Hi sukhman,
If this were actually a GMAT question, then it would use the word 'approximately' in its wording. This question really comes down to staying organized and keeping track of the ratios at each 'step' of the calculation.
To start, we have 10 liters of water. 3 liters of water are removed and 3 liters of milk are put in, which gives us:
7 liters water and 3 liters milk.
With the 2nd removal of 3 liters, we get a 'mix' of water and milk removed. Since we're talking about 30% of the mixture, we're taking out...
30% of 7 liters of water = 2.1 liters of water removed
30% of 3 liters of milk = 0.9 liters of milk removed
THEN 3 liters of milk are put back in, which gives us:
4.9 liters of water and 5.1 liters of milk.
With the 3rd removal of 3 liters, we again get a 'mix' of water and milk removed. Since we're talking about 30% of the mixture, we're taking out...
30% of 4.9 liters of water = 1.47 liters of water removed
30% of 5.1 liters of milk = 1.53 liters of milk removed
THEN 3 liters of milk are put back in, which gives us:
3.43 liters of water and 6.57 liters of milk.
That gives us an approximate ratio of 7 to 13.
Final Answer: E
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Given the answer choices, I suspect that the question stem should read as follows:
At the end of the third process, what is the APPROXIMATE ratio of water to milk?
Each time 3 liters are removed from the 10-liter vessel, 7/10 of the water in the vessel remains.
Since the answer choices are RATIOS, the capacity of the vessel can be ANY VALUE.
To make the math easier, let the capacity of the vessel = 1000 liters.
Remaining water at the end of the 1st process = (7/10)(1000) = 700 liters.
Remaining water at the end of the 2nd process = (7/10)(700) = 490 liters.
Remaining water at the end of the 3rd process = (7/10)(490) ≈ 350 liters.
Since the vessel now contains about 350 liters of water, the approximate amount of milk in the vessel = 1000-350 = 650 liters.
Approximate resulting ratio of water to milk:
350:650 = 7:13.
The correct answer is E.
At the end of the third process, what is the APPROXIMATE ratio of water to milk?
Each time 3 liters are removed from the 10-liter vessel, 7/10 of the water in the vessel remains.
Since the answer choices are RATIOS, the capacity of the vessel can be ANY VALUE.
To make the math easier, let the capacity of the vessel = 1000 liters.
Remaining water at the end of the 1st process = (7/10)(1000) = 700 liters.
Remaining water at the end of the 2nd process = (7/10)(700) = 490 liters.
Remaining water at the end of the 3rd process = (7/10)(490) ≈ 350 liters.
Since the vessel now contains about 350 liters of water, the approximate amount of milk in the vessel = 1000-350 = 650 liters.
Approximate resulting ratio of water to milk:
350:650 = 7:13.
The correct answer is E.
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