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For what percent of those tested for a certain infection [#permalink]

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06 Jan 2013, 02:59

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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.

Re: For what percent of those tested for a certain infection [#permalink]

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06 Jan 2013, 03:19

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gmatbull wrote:

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.

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

Re: For what percent of those tested for a certain infection [#permalink]

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09 Jan 2013, 10:25

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gmatbull wrote:

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.

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.

Re: For what percent of those tested for a certain infection [#permalink]

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18 Jan 2013, 12:17

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fozzzy wrote:

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

Attachment:

Infection tests.jpg [ 122.08 KiB | Viewed 6478 times ]

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)

Re: For what percent of those tested for a certain infection [#permalink]

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29 Jan 2014, 16:14

Hello from the GMAT Club BumpBot!

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Re: For what percent of those tested for a certain infection [#permalink]

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20 Apr 2015, 21:13

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: For what percent of those tested for a certain infection [#permalink]

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15 May 2015, 02:28

think simple.

we need to know the fraction of nagative result and the fraction of positive result. we also need to know for each fraction, how many percent of each fraction is fake.

that is all
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Re: For what percent of those tested for a certain infection [#permalink]

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23 Feb 2017, 08:06

Hello from the GMAT Club BumpBot!

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Re: For what percent of those tested for a certain infection [#permalink]

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01 Aug 2017, 07:00

Bunuel I understood the explanations but since from statement 1 the fraction for not having the infection of those tested positive is 1/8 then those tested positive and the result being accurate is 7/8 , So since the positive and accurate results are 7/8 then can we not consider 1/8 to be the fraction for negative and accurate.Thanks in advance

Re: For what percent of those tested for a certain infection [#permalink]

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14 Aug 2017, 09:57

(1) Of those who tested positive for the infection,1/8 did not have the infection: Insufficient data. No numerical/ratio info is given about those who tested positive. (2) Of those tested for the infection, 90 percent tested negative : 9/10 -ve & 1/10 +ve. No other information about the certainty is provided. hence insufficient.

1 & 2 together, 1/8 X 1/10 = 1/80 did not have but still tested +ve. 1/10-1/80 = 7/80 did have and tested positive. but no info is provided about those who tested negative. hence 1 & 2 together insufficient.

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.

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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