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During the past week, a local medical clinic tested N individuals for

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During the past week, a local medical clinic tested N individuals for  [#permalink]

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New post Updated on: 17 Aug 2015, 02:04
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During the past week, a local medical clinic tested N individuals for two infections. If 1/3 of those tested had infection A and, of those with infection A, 1/5 also had infection B, how many individuals did not have both infection A and B?

A. N/15
B. 4N/15
C. 14N/15
D. N/5
E. 4N/5

Originally posted by asaar on 17 Aug 2015, 00:13.
Last edited by Bunuel on 17 Aug 2015, 02:04, edited 1 time in total.
Renamed the topic and edited the question.
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Re: During the past week, a local medical clinic tested N individuals for  [#permalink]

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New post 17 Aug 2015, 00:33
Bunuel Please help explain this sum

asaar wrote:
During the past week, a local medical clinic tested N individuals for two infections. If 1/3 of those tested had infection A and, of those with A, 1/5 also had infection B, how many individuals did not have both infections A & B?

A. N/15
B. 4N/15
C. 14N/15
D. N/5
E. 4N/5
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Re: During the past week, a local medical clinic tested N individuals for  [#permalink]

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New post 17 Aug 2015, 02:10
asaar wrote:
During the past week, a local medical clinic tested N individuals for two infections. If 1/3 of those tested had infection A and, of those with infection A, 1/5 also had infection B, how many individuals did not have both infection A and B?

A. N/15
B. 4N/15
C. 14N/15
D. N/5
E. 4N/5


1/3 of tested had infection A, thus N/3 had infection A;
Of those with infection A, 1/5 also had infection B, thus 1/5*N/3 = N/15 had both infections A and B.

Therefore, N - N/15 = 14N/15 did not have both infection A and B.

Answer: C.
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Re: During the past week, a local medical clinic tested N individuals for  [#permalink]

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New post 17 Aug 2015, 02:31
Bunuel wrote:
asaar wrote:
During the past week, a local medical clinic tested N individuals for two infections. If 1/3 of those tested had infection A and, of those with infection A, 1/5 also had infection B, how many individuals did not have both infection A and B?

A. N/15
B. 4N/15
C. 14N/15
D. N/5
E. 4N/5


1/3 of tested had infection A, thus N/3 had infection A;
Of those with infection A, 1/5 also had infection B, thus 1/5*N/3 = N/15 had both infections A and B.

Therefore, N - N/15 = 14N/15 did not have both infection A and B.

Answer: C.


Thanks a lot &Bunuel
Does the statement "..1/5 also had infection B" warrant that that was the only no. of people with infection B? Or that there were no other people infected only with B but not with A?
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Re: During the past week, a local medical clinic tested N individuals for  [#permalink]

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New post 17 Aug 2015, 02:39
asaar wrote:
Bunuel wrote:
asaar wrote:
During the past week, a local medical clinic tested N individuals for two infections. If 1/3 of those tested had infection A and, of those with infection A, 1/5 also had infection B, how many individuals did not have both infection A and B?

A. N/15
B. 4N/15
C. 14N/15
D. N/5
E. 4N/5


1/3 of tested had infection A, thus N/3 had infection A;
Of those with infection A, 1/5 also had infection B, thus 1/5*N/3 = N/15 had both infections A and B.

Therefore, N - N/15 = 14N/15 did not have both infection A and B.

Answer: C.


Thanks a lot &Bunuel
Does the statement "..1/5 also had infection B" warrant that that was the only no. of people with infection B? Or that there were no other people infected only with B but not with A?


To get the number of people who did not have both infection A and B, only thing we need to know is the number of people who had both infection A and B, which is N/15.
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Re: During the past week, a local medical clinic tested N individuals for  [#permalink]

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New post 13 Mar 2016, 07:45
Hi brunel, could you tell me what is the question to calculate the individuals "?" in table? (Please see attachment file.) Thank you.
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During the past week, a local medical clinic tested N individuals for  [#permalink]

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New post 04 Jun 2017, 21:40
oanhnguyen1116 wrote:
Hi brunel, could you tell me what is the question to calculate the individuals "?" in table? (Please see attachment file.) Thank you.


Hi, 1 year and a half passed and I'm not sure you will need it now lol. Just wanna share my thoughts.

IMO, the answer to your question (NOT A + NOT B) cannot be deduced from information given. If any, we could figure out 2 values (A + NOT B) and (NOT A) only. In order to calculate (NOT A + NOT B), at least, we need one more value among 3 following (B + NOT A), (B), or (NOT B).

By the way, your concern (NOT A + NOT B) is actually not what the question is asking. In fact, the question asks about "what is not (A+B)", in other words, what is " Total - (A+B)". FYI, it is the sum of 3 values (NOT A + B), (NOT B + A), and (NOT A + NOT B). However, we don't need to calculate this sum, because there is not enough hint to solve that way. We can just solve the question very fast by calculate this way [Total - (A+B)] = N - N/15 = 14N/15.
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Re: During the past week, a local medical clinic tested N individuals for  [#permalink]

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New post 02 Dec 2019, 15:26
Hi All,

We're told that a local medical clinic tested N individuals for two infections; 1/3 of those tested had infection A and, of those with infection A, 1/5 also had infection B. We're asked for the number of individuals who did NOT have BOTH infection A and B. This question can be solved in a couple of different ways, including by TESTing VALUES.

The 5 answer choices have a common denominator of 15, so that will likely be a good number to TEST.

IF.... N = 15
then (1/3)(15) = 5 people had infection A
and (1/5)(5) = 1 person ALSO had infection B

This means that 15 - 1 = 14 people did NOT have BOTH infections, so we're looking for an answer that equals 14 when N = 15. There's only one answer that matches...

Final Answer:

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Re: During the past week, a local medical clinic tested N individuals for   [#permalink] 02 Dec 2019, 15:26
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