability?
4 chapters, containing 21 topics and 43 sub-topics. The largest chapter is Arithmetic, with 6 topics.
Are there flashcards for XAT Quantitative Ability?
Yes — a 51-card Quantitative Ability 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.