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

Question

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.

ENGRTOMBA2018 · Accepted Answer

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.

B is the correct answer.

fskilnik · Answer

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

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

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

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

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

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

Regards,
Fabio.

dvishal387 · Answer

Since the mixture contains oil, water, and vinegar of which 10% is oil. So, 90% is water+vinegar.
When water evaporates only water+vinegar remains.
From stat 1 we cannot conclude the volume of vinegar hence not suff.
In stat 2 we are given % of vinegar. So we can say that since water=50% ,vinegar=40% and oil=10%
when water evaporates we can calculate % of oil.Hence B is correct choice.

gmexamtaker1 · Answer

Gladiator59

Hey gladi could you please shed some light on my issue on this one?
My query is that do the proportions remain the same after water evaporation? I mean beforehand vinegar accounted for 40% of the mixture and oil 10% but after the water is evaporated will it still account for 40% ?

For instance lets say a mixture which is consisted of a, b and c liquids a=5 b=4 c=5 at first b accounts for 40% of the mixture a+b+c but when c is removed b accounts for 80% of the mixture.

Gladiator59 · Answer

Hi there  UNSTOPPABLE12 ,

To answer your question - No. Think of it like this - Statement B says that Vinegar is 40% while oil is 10%.. so water will be the remaining or 50% of the mixture.

Assuming that only water evaporates -  only vinegar and oil will remain...
So now vinegar will be 40% out of 50% total or Vinegar will be 80% of the new mixture whereas oil will be 20%.  Their relative percentages double as the mixture becomes half of original

Hope it is clear.

gmexamtaker1 · Answer

Gladiator59

Thanks gladi brilliant remarks as usual.

Hoozan · Answer

Bunuel  please could you correct me in my understanding

(1) No information on the elements of the mixture - Insuff

(2) let's say the total volume was 100. So oil : water : vinegar = 10 : 40 : 60

Now 60 (water) evaporates. So we are left with 10 : 40 ---> Total - 50

% oil = 1/5 * 100 = 20% (B)

WheatyPie · Answer

This is not a great question - if the water evaporates, a large but unspecified portion of the vinegar would evaporate as well. The answer to the question as written should be E. We shouldn't have to make unrealistic assumptions to answer a question.

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