CAT Quantitative Aptitude Syllabus

Quantitative Aptitude syllabus — full chapter and topic list

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

1. 1

   Number System

   5 topics

   • Divisibility Rules
   • Factors and Multiples
   • HCF and LCM
   • Prime Numbers
   • Remainders
2. 2

   Algebra

   5 topics

   • Linear Equations
   • Quadratic Equations
   • Polynomials
   • Inequalities
   • Progressions
3. 3

   Geometry

   5 topics

   • Lines and Angles
   • Triangles
   • Circles
   • Quadrilaterals
   • Mensuration
4. 4

   Arithmetic

   5 topics

   • Percentages
   • Profit and Loss
   • Simple and Compound Interest
   • Ratio and Proportion
   • Time, Speed, and Distance
5. 5

   Modern Math

   5 topics

   • Permutation and Combination
   • Probability
   • Set Theory
   • Functions
   • Logarithms

Quantitative Aptitude flashcards for CAT

21 of 51 cards from the Quantitative Aptitude 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. State the divisibility rule for 11.

   A number is divisible by 11 if the difference between the sum of digits in odd positions and the sum of digits in even positions is 0 or a multiple of 11.

3. How many factors does a number N = p^a x q^b x r^c (p, q, r prime) have?

   The total number of factors is (a+1)(b+1)(c+1).

4. What is the sum of all factors of N = p^a x q^b?

   Sum of factors = [(p^(a+1) - 1)/(p - 1)] x [(q^(b+1) - 1)/(q - 1)].

5. What is the fundamental relationship between HCF, LCM, and two numbers a and b?

   HCF(a, b) x LCM(a, b) = a x b.

6. How do you find the HCF and LCM of two fractions?

   HCF of fractions = HCF(numerators)/LCM(denominators); LCM of fractions = LCM(numerators)/HCF(denominators).

7. How many prime numbers are there below 20, and list them.

   There are 8: 2, 3, 5, 7, 11, 13, 17, 19.

8. What is the only even prime number, and why is 1 not prime?

   2 is the only even prime. 1 is not prime because it has only one factor (itself), whereas a prime must have exactly two distinct factors.

9. State Fermat's Little Theorem for finding remainders.

   If p is prime and a is not divisible by p, then a^(p-1) ≡ 1 (mod p).

10. What does Wilson's Theorem state about (p-1)! mod p?

    For a prime p, (p-1)! ≡ -1 (mod p), i.e. (p-1)! + 1 is divisible by p.

11. How do you find the unit digit of a power, e.g. the cyclicity of digit 2?

    Unit digits repeat in cycles. For 2 the cycle is 2, 4, 8, 6 (length 4); find the remainder of the exponent divided by 4 to pick the unit digit.

12. What is the general form and solution method for a pair of linear equations a1x+b1y=c1 and a2x+b2y=c2?

    A unique solution exists when a1/a2 != b1/b2. Solve by substitution, elimination, or cross-multiplication: x/(b1c2-b2c1) = y/(c1a2-c2a1) = 1/(a1b2-a2b1).

13. When does a system of two linear equations have no solution or infinitely many solutions?

    No solution when a1/a2 = b1/b2 != c1/c2 (parallel lines); infinitely many when a1/a2 = b1/b2 = c1/c2 (same line).

14. What is the quadratic formula for ax^2 + bx + c = 0?

    x = [-b ± sqrt(b^2 - 4ac)] / (2a).

15. 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.

16. 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 real roots; D < 0: two complex conjugate roots.

17. State the Remainder Theorem for polynomials.

    When a polynomial p(x) is divided by (x - a), the remainder is p(a).

18. State the Factor Theorem.

    (x - a) is a factor of polynomial p(x) if and only if p(a) = 0.

19. How does multiplying or dividing an inequality by a negative number affect it?

    The direction of the inequality sign reverses (e.g. if a < b, then -a > -b).

20. State the AM-GM inequality for two positive numbers a and b.

    (a + b)/2 >= sqrt(ab), with equality when a = b. The arithmetic mean is always at least the geometric mean.

21. What is the formula for the nth term and sum of n terms of an arithmetic progression (AP)?

    nth term: a_n = a + (n-1)d; Sum: S_n = n/2 [2a + (n-1)d] = n/2 (first + last term).

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