GMAT Quant: Arithmetic Formula

GMAT QUANT ARITHMETIC FORMULA

Other than Algebra and Geometry, GMAT Quant consists sums oriented to numbers, traditional operations between them like addition, subtraction, multiplication and division. Some major Arithmetic topics & their formulas are as follows –

Combinatorics – Factorials, Permutations & Combinations

Factorials –

x factorial = x! = x (x-1) (x-2) … (3) (2) (1) (or)

n! = 1.2.3 …. (n-2) (n-1) n

0! = 1

Permutations –

\(_{n}P_{k} = \frac{n!}{(n-k)!}\)

Where, n = the number of objects to choose from and k = the number of objects selected

Combinations –

\(_{n}C_{k} = \frac{n!}{(n-k)!k!}\)

Where, n = the number of objects to choose from and k = the number of objects selected

Permutations & Combinations

Permutations – \(^{a}P_{b}\)

Combinations – \(^{a}C_{b}\)

Where, a, b are Whole Numbers

 

Some Important Combinatorics Formulas

  1. \(^{n}P_{n} = n!\)
  2. \(^{n}P_{m} = \frac{n!}{(n-m)!}\)
  3. Binomial Coefficient

\(^{n}C_{m} = \frac{n}{m} = \frac{n!}{m! (n-m)!}\)

  1. \(^{n}C_{m} = \; ^{n}C_{n-m}\)
  2. \(^{n}C_{m} + \; ^{n}C_{m+1} = \; ^{n+1}C_{m+1}\)
  3. \(^{n}C_{0} + ^{n}C_{1} + ^{n}C_{2} + ….. + ^{n}C_{n} = 2^{n}\)

Fractions

Adding Fractions –

\(\frac{a}{b} + \frac{c}{d} = \frac{(ad + bc)}{bd}\)

Subtracting Fractions –

\(\frac{a}{b} – \frac{c}{d} = \frac{(ad – bc)}{bd}\)

Multiplying Fractions –

\(\frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}\)

Dividing Fractions –

\(\frac{\frac{a}{b}}{\frac{c}{d}} = \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}\)

Formula for a proportion –

\(\frac{a}{b} = \frac{c}{d}\)

In a proportion, the product of the extremes (ad) equal the product of the means(bc), Thus, ad = bc

Percents

Converting Percentage into Decimal

\(20 \% = \frac{20}{100} = 0.5\)

Converting Decimal Into Percentage

\(0.25 = (0.25 \times 100) \% = 25 \%\)

\(1.50 = (1.50 \times 100) \% = 150 \%\)

Percent Change

\(Percent \; Change = \frac{(End \; Value) – (Start \; Value)}{(Start \; Value)} * 100\)

\(Percent \; Change (as \; decimal)= \frac{(End \; Value) – (Start \; Value)}{(Start \; Value)}\)

Percentage Increase/Decrease

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:

\(\left [ \frac{R}{(100 + R)} \times 100 \right ]\%\)

If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

\(\left [ \frac{R}{(100 – R)} \times 100 \right ]\%\)

Percentage Formula for Population Sums

For Present Population P and suppose it increases at the rate of R% per annum, then:

\(Population \; after \; n \; years = P \left ( 1 + \frac{R}{100} \right )^{n}\)

\(Population \; n \; years \; ago = \frac{P}{\left ( 1 + \frac{R}{100} \right )^{n}}\)

Shortcuts to solve Percentage

It is Advisable to memorize the following values. It will save your while solving GMAT Quant –

Percent Decimal Fraction
\(1\%\) 0.01 \(\frac{1}{100}\)
\(5\%\) 0.05 \(\frac{1}{20}\)
\(10\%\) 0.1 \(\frac{1}{10}\)
\(12\frac{1}{2}\%\) 0.125 \(\frac{1}{8}\)
\(20\%\) 0.2 \(\frac{1}{5}\)
\(25\%\) 0.25 \(\frac{1}{4}\)
\(33\frac{1}{3}\%\) 0.333 \(\frac{1}{3}\)
\(50\%\) 0.5 \(\frac{1}{2}\)
\(75\%\) 0.75 \(\frac{3}{4}\)
\(80\%\) 0.8 \(\frac{4}{5}\)
\(90\%\) 0.9 \(\frac{9}{100}\)
\(99\%\) 0.99 \(\frac{99}{100}\)
\(100\%\) 1
\(125\%\) 1.25 \(\frac{5}{4}\)
\(150\%\) 1.5 \(\frac{3}{2}\)
\(200\%\) 2

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