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# What is the volume of milk present in a mixture of milk and water?

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Math Expert
Joined: 02 Sep 2009
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What is the volume of milk present in a mixture of milk and water?  [#permalink]

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16 Oct 2018, 23:47
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Difficulty:

35% (medium)

Question Stats:

73% (01:24) correct 27% (01:24) wrong based on 85 sessions

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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.

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Re: What is the volume of milk present in a mixture of milk and water?  [#permalink]

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17 Oct 2018, 03:12
Bunuel wrote:
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.

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.

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Re: What is the volume of milk present in a mixture of milk and water?  [#permalink]

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17 Oct 2018, 12:02
Bunuel wrote:
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.

$$\left\{ \matrix{ \,m\,\,:\,\,{\rm{milk}}\, \hfill \cr \,w\,\,\,:\,\,{\rm{water}}\,\,\, \hfill \cr} \right.\,\,\,\left( {\,{\rm{volumes}}\,\,{\rm{in}}\,\,{\rm{liters}}\,} \right)\,\,\,\,$$

$$? = m\,\,$$

$$\left( 1 \right)\,\,\,\,m + 2 = w\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {1,3} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 1\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {2,4} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 2\,\, \hfill \cr} \right.$$

$$\left( 2 \right)\,\,\,{m \over w} = {1 \over 2}\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {1,2} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 1\,\, \hfill \cr \,{\rm{Take}}\,\,\left( {m,w} \right) = \left( {2,4} \right)\,\,\,\,\,\, \Rightarrow \,\,\,? = 2\,\, \hfill \cr} \right.$$

$$\left( {1 + 2} \right)\,\,\,\,w\,\,\mathop = \limits^{\left( 2 \right)} \,\,2m\,\,\,\,\,\mathop \Rightarrow \limits^{\left( 1 \right)} \,\,\,\,\,m + 2 = 2m\,\,\,\,\, \Rightarrow \,\,\,\,m\,\,\,{\rm{unique}}$$

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

Regards,
Fabio.
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Re: What is the volume of milk present in a mixture of milk and water?   [#permalink] 17 Oct 2018, 12:02
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