BTGmoderatorDC wrote:At a certain university, the ratio of undergraduate students with an associate's degree to those without an associate's degree is 1:3. Additionally, the ratio of graduate students to undergraduate students is 1:5. If all students at the university are either undergraduate or graduate students, what is the ratio of undergraduates without an associate's degree compared with the entire student body?
A. 1:15
B. 1:5
C. 3:8
D. 5:8
E. 4:5
OA D
Source: Princeton Review
Say there are D numbers of undergraduate students with an associate's degree and N numbers of undergraduate students without an associate's degree; thus, we have
D/N = 1/3 => (D + N)/N = 4/3, where (D + N) = Total number of graduates
Again, say there are G numbers of graduate students and U numbers of undergraduate students; thus, we have
G/U = 1/5 => (G + U)/U = 6/5, where (G + U) = entire student body
We know that (D + N) = Total number of graduates; also, we know that G = numbers of graduate students; thus, U = D + N
So, we can write (D + N)/N = 4/3 as U/N = 4/3.
We have to get the value of N/(G + U).
So, we have
U/N = 4/3 ---(1) and
(G + U)/U = 6/5 ---(2)
Multiplying (1) and (2), we get
=> (G + U)/N = 4/3 * 6/5 = 8/5
=> N/(G + U) = 5/8.
The correct answer:
D
Hope this helps!
-Jay
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