MH CET MBA Quantitative Aptitude Syllabus

In a leaking cistern, if an inlet fills in x hours and a leak empties in y hours (y>x), what is the net fill time?

Net rate = 1/x - 1/y, so net time to fill = xy/(y-x) hours.

What does the Rule of Alligation give you, and state the ratio formula?

It finds the ratio in which two ingredients at prices/concentrations are mixed to get a mean value: (Cheaper quantity)/(Dearer quantity) = (Dearer - Mean)/(Mean - Cheaper).

A vessel has 'a' litres of pure liquid; if 'b' litres is removed and replaced with water n times, how much pure liquid remains?

Remaining pure liquid = a x (1 - b/a)^n litres.

What is the formula for the average (arithmetic mean) of n numbers, and what happens to the average if each number increases by k?

Average = (sum of all values)/n. If every value increases by k, the average also increases by k.

If the average age of n people increases by m years when a new person replaces one aged A, what is the new person's age?

New person's age = A + n x m (the change spread over n people).

A father is currently 3 times his son's age; in 12 years he will be twice as old. Set up the key equations.

Let son = x: father = 3x. Then 3x + 12 = 2(x + 12), giving x = 12 (son 12, father 36).

What is the general (standard) form of a quadratic equation and its roots formula?

ax^2 + bx + c = 0 (a ≠ 0); roots x = [-b ± sqrt(b^2 - 4ac)]/(2a).

For a quadratic 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 nature of quadratic roots?

D>0: two distinct real roots; D=0: two equal real roots; D<0: two complex (no real) roots.

State the three basic laws of indices (exponents).

a^m x a^n = a^(m+n); a^m / a^n = a^(m-n); (a^m)^n = a^(mn). Also a^0 = 1 and a^(-n) = 1/a^n.

What is the definition of a logarithm, and state the product and power rules.

If a^x = N then log_a(N) = x. Rules: log(mn) = log m + log n; log(m^p) = p log m; log(m/n) = log m - log n.

How do you rationalize the denominator of a surd like 1/(sqrt(a) - sqrt(b))?

Multiply numerator and denominator by the conjugate (sqrt(a) + sqrt(b)), giving (sqrt(a)+sqrt(b))/(a-b).

When multiplying or dividing both sides of an inequality by a negative number, what must you do?

Reverse (flip) the direction of the inequality sign.

For an Arithmetic Progression with first term a and common difference d, give the nth term and sum of n terms.

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

For a Geometric Progression with first term a and common ratio r, give the nth term and the sum of n terms (r ≠ 1).

nth term = a r^(n-1); Sum S_n = a(r^n - 1)/(r - 1). Infinite sum (|r|<1) = a/(1 - r).

What are the sum of the first n natural numbers and the sum of their squares?

1+2+...+n = n(n+1)/2; 1^2+2^2+...+n^2 = n(n+1)(2n+1)/6.

What is the BODMAS/order-of-operations rule used in simplification?

Brackets, Orders (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

What is the sum of the interior angles of a triangle, and what is the exterior angle property?

Interior angles sum to 180 degrees; an exterior angle equals the sum of the two opposite (remote) interior angles.

State the Pythagoras theorem for a right-angled triangle.

In a right triangle, (hypotenuse)^2 = (base)^2 + (perpendicular)^2.

What is the relationship between a central angle and an inscribed angle subtending the same arc of a circle?

The central angle is twice the inscribed (angle at circumference) angle subtending the same arc.

What is the sum of the interior angles of an n-sided polygon, and the sum of its exterior angles?

Sum of interior angles = (n - 2) x 180 degrees; sum of exterior angles is always 360 degrees.

What is the distance formula between two points (x1, y1) and (x2, y2)?

Distance = sqrt[(x2 - x1)^2 + (y2 - y1)^2].

Give the midpoint formula and the slope formula for two points (x1,y1) and (x2,y2).

Midpoint = ((x1+x2)/2, (y1+y2)/2); Slope m = (y2 - y1)/(x2 - x1).

State the area and perimeter/circumference formulas for a circle and a rectangle.

Circle: area = pi r^2, circumference = 2 pi r. Rectangle: area = length x breadth, perimeter = 2(length + breadth).

What is the area of a triangle given base and height, and using Heron's formula?

Area = (1/2) x base x height; Heron's: Area = sqrt[s(s-a)(s-b)(s-c)], where s = (a+b+c)/2.

Give the volume and total surface area of a cube and a sphere.

Cube: volume = a^3, TSA = 6a^2. Sphere: volume = (4/3) pi r^3, surface area = 4 pi r^2.

Give the volume, curved surface area, and total surface area of a cylinder of radius r and height h.

Volume = pi r^2 h; CSA = 2 pi r h; TSA = 2 pi r (h + r).

State the divisibility rules for 3, 9, and 11.

Divisible by 3 if digit sum is divisible by 3; by 9 if digit sum is divisible by 9; by 11 if the difference of alternate digit sums is 0 or a multiple of 11.

What is the difference between a Permutation and a Combination, with their formulas?

Permutation (order matters): nPr = n!/(n-r)!. Combination (order does not 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, and P(not E) = 1 - P(E).

State the inclusion-exclusion (Venn) formula for the union of two sets, n(A union B).

n(A union B) = n(A) + n(B) - n(A intersection B).

In clock problems, how many degrees do the hour hand and minute hand move per minute, and when are the hands at right angles?

Minute hand moves 6 degrees/min, hour hand 0.5 degrees/min (relative gain 5.5 degrees/min); the hands are perpendicular (90 degrees) 22 times in 12 hours, when the relative angle is 90 degrees.