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For what percent of those tested for a certain infection was

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For what percent of those tested for a certain infection was

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For what percent of those tested for a certain infection was the test accurate; that is, positive for those who had the infection and negative for those who did not have the infection?

(1) Of those who tested positive for the infection,1/8 did not have the infection.
(2) Of those tested for the infection, 90 percent tested negative.

OA E

Source: GMAT Prep

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The best way to approach this question is with a DOUBLE SET MATRIX.

There are 2 relevant questions here:
1. Does a person have the infection or not?
2. Have they tested positive or not?



Accurate results will be those who (had it & tested positive) + (didn't have it and tested negative) as a percentage of all people tested.



Now apply the information from the statements one at a time:

(1) Of those who tested positive for the infection,1/8 did not have the infection.
Let x = total of those who tested positive. Convert 1/8 to 12.5%:



This is clearly not sufficient to answer the question.

Note: be sure to erase info from statement 1 before evaluating statement 2.

(2) Of those tested for the infection, 90 percent tested negative.



This tells us nothing about who had / didn't have the infection. Insufficient.

(1) & (2) Together:
We now know that x = 10% of the total:



We still have no information about those who tested negative & didn't have the infection, though. So we do not have sufficient information.

The answer is E.

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Harvard Graduate School of Education


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