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%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
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% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
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% Document Info
\author{amandineguilbault}
\pdfinfo{
  /Title (gmat-quant.pdf)
  /Creator (Cheatography)
  /Author (amandineguilbault)
  /Subject (GMAT Quant Cheat Sheet)
}

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% Commands
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% Header and Footer
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\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{GMAT Quant Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{amandineguilbault} via \textcolor{DarkBackground}{\uline{cheatography.com/128918/cs/25372/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}amandineguilbault \\
  \uline{cheatography.com/amandineguilbault} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 13th December, 2020.\\
   Updated 13th December, 2020.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

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% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{1.9908 cm} x{2.9862 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Algebra}}  \tn
% Row 0
\SetRowColor{LightBackground}
ax\textasciicircum{}2\textasciicircum{}+bx+c & sum roots: -b/a \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
Δ =b\textasciicircum{}2\textasciicircum{}-4ac & product roots: c/a \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Ratios}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{q1 : q2 = q2-final : q1-final} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{num\textless{}denum so fraction\textless{}1 so (x+1)/(y+1) \textgreater{} x/y} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{num\textgreater{}denum so fraction\textgreater{}1 so (x+1)/(y+1) \textless{} x/y} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{from exercise:}} a-10 + b-20 + c-15 = 11k + 18k + 24k so 1105-45=53k (ratios gains)} \tn 
% Row Count 5 (+ 2)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{efficacy=1/t (inverse proportionnality) \{\{nl\}\} 1/t1 : 1/t2 : 1/t3 \{\{nl\}\} take LCM = k so you have k/t1 : k/t2 : k/t3 \{\{nl\}\} compute to get x : y : z form \{\{nl\}\} then do x + y + z and cross product} \tn 
% Row Count 9 (+ 4)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Rate of interest = \seqsplit{interestperyear/principalinvested}  * 100} \tn 
% Row Count 11 (+ 2)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{When compared, use compared amount as the base \{\{nl\}\} so you have Δ / base * 100} \tn 
% Row Count 13 (+ 2)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Use quantity as unit of q, the percentage change is \{\{nl\}\} Δ = increased or decrease quantity  \{\{nl\}\} Δ/1(original amount) * 100} \tn 
% Row Count 16 (+ 3)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{To make a profit, take initial price and add the desired profit so that: {\bf{new price per unit = initial (1+profit)}}} \tn 
% Row Count 19 (+ 3)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Always find a 100 that makes the calculation easy = if it's not marked price it's cost price etc.} \tn 
% Row Count 21 (+ 2)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{On Y1, simple and compound interests are the same \{\{nl\}\}Find interest rate w/ difference and interest on interest} \tn 
% Row Count 24 (+ 3)
% Row 11
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Interest = principal *  rate * time} \tn 
% Row Count 25 (+ 1)
% Row 12
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{discount of marked price = discount / marked price * 100} \tn 
% Row Count 27 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\emph{Usually, these questions include: \{\{nl\}\} 1. ratios of shared amounts, \{\{nl\}\} 2. time to perform a task, \{\{nl\}\}\{\{nl\}\} 3. investments and interests \{\{nl\}\} 4. price increases or decreases \{\{nl\}\} =\textgreater{} FOR PROFITS}}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Number properties}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{remainder of sum = sum of remainders} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{remainder of product = product of remainders} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{nb of trailing zeros = at least nb of 5s} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{number of factors = product of each power + 1 {[}ex: 120 -\textgreater{} 2\textasciicircum{}3\textasciicircum{}*5\textasciicircum{}1\textasciicircum{}*3\textasciicircum{}1\textasciicircum{}-\textgreater{} (1+1)*(1+1)*(3+1) = 16{]}} \tn 
% Row Count 6 (+ 3)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{from exercise:}} {\emph{If remainder of product to find, can work by pairs}}} \tn 
% Row Count 8 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{If two expressions are equal, the exponents must be equal (if 2\textasciicircum{}n+2m\textasciicircum{} = 2\textasciicircum{}3m-1\textasciicircum{} then n+2m = 3m-1)} \tn 
% Row Count 10 (+ 2)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{AP}} Sum of arithmetic progression = (1st + Last / 2) * nb of terms} \tn 
% Row Count 12 (+ 2)
% Row 7
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{AP}} nth term → an = a1 + (n-1) * d (common divisor)} \tn 
% Row Count 14 (+ 2)
% Row 8
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{AP}} sum of the n first terms : n/2 {[}2a1 + (n-1)d{]}} \tn 
% Row Count 16 (+ 2)
% Row 9
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{GP}} sum of first n terms = a(r\textasciicircum{}n\textasciicircum{}-1) / r-1where r is common ratio} \tn 
% Row Count 18 (+ 2)
% Row 10
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Number of ways of selecting two distinct integers from the set of first 100 positive integers = 100C2 ways. \{\{nl\}\}i.e., 100C2 = 100 × 992} \tn 
% Row Count 21 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Sets}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{P(AUB) = P(A) + P(B) - P(A∩B)} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{P(AUBUC) = P(A) + P(B) + P(C) + P(A∩B∩C) - {[}P(A∩B) + P(A∩C) + P(B∩C){]}} \tn 
% Row Count 3 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Statistics and Average}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Standard deviation = mean -\textgreater{} (number-mean)\textasciicircum{}2\textasciicircum{} -\textgreater{} mean -\textgreater{} square root(mean)} \tn 
% Row Count 2 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{p{0.4577 cm} p{0.4577 cm} p{0.4577 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{From video}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{5.377cm}}{\{\{fa-bolt\}\}{\bf{Work and Rate}}\{\{fa-bolt\}\}} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\mymulticolumn{3}{x{5.377cm}}{R=J/T} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{3}{x{5.377cm}}{machines identiques: nR=J/T} \tn 
% Row Count 3 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Geometry / Coordinate Geometry}}  \tn
% Row 0
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{air triangle = 1/2 * products of sides * sin (inside angle)} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{sin 150° = 1/2} \tn 
% Row Count 3 (+ 1)
% Row 2
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{sum of interior angles of polygon = (n-2)*180} \tn 
% Row Count 4 (+ 1)
% Row 3
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{Pythagorean triplets (c is odd, at least 2 prime numbers, 1 even number): (3,4,5) / (5,12,13) / (7,24,25) / (8,15,17) / (9,40,41) / (11,60,61) / (12,35,37)} \tn 
% Row Count 8 (+ 4)
% Row 4
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{area triangle = r (inserted circle) * semi-perimeter triangle} \tn 
% Row Count 10 (+ 2)
% Row 5
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{equation of a circle center (a,b): (x-a)\textasciicircum{}2\textasciicircum{} + (y-b)\textasciicircum{}2\textasciicircum{} = r\textasciicircum{}2\textasciicircum{}} \tn 
% Row Count 12 (+ 2)
% Row 6
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{equation of a line that crosses two intercepts: x/value x + y/value y = 1 so (value x)y + (value y)x = (value x)(value y)} \tn 
% Row Count 15 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}