jjjinapinch 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.

Official Guide question
Answer: E

Say,

the number of patients tested experiencing ONLY relief of cold symptoms = c;
the number of patients tested experiencing ONLY side effects = s;
the number of patients tested experiencing BOTH relief of cold symptoms AND side effects = b; and
the number of patients tested experiencing NEITHER relief of cold symptoms NOR side effects = n

Thus, c + s + b + n = 100

We have to get the value of b.

Statement 1: Of the 1,000 patients tested, 15 percent experienced neither side effects nor relief of cold symptoms.

This gives n = 15. Can't get b. Insufficient!

Statement 2: Of the patients tested, 30 percent experienced relief of cold symptoms without side effects.

This gives c = 30. Can't get b. Insufficient!

Statement 1 & 2:

We have n = 15 and c = 30, thus,

c + s + b + n = 100 => 30 + s + b + 15 = 100 => b = 55 - s. Can't get b. Insufficient!

The correct answer: E

Hope this helps!

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HI jjjinapinch,

This question is an example of a standard Overlapping Sets question. It can be solved using the Overlapping Sets Formula or with the Tic-Tac-Toe Board/Matrix Grid. Here's how you can use the Formula to solve it:

We're told that in a product test of a common cold remedy, X% of the patients tested experienced side effects from the use of the drug and Y% experienced relief of cold symptoms. We're asked for the PERCENT of the patients tested who experienced BOTH side effects and relief of cold symptoms.

The Overlapping Sets Formula is...
Total = (Group 1) + (Group 2) - (Both) + (Neither)

In this question, Group 1 would be those who experienced side effects and Group 2 would be those who experienced relief of symptoms.

1) Of the 1,000 patients tested, 15 percent experienced neither side effects nor relief of cold symptoms.

Using the above Formula and the information in Fact 1, we have....
100% = (X%) + (Y%) - (Both) + (15%)

Without knowing the values of X and Y, there's no way to determine the percent for the "Both" group.
Fact 1 is INSUFFICIENT

2) Of the patients tested, 30 percent experienced relief of cold symptoms without side effects.

Using the above Formula and the information in Fact 2, we have....
100% = (X%) + (30%) - (Both) + (Neither)

Without knowing the values of X and "Neither" group, there's no way to determine the percent for the "Both" group.
Fact 2 is INSUFFICIENT

Combining the information in both Facts, we would have....
100% = (X%) + (30%) - (Both) + (15%)
55% = (X%) - (Both)
Without knowing the value of X, there's no way to determine the percent for the "Both" group.

Final Answer: E

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