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

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

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New post 15 Sep 2018, 00:18
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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
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Re: At a certain university, the ratio of undergraduate students with an a  [#permalink]

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New post 15 Sep 2018, 01:23
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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Re: At a certain university, the ratio of undergraduate students with an a  [#permalink]

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New post 26 Oct 2018, 07:07
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.
PLease help
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At a certain university, the ratio of undergraduate students with an a  [#permalink]

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New post Updated on: 27 Oct 2018, 10:29
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UG = undergraduates
G = graduates
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, 11:30.
Last edited by shtepa on 27 Oct 2018, 10:29, edited 1 time in total.
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Re: At a certain university, the ratio of undergraduate students with an a  [#permalink]

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New post 27 Oct 2018, 10:11
shtepa wrote:
UG = undergraduates
G = graduates
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
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At a certain university, the ratio of undergraduate students with an a  [#permalink]

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New post 18 Jan 2019, 14:59
Here's my answer AashiS :

Plugging values:

Undergraduates are divided into two groups:

Associate’s degree to those without an associate’s degree is 1:3

So x + 3x = 4x; Let the total be 120 because is div by 4.

Hence, 30 + 90 = 120......1)

Graduate students to undergraduate students is 1:5 = x + 5x = 6x.

... 1) x + 120 = 6x

x = 24

Finally, 24 + 120 = 144

Plugging the values:

90/144 = 5/8... 5 : 8.

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At a certain university, the ratio of undergraduate students with an a   [#permalink] 18 Jan 2019, 14:59
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