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What is the volume of milk present in a mixture of milk and water?
(1) When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.
(2) The initial mixture had 2 parts of water to 1 part milk.
(1) When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.
(2) The initial mixture had 2 parts of water to 1 part milk.
17 Oct 2018, 04:12
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Bunuel
What is the volume of milk present in a mixture of milk and water?
(1) When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.
(2) The initial mixture had 2 parts of water to 1 part milk.
(1) When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.
(2) The initial mixture had 2 parts of water to 1 part milk.
We'll translate our question stem into equations, so we understand what we need to do.
This is a Precise approach.
(1) This yields m+2 = w, which we cannot use to solve for m.
Insufficient.
(2) This yields m = 2w, which we also cannot use to solve for m.
Insufficient.
Combined.
2 equations with 2 variables --> one solution!
Sufficient.
(C) is our answer.
17 Oct 2018, 13:02
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Bunuel
What is the volume of milk present in a mixture of milk and water?
(1) When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.
(2) The initial mixture had 2 parts of water to 1 part milk.
\(\left\{ \matrix{\\(1) When 2 liters of milk is added to the mixture, the resultant mixture has equal quantities of milk and water.
(2) The initial mixture had 2 parts of water to 1 part milk.
\,m\,\,:\,\,{\rm{milk}}\, \hfill \cr \\
\,w\,\,\,:\,\,{\rm{water}}\,\,\, \hfill \cr} \right.\,\,\,\left( {\,{\rm{volumes}}\,\,{\rm{in}}\,\,{\rm{liters}}\,} \right)\,\,\,\,\)
\(? = m\,\,\)
\(\left( 1 \right)\,\,\,\,m + 2 = w\,\,\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {1,3} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 1\,\, \hfill \cr \\
\,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {2,4} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 2\,\, \hfill \cr} \right.\)
\(\left( 2 \right)\,\,\,{m \over w} = {1 \over 2}\,\,\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {1,2} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 1\,\, \hfill \cr \\
\,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {2,4} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 2\,\, \hfill \cr} \right.\)
\(\left( {1 + 2} \right)\,\,\,\,w\,\,\mathop = \limits^{\left( 2 \right)} \,\,2m\,\,\,\,\,\mathop \Rightarrow \limits^{\left( 1 \right)} \,\,\,\,\,m + 2 = 2m\,\,\,\,\, \Rightarrow \,\,\,\,m\,\,\,{\rm{unique}}\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
