During the past week, a local medical clinic tested \(N\) in

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

During the past week, a local medical clinic tested \(N\) in

by VJesus12 » Sat Nov 30, 2019 5:08 am

During the past week, a local medical clinic tested \(N\) individuals for two infections. If \(\dfrac13\) of those tested had infection \(A\) and, of those with infection \(A\), \(\dfrac15\) also had infection \(B\), how many individuals did not have both infection \(A\) and \(B?\)

A. \(\dfrac{N}{15}\)
B. \(\dfrac{4N}{15}\)
C. \(\dfrac{14N}{15}\)
D. \(\dfrac{N}5\)
E. \(\dfrac{4N}5\)

[spoiler]OA=C[/spoiler]

Source: EMPOWERgmat

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Source: Beat The GMAT — Problem Solving | Sat Nov 30, 2019 5:08 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Mon Dec 02, 2019 9:30 am

Hi VJesus12,

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

Contact Rich at [email protected]

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8085; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: During the past week, a local medical clinic tested \(N\) in

by Scott@TargetTestPrep » Mon Jan 13, 2020 2:58 pm

VJesus12 wrote: ↑
Sat Nov 30, 2019 5:08 am
During the past week, a local medical clinic tested \(N\) individuals for two infections. If \(\dfrac13\) of those tested had infection \(A\) and, of those with infection \(A\), \(\dfrac15\) also had infection \(B\), how many individuals did not have both infection \(A\) and \(B?\)

A. \(\dfrac{N}{15}\)
B. \(\dfrac{4N}{15}\)
C. \(\dfrac{14N}{15}\)
D. \(\dfrac{N}5\)
E. \(\dfrac{4N}5\)

[spoiler]OA=C[/spoiler]

Source: EMPOWERgmat

We know that N/3 individuals had infection A, and 1/5 of those (1/5 x N/3 = N/15) had both infections A and B. Therefore, N - N/15 = 14N/15 individuals do not have both infections.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]