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

Question

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

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

Bunuel · Answer

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.

asaar · Answer

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?

Bunuel · Answer

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.

oanhnguyen1116 · Answer

Hi  brunel , could you tell me what is the question to calculate the individuals "?" in table? (Please see attachment file.) Thank you.

Lucy Phuong · Answer

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   = N - N/15 = 14N/15.

EMPOWERgmatRichC · Answer

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:  C

GMAT assassins aren't born, they're made, 
Rich

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards