EgmatQuantExpert wrote:

A solution consists of only water and alcohol such that the ratio of alcohol to water in the solution is 7:3. How much amount of water should be added to the solution (in mililiters) so that the resulting solution contains 60% alcohol?

1. Total quantity of the resulting solution is 350 mililiters.

2. The original solution contains 10.5 mililiters of alcohol for every 4.5 mililiters of water.

In the solution below, the unit considered is always milliliters.

Let´s use the

k technique, one of the best tools of our method when dealing with ratios/proportions!

\(\left\{ \matrix{

\,{\rm{water}}\,\,\left( w \right)\,\,\, = \,\,3k \hfill \cr

\,{\rm{alcohol}}\,\,\left( a \right) = 7k \hfill \cr} \right.\,\,\,\,\,\,\left( {k > 0} \right)\,\,\,\,\,\,\,\,\,\,\, \to \,\,\,\,\,\,\,\,\,\left\{ \matrix{

\,{\rm{water}}\,\,\left( w \right)\,\,\, = \,\,3k + x \hfill \cr

\,{\rm{alcohol}}\,\,\left( a \right) = 7k \hfill \cr} \right.\,\,\,\,\,\,\,{\rm{such}}\,\,{\rm{that}}\,\,\,\,\,\,{{7k} \over {10k + x}} = {3 \over 5}\,\,\,\,\,\,\,\,\,\,\mathop \Leftrightarrow \limits^{{\rm{cross - multiply}}} \,\,\,\,\,\,5k = 3x\,\,\,\,\,\left( * \right)\)

\(? = x\)

\(\left( 1 \right)\,\,\,10k + x = 350\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,6x + x = 350\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{SUFF}}.\,\,\,\,\,\,\,\)

\(\left( 2 \right)\,\,{a \over w} = {{10.5} \over {4.5}}\,\,\left( { = {{105} \over {45}} = {7 \over 3}} \right)\,\,\,{\rm{already}}\,\,{\rm{known}}\,\,{\rm{pre - statements}}\,\,\,\,\, \Rightarrow \,\,\,\,\,{\rm{INSUFF}}.\,\,\,\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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