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In 1996, 80% of the students at University Y were undergraduates

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In 1996, 80% of the students at University Y were undergraduates  [#permalink]

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New post 30 Jun 2017, 12:50
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  45% (medium)

Question Stats:

75% (02:52) correct 25% (03:03) wrong based on 76 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  [#permalink]

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New post 30 Jun 2017, 13:01
Assume total number of students in the University Y to be 100.
As 80% of these students are under graduates, we would have 80 UG's
Of the undergraduate students, since 60% are out of state(we would have 48 Oos UG)

Since this is 75%(3/4 rth's of the total Oos), Totol OoS students are x

\(\frac{3x}{4} = 48\)
\(x = \frac{48*4}{3} = 64\)

This makes the total Out of State students(Oos), \(\frac{64}{100} or \frac{16}{25}\) of the total students(Option A)
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Re: In 1996, 80% of the students at University Y were undergraduates  [#permalink]

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New post 08 Jul 2017, 05:41
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Tornikea 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 students be \(= 100\)

Number of undergraduates students at University Y \(= 80\)% of \(100 =\frac{80}{100} * 100 = 80\)

\(60\)% of the undergraduates at University Y were out-of-state students \(= 60\)% of \(80 = \frac{60}{100} * 80 = 48\)

Let number of out-of-students at University Y be \(= x\)

\(75\)% of all out-of-students at University Y were undergraduates.

\(75\)% of \(x = 48\)

\(\frac{75}{100} * x = 48\)

\(x = \frac{48 * 100}{75} = 64\)

Required Fraction = Number of out-of-students / Total number of students

Required Fraction \(= \frac{64}{100} = \frac{16}{25}\)

Answer (A)...

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Re: In 1996, 80% of the students at University Y were undergraduates   [#permalink] 08 Jul 2017, 05:41
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In 1996, 80% of the students at University Y were undergraduates

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