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A mixture of oil, water, and vinegar contains 10% oil. After all of th

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A mixture of oil, water, and vinegar contains 10% oil. After all of th  [#permalink]

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23 Aug 2015, 12:55
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A mixture of oil, water, and vinegar contains 10% oil. After all of the water evaporates, what percent of the mixture is oil?

(1) Before the water evaporated, the mixture exactly filled a one liter bottle.

(2) Before the water evaporated, vinegar accounted for forty percent of the mixture.

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Re: A mixture of oil, water, and vinegar contains 10% oil. After all of th  [#permalink]

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23 Aug 2015, 17:48
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A mixture of oil, water, and vinegar contains 10% oil. After all of the water evaporates, what percent of the mixture is oil?

(1) Before the water evaporated, the mixture exactly filled a one liter bottle.

(2) Before the water evaporated, vinegar accounted for forty percent of the mixture.

Let L,V and W stand for proportions of oil, vinegar and water in the mixture. Given, L/T = 0.1 ---> L = 0.1T. % of L when all water evaporates ---> w=0 --> L/(L+V) = ?

Per statement 1, T=1 liter. Does not provide any information about the proportion of vinegar in the mixture. Not sufficient.

Per statement 2, V = 0.4T ----> ratio : L/(L+0.4T) and from L=0.1T ---> ratio = 0.1T/(0.1T+0.4T) ---> thus you get a sufficient answer. B is sufficient to answer.

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Re: A mixture of oil, water, and vinegar contains 10% oil. After all of th  [#permalink]

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16 Sep 2018, 18:19
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A mixture of oil, water, and vinegar contains 10% oil. After all of the water evaporates, what percent of the mixture is oil?

(1) Before the water evaporated, the mixture exactly filled a one liter bottle.

(2) Before the water evaporated, vinegar accounted for forty percent of the mixture.

$${\text{Before: x}}\,\,{\text{liters}}\,\,\,\,\left\{ \begin{gathered} {\text{oil}}\,\,:0.1x\,\,{\text{liters}} \hfill \\ water\,\,:\,\,k\left( {0.9x} \right)\,\,{\text{liters}} \hfill \\ vinegar\,\,:\,\,\,\left( {1 - k} \right)\left( {0.9x} \right)\,\,{\text{liters}}\,\, \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\left( {0 < k < 1} \right)$$

$${\text{After}}:\,\,\,{\text{x}}\left( {1 - 0.9k} \right)\,\,\,{\text{liters}}\,\,\,\left\{ \begin{gathered} {\text{oil}}\,\,:0.1x\,\,{\text{liters}} \hfill \\ water\,\,:\,\,0\,\,{\text{liters}} \hfill \\ vinegar\,\,:\,\,\,\left( {1 - k} \right)\left( {0.9x} \right)\,\,{\text{liters}}\,\, \hfill \\ \end{gathered} \right.$$

$$? = \frac{{0.1x}}{{x\left( {1 - 0.9k} \right)}} = \frac{{0.1}}{{1 - 0.9k}}\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\boxed{? = k}\,$$

$$\left( 1 \right)\,\,\,x = 1\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,\,k = 0.1 \hfill \\ \,{\text{Take}}\,\,\,k = 0.2 \hfill \\ \end{gathered} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{INSUFF}}.$$

$$\left( 2 \right)\,\,\,\,\,\frac{{\left( {1 - k} \right)\left( {0.9x} \right)\,\,}}{x} = \frac{2}{5}\,\,\,\,\, \Rightarrow \,\,\,\,k\,\,{\text{unique}}\,\,\,\,\, \Rightarrow \,\,\,\,{\text{SUFF}}.\,$$

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

Regards,
Fabio.
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Re: A mixture of oil, water, and vinegar contains 10% oil. After all of th &nbs [#permalink] 16 Sep 2018, 18:19
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