When you're posting, please post the source and the OA (with the answer hidden for spoilers). This way we can evaluate whether the question is in fact a good question.
This prompt, for example, is almost an exact plagiarization of OG #200, but with a bafflingly complicated question. The OG question simply asks for the new volume of water. This question asks what a ratio of the differences between various amounts "can be." That makes for a much more complicated and confusing question.
If the original ratio was 60 : 3 : 120, and the ratio of soap to alcohol was halved, we would take (3/60)(1/2) and get 3/120.
The ratio of alcohol to water tripled, though. Our original ratio was 60/120, or 1/2. Tripling that would give us a ratio of 3/2. So, if our new ratio unit of alcohol is 120, our ratio unit of water must be 80.
Now the ratio we're looking for is:
If we use the values we currently have, that would give us:
We would have 0 in the denominator, which is impossible.
So, let's try doubling all of the values in the new solution:
Now, our ratio is:
This would give us a ratio of 40 : 3. That's not an answer choice. We could try doubling the original instead, but again we get something that's not in the answer choices. This question would be FAR too laborious to actually solve on the real test. Mathematically, we could represent this ratio as:
There is no way to simplify this, and thus no reasonable way of reaching an answer.
The GMAT will never ask you to do something this complicated. Ignore this question, and ignore this source.
