Examius
🇮🇳 CAT · subject
CAT Quantitative Aptitude Syllabus
The Quantitative Aptitude syllabus for CAT in full: 5 chapters and 25 topics, every one listed below, plus 51 Quantitative Aptitude flashcards with answers.
Quantitative Aptitude syllabus: all 5 chapters
Expand any chapter to see its topics and sub-topics.
-
Number System
5 topics- Divisibility Rules
- Factors and Multiples
- HCF and LCM
- Prime Numbers
- Remainders
-
Algebra
5 topics- Linear Equations
- Quadratic Equations
- Polynomials
- Inequalities
- Progressions
-
Geometry
5 topics- Lines and Angles
- Triangles
- Circles
- Quadrilaterals
- Mensuration
-
Arithmetic
5 topics- Percentages
- Profit and Loss
- Simple and Compound Interest
- Ratio and Proportion
- Time, Speed, and Distance
-
Modern Math
5 topics- Permutation and Combination
- Probability
- Set Theory
- Functions
- Logarithms
CAT Quantitative Aptitude flashcards — 51 questions with answers
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.
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.
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).
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)].
What is the fundamental relationship between HCF, LCM, and two numbers a and b?
HCF(a, b) x LCM(a, b) = a x b.
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).
How many prime numbers are there below 20, and list them.
There are 8: 2, 3, 5, 7, 11, 13, 17, 19.
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.
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).
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.
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.
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).
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).
What is the quadratic formula for ax^2 + bx + c = 0?
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 real roots; D < 0: two complex conjugate roots.
State the Remainder Theorem for polynomials.
When a polynomial p(x) is divided by (x - a), the remainder is p(a).
State the Factor Theorem.
(x - a) is a factor of polynomial p(x) if and only if p(a) = 0.
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).
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.
Show the other 31 Quantitative Aptitude flashcards
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).
What is the formula for the nth term and sum of n terms of a geometric progression (GP)?
nth term: a_n = a r^(n-1); Sum (r != 1): S_n = a(r^n - 1)/(r - 1); Sum to infinity (|r| < 1): S = a/(1 - r).
What are complementary angles and supplementary angles?
Complementary angles sum to 90 degrees; supplementary angles sum to 180 degrees.
When two parallel lines are cut by a transversal, what is true of alternate interior angles and co-interior angles?
Alternate interior angles are equal; co-interior (same-side interior) angles are supplementary (sum to 180 degrees).
State the Pythagoras theorem.
In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c^2 = a^2 + b^2.
What is the area of a triangle by Heron's formula?
Area = sqrt[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2 is the semi-perimeter.
State the two main triangle similarity/congruence criteria SAS and AAA.
AAA (or AA): triangles with equal corresponding angles are similar. SAS congruence: two sides and the included angle equal implies congruent triangles.
What is the relationship between the angle at the centre and the angle at the circumference subtended by the same arc?
The angle at the centre is twice the angle subtended at any point on the remaining circumference (same arc).
What is the area and circumference of a circle of radius r?
Area = pi r^2; Circumference = 2 pi r.
What is the sum of interior angles of a polygon with n sides?
Sum of interior angles = (n - 2) x 180 degrees.
What is the area of a trapezium with parallel sides a and b and height h?
Area = 1/2 (a + b) h.
What are the area and the diagonal relationships of a rhombus with diagonals d1 and d2?
Area = 1/2 (d1 x d2); the diagonals bisect each other at right angles.
What is the total surface area and volume of a cylinder of radius r and height h?
Volume = pi r^2 h; Total surface area = 2 pi r (r + h).
What is the volume and total surface area of a sphere of radius r?
Volume = 4/3 pi r^3; Surface area = 4 pi r^2.
What is the volume and curved surface area of a cone with radius r, height h, slant height l?
Volume = 1/3 pi r^2 h; Curved surface area = pi r l, where l = sqrt(r^2 + h^2).
How do you convert a fraction increase/decrease into a percentage change?
Percentage change = (change/original value) x 100%.
If a value increases by x% then decreases by x%, what is the net percentage change?
Net change = -(x^2)/100 % (a net decrease).
What are the formulas for profit percentage and loss percentage?
Profit% = (Profit/Cost Price) x 100; Loss% = (Loss/Cost Price) x 100. Both are computed on the cost price.
How do successive discounts of a% and b% combine into a single equivalent discount?
Equivalent discount = a + b - (ab)/100 percent.
What is the formula for simple interest?
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 for principal P at rate R compounded annually for T years?
Amount A = P(1 + R/100)^T; Compound Interest = A - P.
What is the difference between CI and SI for 2 years on principal P at rate R%?
Difference = P(R/100)^2 for 2 years.
If a:b = 2:3 and b:c = 4:5, what is a:b:c?
a:b:c = 8:12:15 (scale b to a common value 12).
What does it mean for four quantities to be in proportion (a:b :: c:d)?
a:b :: c:d means a/b = c/d, equivalently ad = bc (product of extremes equals product of means).
What is the basic relationship between speed, distance, and time?
Speed = Distance/Time; Distance = Speed x Time; Time = Distance/Speed.
What is the average speed for a round trip covering equal distances at speeds x and y?
Average speed = 2xy/(x + y), the harmonic mean of the two speeds.
What are the relative speeds of two objects moving in the same direction versus opposite directions?
Same direction: relative speed = difference of speeds; Opposite directions: relative speed = sum of speeds.
What are the formulas for permutations nPr and combinations nCr?
nPr = n!/(n-r)! (order matters); nCr = n!/[r!(n-r)!] (order does not matter).
What is the classical (theoretical) probability of an event?
P(E) = (number of favourable outcomes)/(total number of equally likely outcomes), a value between 0 and 1.
State the formula for the number of elements in the union of two sets, n(A union B).
n(A union B) = n(A) + n(B) - n(A intersection B).
What is the definition of a logarithm, and what are the product and power rules?
log_b(x) = y means b^y = x. Product rule: log(mn) = log m + log n; Power rule: log(m^k) = k log m; also log_b(x) = log x / log b (change of base).
CAT Quantitative Aptitude FAQ
What is in the CAT Quantitative Aptitude syllabus?
CAT Quantitative Aptitude is split into 5 chapters: Number System, Algebra, Geometry, Arithmetic and Modern Math. Together they contain 25 topics.
How many chapters are in CAT Quantitative Aptitude?
5 chapters, containing 25 topics. The largest chapter is Number System, with 5 topics.
Are there flashcards for CAT Quantitative Aptitude?
Yes — a 51-card Quantitative Aptitude 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.