In a product test of a common cold remedy, x percent of the patients

This is an overlapping set question. A great way to solve this problem is to set up a table with two main categories: experienced side effects and experienced relief from cold symptoms. More specifically, our table will be labeled as follows:

1) Side Effects

2) No Side Effects

3) Relief

4) No Relief

We are given that x percent of the patients tested experienced side effects from the use of the drug and y percent experienced relief from cold symptoms.

We need to determine what percentage of the patients tested experienced both side effects and relief from cold symptoms.

Let’s fill all of this into a table where each entry is the percentage of the total patients tested.



Statement One Alone:

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

With the information from statement one, we can put 15 in the “No Side Effects and No Relief” cell and, subsequently, the values (in terms of x and y) in the other three cells of our table.



We see that the percentage of patients tested who experienced side effects and relief from cold symptoms is (x + y - 85) percent. However, since we know neither the value of x nor the value of y, we do not have enough information to determine the percentage of people who both experienced relief and had side effects. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

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

With the information from statement two, we can enter 30 in the “Relief and No Side Effects” cell and, subsequently, the values (in terms of x and y) in the other three cells of our table.



We see that the percentage of patients tested who experienced both side effects and relief from cold symptoms is (y - 30) percent. However, since we do not know the value of y, we do not have enough information to determine the percentage of people who both experienced relief and had side effects. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, we have the following:



As we can see, from the “Side Effects” column, we have (y - 30) + (85 - y) = x, and from the “No side Effects” column, we have 30 + 15 = 100 - x. From either equation, we can determine that x = 55. However, since we still don’t know the value of y, we do not have enough information to determine the percentage of people who both experienced relief and had side effects.

Answer: E
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Hi All,

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:

GMAT assassins aren't born, they're made,
Rich

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

total probability = 1.
150 no effects
300 relief
no data about side effects.

E is the answer.

I understood that Y% = (Side Effect w Relief) + (Side Effect without Relief)

Is this a situation that probability rules apply? So...
30% = (1-X%) * Y%

Hi

I am not really sure what you were asking, but I will try to explain. If we assume z% to be those which are common in both (i.e., side effect w relief). then:-

x% = (side effect without relief) + z%
y% = (relief without side effect) + z%
Second statement tells us that (relief without side effect) = 30%, so it makes
y% = 30% + z%

So we can write 30% as = y% - z%

But I am not sure how you have come up with 30% = (1-X%) * Y%

Could this problem be solved using a venn diagram?

Hi

Yes I think we can do this using Venn Diagram also.

I have attempted to do that in the attached pic.

The Overlapping Sets Formula for two:
Total = (Group 1) + (Group 2) - Both(b) + Neither(n)
Here, 100% = x% + y% -b+n


1) 100% (1000) = x% + y% -b+ 15% [x and y are unknown] insufficient.

2) 100% (1000) = x% + 30% - b + 15% [x and b are unknown] insfufficient.


Combining the information in both Facts, we would have....
100% = (X%) + (30%) - (Both) + (15%)
55% = (X%) - (Both)

Still x is unknown.

Answer. E

ScottTargetTestPrep For statement 2 combined, after we get x=55, why can't we plug into (y - 30) + (85 - y) = x to solve for y?

If we were to substitute x = 55 in the equation (y - 30) + (85 - y) = x, then y and -y would cancel out, and we would be left with 55 = 55. The value of x = 55 is actually derived from the equation (y - 30) + (85 - y) = x; hence, it is no surprise that substituting x = 55 back into the same equation tells us nothing new.
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Each statement alone is clearly insufficient.

Combined:

Total = (x) + (y) - (x+y) + (Neither)
1,000 = (x) + (300) - (x+y) + (150)
500 = (x) - (x+y)

We can't determine (x+y); INSUFFICIENT.

Answer is E.
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Answer: Option E

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