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 infections \(A\) and \(B?\)
A. \(\dfrac{N}{15}\)
B. \(\dfrac{4N}{15}\)
C. \(\dfrac{14N}{15}\)
D. \(\dfrac{N}5\)
E. \(\dfrac{4N}5\)
Answer: C
Source: EMPOWERgmat
During the past week, a local medical clinic tested \(N\) individuals for two infections. If \(\dfrac13\) of those teste
This topic has expert replies
-
- Legendary Member
- Posts: 2214
- Joined: Fri Mar 02, 2018 2:22 pm
- Followed by:5 members
Total number of people tested for two infections = N
People with infection A = 1/3 of N = N/3
People with infection B and infection A = 1/5 of N/3 = N/15
Total no. of people who did not have both infection A and B
$$=\frac{N}{1}-\frac{N}{15}=\frac{15N-N}{15}=\frac{14N}{15}$$
Answer = C
People with infection A = 1/3 of N = N/3
People with infection B and infection A = 1/5 of N/3 = N/15
Total no. of people who did not have both infection A and B
$$=\frac{N}{1}-\frac{N}{15}=\frac{15N-N}{15}=\frac{14N}{15}$$
Answer = C
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7242
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Solution:M7MBA wrote: ↑Sun Nov 29, 2020 12:44 pmDuring 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 infections \(A\) and \(B?\)
A. \(\dfrac{N}{15}\)
B. \(\dfrac{4N}{15}\)
C. \(\dfrac{14N}{15}\)
D. \(\dfrac{N}5\)
E. \(\dfrac{4N}5\)
Answer: C
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]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews