After 200 Grams of Water were Added to the 24%- Solution of Alcohol GMAT Problem Solving

Question: After 200 grams of water were added to the 24%- solution of alcohol, the strength of the solution decreased by one- third. What was the weight of the original 24% solution?

1. 180 grams
2. 220 grams
3. 250 grams
4. 350 grams
5. 400 grams

Correct Answer: E

Approach Solution (1):

Let the weight of 24% solution be x grams, then the weight of the alcohol in it would be 0.24x.

Next, as in the final solution strength decreased by\(\frac{1}{3}\) thus the strength of the final mixture became \(24*\frac{2}{3}=16\)%

Set the equation: 0.24x = 0.16 (x + 200), the weight of 16% alcohol in x + 200 grams of new solution comes only from (equals to) 24% alcohol in x grams of strong (initial) solution, as there is 0 grams of alcohol in wate r(0% alcohol solution).

Solving gives: x = 400

Approach Solution (2):

After the water has been added the concentration decrease by\(\frac{1}{3}\).

It means that \(\frac{1}{3}\) of the final mixture contains no alcohol and therefore is water.

Hence, 200g of water = \(\frac{1}{3}\) of final mixture

Final Mixture = 600g which 200g are water and 400 are the initial solution

“After 200 grams of water were added to the 24%- solution of alcohol, the strength of the solution decreased by one- third. What was the weight of the original 24% solution?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills.

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