At a certain university, the ratio of undergraduate students

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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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

We can let the number of undergraduate students = 20 and thus, since the number of undergraduate students is 5 times the number of graduate students, the number of graduate students must be 4. Then, the total number of students is 20 + 4 = 24.

Further, since the ratio of undergraduate students with an associate’s degree to those without an associate’s degree is 1:3, there exists an x such that the number of undergraduate students with an associate degree is x and those without an associate degree is 3x. In total, there will be x + 3x = 4x undergraduate students. Setting 4x = 20, we find that x = 5 students are undergraduates with an associate degree and 20 - 5 = 15 are undergraduates without an associate degree. Thus, the ratio of undergraduates without an associate degree to the entire student body is 15/24 = 5/8.

Answer: D