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On GMAT mixture problems with two elements, track both the component and the total. Build a simple content table, update after each add or remove, then set the ratio or equation. Respect the new base each step to avoid errors and finally solve cleanly, carefully.
Mixture and solution problems are a classic part of aptitude and GMAT-style quantitative reasoning and should be a part of your GMAT prep. They test your ability to balance percentages, proportions, and logical structure. What makes them tricky is that whenever you add or remove one component, the total also changes, and with it, the percentage distribution shifts. If you miss this detail, you will fall into the trap of wrong answers. A clean and reliable way to handle such questions is to create a simple table of content. This approach prevents confusion and keeps track of every element clearly.
Every two-element mixture has three moving parts: the amount of component A, the amount of component B, and the total.
The total equals A + B.
The percent of A equals (A / total) * 100.
When you add or remove any component, update both the affected amount and the new total. If you replace, one goes out and the other comes in.
Build a small content table for each step and keep the base current after every change.
From the target percent or ratio, write a clear equation and solve.
Assuming base 100 often removes variables and keeps arithmetic simple.
200 liters solution contains 40% alcohol. How much alcohol should be added to make it 50% alcohol solution?
The solution of 200 liters contains 40% alcohol.
That means 80 liters of alcohol and 120 liters of water.
Now, if we want this solution to become 50% alcohol, we add alcohol, not water.
Let us call the added alcohol X liters.
The new alcohol quantity becomes 80 + X, and the new total volume becomes 200 + X.
Setting up the equation (80 + X)/(200 + X) = 0.5 gives X = 40.
So, 40 liters of alcohol must be added.
A smarter observation is that if the solution must be 50% alcohol, then it must also be 50% water.
Since water is 120 liters, which is 50% of the total, the total solution should be 240 liters.
From 200 to 240, the increase is 40 liters of alcohol.
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500 liters solution contains 40% alcohol. How much water should be added to make it 30% alcohol solution?
500 liters of solution with 40% alcohol, meaning 200 liters alcohol and 300 liters water.
If we need to reduce alcohol concentration to 30%, then water must be added.
Let the added water be X liters.
The new total is 500 + X, alcohol remains 200, and water becomes 300 + X.
The equation is 200/(500 + X) = 0.3.
Solving gives X = 166.67 liters (or 500/3).
Therefore, 166.67 liters of water must be added.
Mixture problems always demand tracking both the total and the changed part. By organizing data into a table and respecting the new base after each change, you can solve these questions quickly and confidently. Regular practice through GMAT practice tests makes this process intuitive.
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