All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?
A. 30
B. 51
C. 60
D. 85
E. 11
OA is B
OA says B but my answer was option A.Pls an Expert is needed here. Thanks
Arithmetic
This topic has expert replies
-
- Moderator
- Posts: 772
- Joined: Wed Aug 30, 2017 6:29 pm
- Followed by:6 members
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7243
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
BTGmoderatorRO wrote:All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?
A. 30
B. 51
C. 60
D. 85
E. 11
OA is B
OA says B but my answer was option A.Pls an Expert is needed here. Thanks
We can let d, c, b, and n be the number of students in the band, orchestra, both band and orchestra, and school, respectively. We can create the equations:
d + c - b = n,
(d - b) + (c - b) = 0.8n,
d = 119,
and
d - b = 0.5n
Substituting the fourth equation into the second equation, we have:
0.5n + (c - b) = 0.8n
c - b = 0.3n
Substituting the above in the first equation, we have:
d + 0.3n = n
d = 0.7n
Finally substituting the above in the third equation, we have:
0.7n = 119
n = 119/0.7 = 1190/7 = 170
Since orchestra only is c - b, or 0.3n, the number of students in the orchestra only is 0.3 x 170 = 51.
Answer: B
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
GMAT/MBA Expert
- Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
If 80% are in only one group, 20% are in both groups. If 50% are in the band only, then, counting the 20% who are in both groups, 70% of the students are in the band in total. So 30% are only in the orchestra. From here, you can either notice that the ratio of people in the band to people only in the orchestra is 70 to 30, or 7 to 3, so if we have 119 = (17)(7) people in the band, we must have (17)(3) = 51 people in the orchestra only. Or you could notice 119 is 70% of the total number of people, so the total number of people must be 170, and since 30% of all people are only in the orchestra, the answer is 30% of 170, which is 51.BTGmoderatorRO wrote:All of the students of Music High School are in the band, the orchestra, or both. 80 percent of the students are in only one group. There are 119 students in the band. If 50 percent of the students are in the band only, how many students are in the orchestra only?
A. 30
B. 51
C. 60
D. 85
E. 11
OA is B
OA says B but my answer was option A.Pls an Expert is needed here. Thanks
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com