# Formulae

## Formulae

Exam2win.com|Aptitude Fundamental Formulaes

Numbers

• A number is divisible by 2 if the last digit is 0, 2, 4, 6 or 8.
• A number is divisible by 3 if the sum of the digits is divisible by 3.
• A number is divisible by 4 if the number formed by the last two digits is divisible by 4.
• A number is divisible by 5 if the last digit is either 0 or 5.
• A number is divisible by 6 if it is divisible by 2 AND it is divisible by 3.
• A number is divisible by 8 if the number formed by the last three digits is divisible by 8.
• A number is divisible by 9 if the sum of the digits is divisible by 9.
• A number is divisible by 10 if the last digit is 0.

• (1 + 2 + 3 + ... + n) = [n(n + 1)] / 2
• (12 + 22 + 32 + ... + n2) = [n(n + 1)(2n + 1)] / 6
• (13 + 23 + 33 + ... + n3) = [n2(n + 1)2] / 4

Ratio & Proportion

• The equality of two ratios is called a proportion. If a : b = c : d, we write a : b :: c : d and we say that a, b, c, d are in proportion. In a proportion, the first and fourth terms are known as extremes, while the second and third are known as means.
• Product of extremes = Product of means
• Mean proportion between a and b is
• The compounded ratio of the ratios (a : b), (c : d), (e : f) is (ace : bdf)
• a2 : b2 is a duplicate ratio of a : b
• a3 : b3 is a triplicate ratio of a : b
• a1/3 : b1/3 is a sub-triplicate ratio of a : b
• If a / b = c / d, then, (a + b) / b = (c + d) / d, which is called the componendo.
• If a / b = c / d, then, (a - b) / b = (c - d) / d, which is called the dividendo.
• If a / b = c / d, then, (a + b) / (a - b) = (c + d) / (c - d), which is called the componendo & dividendo.
• Variation: We say that x is directly proportional to y if x = ky for some constant k and we write, x a y.
• Also, we say that x is inversely proportional to y if x = k / y for some constant k and we write x a 1 / y.

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