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# At a certain university, the ratio of undergraduate students with an a

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Intern
Joined: 17 Nov 2013
Posts: 38
At a certain university, the ratio of undergraduate students with an a  [#permalink]

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14 Sep 2018, 23:18
3
00:00

Difficulty:

55% (hard)

Question Stats:

64% (02:11) correct 36% (01:46) wrong based on 78 sessions

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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
Manager
Joined: 10 May 2018
Posts: 128
Concentration: Finance, Sustainability
Re: At a certain university, the ratio of undergraduate students with an a  [#permalink]

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15 Sep 2018, 00:23
Graduates = $$G$$
Undergraduates = $$UG$$
UG With Associates Degree = $$UGA$$
UG Without Associates Degree = $$UGWA$$

Given

$$\frac{UGA}{UGWA} = \frac{1}{3}$$

so, $$UGA=\frac{UGWA}{3}$$--- eq. 1

also given, $$\frac{G}{UG} = \frac{1}{5}$$

logically, $$UGA+UGWA = UG$$ --- eq.2

so, $$\frac{G}{UGA+UGWA} = \frac{1}{5}$$ --- eq.3

Let $$S = UG+G$$ ...all students at the university are either undergraduate or graduate students...

so, $$G=S-UG$$

we can rewrite eq.3 as

$$\frac{(S-UG)}{(UGA+UGWA)} = \frac{1}{5}$$

from eq.2,

$$\frac{(S-UGA-UGWA)}{(UGA+UGWA)} = \frac{1}{5}$$

from eq. 1,

$$\frac{(S-1.333UGWA)}{(1.333UGWA)}$$ = $$\frac{1}{5}$$

Divide numerator and denominator by S and separate $$\frac{UGWA}{S}$$ from the other terms to reach the answer.

$$\frac{UGWA}{S} = \frac{5}{8}$$

harish1986 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

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Intern
Joined: 24 Jun 2018
Posts: 12
Re: At a certain university, the ratio of undergraduate students with an a  [#permalink]

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26 Oct 2018, 06:07
I am not able to get the answer.

Ratio of Graduate and Under Graduate= 1:5 - 1x + 5x= 6x
Ratio of Degree Students and Without Degree= 1:3 (which is actually under Graduate, which is 5x of total)
Therefore 1x+3x=4x (5x of total)

Solving by this the answer is coming different.
Intern
Joined: 13 Jan 2018
Posts: 1
Location: Croatia (Hrvatska)
GPA: 3.2
WE: Programming (Computer Software)
At a certain university, the ratio of undergraduate students with an a  [#permalink]

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Updated on: 27 Oct 2018, 09:29
2
A = associates degree
WA = without associates degree
T = total

You can draw a table like this.

_____UG____G____T__
A...|..15...|........|
___|_____|____|_____
WA|..45...|........|
___|_____|____|_____
..T.|..60...|..12...|..72

Sorry for the dots and lines, I can't post images or urls

For the number of undergraduates you can choose a number which is divisible by 4,6 and 5. So if a total number of undergraduates is 60, than the number of undergraduates with associates degree is 15 and the number of undergraduate students without associates degree is 45 ($$\frac{15}{45} = \frac{1}{3}$$). The ratio of graduates and undergraduates is 1/5 and from that you can calculate the number of graduates $$\frac{60}{5} = 12$$. At this point you have the number of undergraduates without degree and the total number of students. The final result is $$\frac{45}{(60 + 12)} = \frac{5}{8}$$

Originally posted by shtepa on 26 Oct 2018, 10:30.
Last edited by shtepa on 27 Oct 2018, 09:29, edited 1 time in total.
Intern
Joined: 24 Jun 2018
Posts: 12
Re: At a certain university, the ratio of undergraduate students with an a  [#permalink]

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27 Oct 2018, 09:11
shtepa wrote:
A = associates degree
WA = without associates degree
T = total

You can draw a table like this.

_____UG____G____T__
A...|..15...|........|
___|_____|____|_____
WA|..45...|........|
___|_____|____|_____
..T.|..60...|..12...|..72

Sorry for the dots and lines, I can't post images or urls

For the number of Under graduates you can choose a number which is divisible by 4,6 and 5. So if a total number of Under graduates is 60, than the number of undergraduates with associates degree is 15 and the number of grad. students without associates degree is 45 ($$\frac{15}{45} = \frac{1}{3}$$). The ratio of graduates and undergraduates is 1/5 and from that you can calculate the number of graduates $$\frac{60}{5} = 12$$. At this point you have the number of undergraduates without degree and the total number of students. The final result is $$\frac{45}{(60 + 12)} = \frac{5}{8}$$

Thanks. It really helped.. i think you missed 'Under' as highlighted... Thanks s much
Re: At a certain university, the ratio of undergraduate students with an a &nbs [#permalink] 27 Oct 2018, 09:11
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