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# In 1996, 80% of the students at University Y were undergraduates. If 6

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Math Expert
Joined: 02 Sep 2009
Posts: 55709
In 1996, 80% of the students at University Y were undergraduates. If 6  [#permalink]

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13 Jun 2019, 00:35
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Difficulty:

45% (medium)

Question Stats:

73% (03:14) correct 27% (02:12) wrong based on 22 sessions

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In 1996, 80% of the students at University Y were undergraduates. If 60% of the undergraduates at University Y were out-of-state students and 75% of all out-of-students at University Y were undergraduates, what fraction of the students at University Y were out-of-state students?

A. 16/25
B. 3/5
C. 1/2
D. 12/15
E. 1/4

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Re: In 1996, 80% of the students at University Y were undergraduates. If 6  [#permalink]

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13 Jun 2019, 02:10
Bunuel wrote:
In 1996, 80% of the students at University Y were undergraduates. If 60% of the undergraduates at University Y were out-of-state students and 75% of all out-of-students at University Y were undergraduates, what fraction of the students at University Y were out-of-state students?

A. 16/25
B. 3/5
C. 1/2
D. 12/15
E. 1/4

60% of 80% = 48% of students are OFS UG. 75 % of OFS are UG. so 100% of OFS = 48%*100%/75%=64%; Fraction of OFS = 64%/100%=16/25 IMO A
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Re: In 1996, 80% of the students at University Y were undergraduates. If 6  [#permalink]

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13 Jun 2019, 04:25
Bunuel wrote:
In 1996, 80% of the students at University Y were undergraduates. If 60% of the undergraduates at University Y were out-of-state students and 75% of all out-of-students at University Y were undergraduates, what fraction of the students at University Y were out-of-state students?

A. 16/25
B. 3/5
C. 1/2
D. 12/15
E. 1/4

Let total number of out of state students = x
75% of all out-of-students at University Y were undergraduates
--> 75% of x = 48 (see the attachment)
--> 75/100*x = 48
--> x = 48*100/75 = 64

So, Fraction of students at University Y were out-of-state students = 64/100 = 16/25

IMO Option A

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Re: In 1996, 80% of the students at University Y were undergraduates. If 6  [#permalink]

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13 Jun 2019, 10:25
Bunuel wrote:
In 1996, 80% of the students at University Y were undergraduates. If 60% of the undergraduates at University Y were out-of-state students and 75% of all out-of-students at University Y were undergraduates, what fraction of the students at University Y were out-of-state students?

A. 16/25
B. 3/5
C. 1/2
D. 12/15
E. 1/4

total students = 100
80 are UG
and 60% of 80 are out of state = 48
75/100 * x=48
x=64 students are UG
64/100 ; 16/25
IMO A
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Re: In 1996, 80% of the students at University Y were undergraduates. If 6  [#permalink]

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13 Jun 2019, 11:19
Lets say, Total no. of Students as 100

Now, Total no. of Undergraduate students = 80% of 100 = 80
Out of this 80 students, 60% are out-of-state too i.e,. Undergrad & out-of-state = 60% of 80 = 48 students

So, in the whole university of 100 students only 48 students are undergraduate & out-of-state

Given, 75% of all out-of-state students (say, x) are undergraduate

So, basically, 75% of x = 48

Solving the equation, x = 64

Fraction required : 64/100 = 16/25

IMO (A)
Re: In 1996, 80% of the students at University Y were undergraduates. If 6   [#permalink] 13 Jun 2019, 11:19
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