VJesus12 wrote:In a product test of a common cold remedy, x percent of the patients tested experienced side effects from the use of the drug and y percent experienced relief of cold symptoms. What percent of the patients tested experienced both side effects and relief of cold symptoms?

(1) Of the 1,000 patients tested, 15 percent experienced neither side effects nor relief of cold symptoms.
(2) Of the patients tested, 30 percent experienced relief of cold symptoms without side effects.

The OA is E.

How can I show that the correct answer is the option E? What is the best approach? I'd be thankful for your explanation here.

You can ignore the variables here. There are four categories:
1) Only relief
2) Only side effects
3) both relief and side effects
4) neither relief nor side effects

We want the number for category 3.

Statement 1: This gives us category 4. (15% or 150 patients.) But now all we know that is that the other three categories sum to 85% or 850 patients. There's no way to know how that 850 is distributed among those categories. Not sufficient.

Statement 2: This gives us category 1. (30% or 300 patients.) Again, all we know is that the other categories will sum to 70%, or 700 patients. No way to know how that 700 is distributed.

Together: We'd have the following -
1) Only relief: 300 patients
2) Only side effects: ?
3) both relief and side effects: ?
4) neither relief nor side effects: 150 patients

We know that categories 1 and 4 sum to 450. So there are 550 more patients to account for. (or 55% of the remaining patients.) But there's no way to know how those 550 are distributed to categories 2 and 3. Could be 50 and 500, or 100 and 400, etc. So even together, the statements are not sufficient to answer the question. The answer is E
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