Solutions A, B, and C are mixed. What is the ratio of alcohol and

Question

Solutions A, B, and C are mixed. What is the ratio of alcohol and water in the resultant solution?
 
(1) A contains 20% alcohol, B contains 20% alcohol, and C contains 80% water.
(2) All solutions contain only water and alcohol.

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sujoykrdatta · Answer

This is a classic trap question

(1) Not sufficient since we have no idea of the constituents (for example, A and B might not have water and C might not have alcohol) (2) Not sufficient since we have no idea of the concentration of alcohol / water in the solutions Combining 1 and 2: If you look carefully, each of A, B and C have only alcohol and water and the percent of alcohol in each of A, B and C is 20% (Note: Percent of alcohol in C is 100 - 80 = 20%) Thus, the quantities of A, B and C are irrelevant and the final mixture will simply have 20% alcohol and 80% water => Ratio = 1:4 Answer C (combining both statements)

ExpertsGlobal5 · Answer

Explanation Video:

https://www.youtube.com/watch?v=ogPqEpfTerQ

rashminuligonda · Answer

But what about proportion of each mixture? What if A is 2 portions, B is 1 and C is one? In the solution everything of equal proportions is assumed. I think tahts loophole on question

Bunuel · Answer

Notice that (1) says:  A contains    20% alcohol   , B contains    20% alcohol   , and C contains    80% water   . 
 
So:

A:   20% alcohol  , and   80% water  .
 B:   20% alcohol  , and   80% water  .
 C:   80% water  , and   20% alcohol  .

Once we combine the statements, A, B, and C all have the same composition: 20% alcohol and 80% water. So no matter how much of each solution is mixed, the resulting mixture will still be 20% alcohol and 80% water.

egmat · Answer

Hi rashminuligonda,

Good instinct to worry about proportions, because usually they matter a lot in a mixture problem. But here's the neat part:  when all three solutions have the  same  alcohol concentration, the proportions don't matter at all.

Remember what combining the statements gives us: A is  20%  alcohol, B is  20%  alcohol, and C - since it's  80%  water and (from statement 2)  only  water and alcohol - is also  20%  alcohol. So every solution is  20%  alcohol /  80%  water.

Now use your own example,  2  parts A,  1  part B,  1  part C (say  200  ml,  100  ml,  100  ml =  400  ml total):

- Alcohol =  20%  of each =  40 + 20 + 20 = 80 ml 
- Water =  160 + 80 + 80 = 320 ml 
- Ratio =  80 : 320 = 1 : 4

The solution never assumed equal portions - it just didn't need the portions at all.

Try a totally different mix , say  3  parts A,  5  parts B,  1  part C ( 300 ,  500 ,  100  ml =  900  ml):

- Alcohol =  20%  of  900  =  180 ml 
- Water =  80%  of  900  =  720 ml 
- Ratio =  1 : 4  again

Why it always lands on  1:4 : if every ingredient is exactly  20%  alcohol, the whole pot is  20%  alcohol no matter how you scale each one - you're just averaging  20%  with  20%  with  20% , which is always  20% .

So there's no loophole. The proportions would only change the answer if the concentrations differed. Since they're identical, the mix is locked at  1:4 , and that's exactly why both statements together are  sufficient  - answer  C .

Answer: C

Solutions A, B, and C are mixed. What is the ratio of alcohol and

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GMAT Data Sufficiency (DS) Questions

Solutions A, B, and C are mixed. What is the ratio of alcohol and

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My Rewards