theCEO wrote:GMATGuruNY wrote:karthikpandian19 wrote:There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 17 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?
PS: I had confusion while translating the bolded portion into equation
(A) 25
(B) 32
(C) 36
(D) 48
(E) 61
We can plug in the answers, which represent the total number of art students.
5 take all three classes, and 20 take art and exactly one of the other two core classes.
ABC + (AB + AC) = 5+20 = 25.
The remaining art students take ONLY art.
The answer choices represent the TOTAL number of art students, implying the following options for the number of students who ONLY art:
25-25 = 0
32-25 = 7
36-25 = 11
48-25 = 23
61-25 = 36.
Since the number of students who take only art is 3 TIMES another value in the problem, the number of students who take only art must be a multiple of 3.
Only answer choice
E is viable.
The correct answer is
E.
GMATGuruNY
What happens if the choices had more than one number that were mulitiples of three. How would you solve the problem?
One formula for triple-overlapping groups is as follows:
T = Only A + Only B + Only C + AB + AC + BC + ABC
The problem give values for every grouping in the formula but Only A and BC.
Thus:
Only A + BC = 100 - (17+10+5+20) = 48.
Further, it is stated that Only A : BC = 3:1.
Let's say answer choices C, D and E offered the following values for the total number of art students, with the result that Only A must be one of the values in red:
C) 43-25 =
18
D) 49-25 =
24
E) 61-25 =
36
Answer choice C:
If Only A = 18, then BC = 6, for a total of 18+6 = 24.
Since the problem dictates that Only A + BC = 48 -- double the result here -- the correct answer must be E, which doubles the value of Only A to 36.
The correct answer is
E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
