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CAT: Number System, Arithmetic and DI Quick Rules

Flashcards on number-system rules, arithmetic shortcuts and data interpretation formulas for the CAT. Original study material.

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Number of divisors of

p^{a} q^{b}

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Number of divisors of

p^{a} q^{b}

(a + 1) (b + 1)

Product of two numbers

HCF × LCM.

Trailing zeroes in n!

⌊ n /5 ⌋ + ⌊ n /25 ⌋ + ⌊ n /125 ⌋ + \dots

Net percentage change after +a% and −b%

a - b - \frac{ab}{100}

percent.

Compound interest amount

A = P (1 + \frac{r}{100})^{n}

Simple interest

\frac{P R T}{100}

Time for two workers together

\frac{ab}{a + b}

days.

Average speed over equal distances

\frac{2 v _{1} v _{2}}{v _{1} + v _{2}}

Downstream and upstream speeds

u + v

and

u - v

, with

u

the boat speed and

v

the stream speed.

Train crossing a platform

Distance = length of train + length of platform.

km/h to m/s

Multiply by 5/18.

Heron's formula

s (s - a) (s - b) (s - c)

with

s

the semi-perimeter.

Sum of an AP

\frac{n}{2} [2 a + (n - 1) d]

Sum of a GP

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

Permutations of n objects with repeats

\frac{n !}{p ! q ! r !}

Combinations

(r n) = \frac{n !}{r ! ( n - r )!}

Alligation rule

Cheaper : dearer = (dearer − mean) : (mean − cheaper).

Percentage growth

\frac{new - old}{old} \times 100

Pie chart sector angle

Percentage × 3.6 degrees.

Weighted average

\frac{\sum n _{i} x _{i}}{\sum n _{i}}

Remainder cycle

Powers of a number repeat in a cycle modulo m; reduce the exponent by the cycle length.

Sum of 1 to n

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

Sum of squares 1 to n

\frac{n ( n + 1 ) ( 2 n + 1 )}{6}

Handshakes among n people

\frac{n ( n - 1 )}{2}

Angle between clock hands

∣30 H - 5.5 M ∣

degrees.

Sentence with 'neither … nor'

The verb agrees with the nearer subject.

'The number of' and 'a number of'

Singular verb; plural verb.

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