25 cardsSSC CGL

SSC CGL Quantitative Aptitude Key Rules

Essential arithmetic shortcuts, algebra identities, geometry theorems, and mensuration formulas for SSC CGL preparation.

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Algebraic Identity:

a + b + c = 0

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Algebraic Identity:

a + b + c = 0

a + b + c = 0

, then

a^{3} + b^{3} + c^{3} = 3 ab c

Power of Reciprocal Squared

x + \frac{1}{x} = k

, then

x^{2} + \frac{1}{x ^{2}} = k^{2} - 2

Power of Reciprocal Cubed

x + \frac{1}{x} = k

, then

x^{3} + \frac{1}{x ^{3}} = k^{3} - 3 k

Successive Percentage Change Formula

Net change is

a + b + \frac{ab}{100} %

, with negative signs for reductions.

Relationship Between CP and MP

\frac{Marked Price}{Cost Price} = \frac{100 + Profit %}{100 - Discount %}

CI and SI Difference for 2 Years

CI - SI = P (\frac{R}{100})^{2}

for principal

P

and rate

R %

Work-Men-Days Formula

\frac{M _{1} D _{1} H _{1}}{W _{1}} = \frac{M _{2} D _{2} H _{2}}{W _{2}}

, equating labor efficiency across tasks.

Relative Speed (Opposite Directions)

Relative speed is

S_{1} + S_{2}

when two objects travel towards each other.

Average Speed for Equal Distances

Average Speed = \frac{2 x y}{x + y}

for speeds

x

and

y

Angle Subtended by Arc at Center vs Circumference

Angle subtended at the center is exactly twice the angle subtended at the circumference.

Tangent-Secant Theorem

If tangent

P T

and secant

P A B

meet outside a circle,

P T^{2} = P A \cdot P B

Inradius of Right Triangle (

a, b, c

)

r = \frac{a + b - c}{2}

, where

c

is the hypotenuse.

Circumradius of Right Triangle (

a, b, c

)

R = \frac{c}{2}

, with the circumcenter located at the midpoint of hypotenuse.

Area of Equilateral Triangle of Side

a

Area = \frac{3}{4} a^{2}

, and height

h = \frac{3}{2} a

Centroid Division of Median

The centroid divides each median in the ratio

2 : 1

from vertex to midpoint.

Cyclic Quadrilateral Opposite Angles

Opposite interior angles sum to

18 0^{\circ}

(supplementary).

Total Surface Area of Right Circular Cone

TSA = π r (r + l)

, where slant height

l = r^{2} + h^{2}

Volume of a Solid Sphere

V = \frac{4}{3} π r^{3}

, and surface area

A = 4 π r^{2}

Trigonometric Secant-Tangent Identity

sec^{2} θ - tan^{2} θ = 1

, implying

(sec θ + tan θ) (sec θ - tan θ) = 1

Exact Value of

sin 1 5^{\circ}

sin 1 5^{\circ} = \frac{6 - 2}{4} = cos 7 5^{\circ}

Divisibility Rule for 11

Difference between sum of odd-place digits and even-place digits is

0

or multiple of

11

Number of Factors of

N = p_{1}^{a} p_{2}^{b} p_{3}^{c}

Total factors count is

(a + 1) (b + 1) (c + 1)

for prime factorization.

Polynomial Remainder Theorem

When polynomial

P (x)

is divided by

(x - a)

, the remainder is

P (a)

Product of HCF and LCM Rule

HCF (A, B) \times LCM (A, B) = A \times B

for two numbers.

Euler Formula for Distance Between Centers

d = R (R - 2 r)

, where

R

is circumradius and

r

is inradius.

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