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For what percent of those tested for a certain infection

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by Needgmat » Mon Sep 26, 2016 8:18 am
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 who tested for the infection, 90 percent tested negative.

OAE

Please explain.

Many thanks in advance
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Source: — Data Sufficiency |

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by [email protected] » Mon Sep 26, 2016 10:08 am
Hi Needgmat,

This DS question essentially refers to 4 different types who were tested for an infection:

1) Tested positive AND were positive
2) Tested positive BUT were negative

3) Tested negative AND were negative
4) Tested negative BUT were positive

The question asks us what percent of the total were groups 1 and 3 (combined).

To properly answer this question, we would need LOTS of information.

1) Of those who tested positive for the infection, 1/8 did not have the infection.
Fact 1 gives us a breakdown of those who tested positive, but doesn't give us any sense of how many (or even what percent) Tested positive or negative. Fact 1 is INSUFFICIENT.

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

Fact 2 gives us 90% tested negative, thus 10% tested positive, but doesn't give us any info on the "accuracy" of the tests.
Fact 2 is INSUFFICIENT

Combined, we're still missing the "breakdown" for those who tested negative, so there's no way to answer the question.
Combined, INSUFFICIENT

Final Answer: E

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by Needgmat » Mon Sep 26, 2016 9:34 pm
Hi Rich ,

Thank you so much for your explanation.

Is there any algebraic approach to solve this question.

Many thanks in advance.

Kavin
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by [email protected] » Tue Sep 27, 2016 10:36 am
Hi Kavin,

Yes, you could set this up algebraically, but you'd have to keep track of 4 different variables. Here's how:

A = Percent who tested positive AND were positive
B = Percent who tested positive BUT were negative
C = Percent who tested negative AND were negative
D = Percent who tested negative BUT were positive

100% = A + B + C + D

The question asks us for the sum of A and C.

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

This Fact refers to a sub-group (A+B) and tells us that 1/8 of this group did not have the infection. With this information, we now know that...

B = (1/8)(A + B)
7B = A
B = A/7

100% = A + A/7 + C + D

We still don't know the value of any of the variables, so we cannot answer the question.
Fact 1 is INSUFFICIENT

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

With this information, the equation becomes...

100% = A + B + 90%

We cannot determine the value of "A" or "C", so we cannot answer the question.
Fact 2 is INSUFFICIENT

Combined, we would have...

100% = A + (A/7) + 90%

We can figure out the value of 'A', but we still don't know the value of 'C'
Combined, INSUFFICIENT

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by Jeff@TargetTestPrep » Tue Jan 02, 2018 8:56 am
Needgmat 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 who 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

Jeffrey Miller
Head of GMAT Instruction
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