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Qudurat GAT Quantitative Formulas & Shortcuts

Essential mental arithmetic shortcuts, algebra factorizations, geometry rules, and rate formulas for Saudi Qudurat GAT.

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Difference of Squares Formula

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Difference of Squares Formula

a^{2} - b^{2} = (a - b) (a + b)

Square of a Sum and Difference

(a + b)^{2} = a^{2} + 2 ab + b^{2}

and

(a - b)^{2} = a^{2} - 2 ab + b^{2}

Exponent Addition Rule

a^{m} \times a^{n} = a^{m + n}

and

\frac{a ^{m}}{a ^{n}} = a^{m - n}

(

a \neq = 0

Negative and Fractional Exponents

a^{- n} = \frac{1}{a ^{n}}

and

a^{1/ n} = n a

Sum of Powers of 2 Shortcut

2^{n} + 2^{n} = 2 \times 2^{n} = 2^{n + 1}

(e.g.,

2^{7} + 2^{7} = 2^{8} = 256

Speed, Distance, and Time Relations

Distance = Speed \times Time

;

Speed = \frac{Distance}{Time}

Average Speed for Equal Distances

v_{avg} = \frac{2 v _{1} v _{2}}{v _{1} + v _{2}}

(harmonic mean of two speeds).

Combined Work Rate Formula

\frac{1}{T} = \frac{1}{T _{1}} + \frac{1}{T _{2}} ⟹ T = \frac{T _{1} \times T _{2}}{T _{1} + T _{2}}

Sum of Angles in Any Triangle

The sum of interior angles in any triangle is always

18 0^{\circ}

Sum of Interior Angles of an

n

-gon

Sum = (n - 2) \times 18 0^{\circ}

(e.g., quadrilateral

36 0^{\circ}

, pentagon

54 0^{\circ}

, hexagon

72 0^{\circ}

Pythagorean Triples to Memorize

3 - 4 - 5

5 - 12 - 13

7 - 24 - 25

8 - 15 - 17

, and their multiples (e.g.,

6 - 8 - 10

Special Right Triangle:

3 0^{\circ} - 6 0^{\circ} - 9 0^{\circ}

Side lengths are in the ratio

1 : 3 : 2

opposite to

3 0^{\circ}, 6 0^{\circ}, 9 0^{\circ}

respectively.

Special Right Triangle:

4 5^{\circ} - 4 5^{\circ} - 9 0^{\circ}

Legs are equal: ratio of sides is

1 : 1 : 2

Area and Circumference of a Circle

Area = π r^{2}

and

Circumference = 2 π r = π d

Area of a Triangle

Area = \frac{1}{2} \times base \times height

Area and Perimeter of a Rectangle

Area = l \times w

;

Perimeter = 2 (l + w)

Volume and Surface Area of a Cube

Volume = s^{3}

;

Surface Area = 6 s^{2}

Volume of a Cylinder

Volume = π r^{2} h

;

Curved Surface Area = 2 π r h

Arithmetic Mean (Average)

Average = \frac{Sum of values}{Number of values} ⟹ Sum = Average \times Count

Percentage Change Formula

Percentage Change = \frac{New - Old}{Old} \times 100%

Successive Discounts Shortcut

Discounts

d_{1} %

and

d_{2} %

give net price factor

(1 - d_{1}) (1 - d_{2})

(e.g.,

20%

then

10% ⟹ 0.80 \times 0.90 = 0.72 ⟹ 28%

net discount).

Divisibility Rule for 3 and 9

A number is divisible by 3 (or 9) if the sum of its individual digits is divisible by 3 (or 9).

Divisibility Rule for 4

A number is divisible by 4 if the number formed by its last two digits is divisible by 4.

Sum of First

n

Consecutive Integers

Sum = \frac{n ( n + 1 )}{2}

(e.g.,

1 + 2 + \dots + 10 = \frac{10 \times 11}{2} = 55

Probability of an Event

P (E) = \frac{Number of favorable outcomes}{Total number of possible outcomes}

, where

0 \leq P (E) \leq 1

Qudurat GAT (Saudi Arabia) in Saudi Arabia

In Saudi Arabia, Qudurat GAT (Saudi Arabia) is part of: University entrance.

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