XAT Quantitative Ability Syllabus

Quantitative Ability syllabus — full chapter and topic list

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

1. 1

   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
2. 2

   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
3. 3

   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
4. 4

   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

Quantitative Ability flashcards for XAT

25 of 51 cards from the Quantitative Ability deck — real questions with worked answers.

1. 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.

2. 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)].

3. 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.)

4. 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.

5. What is the formula for successive percentage change of a% then b%?

   Net change = a + b + (ab/100) percent. Use negative signs for decreases.

6. If a quantity increases by x%, by what % must it decrease to return to the original value?

   Required decrease = [x/(100+x)] × 100 percent.

7. 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).

8. 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.

9. 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.

10. 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 %.

11. 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].

12. 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).

13. 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).

14. 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).

15. 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.

16. 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.

17. 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.

18. 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.

19. 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.

20. 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.)

21. 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.

22. 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).

23. 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).

24. 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).

25. 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.

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