For what percent of those tested for a certain infection was the test

I think this problem goes beyond 2 variables. You can use the overlapping sets table, as there can be 4 possibilities for patient to be infected/not-infected:
Tests are Positive & Accurate -> Patient is infected
Tests are Positive & Inaccurate -> Patient is NOT infected
Tests are Negative & Accurate -> Patient is NOT infected
Tests are Negative & Inaccurate -> Patient is infected

Our objective is to identify the value of cell marked in yellow (i.e. Accurate tests) hence find its ratio to TOTAL tests (i.e. % Accuracy)

(1) Of those who tested positive for the infection,1/8 did not have the infection.
INSUFFICIENT: Refer to the diagram, this gives no info to derive the value for yellow cell (i.e. Accurate tests)
(2) Of those tested for the infection, 90 percent tested negative.
INSUFFICIENT: Refer to the diagram, this gives no info to derive the value for yellow cell (i.e. Accurate tests)

Combining (1) & (2)
INSUFFICIENT: Even after combining the statements are INSUFFICIENT to derive the value for yellow cell (i.e. Accurate tests)

Hence Choice(E) is the answer.

For my simplicity I took a smart number as 80.
In the attached diagram, we are supposed to find the red area.

We don't have sufficient information to find the red area.
+1E

I approached as shown below:

The question asks for %age of accuracy.
1. This option is doesn't give complete information. It says 1/8th did not have infection, but OUT OF HOW MANY POSITIVES. And another detail that is missing here is about accuracy of those who are tested negative. so, INSUFFICIENT.

2. 90% are negative, but what is the accuracy of those tested negative/positive? This information is not present. so, INSUFFICIENT.

(1+2) for positives accuracy is 1/8th of 10% (100 minus 90). For negatives, we dont know accuracy. so, INSUFFICIENT.

Answer E

isn't this question asking for 2 variables? I got the answer E

Statement One Alone:

Of those who tested positive for the infection,1/8 did not have the infection.

We can let the total people who tested positive for the infection = p; thus, (7/8)p tested positive and had the infection. However, since we know nothing about those who tested negative, we cannot determine an answer. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

Of those tested for the infection, 90 percent tested negative.

Using the information in statement two, we know that 90 percent tested negative and 10 percent tested positive. However, we still do not have enough information to answer the question.

Statements One and Two Together:

Using both statements, we still do not have information about those who did not have the infection and tested negative; we cannot determine an answer.

Answer: E
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hey there

why no one used overlapping sets formula ?

chetan2u, VeritasKarishma any idea when do we need to use matrix vs overlapping circles ?


have a good Sunday

Hi...

Overlapping sets is best used when you have two unknowns..
Say in this question we just had positive and accurate results.so this would have meant two circles one for accurate and other for positive and overlapped area would give us the positive results that were accurately determined.
However here there are four unknowns - accurately determined positive, inaccurately determined positive, accurately determined negative and inaccurately determined negative.
So a matrix 2*2 is the best here
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