There are 70 students in Math or English or German. Exactly 40 are in Math, 30 in German, 35 in English and 15 in all three courses. How many students are enrolled in exactly two of the courses? Math, English and German.
a. 5
b. 10
c. 50
d. 75
e. 40
correct option is A
How does Exactly influenced your answer in this context. kindly present a mathematically analogy to this and defend your choice of answer. option B seem so close and may be the correct option
Set problem
This topic has expert replies
-
- Moderator
- Posts: 772
- Joined: Wed Aug 30, 2017 6:29 pm
- Followed by:6 members
GMAT/MBA Expert
- Jay@ManhattanReview
- GMAT Instructor
- Posts: 3008
- Joined: Mon Aug 22, 2016 6:19 am
- Location: Grand Central / New York
- Thanked: 470 times
- Followed by:34 members
Total number of students = 70Roland2rule wrote:There are 70 students in Math or English or German. Exactly 40 are in Math, 30 in German, 35 in English and 15 in all three courses. How many students are enrolled in exactly two of the courses? Math, English and German.
a. 5
b. 10
c. 50
d. 75
e. 40
correct option is A
How does Exactly influenced your answer in this context. kindly present a mathematically analogy to this and defend your choice of answer. option B seem so close and may be the correct option
Number of students enrolled in one course = 40 + 30 + 35 = 105
Number of students enrolled in all the three courses = 15
We know that
Total = # of students enrolled in one course - # of students enrolled in two courses + # of students enrolled in all the three courses
70 = 105 - Number of students enrolled in two courses + 15
=> Number of students enrolled in two courses = 120 - 70 = 50
However, this is not the answer to the question.
'50' is the number of students enrolled in two courses including the number of students enrolled in all the three courses
Thus, the number of students enrolled in EXACTLY two courses = 50 - 15 - 15 -15 = 5.
We deducted '15' thrice for each for the three courses.
The correct answer: A
Hope this helps!
Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide
-Jay
_________________
Manhattan Review GMAT Prep
Locations: New York | Jakarta | Nanjing | Berlin | and many more...
Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7251
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
Letting M = math, E = English, and G = German, we can use the formula for a 3-category scenario:BTGmoderatorRO wrote: ↑Sun Sep 10, 2017 2:11 pmThere are 70 students in Math or English or German. Exactly 40 are in Math, 30 in German, 35 in English and 15 in all three courses. How many students are enrolled in exactly two of the courses? Math, English and German.
a. 5
b. 10
c. 50
d. 75
e. 40
correct option is A
How does Exactly influenced your answer in this context. kindly present a mathematically analogy to this and defend your choice of answer. option B seem so close and may be the correct option
Total = n(M) + n(E) + n(G) - n(M and E) - n(M and G) - n(E and G) + n(all 3) - n(none)
70 = 40 + 35 + 30 - n(M and E) - n(M and G) - n(E and G) + 15 - 0
70 = 120 - n(M and E) - n(M and G) - n(E and G)
50 = n(M and E) + n(M and G) + n(E and G)
Note that the term n(M and E) includes those taking M and E, but it also includes the 15 who are taking all three. Similarly, the term n(M and G) includes those taking M and G, but it also includes the 15 who are taking all three. And, finally, the term n(E and G) includes those taking E and G, but it also includes the 15 who are taking all three.
Thus, we have added an extra 15 individuals three times. The total taking exactly 2 courses is not 50. Rather, it is
50 - 15 x 3 = 50 - 45 = 5.
Answer: A
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