Problem Solving

Two glasses contain milk and water. In the first glass the ratio of milk to water is 3 : 2 and in the second glass the ratio of milk and water is reverse of that in first glass. What part of the mixture from first glass should be drawn out and added to the second glass, so that milk and water will be in equal quantities in the second glass?

A. 1/3
B. 1/4
C. 2/5
D. 1/2

gmatter2012 wrote:Two glasses contain milk and water. In the first glass the ratio of milk to water is 3 : 2 and in the second glass the ratio of milk and water is reverse of that in first glass. What part of the mixture from first glass should be drawn out and added to the second glass, so that milk and water will be in equal quantities in the second glass?

A. 1/3
B. 1/4
C. 2/5
D. 1/2

The question as written above does not have sufficient data to determine a unique solution. All answers are potentially correct. Please check the question from the official source.

eagleeye wrote:The question as written above does not have sufficient data to determine a unique solution. All answers are potentially correct. Please check the question from the official source.

Just a brief follow up - the problem is that we don't know how much liquid was in each glass to start - without that info (or at least the relative volumes of the glasses), there's no way to answer the question.

The fact that there are only 4 answer choices should also raise red flags, since a lack of 5 options clearly indicates that it's not a GMAT question.

lets say that both the glasses have same volume , does that help?

Here is my humble attempt to solve this:


M: W is 3:2

W: M is 2:3

to make the ratio W:M the same we need to add some extra water in the second glass 2+N:3 (as we can see that milk is more in the second glass)

2+N = 3. => N = 1...but 1 is 1/2 of the the water portion in the first glass..

I am assuming that the glasses are same size..

please tell me,if this looks incorrect.

gmatter2012 wrote:lets say that both the glasses have same volume , does that help?

Here is my humble attempt to solve this:


M: W is 3:2

W: M is 2:3

to make the ratio W:M the same we need to add some extra water in the second glass 2+N:3 (as we can see that milk is more in the second glass)

2+N = 3. => N = 1...but 1 is 1/2 of the the water portion in the first glass..

I am assuming that the glasses are same size..

please tell me,if this looks incorrect.

Since the ratios are RECIPROCALS, an equal amount from each glass is needed to yield a ratio of 1:1.
Thus, if each glass contains the same volume, ALL of the liquid in the first glass must be poured into the second glass to yield M:W = 1:1.
To illustrate:
Let the total volume of each glass = 5 units.
First glass = 3 units of milk and 2 units of water.
Second glass = 2 units of milk and 3 units of water.
Thus, pouring the entirety of the first glass into the second glass will yield a mixture of 5 units of milk and 5 units of water:
M:W = 5:5 = 1:1.

Another way to view the problem:
In the first glass, of every 5 units, 3 units are milk:
M = 3/5 = 60%.
In the second glass, of every 5 units, 2 units are milk:
M = 2/5 = 40%.
Thus, for milk to be 50% of the mixture -- HALFWAY between 60% and 40% -- we must combine EQUAL amounts of the 60% solution and the 40% solution:
(60+40)/2 = 50%.

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I greet